TSTP Solution File: REL050-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL050-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 19:46:17 EDT 2022
% Result : Unsatisfiable 25.40s 25.56s
% Output : CNFRefutation 25.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 116
% Number of leaves : 483
% Syntax : Number of clauses : 1939 ( 956 unt; 0 nHn;1178 RR)
% Number of literals : 3361 (3360 equ;1424 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 2081 ( 18 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_14,negated_conjecture,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_4,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_3]) ).
cnf(refute_0_5,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_6,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
introduced(tautology,[equality,[$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_7,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( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_7]) ).
cnf(refute_0_9,plain,
join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(composition(complement(converse(composition(X_670,top))),composition(X_670,top))))) = complement(composition(X_670,top)),
inference(subst,[],[refute_0_8:[bind(A,$fot(complement(converse(composition(X_670,top))))),bind(B,$fot(composition(X_670,top)))]]) ).
cnf(refute_0_10,plain,
join(complement(top),composition(converse(converse(X_89)),complement(composition(converse(X_89),top)))) = complement(top),
inference(subst,[],[refute_0_8:[bind(A,$fot(converse(X_89))),bind(B,$fot(top))]]) ).
cnf(refute_0_11,plain,
converse(composition(converse(A),X_7)) = composition(converse(X_7),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_7))]]) ).
cnf(refute_0_12,plain,
( converse(composition(converse(A),X_7)) != composition(converse(X_7),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_7)) = composition(converse(X_7),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_7)),composition(converse(X_7),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_13,plain,
( converse(composition(converse(A),X_7)) != composition(converse(X_7),converse(converse(A)))
| converse(composition(converse(A),X_7)) = composition(converse(X_7),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_12]) ).
cnf(refute_0_14,plain,
converse(composition(converse(A),X_7)) = composition(converse(X_7),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_7)),composition(converse(X_7),converse(converse(A)))) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
converse(composition(converse(top),X_7)) = composition(converse(X_7),top),
inference(subst,[],[refute_0_14:[bind(A,$fot(top))]]) ).
cnf(refute_0_16,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_17,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_18,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| converse(join(A,B)) = join(converse(B),converse(A)) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(B)),join(converse(B),converse(A))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
converse(join(A,B)) = join(converse(B),converse(A)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_18]) ).
cnf(refute_0_20,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(join(converse(A),converse(B))))]]) ).
cnf(refute_0_21,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_20]) ).
cnf(refute_0_22,plain,
join(converse(B),converse(A)) = converse(join(B,A)),
inference(subst,[],[refute_0_21:[bind(A,$fot(B)),bind(B,$fot(A))]]) ).
cnf(refute_0_23,plain,
( converse(join(A,B)) != join(converse(B),converse(A))
| join(converse(B),converse(A)) != converse(join(B,A))
| converse(join(A,B)) = converse(join(B,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(A,B)),converse(join(B,A))) ),[0],$fot(join(converse(B),converse(A)))]]) ).
cnf(refute_0_24,plain,
( converse(join(A,B)) != join(converse(B),converse(A))
| converse(join(A,B)) = converse(join(B,A)) ),
inference(resolve,[$cnf( $equal(join(converse(B),converse(A)),converse(join(B,A))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
converse(join(A,B)) = converse(join(B,A)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(B),converse(A))) )],[refute_0_19,refute_0_24]) ).
cnf(refute_0_26,plain,
converse(join(converse(top),top)) = converse(join(top,converse(top))),
inference(subst,[],[refute_0_25:[bind(A,$fot(converse(top))),bind(B,$fot(top))]]) ).
cnf(refute_0_27,plain,
join(top,join(top,X_81)) = join(join(top,top),X_81),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(top)),bind(B,$fot(top)),bind(C,$fot(X_81))]]) ).
cnf(refute_0_28,plain,
join(join(top,top),complement(zero)) = join(complement(zero),join(top,top)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(top,top))),bind(B,$fot(complement(zero)))]]) ).
cnf(refute_0_29,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_30,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_31,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( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_31]) ).
cnf(refute_0_33,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_34,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_35,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_34]) ).
cnf(refute_0_36,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_37,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_38,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_41,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_40]) ).
cnf(refute_0_42,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_41:[bind(X,$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_43,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_33,refute_0_43]) ).
cnf(refute_0_45,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$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_46,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_32,refute_0_46]) ).
cnf(refute_0_48,plain,
X_35 = join(meet(X_35,complement(B)),complement(join(complement(X_35),complement(B)))),
inference(subst,[],[refute_0_47:[bind(A,$fot(X_35)),bind(B,$fot(complement(B)))]]) ).
cnf(refute_0_49,plain,
meet(X_35,B) = complement(join(complement(X_35),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_35))]]) ).
cnf(refute_0_50,plain,
( meet(X_35,B) != complement(join(complement(X_35),complement(B)))
| complement(join(complement(X_35),complement(B))) = meet(X_35,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_35,B))),bind(Y,$fot(complement(join(complement(X_35),complement(B)))))]]) ).
cnf(refute_0_51,plain,
complement(join(complement(X_35),complement(B))) = meet(X_35,B),
inference(resolve,[$cnf( $equal(meet(X_35,B),complement(join(complement(X_35),complement(B)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( X_35 != join(meet(X_35,complement(B)),complement(join(complement(X_35),complement(B))))
| complement(join(complement(X_35),complement(B))) != meet(X_35,B)
| X_35 = join(meet(X_35,complement(B)),meet(X_35,B)) ),
introduced(tautology,[equality,[$cnf( $equal(X_35,join(meet(X_35,complement(B)),complement(join(complement(X_35),complement(B))))) ),[1,1],$fot(meet(X_35,B))]]) ).
cnf(refute_0_53,plain,
( X_35 != join(meet(X_35,complement(B)),complement(join(complement(X_35),complement(B))))
| X_35 = join(meet(X_35,complement(B)),meet(X_35,B)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_35),complement(B))),meet(X_35,B)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
X_35 = join(meet(X_35,complement(B)),meet(X_35,B)),
inference(resolve,[$cnf( $equal(X_35,join(meet(X_35,complement(B)),complement(join(complement(X_35),complement(B))))) )],[refute_0_48,refute_0_53]) ).
cnf(refute_0_55,plain,
join(meet(X_35,complement(B)),meet(X_35,B)) = join(meet(X_35,B),meet(X_35,complement(B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(X_35,B))),bind(B,$fot(meet(X_35,complement(B))))]]) ).
cnf(refute_0_56,plain,
( X_35 != join(meet(X_35,complement(B)),meet(X_35,B))
| join(meet(X_35,complement(B)),meet(X_35,B)) != join(meet(X_35,B),meet(X_35,complement(B)))
| X_35 = join(meet(X_35,B),meet(X_35,complement(B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_35,join(meet(X_35,B),meet(X_35,complement(B)))) ),[0],$fot(join(meet(X_35,complement(B)),meet(X_35,B)))]]) ).
cnf(refute_0_57,plain,
( X_35 != join(meet(X_35,complement(B)),meet(X_35,B))
| X_35 = join(meet(X_35,B),meet(X_35,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_35,complement(B)),meet(X_35,B)),join(meet(X_35,B),meet(X_35,complement(B)))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
X_35 = join(meet(X_35,B),meet(X_35,complement(B))),
inference(resolve,[$cnf( $equal(X_35,join(meet(X_35,complement(B)),meet(X_35,B))) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
X_50 = join(meet(X_50,top),meet(X_50,complement(top))),
inference(subst,[],[refute_0_58:[bind(B,$fot(top)),bind(X_35,$fot(X_50))]]) ).
cnf(refute_0_60,plain,
meet(A,top) = complement(join(complement(A),complement(top))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(top))]]) ).
cnf(refute_0_61,plain,
zero = meet(join(complement(X_14),complement(X_15)),complement(join(complement(X_14),complement(X_15)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_14),complement(X_15))))]]) ).
cnf(refute_0_62,plain,
meet(X_14,X_15) = complement(join(complement(X_14),complement(X_15))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_14)),bind(B,$fot(X_15))]]) ).
cnf(refute_0_63,plain,
( meet(X_14,X_15) != complement(join(complement(X_14),complement(X_15)))
| complement(join(complement(X_14),complement(X_15))) = meet(X_14,X_15) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_14,X_15))),bind(Y,$fot(complement(join(complement(X_14),complement(X_15)))))]]) ).
cnf(refute_0_64,plain,
complement(join(complement(X_14),complement(X_15))) = meet(X_14,X_15),
inference(resolve,[$cnf( $equal(meet(X_14,X_15),complement(join(complement(X_14),complement(X_15)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( complement(join(complement(X_14),complement(X_15))) != meet(X_14,X_15)
| zero != meet(join(complement(X_14),complement(X_15)),complement(join(complement(X_14),complement(X_15))))
| zero = meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_14),complement(X_15)),complement(join(complement(X_14),complement(X_15))))) ),[1,1],$fot(meet(X_14,X_15))]]) ).
cnf(refute_0_66,plain,
( zero != meet(join(complement(X_14),complement(X_15)),complement(join(complement(X_14),complement(X_15))))
| zero = meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_14),complement(X_15))),meet(X_14,X_15)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
zero = meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_14),complement(X_15)),complement(join(complement(X_14),complement(X_15))))) )],[refute_0_61,refute_0_66]) ).
cnf(refute_0_68,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_69,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_68]) ).
cnf(refute_0_70,plain,
join(meet(X_14,X_15),complement(meet(X_14,X_15))) = top,
inference(subst,[],[refute_0_69:[bind(A,$fot(meet(X_14,X_15)))]]) ).
cnf(refute_0_71,plain,
complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))) = complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))))]]) ).
cnf(refute_0_72,plain,
( complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))) != complement(join(meet(X_14,X_15),complement(meet(X_14,X_15))))
| join(meet(X_14,X_15),complement(meet(X_14,X_15))) != top
| complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))),complement(join(meet(X_14,X_15),complement(meet(X_14,X_15))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_73,plain,
( join(meet(X_14,X_15),complement(meet(X_14,X_15))) != top
| complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))),complement(join(meet(X_14,X_15),complement(meet(X_14,X_15))))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_14,X_15),complement(meet(X_14,X_15))),top) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
meet(join(complement(X_14),complement(X_15)),B) = complement(join(complement(join(complement(X_14),complement(X_15))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_14),complement(X_15))))]]) ).
cnf(refute_0_76,plain,
( complement(join(complement(X_14),complement(X_15))) != meet(X_14,X_15)
| meet(join(complement(X_14),complement(X_15)),B) != complement(join(complement(join(complement(X_14),complement(X_15))),complement(B)))
| meet(join(complement(X_14),complement(X_15)),B) = complement(join(meet(X_14,X_15),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_14),complement(X_15)),B),complement(join(complement(join(complement(X_14),complement(X_15))),complement(B)))) ),[1,0,0],$fot(meet(X_14,X_15))]]) ).
cnf(refute_0_77,plain,
( meet(join(complement(X_14),complement(X_15)),B) != complement(join(complement(join(complement(X_14),complement(X_15))),complement(B)))
| meet(join(complement(X_14),complement(X_15)),B) = complement(join(meet(X_14,X_15),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_14),complement(X_15))),meet(X_14,X_15)) )],[refute_0_64,refute_0_76]) ).
cnf(refute_0_78,plain,
meet(join(complement(X_14),complement(X_15)),B) = complement(join(meet(X_14,X_15),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_14),complement(X_15)),B),complement(join(complement(join(complement(X_14),complement(X_15))),complement(B)))) )],[refute_0_75,refute_0_77]) ).
cnf(refute_0_79,plain,
meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) = complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))),
inference(subst,[],[refute_0_78:[bind(B,$fot(meet(X_14,X_15)))]]) ).
cnf(refute_0_80,plain,
( complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))) != complement(top)
| meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) != complement(join(meet(X_14,X_15),complement(meet(X_14,X_15))))
| meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) = complement(top) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)))),bind(Y,$fot(complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_81,plain,
( complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))) != complement(top)
| meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)),complement(join(meet(X_14,X_15),complement(meet(X_14,X_15))))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_14,X_15),complement(meet(X_14,X_15)))),complement(top)) )],[refute_0_74,refute_0_81]) ).
cnf(refute_0_83,plain,
( meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) != complement(top)
| zero != meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_84,plain,
( zero != meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15)),complement(top)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_14),complement(X_15)),meet(X_14,X_15))) )],[refute_0_67,refute_0_84]) ).
cnf(refute_0_86,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_87,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( complement(top) != zero
| meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_89,plain,
( meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
meet(A,top) = complement(join(complement(A),zero)),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) )],[refute_0_60,refute_0_89]) ).
cnf(refute_0_91,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_92,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_93,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_92]) ).
cnf(refute_0_94,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_91,refute_0_93]) ).
cnf(refute_0_95,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) = meet(top,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,B))),bind(Y,$fot(complement(join(zero,complement(B)))))]]) ).
cnf(refute_0_96,plain,
complement(join(zero,complement(B))) = meet(top,B),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
complement(join(zero,complement(A))) = meet(top,A),
inference(subst,[],[refute_0_96:[bind(B,$fot(A))]]) ).
cnf(refute_0_98,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_99,plain,
complement(join(complement(A),zero)) = complement(join(complement(A),zero)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),zero)))]]) ).
cnf(refute_0_100,plain,
( complement(join(complement(A),zero)) != complement(join(complement(A),zero))
| join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) ),[1,0],$fot(join(zero,complement(A)))]]) ).
cnf(refute_0_101,plain,
( join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
complement(join(complement(A),zero)) = complement(join(zero,complement(A))),
inference(resolve,[$cnf( $equal(join(complement(A),zero),join(zero,complement(A))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
( complement(join(complement(A),zero)) != complement(join(zero,complement(A)))
| complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(complement(join(complement(A),zero)))),bind(Y,$fot(complement(join(zero,complement(A))))),bind(Z,$fot(meet(top,A)))]]) ).
cnf(refute_0_104,plain,
( complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(zero,complement(A)))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
complement(join(complement(A),zero)) = meet(top,A),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(A))),meet(top,A)) )],[refute_0_97,refute_0_104]) ).
cnf(refute_0_106,plain,
( complement(join(complement(A),zero)) != meet(top,A)
| meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) ),[1],$fot(meet(top,A))]]) ).
cnf(refute_0_107,plain,
( meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),meet(top,A)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
meet(A,top) = meet(top,A),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) )],[refute_0_90,refute_0_107]) ).
cnf(refute_0_109,plain,
meet(X_50,top) = meet(top,X_50),
inference(subst,[],[refute_0_108:[bind(A,$fot(X_50))]]) ).
cnf(refute_0_110,plain,
( X_50 != join(meet(X_50,top),meet(X_50,complement(top)))
| meet(X_50,top) != meet(top,X_50)
| X_50 = join(meet(top,X_50),meet(X_50,complement(top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_50,join(meet(X_50,top),meet(X_50,complement(top)))) ),[1,0],$fot(meet(top,X_50))]]) ).
cnf(refute_0_111,plain,
( X_50 != join(meet(X_50,top),meet(X_50,complement(top)))
| X_50 = join(meet(top,X_50),meet(X_50,complement(top))) ),
inference(resolve,[$cnf( $equal(meet(X_50,top),meet(top,X_50)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
X_50 = join(meet(top,X_50),meet(X_50,complement(top))),
inference(resolve,[$cnf( $equal(X_50,join(meet(X_50,top),meet(X_50,complement(top)))) )],[refute_0_59,refute_0_111]) ).
cnf(refute_0_113,plain,
meet(X_50,complement(top)) = meet(X_50,complement(top)),
introduced(tautology,[refl,[$fot(meet(X_50,complement(top)))]]) ).
cnf(refute_0_114,plain,
( complement(top) != zero
| meet(X_50,complement(top)) != meet(X_50,complement(top))
| meet(X_50,complement(top)) = meet(X_50,zero) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_50,complement(top)),meet(X_50,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_115,plain,
( complement(top) != zero
| meet(X_50,complement(top)) = meet(X_50,zero) ),
inference(resolve,[$cnf( $equal(meet(X_50,complement(top)),meet(X_50,complement(top))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
meet(X_50,complement(top)) = meet(X_50,zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_115]) ).
cnf(refute_0_117,plain,
join(meet(top,X_50),meet(X_50,complement(top))) = join(meet(top,X_50),meet(X_50,complement(top))),
introduced(tautology,[refl,[$fot(join(meet(top,X_50),meet(X_50,complement(top))))]]) ).
cnf(refute_0_118,plain,
( join(meet(top,X_50),meet(X_50,complement(top))) != join(meet(top,X_50),meet(X_50,complement(top)))
| meet(X_50,complement(top)) != meet(X_50,zero)
| join(meet(top,X_50),meet(X_50,complement(top))) = join(meet(top,X_50),meet(X_50,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_50),meet(X_50,complement(top))),join(meet(top,X_50),meet(X_50,complement(top)))) ),[1,1],$fot(meet(X_50,zero))]]) ).
cnf(refute_0_119,plain,
( meet(X_50,complement(top)) != meet(X_50,zero)
| join(meet(top,X_50),meet(X_50,complement(top))) = join(meet(top,X_50),meet(X_50,zero)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_50),meet(X_50,complement(top))),join(meet(top,X_50),meet(X_50,complement(top)))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
join(meet(top,X_50),meet(X_50,complement(top))) = join(meet(top,X_50),meet(X_50,zero)),
inference(resolve,[$cnf( $equal(meet(X_50,complement(top)),meet(X_50,zero)) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
( X_50 != join(meet(top,X_50),meet(X_50,complement(top)))
| join(meet(top,X_50),meet(X_50,complement(top))) != join(meet(top,X_50),meet(X_50,zero))
| X_50 = join(meet(top,X_50),meet(X_50,zero)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_50,join(meet(top,X_50),meet(X_50,zero))) ),[0],$fot(join(meet(top,X_50),meet(X_50,complement(top))))]]) ).
cnf(refute_0_122,plain,
( X_50 != join(meet(top,X_50),meet(X_50,complement(top)))
| X_50 = join(meet(top,X_50),meet(X_50,zero)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_50),meet(X_50,complement(top))),join(meet(top,X_50),meet(X_50,zero))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
X_50 = join(meet(top,X_50),meet(X_50,zero)),
inference(resolve,[$cnf( $equal(X_50,join(meet(top,X_50),meet(X_50,complement(top)))) )],[refute_0_112,refute_0_122]) ).
cnf(refute_0_124,plain,
join(complement(zero),join(top,top)) = join(meet(top,join(complement(zero),join(top,top))),meet(join(complement(zero),join(top,top)),zero)),
inference(subst,[],[refute_0_123:[bind(X_50,$fot(join(complement(zero),join(top,top))))]]) ).
cnf(refute_0_125,plain,
meet(top,join(complement(zero),join(top,top))) = complement(join(zero,complement(join(complement(zero),join(top,top))))),
inference(subst,[],[refute_0_94:[bind(B,$fot(join(complement(zero),join(top,top))))]]) ).
cnf(refute_0_126,plain,
zero = join(meet(zero,join(top,top)),complement(join(complement(zero),join(top,top)))),
inference(subst,[],[refute_0_47:[bind(A,$fot(zero)),bind(B,$fot(join(top,top)))]]) ).
cnf(refute_0_127,plain,
meet(zero,join(top,top)) = complement(join(complement(zero),complement(join(top,top)))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(zero)),bind(B,$fot(join(top,top)))]]) ).
cnf(refute_0_128,plain,
top = join(meet(top,X_36),complement(join(complement(top),X_36))),
inference(subst,[],[refute_0_47:[bind(A,$fot(top)),bind(B,$fot(X_36))]]) ).
cnf(refute_0_129,plain,
( complement(top) != zero
| top != join(meet(top,X_36),complement(join(complement(top),X_36)))
| top = join(meet(top,X_36),complement(join(zero,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,X_36),complement(join(complement(top),X_36)))) ),[1,1,0,0],$fot(zero)]]) ).
cnf(refute_0_130,plain,
( top != join(meet(top,X_36),complement(join(complement(top),X_36)))
| top = join(meet(top,X_36),complement(join(zero,X_36))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_129]) ).
cnf(refute_0_131,plain,
top = join(meet(top,X_36),complement(join(zero,X_36))),
inference(resolve,[$cnf( $equal(top,join(meet(top,X_36),complement(join(complement(top),X_36)))) )],[refute_0_128,refute_0_130]) ).
cnf(refute_0_132,plain,
top = join(meet(top,X_45),complement(join(zero,X_45))),
inference(subst,[],[refute_0_131:[bind(X_36,$fot(X_45))]]) ).
cnf(refute_0_133,plain,
join(X_45,zero) = join(zero,X_45),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_45)),bind(B,$fot(zero))]]) ).
cnf(refute_0_134,plain,
( join(X_45,zero) != join(zero,X_45)
| join(zero,X_45) = join(X_45,zero) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_45,zero))),bind(Y,$fot(join(zero,X_45)))]]) ).
cnf(refute_0_135,plain,
join(zero,X_45) = join(X_45,zero),
inference(resolve,[$cnf( $equal(join(X_45,zero),join(zero,X_45)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
( join(zero,X_45) != join(X_45,zero)
| top != join(meet(top,X_45),complement(join(zero,X_45)))
| top = join(meet(top,X_45),complement(join(X_45,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,X_45),complement(join(zero,X_45)))) ),[1,1,0],$fot(join(X_45,zero))]]) ).
cnf(refute_0_137,plain,
( top != join(meet(top,X_45),complement(join(zero,X_45)))
| top = join(meet(top,X_45),complement(join(X_45,zero))) ),
inference(resolve,[$cnf( $equal(join(zero,X_45),join(X_45,zero)) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
top = join(meet(top,X_45),complement(join(X_45,zero))),
inference(resolve,[$cnf( $equal(top,join(meet(top,X_45),complement(join(zero,X_45)))) )],[refute_0_132,refute_0_137]) ).
cnf(refute_0_139,plain,
top = join(meet(top,join(top,complement(zero))),complement(join(join(top,complement(zero)),zero))),
inference(subst,[],[refute_0_138:[bind(X_45,$fot(join(top,complement(zero))))]]) ).
cnf(refute_0_140,plain,
meet(top,join(top,complement(zero))) = complement(join(zero,complement(join(top,complement(zero))))),
inference(subst,[],[refute_0_94:[bind(B,$fot(join(top,complement(zero))))]]) ).
cnf(refute_0_141,plain,
X_35 = join(meet(X_35,top),complement(join(complement(X_35),top))),
inference(subst,[],[refute_0_47:[bind(A,$fot(X_35)),bind(B,$fot(top))]]) ).
cnf(refute_0_142,plain,
meet(X_35,top) = meet(top,X_35),
inference(subst,[],[refute_0_108:[bind(A,$fot(X_35))]]) ).
cnf(refute_0_143,plain,
( X_35 != join(meet(X_35,top),complement(join(complement(X_35),top)))
| meet(X_35,top) != meet(top,X_35)
| X_35 = join(meet(top,X_35),complement(join(complement(X_35),top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_35,join(meet(X_35,top),complement(join(complement(X_35),top)))) ),[1,0],$fot(meet(top,X_35))]]) ).
cnf(refute_0_144,plain,
( X_35 != join(meet(X_35,top),complement(join(complement(X_35),top)))
| X_35 = join(meet(top,X_35),complement(join(complement(X_35),top))) ),
inference(resolve,[$cnf( $equal(meet(X_35,top),meet(top,X_35)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
X_35 = join(meet(top,X_35),complement(join(complement(X_35),top))),
inference(resolve,[$cnf( $equal(X_35,join(meet(X_35,top),complement(join(complement(X_35),top)))) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
join(complement(X_35),top) = join(top,complement(X_35)),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(complement(X_35)))]]) ).
cnf(refute_0_147,plain,
complement(join(complement(X_35),top)) = complement(join(complement(X_35),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(X_35),top)))]]) ).
cnf(refute_0_148,plain,
( complement(join(complement(X_35),top)) != complement(join(complement(X_35),top))
| join(complement(X_35),top) != join(top,complement(X_35))
| complement(join(complement(X_35),top)) = complement(join(top,complement(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X_35),top)),complement(join(complement(X_35),top))) ),[1,0],$fot(join(top,complement(X_35)))]]) ).
cnf(refute_0_149,plain,
( join(complement(X_35),top) != join(top,complement(X_35))
| complement(join(complement(X_35),top)) = complement(join(top,complement(X_35))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_35),top)),complement(join(complement(X_35),top))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
complement(join(complement(X_35),top)) = complement(join(top,complement(X_35))),
inference(resolve,[$cnf( $equal(join(complement(X_35),top),join(top,complement(X_35))) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
join(meet(top,X_35),complement(join(complement(X_35),top))) = join(meet(top,X_35),complement(join(complement(X_35),top))),
introduced(tautology,[refl,[$fot(join(meet(top,X_35),complement(join(complement(X_35),top))))]]) ).
cnf(refute_0_152,plain,
( complement(join(complement(X_35),top)) != complement(join(top,complement(X_35)))
| join(meet(top,X_35),complement(join(complement(X_35),top))) != join(meet(top,X_35),complement(join(complement(X_35),top)))
| join(meet(top,X_35),complement(join(complement(X_35),top))) = join(meet(top,X_35),complement(join(top,complement(X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_35),complement(join(complement(X_35),top))),join(meet(top,X_35),complement(join(complement(X_35),top)))) ),[1,1],$fot(complement(join(top,complement(X_35))))]]) ).
cnf(refute_0_153,plain,
( complement(join(complement(X_35),top)) != complement(join(top,complement(X_35)))
| join(meet(top,X_35),complement(join(complement(X_35),top))) = join(meet(top,X_35),complement(join(top,complement(X_35)))) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_35),complement(join(complement(X_35),top))),join(meet(top,X_35),complement(join(complement(X_35),top)))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
join(meet(top,X_35),complement(join(complement(X_35),top))) = join(meet(top,X_35),complement(join(top,complement(X_35)))),
inference(resolve,[$cnf( $equal(complement(join(complement(X_35),top)),complement(join(top,complement(X_35)))) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
( X_35 != join(meet(top,X_35),complement(join(complement(X_35),top)))
| join(meet(top,X_35),complement(join(complement(X_35),top))) != join(meet(top,X_35),complement(join(top,complement(X_35))))
| X_35 = join(meet(top,X_35),complement(join(top,complement(X_35)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_35,join(meet(top,X_35),complement(join(top,complement(X_35))))) ),[0],$fot(join(meet(top,X_35),complement(join(complement(X_35),top))))]]) ).
cnf(refute_0_156,plain,
( X_35 != join(meet(top,X_35),complement(join(complement(X_35),top)))
| X_35 = join(meet(top,X_35),complement(join(top,complement(X_35)))) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_35),complement(join(complement(X_35),top))),join(meet(top,X_35),complement(join(top,complement(X_35))))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
X_35 = join(meet(top,X_35),complement(join(top,complement(X_35)))),
inference(resolve,[$cnf( $equal(X_35,join(meet(top,X_35),complement(join(complement(X_35),top)))) )],[refute_0_145,refute_0_156]) ).
cnf(refute_0_158,plain,
complement(top) = join(meet(top,complement(top)),complement(join(top,complement(complement(top))))),
inference(subst,[],[refute_0_157:[bind(X_35,$fot(complement(top)))]]) ).
cnf(refute_0_159,plain,
zero = meet(top,complement(top)),
inference(subst,[],[def_zero_13:[bind(A,$fot(top))]]) ).
cnf(refute_0_160,plain,
( zero != meet(top,complement(top))
| meet(top,complement(top)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(top,complement(top))))]]) ).
cnf(refute_0_161,plain,
meet(top,complement(top)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(top,complement(top))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( complement(top) != join(meet(top,complement(top)),complement(join(top,complement(complement(top)))))
| meet(top,complement(top)) != zero
| complement(top) = join(zero,complement(join(top,complement(complement(top))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(top),join(meet(top,complement(top)),complement(join(top,complement(complement(top)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_163,plain,
( complement(top) != join(meet(top,complement(top)),complement(join(top,complement(complement(top)))))
| complement(top) = join(zero,complement(join(top,complement(complement(top))))) ),
inference(resolve,[$cnf( $equal(meet(top,complement(top)),zero) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
complement(top) = join(zero,complement(join(top,complement(complement(top))))),
inference(resolve,[$cnf( $equal(complement(top),join(meet(top,complement(top)),complement(join(top,complement(complement(top)))))) )],[refute_0_158,refute_0_163]) ).
cnf(refute_0_165,plain,
( complement(top) != join(zero,complement(join(top,complement(complement(top)))))
| complement(top) != zero
| zero = join(zero,complement(join(top,complement(complement(top))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(top),join(zero,complement(join(top,complement(complement(top)))))) ),[0],$fot(zero)]]) ).
cnf(refute_0_166,plain,
( complement(top) != join(zero,complement(join(top,complement(complement(top)))))
| zero = join(zero,complement(join(top,complement(complement(top))))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_165]) ).
cnf(refute_0_167,plain,
complement(complement(top)) = complement(complement(top)),
introduced(tautology,[refl,[$fot(complement(complement(top)))]]) ).
cnf(refute_0_168,plain,
( complement(complement(top)) != complement(complement(top))
| complement(top) != zero
| complement(complement(top)) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),complement(complement(top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_169,plain,
( complement(top) != zero
| complement(complement(top)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(complement(top))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
complement(complement(top)) = complement(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_169]) ).
cnf(refute_0_171,plain,
join(top,complement(complement(top))) = join(top,complement(complement(top))),
introduced(tautology,[refl,[$fot(join(top,complement(complement(top))))]]) ).
cnf(refute_0_172,plain,
( complement(complement(top)) != complement(zero)
| join(top,complement(complement(top))) != join(top,complement(complement(top)))
| join(top,complement(complement(top))) = join(top,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,complement(complement(top))),join(top,complement(complement(top)))) ),[1,1],$fot(complement(zero))]]) ).
cnf(refute_0_173,plain,
( complement(complement(top)) != complement(zero)
| join(top,complement(complement(top))) = join(top,complement(zero)) ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(top))),join(top,complement(complement(top)))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
join(top,complement(complement(top))) = join(top,complement(zero)),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
complement(join(top,complement(complement(top)))) = complement(join(top,complement(complement(top)))),
introduced(tautology,[refl,[$fot(complement(join(top,complement(complement(top)))))]]) ).
cnf(refute_0_176,plain,
( complement(join(top,complement(complement(top)))) != complement(join(top,complement(complement(top))))
| join(top,complement(complement(top))) != join(top,complement(zero))
| complement(join(top,complement(complement(top)))) = complement(join(top,complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(top,complement(complement(top)))),complement(join(top,complement(complement(top))))) ),[1,0],$fot(join(top,complement(zero)))]]) ).
cnf(refute_0_177,plain,
( join(top,complement(complement(top))) != join(top,complement(zero))
| complement(join(top,complement(complement(top)))) = complement(join(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(complement(top)))),complement(join(top,complement(complement(top))))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
complement(join(top,complement(complement(top)))) = complement(join(top,complement(zero))),
inference(resolve,[$cnf( $equal(join(top,complement(complement(top))),join(top,complement(zero))) )],[refute_0_174,refute_0_177]) ).
cnf(refute_0_179,plain,
join(zero,complement(join(top,complement(complement(top))))) = join(zero,complement(join(top,complement(complement(top))))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(top,complement(complement(top))))))]]) ).
cnf(refute_0_180,plain,
( complement(join(top,complement(complement(top)))) != complement(join(top,complement(zero)))
| join(zero,complement(join(top,complement(complement(top))))) != join(zero,complement(join(top,complement(complement(top)))))
| join(zero,complement(join(top,complement(complement(top))))) = join(zero,complement(join(top,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(top,complement(complement(top))))),join(zero,complement(join(top,complement(complement(top)))))) ),[1,1],$fot(complement(join(top,complement(zero))))]]) ).
cnf(refute_0_181,plain,
( complement(join(top,complement(complement(top)))) != complement(join(top,complement(zero)))
| join(zero,complement(join(top,complement(complement(top))))) = join(zero,complement(join(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(top,complement(complement(top))))),join(zero,complement(join(top,complement(complement(top)))))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
join(zero,complement(join(top,complement(complement(top))))) = join(zero,complement(join(top,complement(zero)))),
inference(resolve,[$cnf( $equal(complement(join(top,complement(complement(top)))),complement(join(top,complement(zero)))) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
( join(zero,complement(join(top,complement(complement(top))))) != join(zero,complement(join(top,complement(zero))))
| zero != join(zero,complement(join(top,complement(complement(top)))))
| zero = join(zero,complement(join(top,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(zero,complement(join(top,complement(complement(top)))))) ),[1],$fot(join(zero,complement(join(top,complement(zero)))))]]) ).
cnf(refute_0_184,plain,
( zero != join(zero,complement(join(top,complement(complement(top)))))
| zero = join(zero,complement(join(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(top,complement(complement(top))))),join(zero,complement(join(top,complement(zero))))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
( complement(top) != join(zero,complement(join(top,complement(complement(top)))))
| zero = join(zero,complement(join(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(zero,join(zero,complement(join(top,complement(complement(top)))))) )],[refute_0_166,refute_0_184]) ).
cnf(refute_0_186,plain,
zero = join(zero,complement(join(top,complement(zero)))),
inference(resolve,[$cnf( $equal(complement(top),join(zero,complement(join(top,complement(complement(top)))))) )],[refute_0_164,refute_0_185]) ).
cnf(refute_0_187,plain,
( zero != join(zero,complement(join(top,complement(zero))))
| join(zero,complement(join(top,complement(zero)))) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(join(zero,complement(join(top,complement(zero))))))]]) ).
cnf(refute_0_188,plain,
join(zero,complement(join(top,complement(zero)))) = zero,
inference(resolve,[$cnf( $equal(zero,join(zero,complement(join(top,complement(zero))))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
( join(zero,complement(join(top,complement(zero)))) != zero
| meet(top,join(top,complement(zero))) != complement(join(zero,complement(join(top,complement(zero)))))
| meet(top,join(top,complement(zero))) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(top,complement(zero))),complement(join(zero,complement(join(top,complement(zero)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_190,plain,
( meet(top,join(top,complement(zero))) != complement(join(zero,complement(join(top,complement(zero)))))
| meet(top,join(top,complement(zero))) = complement(zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(top,complement(zero)))),zero) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
meet(top,join(top,complement(zero))) = complement(zero),
inference(resolve,[$cnf( $equal(meet(top,join(top,complement(zero))),complement(join(zero,complement(join(top,complement(zero)))))) )],[refute_0_140,refute_0_190]) ).
cnf(refute_0_192,plain,
( meet(top,join(top,complement(zero))) != complement(zero)
| top != join(meet(top,join(top,complement(zero))),complement(join(join(top,complement(zero)),zero)))
| top = join(complement(zero),complement(join(join(top,complement(zero)),zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,join(top,complement(zero))),complement(join(join(top,complement(zero)),zero)))) ),[1,0],$fot(complement(zero))]]) ).
cnf(refute_0_193,plain,
( top != join(meet(top,join(top,complement(zero))),complement(join(join(top,complement(zero)),zero)))
| top = join(complement(zero),complement(join(join(top,complement(zero)),zero))) ),
inference(resolve,[$cnf( $equal(meet(top,join(top,complement(zero))),complement(zero)) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
top = join(complement(zero),complement(join(join(top,complement(zero)),zero))),
inference(resolve,[$cnf( $equal(top,join(meet(top,join(top,complement(zero))),complement(join(join(top,complement(zero)),zero)))) )],[refute_0_139,refute_0_193]) ).
cnf(refute_0_195,plain,
join(zero,complement(zero)) = top,
inference(subst,[],[refute_0_69:[bind(A,$fot(zero))]]) ).
cnf(refute_0_196,plain,
join(complement(zero),zero) = join(zero,complement(zero)),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(zero)))]]) ).
cnf(refute_0_197,plain,
( join(complement(zero),zero) != join(zero,complement(zero))
| join(zero,complement(zero)) != top
| join(complement(zero),zero) = top ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(zero),zero))),bind(Y,$fot(join(zero,complement(zero)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_198,plain,
( join(zero,complement(zero)) != top
| join(complement(zero),zero) = top ),
inference(resolve,[$cnf( $equal(join(complement(zero),zero),join(zero,complement(zero))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
join(complement(zero),zero) = top,
inference(resolve,[$cnf( $equal(join(zero,complement(zero)),top) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
join(top,join(complement(zero),zero)) = join(top,join(complement(zero),zero)),
introduced(tautology,[refl,[$fot(join(top,join(complement(zero),zero)))]]) ).
cnf(refute_0_201,plain,
( join(complement(zero),zero) != top
| join(top,join(complement(zero),zero)) != join(top,join(complement(zero),zero))
| join(top,join(complement(zero),zero)) = join(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(complement(zero),zero)),join(top,join(complement(zero),zero))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_202,plain,
( join(complement(zero),zero) != top
| join(top,join(complement(zero),zero)) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(top,join(complement(zero),zero)),join(top,join(complement(zero),zero))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
join(top,join(complement(zero),zero)) = join(top,top),
inference(resolve,[$cnf( $equal(join(complement(zero),zero),top) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_205,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_204]) ).
cnf(refute_0_206,plain,
join(join(top,complement(zero)),zero) = join(top,join(complement(zero),zero)),
inference(subst,[],[refute_0_205:[bind(A,$fot(top)),bind(B,$fot(complement(zero))),bind(C,$fot(zero))]]) ).
cnf(refute_0_207,plain,
( join(join(top,complement(zero)),zero) != join(top,join(complement(zero),zero))
| join(top,join(complement(zero),zero)) != join(top,top)
| join(join(top,complement(zero)),zero) = join(top,top) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(join(top,complement(zero)),zero))),bind(Y,$fot(join(top,join(complement(zero),zero)))),bind(Z,$fot(join(top,top)))]]) ).
cnf(refute_0_208,plain,
( join(top,join(complement(zero),zero)) != join(top,top)
| join(join(top,complement(zero)),zero) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(join(top,complement(zero)),zero),join(top,join(complement(zero),zero))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
join(join(top,complement(zero)),zero) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,join(complement(zero),zero)),join(top,top)) )],[refute_0_203,refute_0_208]) ).
cnf(refute_0_210,plain,
complement(join(join(top,complement(zero)),zero)) = complement(join(join(top,complement(zero)),zero)),
introduced(tautology,[refl,[$fot(complement(join(join(top,complement(zero)),zero)))]]) ).
cnf(refute_0_211,plain,
( complement(join(join(top,complement(zero)),zero)) != complement(join(join(top,complement(zero)),zero))
| join(join(top,complement(zero)),zero) != join(top,top)
| complement(join(join(top,complement(zero)),zero)) = complement(join(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(join(top,complement(zero)),zero)),complement(join(join(top,complement(zero)),zero))) ),[1,0],$fot(join(top,top))]]) ).
cnf(refute_0_212,plain,
( join(join(top,complement(zero)),zero) != join(top,top)
| complement(join(join(top,complement(zero)),zero)) = complement(join(top,top)) ),
inference(resolve,[$cnf( $equal(complement(join(join(top,complement(zero)),zero)),complement(join(join(top,complement(zero)),zero))) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
complement(join(join(top,complement(zero)),zero)) = complement(join(top,top)),
inference(resolve,[$cnf( $equal(join(join(top,complement(zero)),zero),join(top,top)) )],[refute_0_209,refute_0_212]) ).
cnf(refute_0_214,plain,
join(complement(zero),complement(join(join(top,complement(zero)),zero))) = join(complement(zero),complement(join(join(top,complement(zero)),zero))),
introduced(tautology,[refl,[$fot(join(complement(zero),complement(join(join(top,complement(zero)),zero))))]]) ).
cnf(refute_0_215,plain,
( complement(join(join(top,complement(zero)),zero)) != complement(join(top,top))
| join(complement(zero),complement(join(join(top,complement(zero)),zero))) != join(complement(zero),complement(join(join(top,complement(zero)),zero)))
| join(complement(zero),complement(join(join(top,complement(zero)),zero))) = join(complement(zero),complement(join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),complement(join(join(top,complement(zero)),zero))),join(complement(zero),complement(join(join(top,complement(zero)),zero)))) ),[1,1],$fot(complement(join(top,top)))]]) ).
cnf(refute_0_216,plain,
( complement(join(join(top,complement(zero)),zero)) != complement(join(top,top))
| join(complement(zero),complement(join(join(top,complement(zero)),zero))) = join(complement(zero),complement(join(top,top))) ),
inference(resolve,[$cnf( $equal(join(complement(zero),complement(join(join(top,complement(zero)),zero))),join(complement(zero),complement(join(join(top,complement(zero)),zero)))) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
join(complement(zero),complement(join(join(top,complement(zero)),zero))) = join(complement(zero),complement(join(top,top))),
inference(resolve,[$cnf( $equal(complement(join(join(top,complement(zero)),zero)),complement(join(top,top))) )],[refute_0_213,refute_0_216]) ).
cnf(refute_0_218,plain,
( join(complement(zero),complement(join(join(top,complement(zero)),zero))) != join(complement(zero),complement(join(top,top)))
| top != join(complement(zero),complement(join(join(top,complement(zero)),zero)))
| top = join(complement(zero),complement(join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(zero),complement(join(join(top,complement(zero)),zero)))) ),[1],$fot(join(complement(zero),complement(join(top,top))))]]) ).
cnf(refute_0_219,plain,
( top != join(complement(zero),complement(join(join(top,complement(zero)),zero)))
| top = join(complement(zero),complement(join(top,top))) ),
inference(resolve,[$cnf( $equal(join(complement(zero),complement(join(join(top,complement(zero)),zero))),join(complement(zero),complement(join(top,top)))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
top = join(complement(zero),complement(join(top,top))),
inference(resolve,[$cnf( $equal(top,join(complement(zero),complement(join(join(top,complement(zero)),zero)))) )],[refute_0_194,refute_0_219]) ).
cnf(refute_0_221,plain,
( top != join(complement(zero),complement(join(top,top)))
| join(complement(zero),complement(join(top,top))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(zero),complement(join(top,top)))))]]) ).
cnf(refute_0_222,plain,
join(complement(zero),complement(join(top,top))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(zero),complement(join(top,top)))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
( join(complement(zero),complement(join(top,top))) != top
| meet(zero,join(top,top)) != complement(join(complement(zero),complement(join(top,top))))
| meet(zero,join(top,top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,join(top,top)),complement(join(complement(zero),complement(join(top,top))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_224,plain,
( meet(zero,join(top,top)) != complement(join(complement(zero),complement(join(top,top))))
| meet(zero,join(top,top)) = complement(top) ),
inference(resolve,[$cnf( $equal(join(complement(zero),complement(join(top,top))),top) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
meet(zero,join(top,top)) = complement(top),
inference(resolve,[$cnf( $equal(meet(zero,join(top,top)),complement(join(complement(zero),complement(join(top,top))))) )],[refute_0_127,refute_0_224]) ).
cnf(refute_0_226,plain,
( complement(top) != zero
| meet(zero,join(top,top)) != complement(top)
| meet(zero,join(top,top)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,join(top,top)),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_227,plain,
( meet(zero,join(top,top)) != complement(top)
| meet(zero,join(top,top)) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_226]) ).
cnf(refute_0_228,plain,
meet(zero,join(top,top)) = zero,
inference(resolve,[$cnf( $equal(meet(zero,join(top,top)),complement(top)) )],[refute_0_225,refute_0_227]) ).
cnf(refute_0_229,plain,
( meet(zero,join(top,top)) != zero
| zero != join(meet(zero,join(top,top)),complement(join(complement(zero),join(top,top))))
| zero = join(zero,complement(join(complement(zero),join(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(meet(zero,join(top,top)),complement(join(complement(zero),join(top,top))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_230,plain,
( zero != join(meet(zero,join(top,top)),complement(join(complement(zero),join(top,top))))
| zero = join(zero,complement(join(complement(zero),join(top,top)))) ),
inference(resolve,[$cnf( $equal(meet(zero,join(top,top)),zero) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
zero = join(zero,complement(join(complement(zero),join(top,top)))),
inference(resolve,[$cnf( $equal(zero,join(meet(zero,join(top,top)),complement(join(complement(zero),join(top,top))))) )],[refute_0_126,refute_0_230]) ).
cnf(refute_0_232,plain,
( zero != join(zero,complement(join(complement(zero),join(top,top))))
| join(zero,complement(join(complement(zero),join(top,top)))) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(join(zero,complement(join(complement(zero),join(top,top))))))]]) ).
cnf(refute_0_233,plain,
join(zero,complement(join(complement(zero),join(top,top)))) = zero,
inference(resolve,[$cnf( $equal(zero,join(zero,complement(join(complement(zero),join(top,top))))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
( join(zero,complement(join(complement(zero),join(top,top)))) != zero
| meet(top,join(complement(zero),join(top,top))) != complement(join(zero,complement(join(complement(zero),join(top,top)))))
| meet(top,join(complement(zero),join(top,top))) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(zero),join(top,top))),complement(join(zero,complement(join(complement(zero),join(top,top)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_235,plain,
( meet(top,join(complement(zero),join(top,top))) != complement(join(zero,complement(join(complement(zero),join(top,top)))))
| meet(top,join(complement(zero),join(top,top))) = complement(zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(zero),join(top,top)))),zero) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
meet(top,join(complement(zero),join(top,top))) = complement(zero),
inference(resolve,[$cnf( $equal(meet(top,join(complement(zero),join(top,top))),complement(join(zero,complement(join(complement(zero),join(top,top)))))) )],[refute_0_125,refute_0_235]) ).
cnf(refute_0_237,plain,
( join(complement(zero),join(top,top)) != join(meet(top,join(complement(zero),join(top,top))),meet(join(complement(zero),join(top,top)),zero))
| meet(top,join(complement(zero),join(top,top))) != complement(zero)
| join(complement(zero),join(top,top)) = join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),join(top,top)),join(meet(top,join(complement(zero),join(top,top))),meet(join(complement(zero),join(top,top)),zero))) ),[1,0],$fot(complement(zero))]]) ).
cnf(refute_0_238,plain,
( join(complement(zero),join(top,top)) != join(meet(top,join(complement(zero),join(top,top))),meet(join(complement(zero),join(top,top)),zero))
| join(complement(zero),join(top,top)) = join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) ),
inference(resolve,[$cnf( $equal(meet(top,join(complement(zero),join(top,top))),complement(zero)) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
join(complement(zero),join(top,top)) = join(complement(zero),meet(join(complement(zero),join(top,top)),zero)),
inference(resolve,[$cnf( $equal(join(complement(zero),join(top,top)),join(meet(top,join(complement(zero),join(top,top))),meet(join(complement(zero),join(top,top)),zero))) )],[refute_0_124,refute_0_238]) ).
cnf(refute_0_240,plain,
meet(zero,join(complement(zero),join(top,top))) = complement(join(complement(zero),complement(join(complement(zero),join(top,top))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(zero)),bind(B,$fot(join(complement(zero),join(top,top))))]]) ).
cnf(refute_0_241,plain,
top = join(meet(top,complement(join(complement(zero),join(top,top)))),complement(join(zero,complement(join(complement(zero),join(top,top)))))),
inference(subst,[],[refute_0_131:[bind(X_36,$fot(complement(join(complement(zero),join(top,top)))))]]) ).
cnf(refute_0_242,plain,
( join(zero,complement(join(complement(zero),join(top,top)))) != zero
| top != join(meet(top,complement(join(complement(zero),join(top,top)))),complement(join(zero,complement(join(complement(zero),join(top,top))))))
| top = join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,complement(join(complement(zero),join(top,top)))),complement(join(zero,complement(join(complement(zero),join(top,top))))))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_243,plain,
( top != join(meet(top,complement(join(complement(zero),join(top,top)))),complement(join(zero,complement(join(complement(zero),join(top,top))))))
| top = join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(zero),join(top,top)))),zero) )],[refute_0_233,refute_0_242]) ).
cnf(refute_0_244,plain,
top = join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)),
inference(resolve,[$cnf( $equal(top,join(meet(top,complement(join(complement(zero),join(top,top)))),complement(join(zero,complement(join(complement(zero),join(top,top))))))) )],[refute_0_241,refute_0_243]) ).
cnf(refute_0_245,plain,
meet(top,complement(X_37)) = complement(join(zero,complement(complement(X_37)))),
inference(subst,[],[refute_0_94:[bind(B,$fot(complement(X_37)))]]) ).
cnf(refute_0_246,plain,
X_35 = join(meet(X_35,complement(X_35)),complement(join(complement(X_35),complement(X_35)))),
inference(subst,[],[refute_0_47:[bind(A,$fot(X_35)),bind(B,$fot(complement(X_35)))]]) ).
cnf(refute_0_247,plain,
join(complement(X_32),composition(converse(one),complement(composition(one,X_32)))) = complement(X_32),
inference(subst,[],[refute_0_8:[bind(A,$fot(one)),bind(B,$fot(X_32))]]) ).
cnf(refute_0_248,plain,
converse(composition(converse(X_24),one)) = composition(converse(one),X_24),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_24)),bind(X_7,$fot(one))]]) ).
cnf(refute_0_249,plain,
composition(converse(X_24),one) = converse(X_24),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_24)))]]) ).
cnf(refute_0_250,plain,
( composition(converse(X_24),one) != converse(X_24)
| converse(composition(converse(X_24),one)) != composition(converse(one),X_24)
| converse(converse(X_24)) = composition(converse(one),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_24),one)),composition(converse(one),X_24)) ),[0,0],$fot(converse(X_24))]]) ).
cnf(refute_0_251,plain,
( converse(composition(converse(X_24),one)) != composition(converse(one),X_24)
| converse(converse(X_24)) = composition(converse(one),X_24) ),
inference(resolve,[$cnf( $equal(composition(converse(X_24),one),converse(X_24)) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
converse(converse(X_24)) = composition(converse(one),X_24),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_24),one)),composition(converse(one),X_24)) )],[refute_0_248,refute_0_251]) ).
cnf(refute_0_253,plain,
converse(converse(X_24)) = X_24,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_24))]]) ).
cnf(refute_0_254,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_255,plain,
( converse(converse(X_24)) != composition(converse(one),X_24)
| X_24 = composition(converse(one),X_24) ),
inference(resolve,[$cnf( $equal(converse(converse(X_24)),X_24) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
X_24 = composition(converse(one),X_24),
inference(resolve,[$cnf( $equal(converse(converse(X_24)),composition(converse(one),X_24)) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_258,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_256:[bind(X_24,$fot(one))]]) ).
cnf(refute_0_259,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_260,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_262,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_257,refute_0_262]) ).
cnf(refute_0_264,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_265,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
composition(converse(one),X_24) = composition(converse(one),X_24),
introduced(tautology,[refl,[$fot(composition(converse(one),X_24))]]) ).
cnf(refute_0_267,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_268,plain,
( converse(one) != one
| composition(converse(one),X_24) = composition(one,X_24) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_24),composition(converse(one),X_24)) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
composition(converse(one),X_24) = composition(one,X_24),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
( X_24 != composition(converse(one),X_24)
| composition(converse(one),X_24) != composition(one,X_24)
| X_24 = composition(one,X_24) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,composition(one,X_24)) ),[0],$fot(composition(converse(one),X_24))]]) ).
cnf(refute_0_271,plain,
( X_24 != composition(converse(one),X_24)
| X_24 = composition(one,X_24) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_24),composition(one,X_24)) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
X_24 = composition(one,X_24),
inference(resolve,[$cnf( $equal(X_24,composition(converse(one),X_24)) )],[refute_0_256,refute_0_271]) ).
cnf(refute_0_273,plain,
X_32 = composition(one,X_32),
inference(subst,[],[refute_0_272:[bind(X_24,$fot(X_32))]]) ).
cnf(refute_0_274,plain,
( X_32 != composition(one,X_32)
| composition(one,X_32) = X_32 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_32)),bind(Y,$fot(composition(one,X_32)))]]) ).
cnf(refute_0_275,plain,
composition(one,X_32) = X_32,
inference(resolve,[$cnf( $equal(X_32,composition(one,X_32)) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
( composition(one,X_32) != X_32
| join(complement(X_32),composition(converse(one),complement(composition(one,X_32)))) != complement(X_32)
| join(complement(X_32),composition(converse(one),complement(X_32))) = complement(X_32) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_32),composition(converse(one),complement(composition(one,X_32)))),complement(X_32)) ),[0,1,1,0],$fot(X_32)]]) ).
cnf(refute_0_277,plain,
( join(complement(X_32),composition(converse(one),complement(composition(one,X_32)))) != complement(X_32)
| join(complement(X_32),composition(converse(one),complement(X_32))) = complement(X_32) ),
inference(resolve,[$cnf( $equal(composition(one,X_32),X_32) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
join(complement(X_32),composition(converse(one),complement(X_32))) = complement(X_32),
inference(resolve,[$cnf( $equal(join(complement(X_32),composition(converse(one),complement(composition(one,X_32)))),complement(X_32)) )],[refute_0_247,refute_0_277]) ).
cnf(refute_0_279,plain,
( X_24 != composition(one,X_24)
| composition(one,X_24) = X_24 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_24)),bind(Y,$fot(composition(one,X_24)))]]) ).
cnf(refute_0_280,plain,
composition(one,X_24) = X_24,
inference(resolve,[$cnf( $equal(X_24,composition(one,X_24)) )],[refute_0_272,refute_0_279]) ).
cnf(refute_0_281,plain,
composition(one,complement(X_32)) = complement(X_32),
inference(subst,[],[refute_0_280:[bind(X_24,$fot(complement(X_32)))]]) ).
cnf(refute_0_282,plain,
composition(converse(one),complement(X_32)) = composition(converse(one),complement(X_32)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(X_32)))]]) ).
cnf(refute_0_283,plain,
( composition(converse(one),complement(X_32)) != composition(converse(one),complement(X_32))
| converse(one) != one
| composition(converse(one),complement(X_32)) = composition(one,complement(X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(X_32)),composition(converse(one),complement(X_32))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_284,plain,
( converse(one) != one
| composition(converse(one),complement(X_32)) = composition(one,complement(X_32)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_32)),composition(converse(one),complement(X_32))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
composition(converse(one),complement(X_32)) = composition(one,complement(X_32)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_265,refute_0_284]) ).
cnf(refute_0_286,plain,
( composition(converse(one),complement(X_32)) != composition(one,complement(X_32))
| composition(one,complement(X_32)) != complement(X_32)
| composition(converse(one),complement(X_32)) = complement(X_32) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(composition(converse(one),complement(X_32)))),bind(Y,$fot(composition(one,complement(X_32)))),bind(Z,$fot(complement(X_32)))]]) ).
cnf(refute_0_287,plain,
( composition(one,complement(X_32)) != complement(X_32)
| composition(converse(one),complement(X_32)) = complement(X_32) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_32)),composition(one,complement(X_32))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
composition(converse(one),complement(X_32)) = complement(X_32),
inference(resolve,[$cnf( $equal(composition(one,complement(X_32)),complement(X_32)) )],[refute_0_281,refute_0_287]) ).
cnf(refute_0_289,plain,
join(complement(X_32),composition(converse(one),complement(X_32))) = join(complement(X_32),composition(converse(one),complement(X_32))),
introduced(tautology,[refl,[$fot(join(complement(X_32),composition(converse(one),complement(X_32))))]]) ).
cnf(refute_0_290,plain,
( composition(converse(one),complement(X_32)) != complement(X_32)
| join(complement(X_32),composition(converse(one),complement(X_32))) != join(complement(X_32),composition(converse(one),complement(X_32)))
| join(complement(X_32),composition(converse(one),complement(X_32))) = join(complement(X_32),complement(X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_32),composition(converse(one),complement(X_32))),join(complement(X_32),composition(converse(one),complement(X_32)))) ),[1,1],$fot(complement(X_32))]]) ).
cnf(refute_0_291,plain,
( composition(converse(one),complement(X_32)) != complement(X_32)
| join(complement(X_32),composition(converse(one),complement(X_32))) = join(complement(X_32),complement(X_32)) ),
inference(resolve,[$cnf( $equal(join(complement(X_32),composition(converse(one),complement(X_32))),join(complement(X_32),composition(converse(one),complement(X_32)))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
join(complement(X_32),composition(converse(one),complement(X_32))) = join(complement(X_32),complement(X_32)),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_32)),complement(X_32)) )],[refute_0_288,refute_0_291]) ).
cnf(refute_0_293,plain,
( join(complement(X_32),composition(converse(one),complement(X_32))) != complement(X_32)
| join(complement(X_32),composition(converse(one),complement(X_32))) != join(complement(X_32),complement(X_32))
| join(complement(X_32),complement(X_32)) = complement(X_32) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_32),composition(converse(one),complement(X_32))),complement(X_32)) ),[0],$fot(join(complement(X_32),complement(X_32)))]]) ).
cnf(refute_0_294,plain,
( join(complement(X_32),composition(converse(one),complement(X_32))) != complement(X_32)
| join(complement(X_32),complement(X_32)) = complement(X_32) ),
inference(resolve,[$cnf( $equal(join(complement(X_32),composition(converse(one),complement(X_32))),join(complement(X_32),complement(X_32))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
join(complement(X_32),complement(X_32)) = complement(X_32),
inference(resolve,[$cnf( $equal(join(complement(X_32),composition(converse(one),complement(X_32))),complement(X_32)) )],[refute_0_278,refute_0_294]) ).
cnf(refute_0_296,plain,
join(complement(X_35),complement(X_35)) = complement(X_35),
inference(subst,[],[refute_0_295:[bind(X_32,$fot(X_35))]]) ).
cnf(refute_0_297,plain,
( X_35 != join(meet(X_35,complement(X_35)),complement(join(complement(X_35),complement(X_35))))
| join(complement(X_35),complement(X_35)) != complement(X_35)
| X_35 = join(meet(X_35,complement(X_35)),complement(complement(X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(X_35,join(meet(X_35,complement(X_35)),complement(join(complement(X_35),complement(X_35))))) ),[1,1,0],$fot(complement(X_35))]]) ).
cnf(refute_0_298,plain,
( X_35 != join(meet(X_35,complement(X_35)),complement(join(complement(X_35),complement(X_35))))
| X_35 = join(meet(X_35,complement(X_35)),complement(complement(X_35))) ),
inference(resolve,[$cnf( $equal(join(complement(X_35),complement(X_35)),complement(X_35)) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
X_35 = join(meet(X_35,complement(X_35)),complement(complement(X_35))),
inference(resolve,[$cnf( $equal(X_35,join(meet(X_35,complement(X_35)),complement(join(complement(X_35),complement(X_35))))) )],[refute_0_246,refute_0_298]) ).
cnf(refute_0_300,plain,
join(complement(complement(X_35)),zero) = join(zero,complement(complement(X_35))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(complement(X_35))))]]) ).
cnf(refute_0_301,plain,
( zero != meet(A,complement(A))
| meet(A,complement(A)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(A,complement(A))))]]) ).
cnf(refute_0_302,plain,
meet(A,complement(A)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(A,complement(A))) )],[def_zero_13,refute_0_301]) ).
cnf(refute_0_303,plain,
meet(X_35,complement(X_35)) = zero,
inference(subst,[],[refute_0_302:[bind(A,$fot(X_35))]]) ).
cnf(refute_0_304,plain,
join(complement(complement(X_35)),meet(X_35,complement(X_35))) = join(complement(complement(X_35)),meet(X_35,complement(X_35))),
introduced(tautology,[refl,[$fot(join(complement(complement(X_35)),meet(X_35,complement(X_35))))]]) ).
cnf(refute_0_305,plain,
( join(complement(complement(X_35)),meet(X_35,complement(X_35))) != join(complement(complement(X_35)),meet(X_35,complement(X_35)))
| meet(X_35,complement(X_35)) != zero
| join(complement(complement(X_35)),meet(X_35,complement(X_35))) = join(complement(complement(X_35)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_35)),meet(X_35,complement(X_35))),join(complement(complement(X_35)),meet(X_35,complement(X_35)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_306,plain,
( meet(X_35,complement(X_35)) != zero
| join(complement(complement(X_35)),meet(X_35,complement(X_35))) = join(complement(complement(X_35)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_35)),meet(X_35,complement(X_35))),join(complement(complement(X_35)),meet(X_35,complement(X_35)))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
join(complement(complement(X_35)),meet(X_35,complement(X_35))) = join(complement(complement(X_35)),zero),
inference(resolve,[$cnf( $equal(meet(X_35,complement(X_35)),zero) )],[refute_0_303,refute_0_306]) ).
cnf(refute_0_308,plain,
( join(complement(complement(X_35)),meet(X_35,complement(X_35))) != join(complement(complement(X_35)),zero)
| join(complement(complement(X_35)),zero) != join(zero,complement(complement(X_35)))
| join(complement(complement(X_35)),meet(X_35,complement(X_35))) = join(zero,complement(complement(X_35))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(complement(X_35)),meet(X_35,complement(X_35))))),bind(Y,$fot(join(complement(complement(X_35)),zero))),bind(Z,$fot(join(zero,complement(complement(X_35)))))]]) ).
cnf(refute_0_309,plain,
( join(complement(complement(X_35)),zero) != join(zero,complement(complement(X_35)))
| join(complement(complement(X_35)),meet(X_35,complement(X_35))) = join(zero,complement(complement(X_35))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_35)),meet(X_35,complement(X_35))),join(complement(complement(X_35)),zero)) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
join(complement(complement(X_35)),meet(X_35,complement(X_35))) = join(zero,complement(complement(X_35))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_35)),zero),join(zero,complement(complement(X_35)))) )],[refute_0_300,refute_0_309]) ).
cnf(refute_0_311,plain,
join(meet(X_35,complement(X_35)),complement(complement(X_35))) = join(complement(complement(X_35)),meet(X_35,complement(X_35))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(complement(X_35)))),bind(B,$fot(meet(X_35,complement(X_35))))]]) ).
cnf(refute_0_312,plain,
( join(complement(complement(X_35)),meet(X_35,complement(X_35))) != join(zero,complement(complement(X_35)))
| join(meet(X_35,complement(X_35)),complement(complement(X_35))) != join(complement(complement(X_35)),meet(X_35,complement(X_35)))
| join(meet(X_35,complement(X_35)),complement(complement(X_35))) = join(zero,complement(complement(X_35))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(meet(X_35,complement(X_35)),complement(complement(X_35))))),bind(Y,$fot(join(complement(complement(X_35)),meet(X_35,complement(X_35))))),bind(Z,$fot(join(zero,complement(complement(X_35)))))]]) ).
cnf(refute_0_313,plain,
( join(complement(complement(X_35)),meet(X_35,complement(X_35))) != join(zero,complement(complement(X_35)))
| join(meet(X_35,complement(X_35)),complement(complement(X_35))) = join(zero,complement(complement(X_35))) ),
inference(resolve,[$cnf( $equal(join(meet(X_35,complement(X_35)),complement(complement(X_35))),join(complement(complement(X_35)),meet(X_35,complement(X_35)))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
join(meet(X_35,complement(X_35)),complement(complement(X_35))) = join(zero,complement(complement(X_35))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_35)),meet(X_35,complement(X_35))),join(zero,complement(complement(X_35)))) )],[refute_0_310,refute_0_313]) ).
cnf(refute_0_315,plain,
( X_35 != join(meet(X_35,complement(X_35)),complement(complement(X_35)))
| join(meet(X_35,complement(X_35)),complement(complement(X_35))) != join(zero,complement(complement(X_35)))
| X_35 = join(zero,complement(complement(X_35))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_35,join(zero,complement(complement(X_35)))) ),[0],$fot(join(meet(X_35,complement(X_35)),complement(complement(X_35))))]]) ).
cnf(refute_0_316,plain,
( X_35 != join(meet(X_35,complement(X_35)),complement(complement(X_35)))
| X_35 = join(zero,complement(complement(X_35))) ),
inference(resolve,[$cnf( $equal(join(meet(X_35,complement(X_35)),complement(complement(X_35))),join(zero,complement(complement(X_35)))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
X_35 = join(zero,complement(complement(X_35))),
inference(resolve,[$cnf( $equal(X_35,join(meet(X_35,complement(X_35)),complement(complement(X_35)))) )],[refute_0_299,refute_0_316]) ).
cnf(refute_0_318,plain,
X_37 = join(zero,complement(complement(X_37))),
inference(subst,[],[refute_0_317:[bind(X_35,$fot(X_37))]]) ).
cnf(refute_0_319,plain,
( X_37 != join(zero,complement(complement(X_37)))
| join(zero,complement(complement(X_37))) = X_37 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_37)),bind(Y,$fot(join(zero,complement(complement(X_37)))))]]) ).
cnf(refute_0_320,plain,
join(zero,complement(complement(X_37))) = X_37,
inference(resolve,[$cnf( $equal(X_37,join(zero,complement(complement(X_37)))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
( join(zero,complement(complement(X_37))) != X_37
| meet(top,complement(X_37)) != complement(join(zero,complement(complement(X_37))))
| meet(top,complement(X_37)) = complement(X_37) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(X_37)),complement(join(zero,complement(complement(X_37))))) ),[1,0],$fot(X_37)]]) ).
cnf(refute_0_322,plain,
( meet(top,complement(X_37)) != complement(join(zero,complement(complement(X_37))))
| meet(top,complement(X_37)) = complement(X_37) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_37))),X_37) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
meet(top,complement(X_37)) = complement(X_37),
inference(resolve,[$cnf( $equal(meet(top,complement(X_37)),complement(join(zero,complement(complement(X_37))))) )],[refute_0_245,refute_0_322]) ).
cnf(refute_0_324,plain,
meet(top,complement(join(complement(zero),join(top,top)))) = complement(join(complement(zero),join(top,top))),
inference(subst,[],[refute_0_323:[bind(X_37,$fot(join(complement(zero),join(top,top))))]]) ).
cnf(refute_0_325,plain,
join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))) = join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))),
introduced(tautology,[refl,[$fot(join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))))]]) ).
cnf(refute_0_326,plain,
( join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))) != join(complement(zero),meet(top,complement(join(complement(zero),join(top,top)))))
| meet(top,complement(join(complement(zero),join(top,top)))) != complement(join(complement(zero),join(top,top)))
| join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))) = join(complement(zero),complement(join(complement(zero),join(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))),join(complement(zero),meet(top,complement(join(complement(zero),join(top,top)))))) ),[1,1],$fot(complement(join(complement(zero),join(top,top))))]]) ).
cnf(refute_0_327,plain,
( meet(top,complement(join(complement(zero),join(top,top)))) != complement(join(complement(zero),join(top,top)))
| join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))) = join(complement(zero),complement(join(complement(zero),join(top,top)))) ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))),join(complement(zero),meet(top,complement(join(complement(zero),join(top,top)))))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))) = join(complement(zero),complement(join(complement(zero),join(top,top)))),
inference(resolve,[$cnf( $equal(meet(top,complement(join(complement(zero),join(top,top)))),complement(join(complement(zero),join(top,top)))) )],[refute_0_324,refute_0_327]) ).
cnf(refute_0_329,plain,
join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)) = join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(zero))),bind(B,$fot(meet(top,complement(join(complement(zero),join(top,top))))))]]) ).
cnf(refute_0_330,plain,
( join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))) != join(complement(zero),complement(join(complement(zero),join(top,top))))
| join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)) != join(complement(zero),meet(top,complement(join(complement(zero),join(top,top)))))
| join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)) = join(complement(zero),complement(join(complement(zero),join(top,top)))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)))),bind(Y,$fot(join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))))),bind(Z,$fot(join(complement(zero),complement(join(complement(zero),join(top,top))))))]]) ).
cnf(refute_0_331,plain,
( join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))) != join(complement(zero),complement(join(complement(zero),join(top,top))))
| join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)) = join(complement(zero),complement(join(complement(zero),join(top,top)))) ),
inference(resolve,[$cnf( $equal(join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)),join(complement(zero),meet(top,complement(join(complement(zero),join(top,top)))))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)) = join(complement(zero),complement(join(complement(zero),join(top,top)))),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(top,complement(join(complement(zero),join(top,top))))),join(complement(zero),complement(join(complement(zero),join(top,top))))) )],[refute_0_328,refute_0_331]) ).
cnf(refute_0_333,plain,
( join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)) != join(complement(zero),complement(join(complement(zero),join(top,top))))
| top != join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero))
| top = join(complement(zero),complement(join(complement(zero),join(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero))) ),[1],$fot(join(complement(zero),complement(join(complement(zero),join(top,top)))))]]) ).
cnf(refute_0_334,plain,
( top != join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero))
| top = join(complement(zero),complement(join(complement(zero),join(top,top)))) ),
inference(resolve,[$cnf( $equal(join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero)),join(complement(zero),complement(join(complement(zero),join(top,top))))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
top = join(complement(zero),complement(join(complement(zero),join(top,top)))),
inference(resolve,[$cnf( $equal(top,join(meet(top,complement(join(complement(zero),join(top,top)))),complement(zero))) )],[refute_0_244,refute_0_334]) ).
cnf(refute_0_336,plain,
( top != join(complement(zero),complement(join(complement(zero),join(top,top))))
| join(complement(zero),complement(join(complement(zero),join(top,top)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(zero),complement(join(complement(zero),join(top,top))))))]]) ).
cnf(refute_0_337,plain,
join(complement(zero),complement(join(complement(zero),join(top,top)))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(zero),complement(join(complement(zero),join(top,top))))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
( join(complement(zero),complement(join(complement(zero),join(top,top)))) != top
| meet(zero,join(complement(zero),join(top,top))) != complement(join(complement(zero),complement(join(complement(zero),join(top,top)))))
| meet(zero,join(complement(zero),join(top,top))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,join(complement(zero),join(top,top))),complement(join(complement(zero),complement(join(complement(zero),join(top,top)))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_339,plain,
( meet(zero,join(complement(zero),join(top,top))) != complement(join(complement(zero),complement(join(complement(zero),join(top,top)))))
| meet(zero,join(complement(zero),join(top,top))) = complement(top) ),
inference(resolve,[$cnf( $equal(join(complement(zero),complement(join(complement(zero),join(top,top)))),top) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
meet(zero,join(complement(zero),join(top,top))) = complement(top),
inference(resolve,[$cnf( $equal(meet(zero,join(complement(zero),join(top,top))),complement(join(complement(zero),complement(join(complement(zero),join(top,top)))))) )],[refute_0_240,refute_0_339]) ).
cnf(refute_0_341,plain,
( complement(top) != zero
| meet(zero,join(complement(zero),join(top,top))) != complement(top)
| meet(zero,join(complement(zero),join(top,top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,join(complement(zero),join(top,top))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_342,plain,
( meet(zero,join(complement(zero),join(top,top))) != complement(top)
| meet(zero,join(complement(zero),join(top,top))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_341]) ).
cnf(refute_0_343,plain,
meet(zero,join(complement(zero),join(top,top))) = zero,
inference(resolve,[$cnf( $equal(meet(zero,join(complement(zero),join(top,top))),complement(top)) )],[refute_0_340,refute_0_342]) ).
cnf(refute_0_344,plain,
join(complement(X_15),complement(X_14)) = join(complement(X_14),complement(X_15)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_15))),bind(B,$fot(complement(X_14)))]]) ).
cnf(refute_0_345,plain,
( join(complement(X_15),complement(X_14)) != join(complement(X_14),complement(X_15))
| join(complement(X_14),complement(X_15)) = join(complement(X_15),complement(X_14)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_15),complement(X_14)))),bind(Y,$fot(join(complement(X_14),complement(X_15))))]]) ).
cnf(refute_0_346,plain,
join(complement(X_14),complement(X_15)) = join(complement(X_15),complement(X_14)),
inference(resolve,[$cnf( $equal(join(complement(X_15),complement(X_14)),join(complement(X_14),complement(X_15))) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
( join(complement(X_14),complement(X_15)) != join(complement(X_15),complement(X_14))
| meet(X_14,X_15) != complement(join(complement(X_14),complement(X_15)))
| meet(X_14,X_15) = complement(join(complement(X_15),complement(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_14,X_15),complement(join(complement(X_14),complement(X_15)))) ),[1,0],$fot(join(complement(X_15),complement(X_14)))]]) ).
cnf(refute_0_348,plain,
( meet(X_14,X_15) != complement(join(complement(X_14),complement(X_15)))
| meet(X_14,X_15) = complement(join(complement(X_15),complement(X_14))) ),
inference(resolve,[$cnf( $equal(join(complement(X_14),complement(X_15)),join(complement(X_15),complement(X_14))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
meet(X_14,X_15) = complement(join(complement(X_15),complement(X_14))),
inference(resolve,[$cnf( $equal(meet(X_14,X_15),complement(join(complement(X_14),complement(X_15)))) )],[refute_0_62,refute_0_348]) ).
cnf(refute_0_350,plain,
complement(join(complement(X_15),complement(X_14))) = meet(X_15,X_14),
inference(subst,[],[refute_0_35:[bind(A,$fot(X_15)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_351,plain,
( complement(join(complement(X_15),complement(X_14))) != meet(X_15,X_14)
| meet(X_14,X_15) != complement(join(complement(X_15),complement(X_14)))
| meet(X_14,X_15) = meet(X_15,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_14,X_15),complement(join(complement(X_15),complement(X_14)))) ),[1],$fot(meet(X_15,X_14))]]) ).
cnf(refute_0_352,plain,
( meet(X_14,X_15) != complement(join(complement(X_15),complement(X_14)))
| meet(X_14,X_15) = meet(X_15,X_14) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_15),complement(X_14))),meet(X_15,X_14)) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
meet(X_14,X_15) = meet(X_15,X_14),
inference(resolve,[$cnf( $equal(meet(X_14,X_15),complement(join(complement(X_15),complement(X_14)))) )],[refute_0_349,refute_0_352]) ).
cnf(refute_0_354,plain,
( meet(X_14,X_15) != meet(X_15,X_14)
| meet(X_15,X_14) = meet(X_14,X_15) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_14,X_15))),bind(Y,$fot(meet(X_15,X_14)))]]) ).
cnf(refute_0_355,plain,
meet(X_15,X_14) = meet(X_14,X_15),
inference(resolve,[$cnf( $equal(meet(X_14,X_15),meet(X_15,X_14)) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
meet(join(complement(zero),join(top,top)),zero) = meet(zero,join(complement(zero),join(top,top))),
inference(subst,[],[refute_0_355:[bind(X_14,$fot(zero)),bind(X_15,$fot(join(complement(zero),join(top,top))))]]) ).
cnf(refute_0_357,plain,
( meet(join(complement(zero),join(top,top)),zero) != meet(zero,join(complement(zero),join(top,top)))
| meet(zero,join(complement(zero),join(top,top))) != zero
| meet(join(complement(zero),join(top,top)),zero) = zero ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(join(complement(zero),join(top,top)),zero))),bind(Y,$fot(meet(zero,join(complement(zero),join(top,top))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_358,plain,
( meet(zero,join(complement(zero),join(top,top))) != zero
| meet(join(complement(zero),join(top,top)),zero) = zero ),
inference(resolve,[$cnf( $equal(meet(join(complement(zero),join(top,top)),zero),meet(zero,join(complement(zero),join(top,top)))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
meet(join(complement(zero),join(top,top)),zero) = zero,
inference(resolve,[$cnf( $equal(meet(zero,join(complement(zero),join(top,top))),zero) )],[refute_0_343,refute_0_358]) ).
cnf(refute_0_360,plain,
join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) = join(complement(zero),meet(join(complement(zero),join(top,top)),zero)),
introduced(tautology,[refl,[$fot(join(complement(zero),meet(join(complement(zero),join(top,top)),zero)))]]) ).
cnf(refute_0_361,plain,
( join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) != join(complement(zero),meet(join(complement(zero),join(top,top)),zero))
| meet(join(complement(zero),join(top,top)),zero) != zero
| join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) = join(complement(zero),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),meet(join(complement(zero),join(top,top)),zero)),join(complement(zero),meet(join(complement(zero),join(top,top)),zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_362,plain,
( meet(join(complement(zero),join(top,top)),zero) != zero
| join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) = join(complement(zero),zero) ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(join(complement(zero),join(top,top)),zero)),join(complement(zero),meet(join(complement(zero),join(top,top)),zero))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) = join(complement(zero),zero),
inference(resolve,[$cnf( $equal(meet(join(complement(zero),join(top,top)),zero),zero) )],[refute_0_359,refute_0_362]) ).
cnf(refute_0_364,plain,
( join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) != join(complement(zero),zero)
| join(complement(zero),zero) != top
| join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) = top ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(zero),meet(join(complement(zero),join(top,top)),zero)))),bind(Y,$fot(join(complement(zero),zero))),bind(Z,$fot(top))]]) ).
cnf(refute_0_365,plain,
( join(complement(zero),zero) != top
| join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) = top ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(join(complement(zero),join(top,top)),zero)),join(complement(zero),zero)) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) = top,
inference(resolve,[$cnf( $equal(join(complement(zero),zero),top) )],[refute_0_199,refute_0_365]) ).
cnf(refute_0_367,plain,
( join(complement(zero),join(top,top)) != join(complement(zero),meet(join(complement(zero),join(top,top)),zero))
| join(complement(zero),meet(join(complement(zero),join(top,top)),zero)) != top
| join(complement(zero),join(top,top)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(zero),join(top,top)),top) ),[0],$fot(join(complement(zero),meet(join(complement(zero),join(top,top)),zero)))]]) ).
cnf(refute_0_368,plain,
( join(complement(zero),join(top,top)) != join(complement(zero),meet(join(complement(zero),join(top,top)),zero))
| join(complement(zero),join(top,top)) = top ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(join(complement(zero),join(top,top)),zero)),top) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
join(complement(zero),join(top,top)) = top,
inference(resolve,[$cnf( $equal(join(complement(zero),join(top,top)),join(complement(zero),meet(join(complement(zero),join(top,top)),zero))) )],[refute_0_239,refute_0_368]) ).
cnf(refute_0_370,plain,
( join(complement(zero),join(top,top)) != top
| join(join(top,top),complement(zero)) != join(complement(zero),join(top,top))
| join(join(top,top),complement(zero)) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(join(top,top),complement(zero)),join(complement(zero),join(top,top))) ),[1],$fot(top)]]) ).
cnf(refute_0_371,plain,
( join(join(top,top),complement(zero)) != join(complement(zero),join(top,top))
| join(join(top,top),complement(zero)) = top ),
inference(resolve,[$cnf( $equal(join(complement(zero),join(top,top)),top) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
join(join(top,top),complement(zero)) = top,
inference(resolve,[$cnf( $equal(join(join(top,top),complement(zero)),join(complement(zero),join(top,top))) )],[refute_0_28,refute_0_371]) ).
cnf(refute_0_373,plain,
join(top,complement(zero)) = join(meet(top,join(top,complement(zero))),meet(join(top,complement(zero)),zero)),
inference(subst,[],[refute_0_123:[bind(X_50,$fot(join(top,complement(zero))))]]) ).
cnf(refute_0_374,plain,
( join(top,complement(zero)) != join(meet(top,join(top,complement(zero))),meet(join(top,complement(zero)),zero))
| meet(top,join(top,complement(zero))) != complement(zero)
| join(top,complement(zero)) = join(complement(zero),meet(join(top,complement(zero)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,complement(zero)),join(meet(top,join(top,complement(zero))),meet(join(top,complement(zero)),zero))) ),[1,0],$fot(complement(zero))]]) ).
cnf(refute_0_375,plain,
( join(top,complement(zero)) != join(meet(top,join(top,complement(zero))),meet(join(top,complement(zero)),zero))
| join(top,complement(zero)) = join(complement(zero),meet(join(top,complement(zero)),zero)) ),
inference(resolve,[$cnf( $equal(meet(top,join(top,complement(zero))),complement(zero)) )],[refute_0_191,refute_0_374]) ).
cnf(refute_0_376,plain,
join(top,complement(zero)) = join(complement(zero),meet(join(top,complement(zero)),zero)),
inference(resolve,[$cnf( $equal(join(top,complement(zero)),join(meet(top,join(top,complement(zero))),meet(join(top,complement(zero)),zero))) )],[refute_0_373,refute_0_375]) ).
cnf(refute_0_377,plain,
meet(zero,join(top,complement(zero))) = complement(join(complement(zero),complement(join(top,complement(zero))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(zero)),bind(B,$fot(join(top,complement(zero))))]]) ).
cnf(refute_0_378,plain,
meet(X_36,top) = meet(top,X_36),
inference(subst,[],[refute_0_108:[bind(A,$fot(X_36))]]) ).
cnf(refute_0_379,plain,
( meet(X_36,top) != meet(top,X_36)
| meet(top,X_36) = meet(X_36,top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_36,top))),bind(Y,$fot(meet(top,X_36)))]]) ).
cnf(refute_0_380,plain,
meet(top,X_36) = meet(X_36,top),
inference(resolve,[$cnf( $equal(meet(X_36,top),meet(top,X_36)) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
( meet(top,X_36) != meet(X_36,top)
| top != join(meet(top,X_36),complement(join(complement(top),X_36)))
| top = join(meet(X_36,top),complement(join(complement(top),X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,X_36),complement(join(complement(top),X_36)))) ),[1,0],$fot(meet(X_36,top))]]) ).
cnf(refute_0_382,plain,
( top != join(meet(top,X_36),complement(join(complement(top),X_36)))
| top = join(meet(X_36,top),complement(join(complement(top),X_36))) ),
inference(resolve,[$cnf( $equal(meet(top,X_36),meet(X_36,top)) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
top = join(meet(X_36,top),complement(join(complement(top),X_36))),
inference(resolve,[$cnf( $equal(top,join(meet(top,X_36),complement(join(complement(top),X_36)))) )],[refute_0_128,refute_0_382]) ).
cnf(refute_0_384,plain,
join(complement(top),X_36) = join(complement(top),X_36),
introduced(tautology,[refl,[$fot(join(complement(top),X_36))]]) ).
cnf(refute_0_385,plain,
( complement(top) != zero
| join(complement(top),X_36) != join(complement(top),X_36)
| join(complement(top),X_36) = join(zero,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),X_36),join(complement(top),X_36)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_386,plain,
( complement(top) != zero
| join(complement(top),X_36) = join(zero,X_36) ),
inference(resolve,[$cnf( $equal(join(complement(top),X_36),join(complement(top),X_36)) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
join(complement(top),X_36) = join(zero,X_36),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_386]) ).
cnf(refute_0_388,plain,
complement(join(complement(top),X_36)) = complement(join(complement(top),X_36)),
introduced(tautology,[refl,[$fot(complement(join(complement(top),X_36)))]]) ).
cnf(refute_0_389,plain,
( complement(join(complement(top),X_36)) != complement(join(complement(top),X_36))
| join(complement(top),X_36) != join(zero,X_36)
| complement(join(complement(top),X_36)) = complement(join(zero,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(top),X_36)),complement(join(complement(top),X_36))) ),[1,0],$fot(join(zero,X_36))]]) ).
cnf(refute_0_390,plain,
( join(complement(top),X_36) != join(zero,X_36)
| complement(join(complement(top),X_36)) = complement(join(zero,X_36)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(top),X_36)),complement(join(complement(top),X_36))) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
complement(join(complement(top),X_36)) = complement(join(zero,X_36)),
inference(resolve,[$cnf( $equal(join(complement(top),X_36),join(zero,X_36)) )],[refute_0_387,refute_0_390]) ).
cnf(refute_0_392,plain,
join(meet(X_36,top),complement(join(complement(top),X_36))) = join(meet(X_36,top),complement(join(complement(top),X_36))),
introduced(tautology,[refl,[$fot(join(meet(X_36,top),complement(join(complement(top),X_36))))]]) ).
cnf(refute_0_393,plain,
( complement(join(complement(top),X_36)) != complement(join(zero,X_36))
| join(meet(X_36,top),complement(join(complement(top),X_36))) != join(meet(X_36,top),complement(join(complement(top),X_36)))
| join(meet(X_36,top),complement(join(complement(top),X_36))) = join(meet(X_36,top),complement(join(zero,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_36,top),complement(join(complement(top),X_36))),join(meet(X_36,top),complement(join(complement(top),X_36)))) ),[1,1],$fot(complement(join(zero,X_36)))]]) ).
cnf(refute_0_394,plain,
( complement(join(complement(top),X_36)) != complement(join(zero,X_36))
| join(meet(X_36,top),complement(join(complement(top),X_36))) = join(meet(X_36,top),complement(join(zero,X_36))) ),
inference(resolve,[$cnf( $equal(join(meet(X_36,top),complement(join(complement(top),X_36))),join(meet(X_36,top),complement(join(complement(top),X_36)))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
join(meet(X_36,top),complement(join(complement(top),X_36))) = join(meet(X_36,top),complement(join(zero,X_36))),
inference(resolve,[$cnf( $equal(complement(join(complement(top),X_36)),complement(join(zero,X_36))) )],[refute_0_391,refute_0_394]) ).
cnf(refute_0_396,plain,
( join(meet(X_36,top),complement(join(complement(top),X_36))) != join(meet(X_36,top),complement(join(zero,X_36)))
| top != join(meet(X_36,top),complement(join(complement(top),X_36)))
| top = join(meet(X_36,top),complement(join(zero,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(X_36,top),complement(join(complement(top),X_36)))) ),[1],$fot(join(meet(X_36,top),complement(join(zero,X_36))))]]) ).
cnf(refute_0_397,plain,
( top != join(meet(X_36,top),complement(join(complement(top),X_36)))
| top = join(meet(X_36,top),complement(join(zero,X_36))) ),
inference(resolve,[$cnf( $equal(join(meet(X_36,top),complement(join(complement(top),X_36))),join(meet(X_36,top),complement(join(zero,X_36)))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
top = join(meet(X_36,top),complement(join(zero,X_36))),
inference(resolve,[$cnf( $equal(top,join(meet(X_36,top),complement(join(complement(top),X_36)))) )],[refute_0_383,refute_0_397]) ).
cnf(refute_0_399,plain,
top = join(meet(complement(join(top,complement(zero))),top),complement(join(zero,complement(join(top,complement(zero)))))),
inference(subst,[],[refute_0_398:[bind(X_36,$fot(complement(join(top,complement(zero)))))]]) ).
cnf(refute_0_400,plain,
( join(zero,complement(join(top,complement(zero)))) != zero
| top != join(meet(complement(join(top,complement(zero))),top),complement(join(zero,complement(join(top,complement(zero))))))
| top = join(meet(complement(join(top,complement(zero))),top),complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(complement(join(top,complement(zero))),top),complement(join(zero,complement(join(top,complement(zero))))))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_401,plain,
( top != join(meet(complement(join(top,complement(zero))),top),complement(join(zero,complement(join(top,complement(zero))))))
| top = join(meet(complement(join(top,complement(zero))),top),complement(zero)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(top,complement(zero)))),zero) )],[refute_0_188,refute_0_400]) ).
cnf(refute_0_402,plain,
top = join(meet(complement(join(top,complement(zero))),top),complement(zero)),
inference(resolve,[$cnf( $equal(top,join(meet(complement(join(top,complement(zero))),top),complement(join(zero,complement(join(top,complement(zero))))))) )],[refute_0_399,refute_0_401]) ).
cnf(refute_0_403,plain,
meet(top,complement(join(top,complement(zero)))) = complement(join(top,complement(zero))),
inference(subst,[],[refute_0_323:[bind(X_37,$fot(join(top,complement(zero))))]]) ).
cnf(refute_0_404,plain,
meet(complement(join(top,complement(zero))),top) = meet(top,complement(join(top,complement(zero)))),
inference(subst,[],[refute_0_108:[bind(A,$fot(complement(join(top,complement(zero)))))]]) ).
cnf(refute_0_405,plain,
( meet(complement(join(top,complement(zero))),top) != meet(top,complement(join(top,complement(zero))))
| meet(top,complement(join(top,complement(zero)))) != complement(join(top,complement(zero)))
| meet(complement(join(top,complement(zero))),top) = complement(join(top,complement(zero))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(complement(join(top,complement(zero))),top))),bind(Y,$fot(meet(top,complement(join(top,complement(zero)))))),bind(Z,$fot(complement(join(top,complement(zero)))))]]) ).
cnf(refute_0_406,plain,
( meet(top,complement(join(top,complement(zero)))) != complement(join(top,complement(zero)))
| meet(complement(join(top,complement(zero))),top) = complement(join(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(meet(complement(join(top,complement(zero))),top),meet(top,complement(join(top,complement(zero))))) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
meet(complement(join(top,complement(zero))),top) = complement(join(top,complement(zero))),
inference(resolve,[$cnf( $equal(meet(top,complement(join(top,complement(zero)))),complement(join(top,complement(zero)))) )],[refute_0_403,refute_0_406]) ).
cnf(refute_0_408,plain,
join(complement(zero),meet(complement(join(top,complement(zero))),top)) = join(complement(zero),meet(complement(join(top,complement(zero))),top)),
introduced(tautology,[refl,[$fot(join(complement(zero),meet(complement(join(top,complement(zero))),top)))]]) ).
cnf(refute_0_409,plain,
( join(complement(zero),meet(complement(join(top,complement(zero))),top)) != join(complement(zero),meet(complement(join(top,complement(zero))),top))
| meet(complement(join(top,complement(zero))),top) != complement(join(top,complement(zero)))
| join(complement(zero),meet(complement(join(top,complement(zero))),top)) = join(complement(zero),complement(join(top,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),meet(complement(join(top,complement(zero))),top)),join(complement(zero),meet(complement(join(top,complement(zero))),top))) ),[1,1],$fot(complement(join(top,complement(zero))))]]) ).
cnf(refute_0_410,plain,
( meet(complement(join(top,complement(zero))),top) != complement(join(top,complement(zero)))
| join(complement(zero),meet(complement(join(top,complement(zero))),top)) = join(complement(zero),complement(join(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(complement(join(top,complement(zero))),top)),join(complement(zero),meet(complement(join(top,complement(zero))),top))) )],[refute_0_408,refute_0_409]) ).
cnf(refute_0_411,plain,
join(complement(zero),meet(complement(join(top,complement(zero))),top)) = join(complement(zero),complement(join(top,complement(zero)))),
inference(resolve,[$cnf( $equal(meet(complement(join(top,complement(zero))),top),complement(join(top,complement(zero)))) )],[refute_0_407,refute_0_410]) ).
cnf(refute_0_412,plain,
join(meet(complement(join(top,complement(zero))),top),complement(zero)) = join(complement(zero),meet(complement(join(top,complement(zero))),top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(zero))),bind(B,$fot(meet(complement(join(top,complement(zero))),top)))]]) ).
cnf(refute_0_413,plain,
( join(complement(zero),meet(complement(join(top,complement(zero))),top)) != join(complement(zero),complement(join(top,complement(zero))))
| join(meet(complement(join(top,complement(zero))),top),complement(zero)) != join(complement(zero),meet(complement(join(top,complement(zero))),top))
| join(meet(complement(join(top,complement(zero))),top),complement(zero)) = join(complement(zero),complement(join(top,complement(zero)))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(meet(complement(join(top,complement(zero))),top),complement(zero)))),bind(Y,$fot(join(complement(zero),meet(complement(join(top,complement(zero))),top)))),bind(Z,$fot(join(complement(zero),complement(join(top,complement(zero))))))]]) ).
cnf(refute_0_414,plain,
( join(complement(zero),meet(complement(join(top,complement(zero))),top)) != join(complement(zero),complement(join(top,complement(zero))))
| join(meet(complement(join(top,complement(zero))),top),complement(zero)) = join(complement(zero),complement(join(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(meet(complement(join(top,complement(zero))),top),complement(zero)),join(complement(zero),meet(complement(join(top,complement(zero))),top))) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
join(meet(complement(join(top,complement(zero))),top),complement(zero)) = join(complement(zero),complement(join(top,complement(zero)))),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(complement(join(top,complement(zero))),top)),join(complement(zero),complement(join(top,complement(zero))))) )],[refute_0_411,refute_0_414]) ).
cnf(refute_0_416,plain,
( join(meet(complement(join(top,complement(zero))),top),complement(zero)) != join(complement(zero),complement(join(top,complement(zero))))
| top != join(meet(complement(join(top,complement(zero))),top),complement(zero))
| top = join(complement(zero),complement(join(top,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(complement(join(top,complement(zero))),top),complement(zero))) ),[1],$fot(join(complement(zero),complement(join(top,complement(zero)))))]]) ).
cnf(refute_0_417,plain,
( top != join(meet(complement(join(top,complement(zero))),top),complement(zero))
| top = join(complement(zero),complement(join(top,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(meet(complement(join(top,complement(zero))),top),complement(zero)),join(complement(zero),complement(join(top,complement(zero))))) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
top = join(complement(zero),complement(join(top,complement(zero)))),
inference(resolve,[$cnf( $equal(top,join(meet(complement(join(top,complement(zero))),top),complement(zero))) )],[refute_0_402,refute_0_417]) ).
cnf(refute_0_419,plain,
( top != join(complement(zero),complement(join(top,complement(zero))))
| join(complement(zero),complement(join(top,complement(zero)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(zero),complement(join(top,complement(zero))))))]]) ).
cnf(refute_0_420,plain,
join(complement(zero),complement(join(top,complement(zero)))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(zero),complement(join(top,complement(zero))))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
( join(complement(zero),complement(join(top,complement(zero)))) != top
| meet(zero,join(top,complement(zero))) != complement(join(complement(zero),complement(join(top,complement(zero)))))
| meet(zero,join(top,complement(zero))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,join(top,complement(zero))),complement(join(complement(zero),complement(join(top,complement(zero)))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_422,plain,
( meet(zero,join(top,complement(zero))) != complement(join(complement(zero),complement(join(top,complement(zero)))))
| meet(zero,join(top,complement(zero))) = complement(top) ),
inference(resolve,[$cnf( $equal(join(complement(zero),complement(join(top,complement(zero)))),top) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
meet(zero,join(top,complement(zero))) = complement(top),
inference(resolve,[$cnf( $equal(meet(zero,join(top,complement(zero))),complement(join(complement(zero),complement(join(top,complement(zero)))))) )],[refute_0_377,refute_0_422]) ).
cnf(refute_0_424,plain,
( complement(top) != zero
| meet(zero,join(top,complement(zero))) != complement(top)
| meet(zero,join(top,complement(zero))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,join(top,complement(zero))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_425,plain,
( meet(zero,join(top,complement(zero))) != complement(top)
| meet(zero,join(top,complement(zero))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_424]) ).
cnf(refute_0_426,plain,
meet(zero,join(top,complement(zero))) = zero,
inference(resolve,[$cnf( $equal(meet(zero,join(top,complement(zero))),complement(top)) )],[refute_0_423,refute_0_425]) ).
cnf(refute_0_427,plain,
meet(join(top,complement(zero)),zero) = meet(zero,join(top,complement(zero))),
inference(subst,[],[refute_0_355:[bind(X_14,$fot(zero)),bind(X_15,$fot(join(top,complement(zero))))]]) ).
cnf(refute_0_428,plain,
( meet(join(top,complement(zero)),zero) != meet(zero,join(top,complement(zero)))
| meet(zero,join(top,complement(zero))) != zero
| meet(join(top,complement(zero)),zero) = zero ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(join(top,complement(zero)),zero))),bind(Y,$fot(meet(zero,join(top,complement(zero))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_429,plain,
( meet(zero,join(top,complement(zero))) != zero
| meet(join(top,complement(zero)),zero) = zero ),
inference(resolve,[$cnf( $equal(meet(join(top,complement(zero)),zero),meet(zero,join(top,complement(zero)))) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
meet(join(top,complement(zero)),zero) = zero,
inference(resolve,[$cnf( $equal(meet(zero,join(top,complement(zero))),zero) )],[refute_0_426,refute_0_429]) ).
cnf(refute_0_431,plain,
join(complement(zero),meet(join(top,complement(zero)),zero)) = join(complement(zero),meet(join(top,complement(zero)),zero)),
introduced(tautology,[refl,[$fot(join(complement(zero),meet(join(top,complement(zero)),zero)))]]) ).
cnf(refute_0_432,plain,
( join(complement(zero),meet(join(top,complement(zero)),zero)) != join(complement(zero),meet(join(top,complement(zero)),zero))
| meet(join(top,complement(zero)),zero) != zero
| join(complement(zero),meet(join(top,complement(zero)),zero)) = join(complement(zero),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),meet(join(top,complement(zero)),zero)),join(complement(zero),meet(join(top,complement(zero)),zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_433,plain,
( meet(join(top,complement(zero)),zero) != zero
| join(complement(zero),meet(join(top,complement(zero)),zero)) = join(complement(zero),zero) ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(join(top,complement(zero)),zero)),join(complement(zero),meet(join(top,complement(zero)),zero))) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
join(complement(zero),meet(join(top,complement(zero)),zero)) = join(complement(zero),zero),
inference(resolve,[$cnf( $equal(meet(join(top,complement(zero)),zero),zero) )],[refute_0_430,refute_0_433]) ).
cnf(refute_0_435,plain,
( join(complement(zero),meet(join(top,complement(zero)),zero)) != join(complement(zero),zero)
| join(complement(zero),zero) != top
| join(complement(zero),meet(join(top,complement(zero)),zero)) = top ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(zero),meet(join(top,complement(zero)),zero)))),bind(Y,$fot(join(complement(zero),zero))),bind(Z,$fot(top))]]) ).
cnf(refute_0_436,plain,
( join(complement(zero),zero) != top
| join(complement(zero),meet(join(top,complement(zero)),zero)) = top ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(join(top,complement(zero)),zero)),join(complement(zero),zero)) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
join(complement(zero),meet(join(top,complement(zero)),zero)) = top,
inference(resolve,[$cnf( $equal(join(complement(zero),zero),top) )],[refute_0_199,refute_0_436]) ).
cnf(refute_0_438,plain,
( join(complement(zero),meet(join(top,complement(zero)),zero)) != top
| join(top,complement(zero)) != join(complement(zero),meet(join(top,complement(zero)),zero))
| join(top,complement(zero)) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(top,complement(zero)),join(complement(zero),meet(join(top,complement(zero)),zero))) ),[1],$fot(top)]]) ).
cnf(refute_0_439,plain,
( join(top,complement(zero)) != join(complement(zero),meet(join(top,complement(zero)),zero))
| join(top,complement(zero)) = top ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(join(top,complement(zero)),zero)),top) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
join(top,complement(zero)) = top,
inference(resolve,[$cnf( $equal(join(top,complement(zero)),join(complement(zero),meet(join(top,complement(zero)),zero))) )],[refute_0_376,refute_0_439]) ).
cnf(refute_0_441,plain,
join(top,join(top,complement(zero))) = join(top,join(top,complement(zero))),
introduced(tautology,[refl,[$fot(join(top,join(top,complement(zero))))]]) ).
cnf(refute_0_442,plain,
( join(top,complement(zero)) != top
| join(top,join(top,complement(zero))) != join(top,join(top,complement(zero)))
| join(top,join(top,complement(zero))) = join(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(top,complement(zero))),join(top,join(top,complement(zero)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_443,plain,
( join(top,complement(zero)) != top
| join(top,join(top,complement(zero))) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(top,join(top,complement(zero))),join(top,join(top,complement(zero)))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
join(top,join(top,complement(zero))) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,complement(zero)),top) )],[refute_0_440,refute_0_443]) ).
cnf(refute_0_445,plain,
join(join(top,top),complement(zero)) = join(top,join(top,complement(zero))),
inference(subst,[],[refute_0_205:[bind(A,$fot(top)),bind(B,$fot(top)),bind(C,$fot(complement(zero)))]]) ).
cnf(refute_0_446,plain,
( join(join(top,top),complement(zero)) != join(top,join(top,complement(zero)))
| join(top,join(top,complement(zero))) != join(top,top)
| join(join(top,top),complement(zero)) = join(top,top) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(join(top,top),complement(zero)))),bind(Y,$fot(join(top,join(top,complement(zero))))),bind(Z,$fot(join(top,top)))]]) ).
cnf(refute_0_447,plain,
( join(top,join(top,complement(zero))) != join(top,top)
| join(join(top,top),complement(zero)) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(join(top,top),complement(zero)),join(top,join(top,complement(zero)))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
join(join(top,top),complement(zero)) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,join(top,complement(zero))),join(top,top)) )],[refute_0_444,refute_0_447]) ).
cnf(refute_0_449,plain,
( join(join(top,top),complement(zero)) != join(top,top)
| join(join(top,top),complement(zero)) != top
| join(top,top) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(join(top,top),complement(zero)),top) ),[0],$fot(join(top,top))]]) ).
cnf(refute_0_450,plain,
( join(join(top,top),complement(zero)) != top
| join(top,top) = top ),
inference(resolve,[$cnf( $equal(join(join(top,top),complement(zero)),join(top,top)) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
join(top,top) = top,
inference(resolve,[$cnf( $equal(join(join(top,top),complement(zero)),top) )],[refute_0_372,refute_0_450]) ).
cnf(refute_0_452,plain,
( join(top,join(top,X_81)) != join(join(top,top),X_81)
| join(top,top) != top
| join(top,join(top,X_81)) = join(top,X_81) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(top,X_81)),join(join(top,top),X_81)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_453,plain,
( join(top,join(top,X_81)) != join(join(top,top),X_81)
| join(top,join(top,X_81)) = join(top,X_81) ),
inference(resolve,[$cnf( $equal(join(top,top),top) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
join(top,join(top,X_81)) = join(top,X_81),
inference(resolve,[$cnf( $equal(join(top,join(top,X_81)),join(join(top,top),X_81)) )],[refute_0_27,refute_0_453]) ).
cnf(refute_0_455,plain,
join(top,join(top,converse(complement(converse(top))))) = join(top,converse(complement(converse(top)))),
inference(subst,[],[refute_0_454:[bind(X_81,$fot(converse(complement(converse(top)))))]]) ).
cnf(refute_0_456,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_457,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_458,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( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_457]) ).
cnf(refute_0_459,plain,
converse(join(converse(A),X_5)) = join(A,converse(X_5)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_5)),join(converse(converse(A)),converse(X_5))) )],[refute_0_456,refute_0_458]) ).
cnf(refute_0_460,plain,
converse(join(converse(X_21),complement(converse(X_21)))) = join(X_21,converse(complement(converse(X_21)))),
inference(subst,[],[refute_0_459:[bind(A,$fot(X_21)),bind(X_5,$fot(complement(converse(X_21))))]]) ).
cnf(refute_0_461,plain,
top = join(converse(X_21),complement(converse(X_21))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_21)))]]) ).
cnf(refute_0_462,plain,
( top != join(converse(X_21),complement(converse(X_21)))
| join(converse(X_21),complement(converse(X_21))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_21),complement(converse(X_21)))))]]) ).
cnf(refute_0_463,plain,
join(converse(X_21),complement(converse(X_21))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_21),complement(converse(X_21)))) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
( converse(join(converse(X_21),complement(converse(X_21)))) != join(X_21,converse(complement(converse(X_21))))
| join(converse(X_21),complement(converse(X_21))) != top
| converse(top) = join(X_21,converse(complement(converse(X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_21),complement(converse(X_21)))),join(X_21,converse(complement(converse(X_21))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_465,plain,
( converse(join(converse(X_21),complement(converse(X_21)))) != join(X_21,converse(complement(converse(X_21))))
| converse(top) = join(X_21,converse(complement(converse(X_21)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_21),complement(converse(X_21))),top) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
converse(top) = join(X_21,converse(complement(converse(X_21)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_21),complement(converse(X_21)))),join(X_21,converse(complement(converse(X_21))))) )],[refute_0_460,refute_0_465]) ).
cnf(refute_0_467,plain,
converse(top) = join(top,converse(complement(converse(top)))),
inference(subst,[],[refute_0_466:[bind(X_21,$fot(top))]]) ).
cnf(refute_0_468,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_469,plain,
join(top,converse(complement(converse(top)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(top,converse(complement(converse(top))))) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
( join(top,converse(complement(converse(top)))) != converse(top)
| join(top,join(top,converse(complement(converse(top))))) != join(top,converse(complement(converse(top))))
| join(top,converse(top)) = join(top,converse(complement(converse(top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(top,converse(complement(converse(top))))),join(top,converse(complement(converse(top))))) ),[0,1],$fot(converse(top))]]) ).
cnf(refute_0_471,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( $equal(join(top,converse(complement(converse(top)))),converse(top)) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
join(top,converse(top)) = join(top,converse(complement(converse(top)))),
inference(resolve,[$cnf( $equal(join(top,join(top,converse(complement(converse(top))))),join(top,converse(complement(converse(top))))) )],[refute_0_455,refute_0_471]) ).
cnf(refute_0_473,plain,
( join(top,converse(complement(converse(top)))) != converse(top)
| join(top,converse(top)) != join(top,converse(complement(converse(top))))
| join(top,converse(top)) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,converse(top)),join(top,converse(complement(converse(top))))) ),[1],$fot(converse(top))]]) ).
cnf(refute_0_474,plain,
( join(top,converse(top)) != join(top,converse(complement(converse(top))))
| join(top,converse(top)) = converse(top) ),
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(top)))),converse(top)) )],[refute_0_469,refute_0_473]) ).
cnf(refute_0_475,plain,
join(top,converse(top)) = converse(top),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(top,converse(complement(converse(top))))) )],[refute_0_472,refute_0_474]) ).
cnf(refute_0_476,plain,
( converse(join(converse(top),top)) != converse(join(top,converse(top)))
| join(top,converse(top)) != converse(top)
| converse(join(converse(top),top)) = converse(converse(top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(top),top)),converse(join(top,converse(top)))) ),[1,0],$fot(converse(top))]]) ).
cnf(refute_0_477,plain,
( converse(join(converse(top),top)) != converse(join(top,converse(top)))
| converse(join(converse(top),top)) = converse(converse(top)) ),
inference(resolve,[$cnf( $equal(join(top,converse(top)),converse(top)) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
converse(join(converse(top),top)) = converse(converse(top)),
inference(resolve,[$cnf( $equal(converse(join(converse(top),top)),converse(join(top,converse(top)))) )],[refute_0_26,refute_0_477]) ).
cnf(refute_0_479,plain,
join(converse(top),top) = join(top,converse(top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(converse(top)))]]) ).
cnf(refute_0_480,plain,
( join(converse(top),top) != join(top,converse(top))
| join(top,converse(top)) != converse(top)
| join(converse(top),top) = converse(top) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(converse(top),top))),bind(Y,$fot(join(top,converse(top)))),bind(Z,$fot(converse(top)))]]) ).
cnf(refute_0_481,plain,
( join(top,converse(top)) != converse(top)
| join(converse(top),top) = converse(top) ),
inference(resolve,[$cnf( $equal(join(converse(top),top),join(top,converse(top))) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
join(converse(top),top) = converse(top),
inference(resolve,[$cnf( $equal(join(top,converse(top)),converse(top)) )],[refute_0_475,refute_0_481]) ).
cnf(refute_0_483,plain,
converse(join(X_4,converse(A))) = join(converse(X_4),converse(converse(A))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_4)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_484,plain,
( converse(converse(A)) != A
| converse(join(X_4,converse(A))) != join(converse(X_4),converse(converse(A)))
| converse(join(X_4,converse(A))) = join(converse(X_4),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_4,converse(A))),join(converse(X_4),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_485,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( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_484]) ).
cnf(refute_0_486,plain,
converse(join(X_4,converse(A))) = join(converse(X_4),A),
inference(resolve,[$cnf( $equal(converse(join(X_4,converse(A))),join(converse(X_4),converse(converse(A)))) )],[refute_0_483,refute_0_485]) ).
cnf(refute_0_487,plain,
converse(join(top,converse(top))) = join(converse(top),top),
inference(subst,[],[refute_0_486:[bind(A,$fot(top)),bind(X_4,$fot(top))]]) ).
cnf(refute_0_488,plain,
( converse(join(top,converse(top))) != join(converse(top),top)
| join(converse(top),top) != converse(top)
| converse(join(top,converse(top))) = converse(top) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(converse(join(top,converse(top))))),bind(Y,$fot(join(converse(top),top))),bind(Z,$fot(converse(top)))]]) ).
cnf(refute_0_489,plain,
( join(converse(top),top) != converse(top)
| converse(join(top,converse(top))) = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),top)) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
converse(join(top,converse(top))) = converse(top),
inference(resolve,[$cnf( $equal(join(converse(top),top),converse(top)) )],[refute_0_482,refute_0_489]) ).
cnf(refute_0_491,plain,
( converse(join(converse(top),top)) != converse(join(top,converse(top)))
| converse(join(top,converse(top))) != converse(top)
| converse(join(converse(top),top)) = converse(top) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(converse(join(converse(top),top)))),bind(Y,$fot(converse(join(top,converse(top))))),bind(Z,$fot(converse(top)))]]) ).
cnf(refute_0_492,plain,
( converse(join(top,converse(top))) != converse(top)
| converse(join(converse(top),top)) = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(converse(top),top)),converse(join(top,converse(top)))) )],[refute_0_26,refute_0_491]) ).
cnf(refute_0_493,plain,
converse(join(converse(top),top)) = converse(top),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),converse(top)) )],[refute_0_490,refute_0_492]) ).
cnf(refute_0_494,plain,
( converse(join(converse(top),top)) != converse(converse(top))
| converse(join(converse(top),top)) != converse(top)
| converse(top) = converse(converse(top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(top),top)),converse(converse(top))) ),[0],$fot(converse(top))]]) ).
cnf(refute_0_495,plain,
( converse(join(converse(top),top)) != converse(converse(top))
| converse(top) = converse(converse(top)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(top),top)),converse(top)) )],[refute_0_493,refute_0_494]) ).
cnf(refute_0_496,plain,
converse(converse(top)) = top,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(top))]]) ).
cnf(refute_0_497,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_498,plain,
( converse(top) != converse(converse(top))
| converse(top) = top ),
inference(resolve,[$cnf( $equal(converse(converse(top)),top) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
( converse(join(converse(top),top)) != converse(converse(top))
| converse(top) = top ),
inference(resolve,[$cnf( $equal(converse(top),converse(converse(top))) )],[refute_0_495,refute_0_498]) ).
cnf(refute_0_500,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(converse(join(converse(top),top)),converse(converse(top))) )],[refute_0_478,refute_0_499]) ).
cnf(refute_0_501,plain,
( converse(composition(converse(top),X_7)) != composition(converse(X_7),top)
| converse(top) != top
| converse(composition(top,X_7)) = composition(converse(X_7),top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(top),X_7)),composition(converse(X_7),top)) ),[0,0,0],$fot(top)]]) ).
cnf(refute_0_502,plain,
( converse(composition(converse(top),X_7)) != composition(converse(X_7),top)
| converse(composition(top,X_7)) = composition(converse(X_7),top) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
converse(composition(top,X_7)) = composition(converse(X_7),top),
inference(resolve,[$cnf( $equal(converse(composition(converse(top),X_7)),composition(converse(X_7),top)) )],[refute_0_15,refute_0_502]) ).
cnf(refute_0_504,plain,
converse(composition(top,X_89)) = composition(converse(X_89),top),
inference(subst,[],[refute_0_503:[bind(X_7,$fot(X_89))]]) ).
cnf(refute_0_505,plain,
( converse(composition(top,X_89)) != composition(converse(X_89),top)
| composition(converse(X_89),top) = converse(composition(top,X_89)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(top,X_89)))),bind(Y,$fot(composition(converse(X_89),top)))]]) ).
cnf(refute_0_506,plain,
composition(converse(X_89),top) = converse(composition(top,X_89)),
inference(resolve,[$cnf( $equal(converse(composition(top,X_89)),composition(converse(X_89),top)) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
( composition(converse(X_89),top) != converse(composition(top,X_89))
| join(complement(top),composition(converse(converse(X_89)),complement(composition(converse(X_89),top)))) != complement(top)
| join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(converse(X_89)),complement(composition(converse(X_89),top)))),complement(top)) ),[0,1,1,0],$fot(converse(composition(top,X_89)))]]) ).
cnf(refute_0_508,plain,
( join(complement(top),composition(converse(converse(X_89)),complement(composition(converse(X_89),top)))) != complement(top)
| join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = complement(top) ),
inference(resolve,[$cnf( $equal(composition(converse(X_89),top),converse(composition(top,X_89))) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(converse(X_89)),complement(composition(converse(X_89),top)))),complement(top)) )],[refute_0_10,refute_0_508]) ).
cnf(refute_0_510,plain,
X_35 = join(meet(X_35,complement(complement(X_35))),complement(join(complement(X_35),complement(complement(X_35))))),
inference(subst,[],[refute_0_47:[bind(A,$fot(X_35)),bind(B,$fot(complement(complement(X_35))))]]) ).
cnf(refute_0_511,plain,
top = join(complement(X_35),complement(complement(X_35))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_35)))]]) ).
cnf(refute_0_512,plain,
( top != join(complement(X_35),complement(complement(X_35)))
| join(complement(X_35),complement(complement(X_35))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_35),complement(complement(X_35)))))]]) ).
cnf(refute_0_513,plain,
join(complement(X_35),complement(complement(X_35))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_35),complement(complement(X_35)))) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
( X_35 != join(meet(X_35,complement(complement(X_35))),complement(join(complement(X_35),complement(complement(X_35)))))
| join(complement(X_35),complement(complement(X_35))) != top
| X_35 = join(meet(X_35,complement(complement(X_35))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_35,join(meet(X_35,complement(complement(X_35))),complement(join(complement(X_35),complement(complement(X_35)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_515,plain,
( X_35 != join(meet(X_35,complement(complement(X_35))),complement(join(complement(X_35),complement(complement(X_35)))))
| X_35 = join(meet(X_35,complement(complement(X_35))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_35),complement(complement(X_35))),top) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
X_35 = join(meet(X_35,complement(complement(X_35))),complement(top)),
inference(resolve,[$cnf( $equal(X_35,join(meet(X_35,complement(complement(X_35))),complement(join(complement(X_35),complement(complement(X_35)))))) )],[refute_0_510,refute_0_515]) ).
cnf(refute_0_517,plain,
join(complement(top),meet(X_35,complement(complement(X_35)))) = join(complement(top),meet(X_35,complement(complement(X_35)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_35,complement(complement(X_35)))))]]) ).
cnf(refute_0_518,plain,
( complement(top) != zero
| join(complement(top),meet(X_35,complement(complement(X_35)))) != join(complement(top),meet(X_35,complement(complement(X_35))))
| join(complement(top),meet(X_35,complement(complement(X_35)))) = join(zero,meet(X_35,complement(complement(X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_35,complement(complement(X_35)))),join(complement(top),meet(X_35,complement(complement(X_35))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_519,plain,
( complement(top) != zero
| join(complement(top),meet(X_35,complement(complement(X_35)))) = join(zero,meet(X_35,complement(complement(X_35)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_35,complement(complement(X_35)))),join(complement(top),meet(X_35,complement(complement(X_35))))) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
join(complement(top),meet(X_35,complement(complement(X_35)))) = join(zero,meet(X_35,complement(complement(X_35)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_519]) ).
cnf(refute_0_521,plain,
join(meet(X_35,complement(complement(X_35))),complement(top)) = join(complement(top),meet(X_35,complement(complement(X_35)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_35,complement(complement(X_35)))))]]) ).
cnf(refute_0_522,plain,
( join(complement(top),meet(X_35,complement(complement(X_35)))) != join(zero,meet(X_35,complement(complement(X_35))))
| join(meet(X_35,complement(complement(X_35))),complement(top)) != join(complement(top),meet(X_35,complement(complement(X_35))))
| join(meet(X_35,complement(complement(X_35))),complement(top)) = join(zero,meet(X_35,complement(complement(X_35)))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(meet(X_35,complement(complement(X_35))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_35,complement(complement(X_35)))))),bind(Z,$fot(join(zero,meet(X_35,complement(complement(X_35))))))]]) ).
cnf(refute_0_523,plain,
( join(complement(top),meet(X_35,complement(complement(X_35)))) != join(zero,meet(X_35,complement(complement(X_35))))
| join(meet(X_35,complement(complement(X_35))),complement(top)) = join(zero,meet(X_35,complement(complement(X_35)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_35,complement(complement(X_35))),complement(top)),join(complement(top),meet(X_35,complement(complement(X_35))))) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
join(meet(X_35,complement(complement(X_35))),complement(top)) = join(zero,meet(X_35,complement(complement(X_35)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_35,complement(complement(X_35)))),join(zero,meet(X_35,complement(complement(X_35))))) )],[refute_0_520,refute_0_523]) ).
cnf(refute_0_525,plain,
( X_35 != join(meet(X_35,complement(complement(X_35))),complement(top))
| join(meet(X_35,complement(complement(X_35))),complement(top)) != join(zero,meet(X_35,complement(complement(X_35))))
| X_35 = join(zero,meet(X_35,complement(complement(X_35)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_35,join(zero,meet(X_35,complement(complement(X_35))))) ),[0],$fot(join(meet(X_35,complement(complement(X_35))),complement(top)))]]) ).
cnf(refute_0_526,plain,
( X_35 != join(meet(X_35,complement(complement(X_35))),complement(top))
| X_35 = join(zero,meet(X_35,complement(complement(X_35)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_35,complement(complement(X_35))),complement(top)),join(zero,meet(X_35,complement(complement(X_35))))) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
X_35 = join(zero,meet(X_35,complement(complement(X_35)))),
inference(resolve,[$cnf( $equal(X_35,join(meet(X_35,complement(complement(X_35))),complement(top))) )],[refute_0_516,refute_0_526]) ).
cnf(refute_0_528,plain,
meet(B,B) = complement(join(complement(B),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_529,plain,
join(complement(B),complement(B)) = complement(B),
inference(subst,[],[refute_0_295:[bind(X_32,$fot(B))]]) ).
cnf(refute_0_530,plain,
( join(complement(B),complement(B)) != complement(B)
| meet(B,B) != complement(join(complement(B),complement(B)))
| meet(B,B) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(B,B),complement(join(complement(B),complement(B)))) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_531,plain,
( meet(B,B) != complement(join(complement(B),complement(B)))
| meet(B,B) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(join(complement(B),complement(B)),complement(B)) )],[refute_0_529,refute_0_530]) ).
cnf(refute_0_532,plain,
meet(B,B) = complement(complement(B)),
inference(resolve,[$cnf( $equal(meet(B,B),complement(join(complement(B),complement(B)))) )],[refute_0_528,refute_0_531]) ).
cnf(refute_0_533,plain,
meet(top,complement(X_35)) = complement(X_35),
inference(subst,[],[refute_0_323:[bind(X_37,$fot(X_35))]]) ).
cnf(refute_0_534,plain,
complement(meet(top,complement(X_35))) = complement(meet(top,complement(X_35))),
introduced(tautology,[refl,[$fot(complement(meet(top,complement(X_35))))]]) ).
cnf(refute_0_535,plain,
( complement(meet(top,complement(X_35))) != complement(meet(top,complement(X_35)))
| meet(top,complement(X_35)) != complement(X_35)
| complement(meet(top,complement(X_35))) = complement(complement(X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,complement(X_35))),complement(meet(top,complement(X_35)))) ),[1,0],$fot(complement(X_35))]]) ).
cnf(refute_0_536,plain,
( meet(top,complement(X_35)) != complement(X_35)
| complement(meet(top,complement(X_35))) = complement(complement(X_35)) ),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(X_35))),complement(meet(top,complement(X_35)))) )],[refute_0_534,refute_0_535]) ).
cnf(refute_0_537,plain,
complement(meet(top,complement(X_35))) = complement(complement(X_35)),
inference(resolve,[$cnf( $equal(meet(top,complement(X_35)),complement(X_35)) )],[refute_0_533,refute_0_536]) ).
cnf(refute_0_538,plain,
join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B)))))),
inference(subst,[],[refute_0_527:[bind(X_35,$fot(join(zero,complement(B))))]]) ).
cnf(refute_0_539,plain,
( complement(join(zero,complement(B))) != meet(top,B)
| join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))
| join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))) ),[1,1,1,0],$fot(meet(top,B))]]) ).
cnf(refute_0_540,plain,
( join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))
| join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),meet(top,B)) )],[refute_0_96,refute_0_539]) ).
cnf(refute_0_541,plain,
join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))) )],[refute_0_538,refute_0_540]) ).
cnf(refute_0_542,plain,
meet(join(zero,complement(B)),complement(meet(top,B))) = meet(complement(meet(top,B)),join(zero,complement(B))),
inference(subst,[],[refute_0_355:[bind(X_14,$fot(complement(meet(top,B)))),bind(X_15,$fot(join(zero,complement(B))))]]) ).
cnf(refute_0_543,plain,
join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))))]]) ).
cnf(refute_0_544,plain,
( join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) != join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))
| meet(join(zero,complement(B)),complement(meet(top,B))) != meet(complement(meet(top,B)),join(zero,complement(B)))
| join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))) ),[1,1],$fot(meet(complement(meet(top,B)),join(zero,complement(B))))]]) ).
cnf(refute_0_545,plain,
( meet(join(zero,complement(B)),complement(meet(top,B))) != meet(complement(meet(top,B)),join(zero,complement(B)))
| join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(B)),complement(meet(top,B))),meet(complement(meet(top,B)),join(zero,complement(B)))) )],[refute_0_542,refute_0_545]) ).
cnf(refute_0_547,plain,
( join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))
| join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| join(zero,complement(B)) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,complement(B)),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) ),[0],$fot(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))))]]) ).
cnf(refute_0_548,plain,
( join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))
| join(zero,complement(B)) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
join(zero,complement(B)) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))) )],[refute_0_541,refute_0_548]) ).
cnf(refute_0_550,plain,
join(complement(A),complement(B)) = join(zero,complement(complement(join(complement(A),complement(B))))),
inference(subst,[],[refute_0_317:[bind(X_35,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_551,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_552,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( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_35,refute_0_551]) ).
cnf(refute_0_553,plain,
join(complement(A),complement(B)) = join(zero,complement(meet(A,B))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(complement(join(complement(A),complement(B)))))) )],[refute_0_550,refute_0_552]) ).
cnf(refute_0_554,plain,
join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B)))))),
inference(subst,[],[refute_0_527:[bind(X_35,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_555,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))
| join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))) ),[1,1,1,0],$fot(meet(A,B))]]) ).
cnf(refute_0_556,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))
| join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_35,refute_0_555]) ).
cnf(refute_0_557,plain,
join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))) )],[refute_0_554,refute_0_556]) ).
cnf(refute_0_558,plain,
join(complement(complement(meet(A,B))),meet(A,B)) = join(meet(A,B),complement(complement(meet(A,B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(complement(meet(A,B)))))]]) ).
cnf(refute_0_559,plain,
complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(meet(A,B))),meet(A,B))))]]) ).
cnf(refute_0_560,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| join(complement(complement(meet(A,B))),meet(A,B)) != join(meet(A,B),complement(complement(meet(A,B))))
| complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) ),[1,0],$fot(join(meet(A,B),complement(complement(meet(A,B)))))]]) ).
cnf(refute_0_561,plain,
( join(complement(complement(meet(A,B))),meet(A,B)) != join(meet(A,B),complement(complement(meet(A,B))))
| complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))),
inference(resolve,[$cnf( $equal(join(complement(complement(meet(A,B))),meet(A,B)),join(meet(A,B),complement(complement(meet(A,B))))) )],[refute_0_558,refute_0_561]) ).
cnf(refute_0_563,plain,
meet(A,join(complement(X_14),complement(X_15))) = complement(join(complement(A),complement(join(complement(X_14),complement(X_15))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(complement(X_14),complement(X_15))))]]) ).
cnf(refute_0_564,plain,
( complement(join(complement(X_14),complement(X_15))) != meet(X_14,X_15)
| meet(A,join(complement(X_14),complement(X_15))) != complement(join(complement(A),complement(join(complement(X_14),complement(X_15)))))
| meet(A,join(complement(X_14),complement(X_15))) = complement(join(complement(A),meet(X_14,X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_14),complement(X_15))),complement(join(complement(A),complement(join(complement(X_14),complement(X_15)))))) ),[1,0,1],$fot(meet(X_14,X_15))]]) ).
cnf(refute_0_565,plain,
( meet(A,join(complement(X_14),complement(X_15))) != complement(join(complement(A),complement(join(complement(X_14),complement(X_15)))))
| meet(A,join(complement(X_14),complement(X_15))) = complement(join(complement(A),meet(X_14,X_15))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_14),complement(X_15))),meet(X_14,X_15)) )],[refute_0_64,refute_0_564]) ).
cnf(refute_0_566,plain,
meet(A,join(complement(X_14),complement(X_15))) = complement(join(complement(A),meet(X_14,X_15))),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_14),complement(X_15))),complement(join(complement(A),complement(join(complement(X_14),complement(X_15)))))) )],[refute_0_563,refute_0_565]) ).
cnf(refute_0_567,plain,
meet(complement(meet(A,B)),join(complement(A),complement(B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
inference(subst,[],[refute_0_566:[bind(A,$fot(complement(meet(A,B)))),bind(X_14,$fot(A)),bind(X_15,$fot(B))]]) ).
cnf(refute_0_568,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = meet(complement(meet(A,B)),join(complement(A),complement(B))),
inference(subst,[],[refute_0_355:[bind(X_14,$fot(complement(meet(A,B)))),bind(X_15,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_569,plain,
( meet(complement(meet(A,B)),join(complement(A),complement(B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != meet(complement(meet(A,B)),join(complement(A),complement(B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(join(complement(A),complement(B)),complement(meet(A,B))))),bind(Y,$fot(meet(complement(meet(A,B)),join(complement(A),complement(B))))),bind(Z,$fot(complement(join(complement(complement(meet(A,B))),meet(A,B)))))]]) ).
cnf(refute_0_570,plain,
( meet(complement(meet(A,B)),join(complement(A),complement(B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),meet(complement(meet(A,B)),join(complement(A),complement(B)))) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
inference(resolve,[$cnf( $equal(meet(complement(meet(A,B)),join(complement(A),complement(B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_567,refute_0_570]) ).
cnf(refute_0_572,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(join(complement(A),complement(B)),complement(meet(A,B))))),bind(Y,$fot(complement(join(complement(complement(meet(A,B))),meet(A,B))))),bind(Z,$fot(complement(join(meet(A,B),complement(complement(meet(A,B)))))))]]) ).
cnf(refute_0_573,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(meet(A,B),complement(complement(meet(A,B)))))) )],[refute_0_562,refute_0_573]) ).
cnf(refute_0_575,plain,
join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))))]]) ).
cnf(refute_0_576,plain,
( join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) ),[1,1],$fot(complement(join(meet(A,B),complement(complement(meet(A,B))))))]]) ).
cnf(refute_0_577,plain,
( meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),complement(join(meet(A,B),complement(complement(meet(A,B)))))) )],[refute_0_574,refute_0_577]) ).
cnf(refute_0_579,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) ),[0],$fot(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))))]]) ).
cnf(refute_0_580,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) )],[refute_0_578,refute_0_579]) ).
cnf(refute_0_581,plain,
join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) )],[refute_0_557,refute_0_580]) ).
cnf(refute_0_582,plain,
X_35 = join(meet(X_35,X_36),complement(join(complement(X_35),X_36))),
inference(subst,[],[refute_0_47:[bind(A,$fot(X_35)),bind(B,$fot(X_36))]]) ).
cnf(refute_0_583,plain,
meet(X_36,X_35) = meet(X_35,X_36),
inference(subst,[],[refute_0_353:[bind(X_14,$fot(X_36)),bind(X_15,$fot(X_35))]]) ).
cnf(refute_0_584,plain,
( meet(X_36,X_35) != meet(X_35,X_36)
| meet(X_35,X_36) = meet(X_36,X_35) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_36,X_35))),bind(Y,$fot(meet(X_35,X_36)))]]) ).
cnf(refute_0_585,plain,
meet(X_35,X_36) = meet(X_36,X_35),
inference(resolve,[$cnf( $equal(meet(X_36,X_35),meet(X_35,X_36)) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
( X_35 != join(meet(X_35,X_36),complement(join(complement(X_35),X_36)))
| meet(X_35,X_36) != meet(X_36,X_35)
| X_35 = join(meet(X_36,X_35),complement(join(complement(X_35),X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(X_35,join(meet(X_35,X_36),complement(join(complement(X_35),X_36)))) ),[1,0],$fot(meet(X_36,X_35))]]) ).
cnf(refute_0_587,plain,
( X_35 != join(meet(X_35,X_36),complement(join(complement(X_35),X_36)))
| X_35 = join(meet(X_36,X_35),complement(join(complement(X_35),X_36))) ),
inference(resolve,[$cnf( $equal(meet(X_35,X_36),meet(X_36,X_35)) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
X_35 = join(meet(X_36,X_35),complement(join(complement(X_35),X_36))),
inference(resolve,[$cnf( $equal(X_35,join(meet(X_35,X_36),complement(join(complement(X_35),X_36)))) )],[refute_0_582,refute_0_587]) ).
cnf(refute_0_589,plain,
complement(X_60) = join(meet(X_60,complement(X_60)),complement(join(complement(complement(X_60)),X_60))),
inference(subst,[],[refute_0_588:[bind(X_35,$fot(complement(X_60))),bind(X_36,$fot(X_60))]]) ).
cnf(refute_0_590,plain,
zero = meet(X_60,complement(X_60)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_60))]]) ).
cnf(refute_0_591,plain,
( zero != meet(X_60,complement(X_60))
| meet(X_60,complement(X_60)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_60,complement(X_60))))]]) ).
cnf(refute_0_592,plain,
meet(X_60,complement(X_60)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_60,complement(X_60))) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
( complement(X_60) != join(meet(X_60,complement(X_60)),complement(join(complement(complement(X_60)),X_60)))
| meet(X_60,complement(X_60)) != zero
| complement(X_60) = join(zero,complement(join(complement(complement(X_60)),X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_60),join(meet(X_60,complement(X_60)),complement(join(complement(complement(X_60)),X_60)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_594,plain,
( complement(X_60) != join(meet(X_60,complement(X_60)),complement(join(complement(complement(X_60)),X_60)))
| complement(X_60) = join(zero,complement(join(complement(complement(X_60)),X_60))) ),
inference(resolve,[$cnf( $equal(meet(X_60,complement(X_60)),zero) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
complement(X_60) = join(zero,complement(join(complement(complement(X_60)),X_60))),
inference(resolve,[$cnf( $equal(complement(X_60),join(meet(X_60,complement(X_60)),complement(join(complement(complement(X_60)),X_60)))) )],[refute_0_589,refute_0_594]) ).
cnf(refute_0_596,plain,
join(complement(complement(X_60)),X_60) = join(X_60,complement(complement(X_60))),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_60)),bind(B,$fot(complement(complement(X_60))))]]) ).
cnf(refute_0_597,plain,
complement(join(complement(complement(X_60)),X_60)) = complement(join(complement(complement(X_60)),X_60)),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(X_60)),X_60)))]]) ).
cnf(refute_0_598,plain,
( complement(join(complement(complement(X_60)),X_60)) != complement(join(complement(complement(X_60)),X_60))
| join(complement(complement(X_60)),X_60) != join(X_60,complement(complement(X_60)))
| complement(join(complement(complement(X_60)),X_60)) = complement(join(X_60,complement(complement(X_60)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(X_60)),X_60)),complement(join(complement(complement(X_60)),X_60))) ),[1,0],$fot(join(X_60,complement(complement(X_60))))]]) ).
cnf(refute_0_599,plain,
( join(complement(complement(X_60)),X_60) != join(X_60,complement(complement(X_60)))
| complement(join(complement(complement(X_60)),X_60)) = complement(join(X_60,complement(complement(X_60)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_60)),X_60)),complement(join(complement(complement(X_60)),X_60))) )],[refute_0_597,refute_0_598]) ).
cnf(refute_0_600,plain,
complement(join(complement(complement(X_60)),X_60)) = complement(join(X_60,complement(complement(X_60)))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_60)),X_60),join(X_60,complement(complement(X_60)))) )],[refute_0_596,refute_0_599]) ).
cnf(refute_0_601,plain,
join(zero,complement(join(complement(complement(X_60)),X_60))) = join(zero,complement(join(complement(complement(X_60)),X_60))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(complement(X_60)),X_60))))]]) ).
cnf(refute_0_602,plain,
( complement(join(complement(complement(X_60)),X_60)) != complement(join(X_60,complement(complement(X_60))))
| join(zero,complement(join(complement(complement(X_60)),X_60))) != join(zero,complement(join(complement(complement(X_60)),X_60)))
| join(zero,complement(join(complement(complement(X_60)),X_60))) = join(zero,complement(join(X_60,complement(complement(X_60))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(complement(X_60)),X_60))),join(zero,complement(join(complement(complement(X_60)),X_60)))) ),[1,1],$fot(complement(join(X_60,complement(complement(X_60)))))]]) ).
cnf(refute_0_603,plain,
( complement(join(complement(complement(X_60)),X_60)) != complement(join(X_60,complement(complement(X_60))))
| join(zero,complement(join(complement(complement(X_60)),X_60))) = join(zero,complement(join(X_60,complement(complement(X_60))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(complement(X_60)),X_60))),join(zero,complement(join(complement(complement(X_60)),X_60)))) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
join(zero,complement(join(complement(complement(X_60)),X_60))) = join(zero,complement(join(X_60,complement(complement(X_60))))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_60)),X_60)),complement(join(X_60,complement(complement(X_60))))) )],[refute_0_600,refute_0_603]) ).
cnf(refute_0_605,plain,
( complement(X_60) != join(zero,complement(join(complement(complement(X_60)),X_60)))
| join(zero,complement(join(complement(complement(X_60)),X_60))) != join(zero,complement(join(X_60,complement(complement(X_60)))))
| complement(X_60) = join(zero,complement(join(X_60,complement(complement(X_60))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_60),join(zero,complement(join(X_60,complement(complement(X_60)))))) ),[0],$fot(join(zero,complement(join(complement(complement(X_60)),X_60))))]]) ).
cnf(refute_0_606,plain,
( complement(X_60) != join(zero,complement(join(complement(complement(X_60)),X_60)))
| complement(X_60) = join(zero,complement(join(X_60,complement(complement(X_60))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(complement(X_60)),X_60))),join(zero,complement(join(X_60,complement(complement(X_60)))))) )],[refute_0_604,refute_0_605]) ).
cnf(refute_0_607,plain,
complement(X_60) = join(zero,complement(join(X_60,complement(complement(X_60))))),
inference(resolve,[$cnf( $equal(complement(X_60),join(zero,complement(join(complement(complement(X_60)),X_60)))) )],[refute_0_595,refute_0_606]) ).
cnf(refute_0_608,plain,
( complement(X_60) != join(zero,complement(join(X_60,complement(complement(X_60)))))
| join(zero,complement(join(X_60,complement(complement(X_60))))) = complement(X_60) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_60))),bind(Y,$fot(join(zero,complement(join(X_60,complement(complement(X_60)))))))]]) ).
cnf(refute_0_609,plain,
join(zero,complement(join(X_60,complement(complement(X_60))))) = complement(X_60),
inference(resolve,[$cnf( $equal(complement(X_60),join(zero,complement(join(X_60,complement(complement(X_60)))))) )],[refute_0_607,refute_0_608]) ).
cnf(refute_0_610,plain,
join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) = complement(meet(A,B)),
inference(subst,[],[refute_0_609:[bind(X_60,$fot(meet(A,B)))]]) ).
cnf(refute_0_611,plain,
( join(complement(A),complement(B)) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) != complement(meet(A,B))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),complement(meet(A,B))) ),[0],$fot(join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))))]]) ).
cnf(refute_0_612,plain,
( join(complement(A),complement(B)) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),complement(meet(A,B))) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
join(complement(A),complement(B)) = complement(meet(A,B)),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) )],[refute_0_581,refute_0_612]) ).
cnf(refute_0_614,plain,
( join(complement(A),complement(B)) != complement(meet(A,B))
| join(complement(A),complement(B)) != join(zero,complement(meet(A,B)))
| complement(meet(A,B)) = join(zero,complement(meet(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(meet(A,B)))) ),[0],$fot(complement(meet(A,B)))]]) ).
cnf(refute_0_615,plain,
( join(complement(A),complement(B)) != join(zero,complement(meet(A,B)))
| complement(meet(A,B)) = join(zero,complement(meet(A,B))) ),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),complement(meet(A,B))) )],[refute_0_613,refute_0_614]) ).
cnf(refute_0_616,plain,
complement(meet(A,B)) = join(zero,complement(meet(A,B))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(meet(A,B)))) )],[refute_0_553,refute_0_615]) ).
cnf(refute_0_617,plain,
( complement(meet(A,B)) != join(zero,complement(meet(A,B)))
| join(zero,complement(meet(A,B))) = complement(meet(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(meet(A,B)))),bind(Y,$fot(join(zero,complement(meet(A,B)))))]]) ).
cnf(refute_0_618,plain,
join(zero,complement(meet(A,B))) = complement(meet(A,B)),
inference(resolve,[$cnf( $equal(complement(meet(A,B)),join(zero,complement(meet(A,B)))) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
join(zero,complement(meet(top,B))) = complement(meet(top,B)),
inference(subst,[],[refute_0_618:[bind(A,$fot(top))]]) ).
cnf(refute_0_620,plain,
meet(X_32,X_32) = complement(complement(X_32)),
inference(subst,[],[refute_0_532:[bind(B,$fot(X_32))]]) ).
cnf(refute_0_621,plain,
complement(meet(X_32,X_32)) = complement(meet(X_32,X_32)),
introduced(tautology,[refl,[$fot(complement(meet(X_32,X_32)))]]) ).
cnf(refute_0_622,plain,
( complement(meet(X_32,X_32)) != complement(meet(X_32,X_32))
| meet(X_32,X_32) != complement(complement(X_32))
| complement(meet(X_32,X_32)) = complement(complement(complement(X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(X_32,X_32)),complement(meet(X_32,X_32))) ),[1,0],$fot(complement(complement(X_32)))]]) ).
cnf(refute_0_623,plain,
( meet(X_32,X_32) != complement(complement(X_32))
| complement(meet(X_32,X_32)) = complement(complement(complement(X_32))) ),
inference(resolve,[$cnf( $equal(complement(meet(X_32,X_32)),complement(meet(X_32,X_32))) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
complement(meet(X_32,X_32)) = complement(complement(complement(X_32))),
inference(resolve,[$cnf( $equal(meet(X_32,X_32),complement(complement(X_32))) )],[refute_0_620,refute_0_623]) ).
cnf(refute_0_625,plain,
join(complement(X_32),complement(X_32)) = complement(meet(X_32,X_32)),
inference(subst,[],[refute_0_613:[bind(A,$fot(X_32)),bind(B,$fot(X_32))]]) ).
cnf(refute_0_626,plain,
( complement(meet(X_32,X_32)) != complement(complement(complement(X_32)))
| join(complement(X_32),complement(X_32)) != complement(meet(X_32,X_32))
| join(complement(X_32),complement(X_32)) = complement(complement(complement(X_32))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(X_32),complement(X_32)))),bind(Y,$fot(complement(meet(X_32,X_32)))),bind(Z,$fot(complement(complement(complement(X_32)))))]]) ).
cnf(refute_0_627,plain,
( complement(meet(X_32,X_32)) != complement(complement(complement(X_32)))
| join(complement(X_32),complement(X_32)) = complement(complement(complement(X_32))) ),
inference(resolve,[$cnf( $equal(join(complement(X_32),complement(X_32)),complement(meet(X_32,X_32))) )],[refute_0_625,refute_0_626]) ).
cnf(refute_0_628,plain,
join(complement(X_32),complement(X_32)) = complement(complement(complement(X_32))),
inference(resolve,[$cnf( $equal(complement(meet(X_32,X_32)),complement(complement(complement(X_32)))) )],[refute_0_624,refute_0_627]) ).
cnf(refute_0_629,plain,
( join(complement(X_32),complement(X_32)) != complement(X_32)
| join(complement(X_32),complement(X_32)) != complement(complement(complement(X_32)))
| complement(complement(complement(X_32))) = complement(X_32) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_32),complement(X_32)),complement(X_32)) ),[0],$fot(complement(complement(complement(X_32))))]]) ).
cnf(refute_0_630,plain,
( join(complement(X_32),complement(X_32)) != complement(X_32)
| complement(complement(complement(X_32))) = complement(X_32) ),
inference(resolve,[$cnf( $equal(join(complement(X_32),complement(X_32)),complement(complement(complement(X_32)))) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
complement(complement(complement(X_32))) = complement(X_32),
inference(resolve,[$cnf( $equal(join(complement(X_32),complement(X_32)),complement(X_32)) )],[refute_0_295,refute_0_630]) ).
cnf(refute_0_632,plain,
complement(complement(complement(meet(top,B)))) = complement(meet(top,B)),
inference(subst,[],[refute_0_631:[bind(X_32,$fot(meet(top,B)))]]) ).
cnf(refute_0_633,plain,
meet(complement(meet(top,B)),complement(meet(top,B))) = complement(complement(complement(meet(top,B)))),
inference(subst,[],[refute_0_532:[bind(B,$fot(complement(meet(top,B))))]]) ).
cnf(refute_0_634,plain,
( complement(complement(complement(meet(top,B)))) != complement(meet(top,B))
| meet(complement(meet(top,B)),complement(meet(top,B))) != complement(complement(complement(meet(top,B))))
| meet(complement(meet(top,B)),complement(meet(top,B))) = complement(meet(top,B)) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(complement(meet(top,B)),complement(meet(top,B))))),bind(Y,$fot(complement(complement(complement(meet(top,B)))))),bind(Z,$fot(complement(meet(top,B))))]]) ).
cnf(refute_0_635,plain,
( complement(complement(complement(meet(top,B)))) != complement(meet(top,B))
| meet(complement(meet(top,B)),complement(meet(top,B))) = complement(meet(top,B)) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,B)),complement(meet(top,B))),complement(complement(complement(meet(top,B))))) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
meet(complement(meet(top,B)),complement(meet(top,B))) = complement(meet(top,B)),
inference(resolve,[$cnf( $equal(complement(complement(complement(meet(top,B)))),complement(meet(top,B))) )],[refute_0_632,refute_0_635]) ).
cnf(refute_0_637,plain,
meet(A,join(zero,complement(X_17))) = complement(join(complement(A),complement(join(zero,complement(X_17))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(zero,complement(X_17))))]]) ).
cnf(refute_0_638,plain,
meet(top,X_17) = complement(join(zero,complement(X_17))),
inference(subst,[],[refute_0_94:[bind(B,$fot(X_17))]]) ).
cnf(refute_0_639,plain,
( meet(top,X_17) != complement(join(zero,complement(X_17)))
| complement(join(zero,complement(X_17))) = meet(top,X_17) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,X_17))),bind(Y,$fot(complement(join(zero,complement(X_17)))))]]) ).
cnf(refute_0_640,plain,
complement(join(zero,complement(X_17))) = meet(top,X_17),
inference(resolve,[$cnf( $equal(meet(top,X_17),complement(join(zero,complement(X_17)))) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
( complement(join(zero,complement(X_17))) != meet(top,X_17)
| meet(A,join(zero,complement(X_17))) != complement(join(complement(A),complement(join(zero,complement(X_17)))))
| meet(A,join(zero,complement(X_17))) = complement(join(complement(A),meet(top,X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_17))),complement(join(complement(A),complement(join(zero,complement(X_17)))))) ),[1,0,1],$fot(meet(top,X_17))]]) ).
cnf(refute_0_642,plain,
( meet(A,join(zero,complement(X_17))) != complement(join(complement(A),complement(join(zero,complement(X_17)))))
| meet(A,join(zero,complement(X_17))) = complement(join(complement(A),meet(top,X_17))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_17))),meet(top,X_17)) )],[refute_0_640,refute_0_641]) ).
cnf(refute_0_643,plain,
meet(A,join(zero,complement(X_17))) = complement(join(complement(A),meet(top,X_17))),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_17))),complement(join(complement(A),complement(join(zero,complement(X_17)))))) )],[refute_0_637,refute_0_642]) ).
cnf(refute_0_644,plain,
join(complement(X_14),complement(X_15)) = complement(meet(X_14,X_15)),
inference(subst,[],[refute_0_613:[bind(A,$fot(X_14)),bind(B,$fot(X_15))]]) ).
cnf(refute_0_645,plain,
meet(A,join(complement(X_14),complement(X_15))) = meet(A,join(complement(X_14),complement(X_15))),
introduced(tautology,[refl,[$fot(meet(A,join(complement(X_14),complement(X_15))))]]) ).
cnf(refute_0_646,plain,
( join(complement(X_14),complement(X_15)) != complement(meet(X_14,X_15))
| meet(A,join(complement(X_14),complement(X_15))) != meet(A,join(complement(X_14),complement(X_15)))
| meet(A,join(complement(X_14),complement(X_15))) = meet(A,complement(meet(X_14,X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_14),complement(X_15))),meet(A,join(complement(X_14),complement(X_15)))) ),[1,1],$fot(complement(meet(X_14,X_15)))]]) ).
cnf(refute_0_647,plain,
( join(complement(X_14),complement(X_15)) != complement(meet(X_14,X_15))
| meet(A,join(complement(X_14),complement(X_15))) = meet(A,complement(meet(X_14,X_15))) ),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_14),complement(X_15))),meet(A,join(complement(X_14),complement(X_15)))) )],[refute_0_645,refute_0_646]) ).
cnf(refute_0_648,plain,
meet(A,join(complement(X_14),complement(X_15))) = meet(A,complement(meet(X_14,X_15))),
inference(resolve,[$cnf( $equal(join(complement(X_14),complement(X_15)),complement(meet(X_14,X_15))) )],[refute_0_644,refute_0_647]) ).
cnf(refute_0_649,plain,
( meet(A,join(complement(X_14),complement(X_15))) != complement(join(complement(A),meet(X_14,X_15)))
| meet(A,join(complement(X_14),complement(X_15))) != meet(A,complement(meet(X_14,X_15)))
| meet(A,complement(meet(X_14,X_15))) = complement(join(complement(A),meet(X_14,X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_14),complement(X_15))),complement(join(complement(A),meet(X_14,X_15)))) ),[0],$fot(meet(A,complement(meet(X_14,X_15))))]]) ).
cnf(refute_0_650,plain,
( meet(A,join(complement(X_14),complement(X_15))) != complement(join(complement(A),meet(X_14,X_15)))
| meet(A,complement(meet(X_14,X_15))) = complement(join(complement(A),meet(X_14,X_15))) ),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_14),complement(X_15))),meet(A,complement(meet(X_14,X_15)))) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
meet(A,complement(meet(X_14,X_15))) = complement(join(complement(A),meet(X_14,X_15))),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_14),complement(X_15))),complement(join(complement(A),meet(X_14,X_15)))) )],[refute_0_566,refute_0_650]) ).
cnf(refute_0_652,plain,
( meet(A,complement(meet(X_14,X_15))) != complement(join(complement(A),meet(X_14,X_15)))
| complement(join(complement(A),meet(X_14,X_15))) = meet(A,complement(meet(X_14,X_15))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,complement(meet(X_14,X_15))))),bind(Y,$fot(complement(join(complement(A),meet(X_14,X_15)))))]]) ).
cnf(refute_0_653,plain,
complement(join(complement(A),meet(X_14,X_15))) = meet(A,complement(meet(X_14,X_15))),
inference(resolve,[$cnf( $equal(meet(A,complement(meet(X_14,X_15))),complement(join(complement(A),meet(X_14,X_15)))) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
complement(join(complement(A),meet(top,X_17))) = meet(A,complement(meet(top,X_17))),
inference(subst,[],[refute_0_653:[bind(X_14,$fot(top)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_655,plain,
( complement(join(complement(A),meet(top,X_17))) != meet(A,complement(meet(top,X_17)))
| meet(A,join(zero,complement(X_17))) != complement(join(complement(A),meet(top,X_17)))
| meet(A,join(zero,complement(X_17))) = meet(A,complement(meet(top,X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_17))),complement(join(complement(A),meet(top,X_17)))) ),[1],$fot(meet(A,complement(meet(top,X_17))))]]) ).
cnf(refute_0_656,plain,
( meet(A,join(zero,complement(X_17))) != complement(join(complement(A),meet(top,X_17)))
| meet(A,join(zero,complement(X_17))) = meet(A,complement(meet(top,X_17))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),meet(top,X_17))),meet(A,complement(meet(top,X_17)))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
meet(A,join(zero,complement(X_17))) = meet(A,complement(meet(top,X_17))),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_17))),complement(join(complement(A),meet(top,X_17)))) )],[refute_0_643,refute_0_656]) ).
cnf(refute_0_658,plain,
meet(complement(meet(top,B)),join(zero,complement(B))) = meet(complement(meet(top,B)),complement(meet(top,B))),
inference(subst,[],[refute_0_657:[bind(A,$fot(complement(meet(top,B)))),bind(X_17,$fot(B))]]) ).
cnf(refute_0_659,plain,
( meet(complement(meet(top,B)),complement(meet(top,B))) != complement(meet(top,B))
| meet(complement(meet(top,B)),join(zero,complement(B))) != meet(complement(meet(top,B)),complement(meet(top,B)))
| meet(complement(meet(top,B)),join(zero,complement(B))) = complement(meet(top,B)) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(complement(meet(top,B)),join(zero,complement(B))))),bind(Y,$fot(meet(complement(meet(top,B)),complement(meet(top,B))))),bind(Z,$fot(complement(meet(top,B))))]]) ).
cnf(refute_0_660,plain,
( meet(complement(meet(top,B)),complement(meet(top,B))) != complement(meet(top,B))
| meet(complement(meet(top,B)),join(zero,complement(B))) = complement(meet(top,B)) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,B)),join(zero,complement(B))),meet(complement(meet(top,B)),complement(meet(top,B)))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
meet(complement(meet(top,B)),join(zero,complement(B))) = complement(meet(top,B)),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,B)),complement(meet(top,B))),complement(meet(top,B))) )],[refute_0_636,refute_0_660]) ).
cnf(refute_0_662,plain,
join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),
introduced(tautology,[refl,[$fot(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))))]]) ).
cnf(refute_0_663,plain,
( join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| meet(complement(meet(top,B)),join(zero,complement(B))) != complement(meet(top,B))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,complement(meet(top,B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) ),[1,1],$fot(complement(meet(top,B)))]]) ).
cnf(refute_0_664,plain,
( meet(complement(meet(top,B)),join(zero,complement(B))) != complement(meet(top,B))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,complement(meet(top,B))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,complement(meet(top,B))),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,B)),join(zero,complement(B))),complement(meet(top,B))) )],[refute_0_661,refute_0_664]) ).
cnf(refute_0_666,plain,
( join(zero,complement(meet(top,B))) != complement(meet(top,B))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) != join(zero,complement(meet(top,B)))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = complement(meet(top,B)) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))))),bind(Y,$fot(join(zero,complement(meet(top,B))))),bind(Z,$fot(complement(meet(top,B))))]]) ).
cnf(refute_0_667,plain,
( join(zero,complement(meet(top,B))) != complement(meet(top,B))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = complement(meet(top,B)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),join(zero,complement(meet(top,B)))) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = complement(meet(top,B)),
inference(resolve,[$cnf( $equal(join(zero,complement(meet(top,B))),complement(meet(top,B))) )],[refute_0_619,refute_0_667]) ).
cnf(refute_0_669,plain,
( join(zero,complement(B)) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) != complement(meet(top,B))
| join(zero,complement(B)) = complement(meet(top,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,complement(B)),complement(meet(top,B))) ),[0],$fot(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))))]]) ).
cnf(refute_0_670,plain,
( join(zero,complement(B)) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| join(zero,complement(B)) = complement(meet(top,B)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),complement(meet(top,B))) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
join(zero,complement(B)) = complement(meet(top,B)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) )],[refute_0_549,refute_0_670]) ).
cnf(refute_0_672,plain,
join(zero,complement(complement(X_35))) = complement(meet(top,complement(X_35))),
inference(subst,[],[refute_0_671:[bind(B,$fot(complement(X_35)))]]) ).
cnf(refute_0_673,plain,
( complement(meet(top,complement(X_35))) != complement(complement(X_35))
| join(zero,complement(complement(X_35))) != complement(meet(top,complement(X_35)))
| join(zero,complement(complement(X_35))) = complement(complement(X_35)) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(zero,complement(complement(X_35))))),bind(Y,$fot(complement(meet(top,complement(X_35))))),bind(Z,$fot(complement(complement(X_35))))]]) ).
cnf(refute_0_674,plain,
( complement(meet(top,complement(X_35))) != complement(complement(X_35))
| join(zero,complement(complement(X_35))) = complement(complement(X_35)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_35))),complement(meet(top,complement(X_35)))) )],[refute_0_672,refute_0_673]) ).
cnf(refute_0_675,plain,
join(zero,complement(complement(X_35))) = complement(complement(X_35)),
inference(resolve,[$cnf( $equal(complement(meet(top,complement(X_35))),complement(complement(X_35))) )],[refute_0_537,refute_0_674]) ).
cnf(refute_0_676,plain,
( X_35 != join(zero,complement(complement(X_35)))
| join(zero,complement(complement(X_35))) != complement(complement(X_35))
| X_35 = complement(complement(X_35)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_35,complement(complement(X_35))) ),[0],$fot(join(zero,complement(complement(X_35))))]]) ).
cnf(refute_0_677,plain,
( X_35 != join(zero,complement(complement(X_35)))
| X_35 = complement(complement(X_35)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_35))),complement(complement(X_35))) )],[refute_0_675,refute_0_676]) ).
cnf(refute_0_678,plain,
X_35 = complement(complement(X_35)),
inference(resolve,[$cnf( $equal(X_35,join(zero,complement(complement(X_35)))) )],[refute_0_317,refute_0_677]) ).
cnf(refute_0_679,plain,
( X_35 != complement(complement(X_35))
| complement(complement(X_35)) = X_35 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_35)),bind(Y,$fot(complement(complement(X_35))))]]) ).
cnf(refute_0_680,plain,
complement(complement(X_35)) = X_35,
inference(resolve,[$cnf( $equal(X_35,complement(complement(X_35))) )],[refute_0_678,refute_0_679]) ).
cnf(refute_0_681,plain,
complement(complement(B)) = B,
inference(subst,[],[refute_0_680:[bind(X_35,$fot(B))]]) ).
cnf(refute_0_682,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_683,plain,
( meet(B,B) != complement(complement(B))
| meet(B,B) = B ),
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
meet(B,B) = B,
inference(resolve,[$cnf( $equal(meet(B,B),complement(complement(B))) )],[refute_0_532,refute_0_683]) ).
cnf(refute_0_685,plain,
meet(X_35,X_35) = X_35,
inference(subst,[],[refute_0_684:[bind(B,$fot(X_35))]]) ).
cnf(refute_0_686,plain,
meet(X_35,complement(complement(X_35))) = meet(X_35,complement(complement(X_35))),
introduced(tautology,[refl,[$fot(meet(X_35,complement(complement(X_35))))]]) ).
cnf(refute_0_687,plain,
( complement(complement(X_35)) != X_35
| meet(X_35,complement(complement(X_35))) != meet(X_35,complement(complement(X_35)))
| meet(X_35,complement(complement(X_35))) = meet(X_35,X_35) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_35,complement(complement(X_35))),meet(X_35,complement(complement(X_35)))) ),[1,1],$fot(X_35)]]) ).
cnf(refute_0_688,plain,
( complement(complement(X_35)) != X_35
| meet(X_35,complement(complement(X_35))) = meet(X_35,X_35) ),
inference(resolve,[$cnf( $equal(meet(X_35,complement(complement(X_35))),meet(X_35,complement(complement(X_35)))) )],[refute_0_686,refute_0_687]) ).
cnf(refute_0_689,plain,
meet(X_35,complement(complement(X_35))) = meet(X_35,X_35),
inference(resolve,[$cnf( $equal(complement(complement(X_35)),X_35) )],[refute_0_680,refute_0_688]) ).
cnf(refute_0_690,plain,
( meet(X_35,X_35) != X_35
| meet(X_35,complement(complement(X_35))) != meet(X_35,X_35)
| meet(X_35,complement(complement(X_35))) = X_35 ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(X_35,complement(complement(X_35))))),bind(Y,$fot(meet(X_35,X_35))),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_691,plain,
( meet(X_35,X_35) != X_35
| meet(X_35,complement(complement(X_35))) = X_35 ),
inference(resolve,[$cnf( $equal(meet(X_35,complement(complement(X_35))),meet(X_35,X_35)) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
meet(X_35,complement(complement(X_35))) = X_35,
inference(resolve,[$cnf( $equal(meet(X_35,X_35),X_35) )],[refute_0_685,refute_0_691]) ).
cnf(refute_0_693,plain,
join(zero,meet(X_35,complement(complement(X_35)))) = join(zero,meet(X_35,complement(complement(X_35)))),
introduced(tautology,[refl,[$fot(join(zero,meet(X_35,complement(complement(X_35)))))]]) ).
cnf(refute_0_694,plain,
( join(zero,meet(X_35,complement(complement(X_35)))) != join(zero,meet(X_35,complement(complement(X_35))))
| meet(X_35,complement(complement(X_35))) != X_35
| join(zero,meet(X_35,complement(complement(X_35)))) = join(zero,X_35) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_35,complement(complement(X_35)))),join(zero,meet(X_35,complement(complement(X_35))))) ),[1,1],$fot(X_35)]]) ).
cnf(refute_0_695,plain,
( meet(X_35,complement(complement(X_35))) != X_35
| join(zero,meet(X_35,complement(complement(X_35)))) = join(zero,X_35) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_35,complement(complement(X_35)))),join(zero,meet(X_35,complement(complement(X_35))))) )],[refute_0_693,refute_0_694]) ).
cnf(refute_0_696,plain,
join(zero,meet(X_35,complement(complement(X_35)))) = join(zero,X_35),
inference(resolve,[$cnf( $equal(meet(X_35,complement(complement(X_35))),X_35) )],[refute_0_692,refute_0_695]) ).
cnf(refute_0_697,plain,
( X_35 != join(zero,meet(X_35,complement(complement(X_35))))
| join(zero,meet(X_35,complement(complement(X_35)))) != join(zero,X_35)
| X_35 = join(zero,X_35) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_35,join(zero,X_35)) ),[0],$fot(join(zero,meet(X_35,complement(complement(X_35)))))]]) ).
cnf(refute_0_698,plain,
( X_35 != join(zero,meet(X_35,complement(complement(X_35))))
| X_35 = join(zero,X_35) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_35,complement(complement(X_35)))),join(zero,X_35)) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
X_35 = join(zero,X_35),
inference(resolve,[$cnf( $equal(X_35,join(zero,meet(X_35,complement(complement(X_35))))) )],[refute_0_527,refute_0_698]) ).
cnf(refute_0_700,plain,
( X_35 != join(zero,X_35)
| join(zero,X_35) = X_35 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_35)),bind(Y,$fot(join(zero,X_35)))]]) ).
cnf(refute_0_701,plain,
join(zero,X_35) = X_35,
inference(resolve,[$cnf( $equal(X_35,join(zero,X_35)) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
join(zero,composition(X_89,complement(converse(composition(top,X_89))))) = composition(X_89,complement(converse(composition(top,X_89)))),
inference(subst,[],[refute_0_701:[bind(X_35,$fot(composition(X_89,complement(converse(composition(top,X_89))))))]]) ).
cnf(refute_0_703,plain,
converse(converse(X_89)) = X_89,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_89))]]) ).
cnf(refute_0_704,plain,
composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))) = composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))),
introduced(tautology,[refl,[$fot(composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))))]]) ).
cnf(refute_0_705,plain,
( composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))) != composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))
| converse(converse(X_89)) != X_89
| composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))) = composition(X_89,complement(converse(composition(top,X_89)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) ),[1,0],$fot(X_89)]]) ).
cnf(refute_0_706,plain,
( converse(converse(X_89)) != X_89
| composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))) = composition(X_89,complement(converse(composition(top,X_89)))) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))) = composition(X_89,complement(converse(composition(top,X_89)))),
inference(resolve,[$cnf( $equal(converse(converse(X_89)),X_89) )],[refute_0_703,refute_0_706]) ).
cnf(refute_0_708,plain,
join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),
introduced(tautology,[refl,[$fot(join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))))]]) ).
cnf(refute_0_709,plain,
( composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))) != composition(X_89,complement(converse(composition(top,X_89))))
| join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) != join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))))
| join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = join(zero,composition(X_89,complement(converse(composition(top,X_89))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))))) ),[1,1],$fot(composition(X_89,complement(converse(composition(top,X_89)))))]]) ).
cnf(refute_0_710,plain,
( composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))) != composition(X_89,complement(converse(composition(top,X_89))))
| join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = join(zero,composition(X_89,complement(converse(composition(top,X_89))))) ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))))) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = join(zero,composition(X_89,complement(converse(composition(top,X_89))))),
inference(resolve,[$cnf( $equal(composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))),composition(X_89,complement(converse(composition(top,X_89))))) )],[refute_0_707,refute_0_710]) ).
cnf(refute_0_712,plain,
join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),
introduced(tautology,[refl,[$fot(join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))))]]) ).
cnf(refute_0_713,plain,
( complement(top) != zero
| join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) != join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))))
| join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_714,plain,
( complement(top) != zero
| join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))))) )],[refute_0_712,refute_0_713]) ).
cnf(refute_0_715,plain,
join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_714]) ).
cnf(refute_0_716,plain,
( join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) != join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))))
| join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) != join(zero,composition(X_89,complement(converse(composition(top,X_89)))))
| join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = join(zero,composition(X_89,complement(converse(composition(top,X_89))))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))))),bind(Y,$fot(join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))))),bind(Z,$fot(join(zero,composition(X_89,complement(converse(composition(top,X_89)))))))]]) ).
cnf(refute_0_717,plain,
( join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) != join(zero,composition(X_89,complement(converse(composition(top,X_89)))))
| join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = join(zero,composition(X_89,complement(converse(composition(top,X_89))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89)))))) )],[refute_0_715,refute_0_716]) ).
cnf(refute_0_718,plain,
join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = join(zero,composition(X_89,complement(converse(composition(top,X_89))))),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),join(zero,composition(X_89,complement(converse(composition(top,X_89)))))) )],[refute_0_711,refute_0_717]) ).
cnf(refute_0_719,plain,
( join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) != join(zero,composition(X_89,complement(converse(composition(top,X_89)))))
| join(zero,composition(X_89,complement(converse(composition(top,X_89))))) != composition(X_89,complement(converse(composition(top,X_89))))
| join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = composition(X_89,complement(converse(composition(top,X_89)))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))))),bind(Y,$fot(join(zero,composition(X_89,complement(converse(composition(top,X_89))))))),bind(Z,$fot(composition(X_89,complement(converse(composition(top,X_89))))))]]) ).
cnf(refute_0_720,plain,
( join(zero,composition(X_89,complement(converse(composition(top,X_89))))) != composition(X_89,complement(converse(composition(top,X_89))))
| join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = composition(X_89,complement(converse(composition(top,X_89)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),join(zero,composition(X_89,complement(converse(composition(top,X_89)))))) )],[refute_0_718,refute_0_719]) ).
cnf(refute_0_721,plain,
join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) = composition(X_89,complement(converse(composition(top,X_89)))),
inference(resolve,[$cnf( $equal(join(zero,composition(X_89,complement(converse(composition(top,X_89))))),composition(X_89,complement(converse(composition(top,X_89))))) )],[refute_0_702,refute_0_720]) ).
cnf(refute_0_722,plain,
( join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) != complement(top)
| join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) != composition(X_89,complement(converse(composition(top,X_89))))
| composition(X_89,complement(converse(composition(top,X_89)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),complement(top)) ),[0],$fot(composition(X_89,complement(converse(composition(top,X_89)))))]]) ).
cnf(refute_0_723,plain,
( join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) != complement(top)
| composition(X_89,complement(converse(composition(top,X_89)))) = complement(top) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),composition(X_89,complement(converse(composition(top,X_89))))) )],[refute_0_721,refute_0_722]) ).
cnf(refute_0_724,plain,
( complement(top) != zero
| composition(X_89,complement(converse(composition(top,X_89)))) != complement(top)
| composition(X_89,complement(converse(composition(top,X_89)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_89,complement(converse(composition(top,X_89)))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_725,plain,
( composition(X_89,complement(converse(composition(top,X_89)))) != complement(top)
| composition(X_89,complement(converse(composition(top,X_89)))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_724]) ).
cnf(refute_0_726,plain,
( join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))) != complement(top)
| composition(X_89,complement(converse(composition(top,X_89)))) = zero ),
inference(resolve,[$cnf( $equal(composition(X_89,complement(converse(composition(top,X_89)))),complement(top)) )],[refute_0_723,refute_0_725]) ).
cnf(refute_0_727,plain,
composition(X_89,complement(converse(composition(top,X_89)))) = zero,
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(converse(X_89)),complement(converse(composition(top,X_89))))),complement(top)) )],[refute_0_509,refute_0_726]) ).
cnf(refute_0_728,plain,
composition(complement(converse(composition(X_461,top))),complement(converse(composition(top,complement(converse(composition(X_461,top))))))) = zero,
inference(subst,[],[refute_0_727:[bind(X_89,$fot(complement(converse(composition(X_461,top)))))]]) ).
cnf(refute_0_729,plain,
join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,composition(top,X_124))))) = complement(composition(top,X_124)),
inference(subst,[],[refute_0_8:[bind(A,$fot(top)),bind(B,$fot(composition(top,X_124)))]]) ).
cnf(refute_0_730,plain,
composition(top,composition(top,C)) = composition(composition(top,top),C),
inference(subst,[],[composition_associativity_5:[bind(A,$fot(top)),bind(B,$fot(top))]]) ).
cnf(refute_0_731,plain,
composition(join(X_98,one),X_100) = join(composition(X_98,X_100),composition(one,X_100)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_98)),bind(B,$fot(one)),bind(C,$fot(X_100))]]) ).
cnf(refute_0_732,plain,
X_100 = composition(one,X_100),
inference(subst,[],[refute_0_272:[bind(X_24,$fot(X_100))]]) ).
cnf(refute_0_733,plain,
( X_100 != composition(one,X_100)
| composition(one,X_100) = X_100 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_100)),bind(Y,$fot(composition(one,X_100)))]]) ).
cnf(refute_0_734,plain,
composition(one,X_100) = X_100,
inference(resolve,[$cnf( $equal(X_100,composition(one,X_100)) )],[refute_0_732,refute_0_733]) ).
cnf(refute_0_735,plain,
( composition(join(X_98,one),X_100) != join(composition(X_98,X_100),composition(one,X_100))
| composition(one,X_100) != X_100
| composition(join(X_98,one),X_100) = join(composition(X_98,X_100),X_100) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_98,one),X_100),join(composition(X_98,X_100),composition(one,X_100))) ),[1,1],$fot(X_100)]]) ).
cnf(refute_0_736,plain,
( composition(join(X_98,one),X_100) != join(composition(X_98,X_100),composition(one,X_100))
| composition(join(X_98,one),X_100) = join(composition(X_98,X_100),X_100) ),
inference(resolve,[$cnf( $equal(composition(one,X_100),X_100) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
composition(join(X_98,one),X_100) = join(composition(X_98,X_100),X_100),
inference(resolve,[$cnf( $equal(composition(join(X_98,one),X_100),join(composition(X_98,X_100),composition(one,X_100))) )],[refute_0_731,refute_0_736]) ).
cnf(refute_0_738,plain,
join(composition(X_98,X_100),X_100) = join(X_100,composition(X_98,X_100)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_100)),bind(B,$fot(composition(X_98,X_100)))]]) ).
cnf(refute_0_739,plain,
( composition(join(X_98,one),X_100) != join(composition(X_98,X_100),X_100)
| join(composition(X_98,X_100),X_100) != join(X_100,composition(X_98,X_100))
| composition(join(X_98,one),X_100) = join(X_100,composition(X_98,X_100)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_98,one),X_100),join(X_100,composition(X_98,X_100))) ),[0],$fot(join(composition(X_98,X_100),X_100))]]) ).
cnf(refute_0_740,plain,
( composition(join(X_98,one),X_100) != join(composition(X_98,X_100),X_100)
| composition(join(X_98,one),X_100) = join(X_100,composition(X_98,X_100)) ),
inference(resolve,[$cnf( $equal(join(composition(X_98,X_100),X_100),join(X_100,composition(X_98,X_100))) )],[refute_0_738,refute_0_739]) ).
cnf(refute_0_741,plain,
composition(join(X_98,one),X_100) = join(X_100,composition(X_98,X_100)),
inference(resolve,[$cnf( $equal(composition(join(X_98,one),X_100),join(composition(X_98,X_100),X_100)) )],[refute_0_737,refute_0_740]) ).
cnf(refute_0_742,plain,
composition(join(X_98,one),top) = join(top,composition(X_98,top)),
inference(subst,[],[refute_0_741:[bind(X_100,$fot(top))]]) ).
cnf(refute_0_743,plain,
top = join(join(complement(X_14),complement(X_15)),complement(join(complement(X_14),complement(X_15)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(complement(X_14),complement(X_15))))]]) ).
cnf(refute_0_744,plain,
( complement(join(complement(X_14),complement(X_15))) != meet(X_14,X_15)
| top != join(join(complement(X_14),complement(X_15)),complement(join(complement(X_14),complement(X_15))))
| top = join(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_14),complement(X_15)),complement(join(complement(X_14),complement(X_15))))) ),[1,1],$fot(meet(X_14,X_15))]]) ).
cnf(refute_0_745,plain,
( top != join(join(complement(X_14),complement(X_15)),complement(join(complement(X_14),complement(X_15))))
| top = join(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_14),complement(X_15))),meet(X_14,X_15)) )],[refute_0_64,refute_0_744]) ).
cnf(refute_0_746,plain,
top = join(join(complement(X_14),complement(X_15)),meet(X_14,X_15)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_14),complement(X_15)),complement(join(complement(X_14),complement(X_15))))) )],[refute_0_743,refute_0_745]) ).
cnf(refute_0_747,plain,
join(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) = join(complement(X_14),join(complement(X_15),meet(X_14,X_15))),
inference(subst,[],[refute_0_205:[bind(A,$fot(complement(X_14))),bind(B,$fot(complement(X_15))),bind(C,$fot(meet(X_14,X_15)))]]) ).
cnf(refute_0_748,plain,
( join(join(complement(X_14),complement(X_15)),meet(X_14,X_15)) != join(complement(X_14),join(complement(X_15),meet(X_14,X_15)))
| top != join(join(complement(X_14),complement(X_15)),meet(X_14,X_15))
| top = join(complement(X_14),join(complement(X_15),meet(X_14,X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_14),complement(X_15)),meet(X_14,X_15))) ),[1],$fot(join(complement(X_14),join(complement(X_15),meet(X_14,X_15))))]]) ).
cnf(refute_0_749,plain,
( top != join(join(complement(X_14),complement(X_15)),meet(X_14,X_15))
| top = join(complement(X_14),join(complement(X_15),meet(X_14,X_15))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_14),complement(X_15)),meet(X_14,X_15)),join(complement(X_14),join(complement(X_15),meet(X_14,X_15)))) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
top = join(complement(X_14),join(complement(X_15),meet(X_14,X_15))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_14),complement(X_15)),meet(X_14,X_15))) )],[refute_0_746,refute_0_749]) ).
cnf(refute_0_751,plain,
top = join(complement(X_110),join(complement(complement(X_35)),meet(X_110,complement(X_35)))),
inference(subst,[],[refute_0_750:[bind(X_14,$fot(X_110)),bind(X_15,$fot(complement(X_35)))]]) ).
cnf(refute_0_752,plain,
( complement(complement(X_35)) != X_35
| top != join(complement(X_110),join(complement(complement(X_35)),meet(X_110,complement(X_35))))
| top = join(complement(X_110),join(X_35,meet(X_110,complement(X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_110),join(complement(complement(X_35)),meet(X_110,complement(X_35))))) ),[1,1,0],$fot(X_35)]]) ).
cnf(refute_0_753,plain,
( top != join(complement(X_110),join(complement(complement(X_35)),meet(X_110,complement(X_35))))
| top = join(complement(X_110),join(X_35,meet(X_110,complement(X_35)))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_35)),X_35) )],[refute_0_680,refute_0_752]) ).
cnf(refute_0_754,plain,
top = join(complement(X_110),join(X_35,meet(X_110,complement(X_35)))),
inference(resolve,[$cnf( $equal(top,join(complement(X_110),join(complement(complement(X_35)),meet(X_110,complement(X_35))))) )],[refute_0_751,refute_0_753]) ).
cnf(refute_0_755,plain,
top = join(complement(zero),join(X_117,meet(zero,complement(X_117)))),
inference(subst,[],[refute_0_754:[bind(X_110,$fot(zero)),bind(X_35,$fot(X_117))]]) ).
cnf(refute_0_756,plain,
( X_50 != join(meet(X_50,top),meet(X_50,complement(top)))
| complement(top) != zero
| X_50 = join(meet(X_50,top),meet(X_50,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(X_50,join(meet(X_50,top),meet(X_50,complement(top)))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_757,plain,
( X_50 != join(meet(X_50,top),meet(X_50,complement(top)))
| X_50 = join(meet(X_50,top),meet(X_50,zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_756]) ).
cnf(refute_0_758,plain,
X_50 = join(meet(X_50,top),meet(X_50,zero)),
inference(resolve,[$cnf( $equal(X_50,join(meet(X_50,top),meet(X_50,complement(top)))) )],[refute_0_59,refute_0_757]) ).
cnf(refute_0_759,plain,
X_51 = join(meet(X_51,top),meet(X_51,zero)),
inference(subst,[],[refute_0_758:[bind(X_50,$fot(X_51))]]) ).
cnf(refute_0_760,plain,
meet(zero,X_51) = meet(X_51,zero),
inference(subst,[],[refute_0_353:[bind(X_14,$fot(zero)),bind(X_15,$fot(X_51))]]) ).
cnf(refute_0_761,plain,
( meet(zero,X_51) != meet(X_51,zero)
| meet(X_51,zero) = meet(zero,X_51) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(zero,X_51))),bind(Y,$fot(meet(X_51,zero)))]]) ).
cnf(refute_0_762,plain,
meet(X_51,zero) = meet(zero,X_51),
inference(resolve,[$cnf( $equal(meet(zero,X_51),meet(X_51,zero)) )],[refute_0_760,refute_0_761]) ).
cnf(refute_0_763,plain,
( X_51 != join(meet(X_51,top),meet(X_51,zero))
| meet(X_51,zero) != meet(zero,X_51)
| X_51 = join(meet(X_51,top),meet(zero,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(X_51,join(meet(X_51,top),meet(X_51,zero))) ),[1,1],$fot(meet(zero,X_51))]]) ).
cnf(refute_0_764,plain,
( X_51 != join(meet(X_51,top),meet(X_51,zero))
| X_51 = join(meet(X_51,top),meet(zero,X_51)) ),
inference(resolve,[$cnf( $equal(meet(X_51,zero),meet(zero,X_51)) )],[refute_0_762,refute_0_763]) ).
cnf(refute_0_765,plain,
X_51 = join(meet(X_51,top),meet(zero,X_51)),
inference(resolve,[$cnf( $equal(X_51,join(meet(X_51,top),meet(X_51,zero))) )],[refute_0_759,refute_0_764]) ).
cnf(refute_0_766,plain,
complement(zero) = join(meet(complement(zero),top),meet(zero,complement(zero))),
inference(subst,[],[refute_0_765:[bind(X_51,$fot(complement(zero)))]]) ).
cnf(refute_0_767,plain,
zero = meet(zero,complement(zero)),
inference(subst,[],[def_zero_13:[bind(A,$fot(zero))]]) ).
cnf(refute_0_768,plain,
( zero != meet(zero,complement(zero))
| meet(zero,complement(zero)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(zero,complement(zero))))]]) ).
cnf(refute_0_769,plain,
meet(zero,complement(zero)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(zero,complement(zero))) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
( complement(zero) != join(meet(complement(zero),top),meet(zero,complement(zero)))
| meet(zero,complement(zero)) != zero
| complement(zero) = join(meet(complement(zero),top),zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(zero),join(meet(complement(zero),top),meet(zero,complement(zero)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_771,plain,
( complement(zero) != join(meet(complement(zero),top),meet(zero,complement(zero)))
| complement(zero) = join(meet(complement(zero),top),zero) ),
inference(resolve,[$cnf( $equal(meet(zero,complement(zero)),zero) )],[refute_0_769,refute_0_770]) ).
cnf(refute_0_772,plain,
complement(zero) = join(meet(complement(zero),top),zero),
inference(resolve,[$cnf( $equal(complement(zero),join(meet(complement(zero),top),meet(zero,complement(zero)))) )],[refute_0_766,refute_0_771]) ).
cnf(refute_0_773,plain,
meet(top,complement(zero)) = complement(zero),
inference(subst,[],[refute_0_323:[bind(X_37,$fot(zero))]]) ).
cnf(refute_0_774,plain,
meet(complement(zero),top) = meet(top,complement(zero)),
inference(subst,[],[refute_0_108:[bind(A,$fot(complement(zero)))]]) ).
cnf(refute_0_775,plain,
( meet(complement(zero),top) != meet(top,complement(zero))
| meet(top,complement(zero)) != complement(zero)
| meet(complement(zero),top) = complement(zero) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(complement(zero),top))),bind(Y,$fot(meet(top,complement(zero)))),bind(Z,$fot(complement(zero)))]]) ).
cnf(refute_0_776,plain,
( meet(top,complement(zero)) != complement(zero)
| meet(complement(zero),top) = complement(zero) ),
inference(resolve,[$cnf( $equal(meet(complement(zero),top),meet(top,complement(zero))) )],[refute_0_774,refute_0_775]) ).
cnf(refute_0_777,plain,
meet(complement(zero),top) = complement(zero),
inference(resolve,[$cnf( $equal(meet(top,complement(zero)),complement(zero)) )],[refute_0_773,refute_0_776]) ).
cnf(refute_0_778,plain,
join(zero,meet(complement(zero),top)) = join(zero,meet(complement(zero),top)),
introduced(tautology,[refl,[$fot(join(zero,meet(complement(zero),top)))]]) ).
cnf(refute_0_779,plain,
( join(zero,meet(complement(zero),top)) != join(zero,meet(complement(zero),top))
| meet(complement(zero),top) != complement(zero)
| join(zero,meet(complement(zero),top)) = join(zero,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(complement(zero),top)),join(zero,meet(complement(zero),top))) ),[1,1],$fot(complement(zero))]]) ).
cnf(refute_0_780,plain,
( meet(complement(zero),top) != complement(zero)
| join(zero,meet(complement(zero),top)) = join(zero,complement(zero)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(zero),top)),join(zero,meet(complement(zero),top))) )],[refute_0_778,refute_0_779]) ).
cnf(refute_0_781,plain,
join(zero,meet(complement(zero),top)) = join(zero,complement(zero)),
inference(resolve,[$cnf( $equal(meet(complement(zero),top),complement(zero)) )],[refute_0_777,refute_0_780]) ).
cnf(refute_0_782,plain,
( join(zero,complement(zero)) != top
| join(zero,meet(complement(zero),top)) != join(zero,complement(zero))
| join(zero,meet(complement(zero),top)) = top ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(zero,meet(complement(zero),top)))),bind(Y,$fot(join(zero,complement(zero)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_783,plain,
( join(zero,complement(zero)) != top
| join(zero,meet(complement(zero),top)) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(zero),top)),join(zero,complement(zero))) )],[refute_0_781,refute_0_782]) ).
cnf(refute_0_784,plain,
join(zero,meet(complement(zero),top)) = top,
inference(resolve,[$cnf( $equal(join(zero,complement(zero)),top) )],[refute_0_195,refute_0_783]) ).
cnf(refute_0_785,plain,
join(meet(complement(zero),top),zero) = join(zero,meet(complement(zero),top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(meet(complement(zero),top)))]]) ).
cnf(refute_0_786,plain,
( join(meet(complement(zero),top),zero) != join(zero,meet(complement(zero),top))
| join(zero,meet(complement(zero),top)) != top
| join(meet(complement(zero),top),zero) = top ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(meet(complement(zero),top),zero))),bind(Y,$fot(join(zero,meet(complement(zero),top)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_787,plain,
( join(zero,meet(complement(zero),top)) != top
| join(meet(complement(zero),top),zero) = top ),
inference(resolve,[$cnf( $equal(join(meet(complement(zero),top),zero),join(zero,meet(complement(zero),top))) )],[refute_0_785,refute_0_786]) ).
cnf(refute_0_788,plain,
join(meet(complement(zero),top),zero) = top,
inference(resolve,[$cnf( $equal(join(zero,meet(complement(zero),top)),top) )],[refute_0_784,refute_0_787]) ).
cnf(refute_0_789,plain,
( complement(zero) != join(meet(complement(zero),top),zero)
| join(meet(complement(zero),top),zero) != top
| complement(zero) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(zero),top) ),[0],$fot(join(meet(complement(zero),top),zero))]]) ).
cnf(refute_0_790,plain,
( complement(zero) != join(meet(complement(zero),top),zero)
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(join(meet(complement(zero),top),zero),top) )],[refute_0_788,refute_0_789]) ).
cnf(refute_0_791,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(complement(zero),join(meet(complement(zero),top),zero)) )],[refute_0_772,refute_0_790]) ).
cnf(refute_0_792,plain,
( complement(zero) != top
| top != join(complement(zero),join(X_117,meet(zero,complement(X_117))))
| top = join(top,join(X_117,meet(zero,complement(X_117)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(zero),join(X_117,meet(zero,complement(X_117))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_793,plain,
( top != join(complement(zero),join(X_117,meet(zero,complement(X_117))))
| top = join(top,join(X_117,meet(zero,complement(X_117)))) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_791,refute_0_792]) ).
cnf(refute_0_794,plain,
top = join(top,join(X_117,meet(zero,complement(X_117)))),
inference(resolve,[$cnf( $equal(top,join(complement(zero),join(X_117,meet(zero,complement(X_117))))) )],[refute_0_755,refute_0_793]) ).
cnf(refute_0_795,plain,
join(A,zero) = join(zero,A),
inference(subst,[],[maddux1_join_commutativity_1:[bind(B,$fot(zero))]]) ).
cnf(refute_0_796,plain,
A = join(zero,A),
inference(subst,[],[refute_0_699:[bind(X_35,$fot(A))]]) ).
cnf(refute_0_797,plain,
( A != join(zero,A)
| join(zero,A) = A ),
inference(subst,[],[refute_0_2:[bind(X,$fot(A)),bind(Y,$fot(join(zero,A)))]]) ).
cnf(refute_0_798,plain,
join(zero,A) = A,
inference(resolve,[$cnf( $equal(A,join(zero,A)) )],[refute_0_796,refute_0_797]) ).
cnf(refute_0_799,plain,
( join(A,zero) != join(zero,A)
| join(zero,A) != A
| join(A,zero) = A ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,zero),A) ),[0],$fot(join(zero,A))]]) ).
cnf(refute_0_800,plain,
( join(A,zero) != join(zero,A)
| join(A,zero) = A ),
inference(resolve,[$cnf( $equal(join(zero,A),A) )],[refute_0_798,refute_0_799]) ).
cnf(refute_0_801,plain,
join(A,zero) = A,
inference(resolve,[$cnf( $equal(join(A,zero),join(zero,A)) )],[refute_0_795,refute_0_800]) ).
cnf(refute_0_802,plain,
join(X_117,zero) = X_117,
inference(subst,[],[refute_0_801:[bind(A,$fot(X_117))]]) ).
cnf(refute_0_803,plain,
zero = join(meet(X_60,zero),complement(join(complement(zero),X_60))),
inference(subst,[],[refute_0_588:[bind(X_35,$fot(zero)),bind(X_36,$fot(X_60))]]) ).
cnf(refute_0_804,plain,
( complement(zero) != top
| zero != join(meet(X_60,zero),complement(join(complement(zero),X_60)))
| zero = join(meet(X_60,zero),complement(join(top,X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(meet(X_60,zero),complement(join(complement(zero),X_60)))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_0_805,plain,
( zero != join(meet(X_60,zero),complement(join(complement(zero),X_60)))
| zero = join(meet(X_60,zero),complement(join(top,X_60))) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_791,refute_0_804]) ).
cnf(refute_0_806,plain,
zero = join(meet(X_60,zero),complement(join(top,X_60))),
inference(resolve,[$cnf( $equal(zero,join(meet(X_60,zero),complement(join(complement(zero),X_60)))) )],[refute_0_803,refute_0_805]) ).
cnf(refute_0_807,plain,
zero = join(meet(join(X_87,complement(join(top,X_87))),zero),complement(join(top,join(X_87,complement(join(top,X_87)))))),
inference(subst,[],[refute_0_806:[bind(X_60,$fot(join(X_87,complement(join(top,X_87)))))]]) ).
cnf(refute_0_808,plain,
top = join(join(X_79,X_80),complement(join(X_79,X_80))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(X_79,X_80)))]]) ).
cnf(refute_0_809,plain,
join(X_79,join(X_80,complement(join(X_79,X_80)))) = join(join(X_79,X_80),complement(join(X_79,X_80))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_79)),bind(B,$fot(X_80)),bind(C,$fot(complement(join(X_79,X_80))))]]) ).
cnf(refute_0_810,plain,
( join(X_79,join(X_80,complement(join(X_79,X_80)))) != join(join(X_79,X_80),complement(join(X_79,X_80)))
| join(join(X_79,X_80),complement(join(X_79,X_80))) = join(X_79,join(X_80,complement(join(X_79,X_80)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_79,join(X_80,complement(join(X_79,X_80)))))),bind(Y,$fot(join(join(X_79,X_80),complement(join(X_79,X_80)))))]]) ).
cnf(refute_0_811,plain,
join(join(X_79,X_80),complement(join(X_79,X_80))) = join(X_79,join(X_80,complement(join(X_79,X_80)))),
inference(resolve,[$cnf( $equal(join(X_79,join(X_80,complement(join(X_79,X_80)))),join(join(X_79,X_80),complement(join(X_79,X_80)))) )],[refute_0_809,refute_0_810]) ).
cnf(refute_0_812,plain,
( join(join(X_79,X_80),complement(join(X_79,X_80))) != join(X_79,join(X_80,complement(join(X_79,X_80))))
| top != join(join(X_79,X_80),complement(join(X_79,X_80)))
| top = join(X_79,join(X_80,complement(join(X_79,X_80)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(X_79,X_80),complement(join(X_79,X_80)))) ),[1],$fot(join(X_79,join(X_80,complement(join(X_79,X_80)))))]]) ).
cnf(refute_0_813,plain,
( top != join(join(X_79,X_80),complement(join(X_79,X_80)))
| top = join(X_79,join(X_80,complement(join(X_79,X_80)))) ),
inference(resolve,[$cnf( $equal(join(join(X_79,X_80),complement(join(X_79,X_80))),join(X_79,join(X_80,complement(join(X_79,X_80))))) )],[refute_0_811,refute_0_812]) ).
cnf(refute_0_814,plain,
top = join(X_79,join(X_80,complement(join(X_79,X_80)))),
inference(resolve,[$cnf( $equal(top,join(join(X_79,X_80),complement(join(X_79,X_80)))) )],[refute_0_808,refute_0_813]) ).
cnf(refute_0_815,plain,
top = join(top,join(X_87,complement(join(top,X_87)))),
inference(subst,[],[refute_0_814:[bind(X_79,$fot(top)),bind(X_80,$fot(X_87))]]) ).
cnf(refute_0_816,plain,
( top != join(top,join(X_87,complement(join(top,X_87))))
| join(top,join(X_87,complement(join(top,X_87)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,join(X_87,complement(join(top,X_87))))))]]) ).
cnf(refute_0_817,plain,
join(top,join(X_87,complement(join(top,X_87)))) = top,
inference(resolve,[$cnf( $equal(top,join(top,join(X_87,complement(join(top,X_87))))) )],[refute_0_815,refute_0_816]) ).
cnf(refute_0_818,plain,
( join(top,join(X_87,complement(join(top,X_87)))) != top
| zero != join(meet(join(X_87,complement(join(top,X_87))),zero),complement(join(top,join(X_87,complement(join(top,X_87))))))
| zero = join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(meet(join(X_87,complement(join(top,X_87))),zero),complement(join(top,join(X_87,complement(join(top,X_87))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_819,plain,
( zero != join(meet(join(X_87,complement(join(top,X_87))),zero),complement(join(top,join(X_87,complement(join(top,X_87))))))
| zero = join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)) ),
inference(resolve,[$cnf( $equal(join(top,join(X_87,complement(join(top,X_87)))),top) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
zero = join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)),
inference(resolve,[$cnf( $equal(zero,join(meet(join(X_87,complement(join(top,X_87))),zero),complement(join(top,join(X_87,complement(join(top,X_87))))))) )],[refute_0_807,refute_0_819]) ).
cnf(refute_0_821,plain,
join(zero,meet(zero,join(X_87,complement(join(top,X_87))))) = meet(zero,join(X_87,complement(join(top,X_87)))),
inference(subst,[],[refute_0_701:[bind(X_35,$fot(meet(zero,join(X_87,complement(join(top,X_87))))))]]) ).
cnf(refute_0_822,plain,
meet(join(X_87,complement(join(top,X_87))),zero) = meet(zero,join(X_87,complement(join(top,X_87)))),
inference(subst,[],[refute_0_355:[bind(X_14,$fot(zero)),bind(X_15,$fot(join(X_87,complement(join(top,X_87)))))]]) ).
cnf(refute_0_823,plain,
join(zero,meet(join(X_87,complement(join(top,X_87))),zero)) = join(zero,meet(join(X_87,complement(join(top,X_87))),zero)),
introduced(tautology,[refl,[$fot(join(zero,meet(join(X_87,complement(join(top,X_87))),zero)))]]) ).
cnf(refute_0_824,plain,
( join(zero,meet(join(X_87,complement(join(top,X_87))),zero)) != join(zero,meet(join(X_87,complement(join(top,X_87))),zero))
| meet(join(X_87,complement(join(top,X_87))),zero) != meet(zero,join(X_87,complement(join(top,X_87))))
| join(zero,meet(join(X_87,complement(join(top,X_87))),zero)) = join(zero,meet(zero,join(X_87,complement(join(top,X_87))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(X_87,complement(join(top,X_87))),zero)),join(zero,meet(join(X_87,complement(join(top,X_87))),zero))) ),[1,1],$fot(meet(zero,join(X_87,complement(join(top,X_87)))))]]) ).
cnf(refute_0_825,plain,
( meet(join(X_87,complement(join(top,X_87))),zero) != meet(zero,join(X_87,complement(join(top,X_87))))
| join(zero,meet(join(X_87,complement(join(top,X_87))),zero)) = join(zero,meet(zero,join(X_87,complement(join(top,X_87))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(X_87,complement(join(top,X_87))),zero)),join(zero,meet(join(X_87,complement(join(top,X_87))),zero))) )],[refute_0_823,refute_0_824]) ).
cnf(refute_0_826,plain,
join(zero,meet(join(X_87,complement(join(top,X_87))),zero)) = join(zero,meet(zero,join(X_87,complement(join(top,X_87))))),
inference(resolve,[$cnf( $equal(meet(join(X_87,complement(join(top,X_87))),zero),meet(zero,join(X_87,complement(join(top,X_87))))) )],[refute_0_822,refute_0_825]) ).
cnf(refute_0_827,plain,
join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) = join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)))]]) ).
cnf(refute_0_828,plain,
( complement(top) != zero
| join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) != join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero))
| join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) = join(zero,meet(join(X_87,complement(join(top,X_87))),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)),join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_829,plain,
( complement(top) != zero
| join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) = join(zero,meet(join(X_87,complement(join(top,X_87))),zero)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)),join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero))) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) = join(zero,meet(join(X_87,complement(join(top,X_87))),zero)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_829]) ).
cnf(refute_0_831,plain,
( join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) != join(zero,meet(join(X_87,complement(join(top,X_87))),zero))
| join(zero,meet(join(X_87,complement(join(top,X_87))),zero)) != join(zero,meet(zero,join(X_87,complement(join(top,X_87)))))
| join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) = join(zero,meet(zero,join(X_87,complement(join(top,X_87))))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)))),bind(Y,$fot(join(zero,meet(join(X_87,complement(join(top,X_87))),zero)))),bind(Z,$fot(join(zero,meet(zero,join(X_87,complement(join(top,X_87)))))))]]) ).
cnf(refute_0_832,plain,
( join(zero,meet(join(X_87,complement(join(top,X_87))),zero)) != join(zero,meet(zero,join(X_87,complement(join(top,X_87)))))
| join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) = join(zero,meet(zero,join(X_87,complement(join(top,X_87))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)),join(zero,meet(join(X_87,complement(join(top,X_87))),zero))) )],[refute_0_830,refute_0_831]) ).
cnf(refute_0_833,plain,
join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) = join(zero,meet(zero,join(X_87,complement(join(top,X_87))))),
inference(resolve,[$cnf( $equal(join(zero,meet(join(X_87,complement(join(top,X_87))),zero)),join(zero,meet(zero,join(X_87,complement(join(top,X_87)))))) )],[refute_0_826,refute_0_832]) ).
cnf(refute_0_834,plain,
( join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) != join(zero,meet(zero,join(X_87,complement(join(top,X_87)))))
| join(zero,meet(zero,join(X_87,complement(join(top,X_87))))) != meet(zero,join(X_87,complement(join(top,X_87))))
| join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) = meet(zero,join(X_87,complement(join(top,X_87)))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)))),bind(Y,$fot(join(zero,meet(zero,join(X_87,complement(join(top,X_87))))))),bind(Z,$fot(meet(zero,join(X_87,complement(join(top,X_87))))))]]) ).
cnf(refute_0_835,plain,
( join(zero,meet(zero,join(X_87,complement(join(top,X_87))))) != meet(zero,join(X_87,complement(join(top,X_87))))
| join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) = meet(zero,join(X_87,complement(join(top,X_87)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)),join(zero,meet(zero,join(X_87,complement(join(top,X_87)))))) )],[refute_0_833,refute_0_834]) ).
cnf(refute_0_836,plain,
join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) = meet(zero,join(X_87,complement(join(top,X_87)))),
inference(resolve,[$cnf( $equal(join(zero,meet(zero,join(X_87,complement(join(top,X_87))))),meet(zero,join(X_87,complement(join(top,X_87))))) )],[refute_0_821,refute_0_835]) ).
cnf(refute_0_837,plain,
join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)) = join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(join(X_87,complement(join(top,X_87))),zero)))]]) ).
cnf(refute_0_838,plain,
( join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) != meet(zero,join(X_87,complement(join(top,X_87))))
| join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)) != join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero))
| join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)) = meet(zero,join(X_87,complement(join(top,X_87)))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)))),bind(Y,$fot(join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)))),bind(Z,$fot(meet(zero,join(X_87,complement(join(top,X_87))))))]]) ).
cnf(refute_0_839,plain,
( join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)) != meet(zero,join(X_87,complement(join(top,X_87))))
| join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)) = meet(zero,join(X_87,complement(join(top,X_87)))) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)),join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero))) )],[refute_0_837,refute_0_838]) ).
cnf(refute_0_840,plain,
join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)) = meet(zero,join(X_87,complement(join(top,X_87)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(X_87,complement(join(top,X_87))),zero)),meet(zero,join(X_87,complement(join(top,X_87))))) )],[refute_0_836,refute_0_839]) ).
cnf(refute_0_841,plain,
( join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)) != meet(zero,join(X_87,complement(join(top,X_87))))
| zero != join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top))
| zero = meet(zero,join(X_87,complement(join(top,X_87)))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top))) ),[1],$fot(meet(zero,join(X_87,complement(join(top,X_87)))))]]) ).
cnf(refute_0_842,plain,
( zero != join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top))
| zero = meet(zero,join(X_87,complement(join(top,X_87)))) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top)),meet(zero,join(X_87,complement(join(top,X_87))))) )],[refute_0_840,refute_0_841]) ).
cnf(refute_0_843,plain,
zero = meet(zero,join(X_87,complement(join(top,X_87)))),
inference(resolve,[$cnf( $equal(zero,join(meet(join(X_87,complement(join(top,X_87))),zero),complement(top))) )],[refute_0_820,refute_0_842]) ).
cnf(refute_0_844,plain,
join(X_79,join(meet(zero,X_79),X_81)) = join(join(X_79,meet(zero,X_79)),X_81),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_79)),bind(B,$fot(meet(zero,X_79))),bind(C,$fot(X_81))]]) ).
cnf(refute_0_845,plain,
X_52 = join(meet(top,X_52),meet(X_52,zero)),
inference(subst,[],[refute_0_123:[bind(X_50,$fot(X_52))]]) ).
cnf(refute_0_846,plain,
meet(zero,X_52) = meet(X_52,zero),
inference(subst,[],[refute_0_353:[bind(X_14,$fot(zero)),bind(X_15,$fot(X_52))]]) ).
cnf(refute_0_847,plain,
( meet(zero,X_52) != meet(X_52,zero)
| meet(X_52,zero) = meet(zero,X_52) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(zero,X_52))),bind(Y,$fot(meet(X_52,zero)))]]) ).
cnf(refute_0_848,plain,
meet(X_52,zero) = meet(zero,X_52),
inference(resolve,[$cnf( $equal(meet(zero,X_52),meet(X_52,zero)) )],[refute_0_846,refute_0_847]) ).
cnf(refute_0_849,plain,
( X_52 != join(meet(top,X_52),meet(X_52,zero))
| meet(X_52,zero) != meet(zero,X_52)
| X_52 = join(meet(top,X_52),meet(zero,X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(X_52,join(meet(top,X_52),meet(X_52,zero))) ),[1,1],$fot(meet(zero,X_52))]]) ).
cnf(refute_0_850,plain,
( X_52 != join(meet(top,X_52),meet(X_52,zero))
| X_52 = join(meet(top,X_52),meet(zero,X_52)) ),
inference(resolve,[$cnf( $equal(meet(X_52,zero),meet(zero,X_52)) )],[refute_0_848,refute_0_849]) ).
cnf(refute_0_851,plain,
X_52 = join(meet(top,X_52),meet(zero,X_52)),
inference(resolve,[$cnf( $equal(X_52,join(meet(top,X_52),meet(X_52,zero))) )],[refute_0_845,refute_0_850]) ).
cnf(refute_0_852,plain,
join(zero,complement(B)) = complement(B),
inference(subst,[],[refute_0_701:[bind(X_35,$fot(complement(B)))]]) ).
cnf(refute_0_853,plain,
complement(join(zero,complement(B))) = complement(join(zero,complement(B))),
introduced(tautology,[refl,[$fot(complement(join(zero,complement(B))))]]) ).
cnf(refute_0_854,plain,
( complement(join(zero,complement(B))) != complement(join(zero,complement(B)))
| join(zero,complement(B)) != complement(B)
| complement(join(zero,complement(B))) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,complement(B))),complement(join(zero,complement(B)))) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_855,plain,
( join(zero,complement(B)) != complement(B)
| complement(join(zero,complement(B))) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),complement(join(zero,complement(B)))) )],[refute_0_853,refute_0_854]) ).
cnf(refute_0_856,plain,
complement(join(zero,complement(B))) = complement(complement(B)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(B)) )],[refute_0_852,refute_0_855]) ).
cnf(refute_0_857,plain,
( complement(complement(B)) != B
| complement(join(zero,complement(B))) != complement(complement(B))
| complement(join(zero,complement(B))) = B ),
inference(subst,[],[refute_0_41:[bind(X,$fot(complement(join(zero,complement(B))))),bind(Y,$fot(complement(complement(B)))),bind(Z,$fot(B))]]) ).
cnf(refute_0_858,plain,
( complement(complement(B)) != B
| complement(join(zero,complement(B))) = B ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),complement(complement(B))) )],[refute_0_856,refute_0_857]) ).
cnf(refute_0_859,plain,
complement(join(zero,complement(B))) = B,
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_681,refute_0_858]) ).
cnf(refute_0_860,plain,
( complement(join(zero,complement(B))) != B
| meet(top,B) != complement(join(zero,complement(B)))
| meet(top,B) = B ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) ),[1],$fot(B)]]) ).
cnf(refute_0_861,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| meet(top,B) = B ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),B) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
meet(top,B) = B,
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_94,refute_0_861]) ).
cnf(refute_0_863,plain,
meet(top,X_52) = X_52,
inference(subst,[],[refute_0_862:[bind(B,$fot(X_52))]]) ).
cnf(refute_0_864,plain,
join(meet(top,X_52),meet(zero,X_52)) = join(meet(top,X_52),meet(zero,X_52)),
introduced(tautology,[refl,[$fot(join(meet(top,X_52),meet(zero,X_52)))]]) ).
cnf(refute_0_865,plain,
( join(meet(top,X_52),meet(zero,X_52)) != join(meet(top,X_52),meet(zero,X_52))
| meet(top,X_52) != X_52
| join(meet(top,X_52),meet(zero,X_52)) = join(X_52,meet(zero,X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_52),meet(zero,X_52)),join(meet(top,X_52),meet(zero,X_52))) ),[1,0],$fot(X_52)]]) ).
cnf(refute_0_866,plain,
( meet(top,X_52) != X_52
| join(meet(top,X_52),meet(zero,X_52)) = join(X_52,meet(zero,X_52)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_52),meet(zero,X_52)),join(meet(top,X_52),meet(zero,X_52))) )],[refute_0_864,refute_0_865]) ).
cnf(refute_0_867,plain,
join(meet(top,X_52),meet(zero,X_52)) = join(X_52,meet(zero,X_52)),
inference(resolve,[$cnf( $equal(meet(top,X_52),X_52) )],[refute_0_863,refute_0_866]) ).
cnf(refute_0_868,plain,
( X_52 != join(meet(top,X_52),meet(zero,X_52))
| join(meet(top,X_52),meet(zero,X_52)) != join(X_52,meet(zero,X_52))
| X_52 = join(X_52,meet(zero,X_52)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_52,join(X_52,meet(zero,X_52))) ),[0],$fot(join(meet(top,X_52),meet(zero,X_52)))]]) ).
cnf(refute_0_869,plain,
( X_52 != join(meet(top,X_52),meet(zero,X_52))
| X_52 = join(X_52,meet(zero,X_52)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_52),meet(zero,X_52)),join(X_52,meet(zero,X_52))) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
X_52 = join(X_52,meet(zero,X_52)),
inference(resolve,[$cnf( $equal(X_52,join(meet(top,X_52),meet(zero,X_52))) )],[refute_0_851,refute_0_869]) ).
cnf(refute_0_871,plain,
X_79 = join(X_79,meet(zero,X_79)),
inference(subst,[],[refute_0_870:[bind(X_52,$fot(X_79))]]) ).
cnf(refute_0_872,plain,
( X_79 != join(X_79,meet(zero,X_79))
| join(X_79,meet(zero,X_79)) = X_79 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_79)),bind(Y,$fot(join(X_79,meet(zero,X_79))))]]) ).
cnf(refute_0_873,plain,
join(X_79,meet(zero,X_79)) = X_79,
inference(resolve,[$cnf( $equal(X_79,join(X_79,meet(zero,X_79))) )],[refute_0_871,refute_0_872]) ).
cnf(refute_0_874,plain,
( join(X_79,join(meet(zero,X_79),X_81)) != join(join(X_79,meet(zero,X_79)),X_81)
| join(X_79,meet(zero,X_79)) != X_79
| join(X_79,join(meet(zero,X_79),X_81)) = join(X_79,X_81) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_79,join(meet(zero,X_79),X_81)),join(join(X_79,meet(zero,X_79)),X_81)) ),[1,0],$fot(X_79)]]) ).
cnf(refute_0_875,plain,
( join(X_79,join(meet(zero,X_79),X_81)) != join(join(X_79,meet(zero,X_79)),X_81)
| join(X_79,join(meet(zero,X_79),X_81)) = join(X_79,X_81) ),
inference(resolve,[$cnf( $equal(join(X_79,meet(zero,X_79)),X_79) )],[refute_0_873,refute_0_874]) ).
cnf(refute_0_876,plain,
join(X_79,join(meet(zero,X_79),X_81)) = join(X_79,X_81),
inference(resolve,[$cnf( $equal(join(X_79,join(meet(zero,X_79),X_81)),join(join(X_79,meet(zero,X_79)),X_81)) )],[refute_0_844,refute_0_875]) ).
cnf(refute_0_877,plain,
join(X_107,join(meet(zero,X_107),complement(join(complement(zero),X_107)))) = join(X_107,complement(join(complement(zero),X_107))),
inference(subst,[],[refute_0_876:[bind(X_79,$fot(X_107)),bind(X_81,$fot(complement(join(complement(zero),X_107))))]]) ).
cnf(refute_0_878,plain,
zero = join(meet(zero,X_107),complement(join(complement(zero),X_107))),
inference(subst,[],[refute_0_47:[bind(A,$fot(zero)),bind(B,$fot(X_107))]]) ).
cnf(refute_0_879,plain,
( zero != join(meet(zero,X_107),complement(join(complement(zero),X_107)))
| join(meet(zero,X_107),complement(join(complement(zero),X_107))) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(join(meet(zero,X_107),complement(join(complement(zero),X_107)))))]]) ).
cnf(refute_0_880,plain,
join(meet(zero,X_107),complement(join(complement(zero),X_107))) = zero,
inference(resolve,[$cnf( $equal(zero,join(meet(zero,X_107),complement(join(complement(zero),X_107)))) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
( join(X_107,join(meet(zero,X_107),complement(join(complement(zero),X_107)))) != join(X_107,complement(join(complement(zero),X_107)))
| join(meet(zero,X_107),complement(join(complement(zero),X_107))) != zero
| join(X_107,zero) = join(X_107,complement(join(complement(zero),X_107))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_107,join(meet(zero,X_107),complement(join(complement(zero),X_107)))),join(X_107,complement(join(complement(zero),X_107)))) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_882,plain,
( join(X_107,join(meet(zero,X_107),complement(join(complement(zero),X_107)))) != join(X_107,complement(join(complement(zero),X_107)))
| join(X_107,zero) = join(X_107,complement(join(complement(zero),X_107))) ),
inference(resolve,[$cnf( $equal(join(meet(zero,X_107),complement(join(complement(zero),X_107))),zero) )],[refute_0_880,refute_0_881]) ).
cnf(refute_0_883,plain,
join(X_107,zero) = join(X_107,complement(join(complement(zero),X_107))),
inference(resolve,[$cnf( $equal(join(X_107,join(meet(zero,X_107),complement(join(complement(zero),X_107)))),join(X_107,complement(join(complement(zero),X_107)))) )],[refute_0_877,refute_0_882]) ).
cnf(refute_0_884,plain,
join(X_107,zero) = X_107,
inference(subst,[],[refute_0_801:[bind(A,$fot(X_107))]]) ).
cnf(refute_0_885,plain,
( join(X_107,zero) != X_107
| join(X_107,zero) != join(X_107,complement(join(complement(zero),X_107)))
| X_107 = join(X_107,complement(join(complement(zero),X_107))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_107,zero),join(X_107,complement(join(complement(zero),X_107)))) ),[0],$fot(X_107)]]) ).
cnf(refute_0_886,plain,
( join(X_107,zero) != join(X_107,complement(join(complement(zero),X_107)))
| X_107 = join(X_107,complement(join(complement(zero),X_107))) ),
inference(resolve,[$cnf( $equal(join(X_107,zero),X_107) )],[refute_0_884,refute_0_885]) ).
cnf(refute_0_887,plain,
join(complement(zero),X_107) = join(complement(zero),X_107),
introduced(tautology,[refl,[$fot(join(complement(zero),X_107))]]) ).
cnf(refute_0_888,plain,
( complement(zero) != top
| join(complement(zero),X_107) != join(complement(zero),X_107)
| join(complement(zero),X_107) = join(top,X_107) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),X_107),join(complement(zero),X_107)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_889,plain,
( complement(zero) != top
| join(complement(zero),X_107) = join(top,X_107) ),
inference(resolve,[$cnf( $equal(join(complement(zero),X_107),join(complement(zero),X_107)) )],[refute_0_887,refute_0_888]) ).
cnf(refute_0_890,plain,
join(complement(zero),X_107) = join(top,X_107),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_791,refute_0_889]) ).
cnf(refute_0_891,plain,
complement(join(complement(zero),X_107)) = complement(join(complement(zero),X_107)),
introduced(tautology,[refl,[$fot(complement(join(complement(zero),X_107)))]]) ).
cnf(refute_0_892,plain,
( complement(join(complement(zero),X_107)) != complement(join(complement(zero),X_107))
| join(complement(zero),X_107) != join(top,X_107)
| complement(join(complement(zero),X_107)) = complement(join(top,X_107)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(zero),X_107)),complement(join(complement(zero),X_107))) ),[1,0],$fot(join(top,X_107))]]) ).
cnf(refute_0_893,plain,
( join(complement(zero),X_107) != join(top,X_107)
| complement(join(complement(zero),X_107)) = complement(join(top,X_107)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(zero),X_107)),complement(join(complement(zero),X_107))) )],[refute_0_891,refute_0_892]) ).
cnf(refute_0_894,plain,
complement(join(complement(zero),X_107)) = complement(join(top,X_107)),
inference(resolve,[$cnf( $equal(join(complement(zero),X_107),join(top,X_107)) )],[refute_0_890,refute_0_893]) ).
cnf(refute_0_895,plain,
join(X_107,complement(join(complement(zero),X_107))) = join(X_107,complement(join(complement(zero),X_107))),
introduced(tautology,[refl,[$fot(join(X_107,complement(join(complement(zero),X_107))))]]) ).
cnf(refute_0_896,plain,
( complement(join(complement(zero),X_107)) != complement(join(top,X_107))
| join(X_107,complement(join(complement(zero),X_107))) != join(X_107,complement(join(complement(zero),X_107)))
| join(X_107,complement(join(complement(zero),X_107))) = join(X_107,complement(join(top,X_107))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_107,complement(join(complement(zero),X_107))),join(X_107,complement(join(complement(zero),X_107)))) ),[1,1],$fot(complement(join(top,X_107)))]]) ).
cnf(refute_0_897,plain,
( complement(join(complement(zero),X_107)) != complement(join(top,X_107))
| join(X_107,complement(join(complement(zero),X_107))) = join(X_107,complement(join(top,X_107))) ),
inference(resolve,[$cnf( $equal(join(X_107,complement(join(complement(zero),X_107))),join(X_107,complement(join(complement(zero),X_107)))) )],[refute_0_895,refute_0_896]) ).
cnf(refute_0_898,plain,
join(X_107,complement(join(complement(zero),X_107))) = join(X_107,complement(join(top,X_107))),
inference(resolve,[$cnf( $equal(complement(join(complement(zero),X_107)),complement(join(top,X_107))) )],[refute_0_894,refute_0_897]) ).
cnf(refute_0_899,plain,
( X_107 != join(X_107,complement(join(complement(zero),X_107)))
| join(X_107,complement(join(complement(zero),X_107))) != join(X_107,complement(join(top,X_107)))
| X_107 = join(X_107,complement(join(top,X_107))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,join(X_107,complement(join(top,X_107)))) ),[0],$fot(join(X_107,complement(join(complement(zero),X_107))))]]) ).
cnf(refute_0_900,plain,
( X_107 != join(X_107,complement(join(complement(zero),X_107)))
| X_107 = join(X_107,complement(join(top,X_107))) ),
inference(resolve,[$cnf( $equal(join(X_107,complement(join(complement(zero),X_107))),join(X_107,complement(join(top,X_107)))) )],[refute_0_898,refute_0_899]) ).
cnf(refute_0_901,plain,
( join(X_107,zero) != join(X_107,complement(join(complement(zero),X_107)))
| X_107 = join(X_107,complement(join(top,X_107))) ),
inference(resolve,[$cnf( $equal(X_107,join(X_107,complement(join(complement(zero),X_107)))) )],[refute_0_886,refute_0_900]) ).
cnf(refute_0_902,plain,
X_107 = join(X_107,complement(join(top,X_107))),
inference(resolve,[$cnf( $equal(join(X_107,zero),join(X_107,complement(join(complement(zero),X_107)))) )],[refute_0_883,refute_0_901]) ).
cnf(refute_0_903,plain,
( X_107 != join(X_107,complement(join(top,X_107)))
| join(X_107,complement(join(top,X_107))) = X_107 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_107)),bind(Y,$fot(join(X_107,complement(join(top,X_107)))))]]) ).
cnf(refute_0_904,plain,
join(X_107,complement(join(top,X_107))) = X_107,
inference(resolve,[$cnf( $equal(X_107,join(X_107,complement(join(top,X_107)))) )],[refute_0_902,refute_0_903]) ).
cnf(refute_0_905,plain,
join(X_87,complement(join(top,X_87))) = X_87,
inference(subst,[],[refute_0_904:[bind(X_107,$fot(X_87))]]) ).
cnf(refute_0_906,plain,
meet(zero,join(X_87,complement(join(top,X_87)))) = meet(zero,join(X_87,complement(join(top,X_87)))),
introduced(tautology,[refl,[$fot(meet(zero,join(X_87,complement(join(top,X_87)))))]]) ).
cnf(refute_0_907,plain,
( join(X_87,complement(join(top,X_87))) != X_87
| meet(zero,join(X_87,complement(join(top,X_87)))) != meet(zero,join(X_87,complement(join(top,X_87))))
| meet(zero,join(X_87,complement(join(top,X_87)))) = meet(zero,X_87) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,join(X_87,complement(join(top,X_87)))),meet(zero,join(X_87,complement(join(top,X_87))))) ),[1,1],$fot(X_87)]]) ).
cnf(refute_0_908,plain,
( join(X_87,complement(join(top,X_87))) != X_87
| meet(zero,join(X_87,complement(join(top,X_87)))) = meet(zero,X_87) ),
inference(resolve,[$cnf( $equal(meet(zero,join(X_87,complement(join(top,X_87)))),meet(zero,join(X_87,complement(join(top,X_87))))) )],[refute_0_906,refute_0_907]) ).
cnf(refute_0_909,plain,
meet(zero,join(X_87,complement(join(top,X_87)))) = meet(zero,X_87),
inference(resolve,[$cnf( $equal(join(X_87,complement(join(top,X_87))),X_87) )],[refute_0_905,refute_0_908]) ).
cnf(refute_0_910,plain,
( meet(zero,join(X_87,complement(join(top,X_87)))) != meet(zero,X_87)
| zero != meet(zero,join(X_87,complement(join(top,X_87))))
| zero = meet(zero,X_87) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(zero,join(X_87,complement(join(top,X_87))))) ),[1],$fot(meet(zero,X_87))]]) ).
cnf(refute_0_911,plain,
( zero != meet(zero,join(X_87,complement(join(top,X_87))))
| zero = meet(zero,X_87) ),
inference(resolve,[$cnf( $equal(meet(zero,join(X_87,complement(join(top,X_87)))),meet(zero,X_87)) )],[refute_0_909,refute_0_910]) ).
cnf(refute_0_912,plain,
zero = meet(zero,X_87),
inference(resolve,[$cnf( $equal(zero,meet(zero,join(X_87,complement(join(top,X_87))))) )],[refute_0_843,refute_0_911]) ).
cnf(refute_0_913,plain,
( zero != meet(zero,X_87)
| meet(zero,X_87) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(zero,X_87)))]]) ).
cnf(refute_0_914,plain,
meet(zero,X_87) = zero,
inference(resolve,[$cnf( $equal(zero,meet(zero,X_87)) )],[refute_0_912,refute_0_913]) ).
cnf(refute_0_915,plain,
meet(zero,complement(X_117)) = zero,
inference(subst,[],[refute_0_914:[bind(X_87,$fot(complement(X_117)))]]) ).
cnf(refute_0_916,plain,
join(X_117,meet(zero,complement(X_117))) = join(X_117,meet(zero,complement(X_117))),
introduced(tautology,[refl,[$fot(join(X_117,meet(zero,complement(X_117))))]]) ).
cnf(refute_0_917,plain,
( join(X_117,meet(zero,complement(X_117))) != join(X_117,meet(zero,complement(X_117)))
| meet(zero,complement(X_117)) != zero
| join(X_117,meet(zero,complement(X_117))) = join(X_117,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_117,meet(zero,complement(X_117))),join(X_117,meet(zero,complement(X_117)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_918,plain,
( meet(zero,complement(X_117)) != zero
| join(X_117,meet(zero,complement(X_117))) = join(X_117,zero) ),
inference(resolve,[$cnf( $equal(join(X_117,meet(zero,complement(X_117))),join(X_117,meet(zero,complement(X_117)))) )],[refute_0_916,refute_0_917]) ).
cnf(refute_0_919,plain,
join(X_117,meet(zero,complement(X_117))) = join(X_117,zero),
inference(resolve,[$cnf( $equal(meet(zero,complement(X_117)),zero) )],[refute_0_915,refute_0_918]) ).
cnf(refute_0_920,plain,
( join(X_117,meet(zero,complement(X_117))) != join(X_117,zero)
| join(X_117,zero) != X_117
| join(X_117,meet(zero,complement(X_117))) = X_117 ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(X_117,meet(zero,complement(X_117))))),bind(Y,$fot(join(X_117,zero))),bind(Z,$fot(X_117))]]) ).
cnf(refute_0_921,plain,
( join(X_117,zero) != X_117
| join(X_117,meet(zero,complement(X_117))) = X_117 ),
inference(resolve,[$cnf( $equal(join(X_117,meet(zero,complement(X_117))),join(X_117,zero)) )],[refute_0_919,refute_0_920]) ).
cnf(refute_0_922,plain,
join(X_117,meet(zero,complement(X_117))) = X_117,
inference(resolve,[$cnf( $equal(join(X_117,zero),X_117) )],[refute_0_802,refute_0_921]) ).
cnf(refute_0_923,plain,
join(top,join(X_117,meet(zero,complement(X_117)))) = join(top,join(X_117,meet(zero,complement(X_117)))),
introduced(tautology,[refl,[$fot(join(top,join(X_117,meet(zero,complement(X_117)))))]]) ).
cnf(refute_0_924,plain,
( join(X_117,meet(zero,complement(X_117))) != X_117
| join(top,join(X_117,meet(zero,complement(X_117)))) != join(top,join(X_117,meet(zero,complement(X_117))))
| join(top,join(X_117,meet(zero,complement(X_117)))) = join(top,X_117) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(X_117,meet(zero,complement(X_117)))),join(top,join(X_117,meet(zero,complement(X_117))))) ),[1,1],$fot(X_117)]]) ).
cnf(refute_0_925,plain,
( join(X_117,meet(zero,complement(X_117))) != X_117
| join(top,join(X_117,meet(zero,complement(X_117)))) = join(top,X_117) ),
inference(resolve,[$cnf( $equal(join(top,join(X_117,meet(zero,complement(X_117)))),join(top,join(X_117,meet(zero,complement(X_117))))) )],[refute_0_923,refute_0_924]) ).
cnf(refute_0_926,plain,
join(top,join(X_117,meet(zero,complement(X_117)))) = join(top,X_117),
inference(resolve,[$cnf( $equal(join(X_117,meet(zero,complement(X_117))),X_117) )],[refute_0_922,refute_0_925]) ).
cnf(refute_0_927,plain,
( join(top,join(X_117,meet(zero,complement(X_117)))) != join(top,X_117)
| top != join(top,join(X_117,meet(zero,complement(X_117))))
| top = join(top,X_117) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,join(X_117,meet(zero,complement(X_117))))) ),[1],$fot(join(top,X_117))]]) ).
cnf(refute_0_928,plain,
( top != join(top,join(X_117,meet(zero,complement(X_117))))
| top = join(top,X_117) ),
inference(resolve,[$cnf( $equal(join(top,join(X_117,meet(zero,complement(X_117)))),join(top,X_117)) )],[refute_0_926,refute_0_927]) ).
cnf(refute_0_929,plain,
top = join(top,X_117),
inference(resolve,[$cnf( $equal(top,join(top,join(X_117,meet(zero,complement(X_117))))) )],[refute_0_794,refute_0_928]) ).
cnf(refute_0_930,plain,
top = join(top,composition(X_98,top)),
inference(subst,[],[refute_0_929:[bind(X_117,$fot(composition(X_98,top)))]]) ).
cnf(refute_0_931,plain,
( top != join(top,composition(X_98,top))
| join(top,composition(X_98,top)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,composition(X_98,top))))]]) ).
cnf(refute_0_932,plain,
join(top,composition(X_98,top)) = top,
inference(resolve,[$cnf( $equal(top,join(top,composition(X_98,top))) )],[refute_0_930,refute_0_931]) ).
cnf(refute_0_933,plain,
( composition(join(X_98,one),top) != join(top,composition(X_98,top))
| join(top,composition(X_98,top)) != top
| composition(join(X_98,one),top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_98,one),top),top) ),[0],$fot(join(top,composition(X_98,top)))]]) ).
cnf(refute_0_934,plain,
( composition(join(X_98,one),top) != join(top,composition(X_98,top))
| composition(join(X_98,one),top) = top ),
inference(resolve,[$cnf( $equal(join(top,composition(X_98,top)),top) )],[refute_0_932,refute_0_933]) ).
cnf(refute_0_935,plain,
composition(join(X_98,one),top) = top,
inference(resolve,[$cnf( $equal(composition(join(X_98,one),top),join(top,composition(X_98,top))) )],[refute_0_742,refute_0_934]) ).
cnf(refute_0_936,plain,
composition(join(top,one),top) = top,
inference(subst,[],[refute_0_935:[bind(X_98,$fot(top))]]) ).
cnf(refute_0_937,plain,
top = join(top,one),
inference(subst,[],[refute_0_929:[bind(X_117,$fot(one))]]) ).
cnf(refute_0_938,plain,
( top != join(top,one)
| join(top,one) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,one)))]]) ).
cnf(refute_0_939,plain,
join(top,one) = top,
inference(resolve,[$cnf( $equal(top,join(top,one)) )],[refute_0_937,refute_0_938]) ).
cnf(refute_0_940,plain,
( composition(join(top,one),top) != top
| join(top,one) != top
| composition(top,top) = top ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,one),top),top) ),[0,0],$fot(top)]]) ).
cnf(refute_0_941,plain,
( composition(join(top,one),top) != top
| composition(top,top) = top ),
inference(resolve,[$cnf( $equal(join(top,one),top) )],[refute_0_939,refute_0_940]) ).
cnf(refute_0_942,plain,
composition(top,top) = top,
inference(resolve,[$cnf( $equal(composition(join(top,one),top),top) )],[refute_0_936,refute_0_941]) ).
cnf(refute_0_943,plain,
( composition(top,composition(top,C)) != composition(composition(top,top),C)
| composition(top,top) != top
| composition(top,composition(top,C)) = composition(top,C) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(top,C)),composition(composition(top,top),C)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_944,plain,
( composition(top,composition(top,C)) != composition(composition(top,top),C)
| composition(top,composition(top,C)) = composition(top,C) ),
inference(resolve,[$cnf( $equal(composition(top,top),top) )],[refute_0_942,refute_0_943]) ).
cnf(refute_0_945,plain,
composition(top,composition(top,C)) = composition(top,C),
inference(resolve,[$cnf( $equal(composition(top,composition(top,C)),composition(composition(top,top),C)) )],[refute_0_730,refute_0_944]) ).
cnf(refute_0_946,plain,
composition(top,composition(top,X_124)) = composition(top,X_124),
inference(subst,[],[refute_0_945:[bind(C,$fot(X_124))]]) ).
cnf(refute_0_947,plain,
( composition(top,composition(top,X_124)) != composition(top,X_124)
| join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,composition(top,X_124))))) != complement(composition(top,X_124))
| join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) = complement(composition(top,X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,composition(top,X_124))))),complement(composition(top,X_124))) ),[0,1,1,0],$fot(composition(top,X_124))]]) ).
cnf(refute_0_948,plain,
( join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,composition(top,X_124))))) != complement(composition(top,X_124))
| join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) = complement(composition(top,X_124)) ),
inference(resolve,[$cnf( $equal(composition(top,composition(top,X_124)),composition(top,X_124)) )],[refute_0_946,refute_0_947]) ).
cnf(refute_0_949,plain,
join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) = complement(composition(top,X_124)),
inference(resolve,[$cnf( $equal(join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,composition(top,X_124))))),complement(composition(top,X_124))) )],[refute_0_729,refute_0_948]) ).
cnf(refute_0_950,plain,
converse(converse(join(one,join(one,complement(join(one,one)))))) = join(one,join(one,complement(join(one,one)))),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(join(one,join(one,complement(join(one,one))))))]]) ).
cnf(refute_0_951,plain,
converse(top) = join(join(one,one),converse(complement(converse(join(one,one))))),
inference(subst,[],[refute_0_466:[bind(X_21,$fot(join(one,one)))]]) ).
cnf(refute_0_952,plain,
converse(join(converse(one),X_5)) = join(one,converse(X_5)),
inference(subst,[],[refute_0_459:[bind(A,$fot(one))]]) ).
cnf(refute_0_953,plain,
( converse(join(converse(one),X_5)) != join(one,converse(X_5))
| converse(one) != one
| converse(join(one,X_5)) = join(one,converse(X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(one),X_5)),join(one,converse(X_5))) ),[0,0,0],$fot(one)]]) ).
cnf(refute_0_954,plain,
( converse(join(converse(one),X_5)) != join(one,converse(X_5))
| converse(join(one,X_5)) = join(one,converse(X_5)) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_265,refute_0_953]) ).
cnf(refute_0_955,plain,
converse(join(one,X_5)) = join(one,converse(X_5)),
inference(resolve,[$cnf( $equal(converse(join(converse(one),X_5)),join(one,converse(X_5))) )],[refute_0_952,refute_0_954]) ).
cnf(refute_0_956,plain,
converse(join(one,one)) = join(one,converse(one)),
inference(subst,[],[refute_0_955:[bind(X_5,$fot(one))]]) ).
cnf(refute_0_957,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_958,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(join(one,one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_265,refute_0_957]) ).
cnf(refute_0_959,plain,
converse(join(one,one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) )],[refute_0_956,refute_0_958]) ).
cnf(refute_0_960,plain,
( converse(join(one,one)) != join(one,one)
| converse(top) != join(join(one,one),converse(complement(converse(join(one,one)))))
| converse(top) = join(join(one,one),converse(complement(join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(join(one,one),converse(complement(converse(join(one,one)))))) ),[1,1,0,0],$fot(join(one,one))]]) ).
cnf(refute_0_961,plain,
( converse(top) != join(join(one,one),converse(complement(converse(join(one,one)))))
| converse(top) = join(join(one,one),converse(complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_959,refute_0_960]) ).
cnf(refute_0_962,plain,
converse(top) = join(join(one,one),converse(complement(join(one,one)))),
inference(resolve,[$cnf( $equal(converse(top),join(join(one,one),converse(complement(converse(join(one,one)))))) )],[refute_0_951,refute_0_961]) ).
cnf(refute_0_963,plain,
( converse(join(one,X_5)) != join(one,converse(X_5))
| join(one,converse(X_5)) = converse(join(one,X_5)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(one,X_5)))),bind(Y,$fot(join(one,converse(X_5))))]]) ).
cnf(refute_0_964,plain,
join(one,converse(X_5)) = converse(join(one,X_5)),
inference(resolve,[$cnf( $equal(converse(join(one,X_5)),join(one,converse(X_5))) )],[refute_0_955,refute_0_963]) ).
cnf(refute_0_965,plain,
join(one,converse(join(one,complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))),
inference(subst,[],[refute_0_964:[bind(X_5,$fot(join(one,complement(join(one,one)))))]]) ).
cnf(refute_0_966,plain,
join(one,converse(complement(join(one,one)))) = converse(join(one,complement(join(one,one)))),
inference(subst,[],[refute_0_964:[bind(X_5,$fot(complement(join(one,one))))]]) ).
cnf(refute_0_967,plain,
join(one,join(one,converse(complement(join(one,one))))) = join(one,join(one,converse(complement(join(one,one))))),
introduced(tautology,[refl,[$fot(join(one,join(one,converse(complement(join(one,one))))))]]) ).
cnf(refute_0_968,plain,
( join(one,converse(complement(join(one,one)))) != converse(join(one,complement(join(one,one))))
| join(one,join(one,converse(complement(join(one,one))))) != join(one,join(one,converse(complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) = join(one,converse(join(one,complement(join(one,one))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),join(one,join(one,converse(complement(join(one,one)))))) ),[1,1],$fot(converse(join(one,complement(join(one,one)))))]]) ).
cnf(refute_0_969,plain,
( join(one,converse(complement(join(one,one)))) != converse(join(one,complement(join(one,one))))
| join(one,join(one,converse(complement(join(one,one))))) = join(one,converse(join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),join(one,join(one,converse(complement(join(one,one)))))) )],[refute_0_967,refute_0_968]) ).
cnf(refute_0_970,plain,
join(one,join(one,converse(complement(join(one,one))))) = join(one,converse(join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(join(one,converse(complement(join(one,one)))),converse(join(one,complement(join(one,one))))) )],[refute_0_966,refute_0_969]) ).
cnf(refute_0_971,plain,
( join(one,converse(join(one,complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) != join(one,converse(join(one,complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(one,join(one,converse(complement(join(one,one))))))),bind(Y,$fot(join(one,converse(join(one,complement(join(one,one))))))),bind(Z,$fot(converse(join(one,join(one,complement(join(one,one)))))))]]) ).
cnf(refute_0_972,plain,
( join(one,converse(join(one,complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),join(one,converse(join(one,complement(join(one,one)))))) )],[refute_0_970,refute_0_971]) ).
cnf(refute_0_973,plain,
join(one,join(one,converse(complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,complement(join(one,one))))),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_965,refute_0_972]) ).
cnf(refute_0_974,plain,
join(join(one,one),converse(complement(join(one,one)))) = join(one,join(one,converse(complement(join(one,one))))),
inference(subst,[],[refute_0_205:[bind(A,$fot(one)),bind(B,$fot(one)),bind(C,$fot(converse(complement(join(one,one)))))]]) ).
cnf(refute_0_975,plain,
( join(join(one,one),converse(complement(join(one,one)))) != join(one,join(one,converse(complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(join(one,one),converse(complement(join(one,one)))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(join(one,one),converse(complement(join(one,one)))))),bind(Y,$fot(join(one,join(one,converse(complement(join(one,one))))))),bind(Z,$fot(converse(join(one,join(one,complement(join(one,one)))))))]]) ).
cnf(refute_0_976,plain,
( join(one,join(one,converse(complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(join(one,one),converse(complement(join(one,one)))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(complement(join(one,one)))),join(one,join(one,converse(complement(join(one,one)))))) )],[refute_0_974,refute_0_975]) ).
cnf(refute_0_977,plain,
join(join(one,one),converse(complement(join(one,one)))) = converse(join(one,join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_973,refute_0_976]) ).
cnf(refute_0_978,plain,
( converse(top) != join(join(one,one),converse(complement(join(one,one))))
| join(join(one,one),converse(complement(join(one,one)))) != converse(join(one,join(one,complement(join(one,one)))))
| converse(top) = converse(join(one,join(one,complement(join(one,one))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),converse(join(one,join(one,complement(join(one,one)))))) ),[0],$fot(join(join(one,one),converse(complement(join(one,one)))))]]) ).
cnf(refute_0_979,plain,
( converse(top) != join(join(one,one),converse(complement(join(one,one))))
| converse(top) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(complement(join(one,one)))),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_977,refute_0_978]) ).
cnf(refute_0_980,plain,
converse(top) = converse(join(one,join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(converse(top),join(join(one,one),converse(complement(join(one,one))))) )],[refute_0_962,refute_0_979]) ).
cnf(refute_0_981,plain,
( converse(top) != converse(join(one,join(one,complement(join(one,one)))))
| converse(join(one,join(one,complement(join(one,one))))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(converse(join(one,join(one,complement(join(one,one)))))))]]) ).
cnf(refute_0_982,plain,
converse(join(one,join(one,complement(join(one,one))))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_980,refute_0_981]) ).
cnf(refute_0_983,plain,
( converse(converse(join(one,join(one,complement(join(one,one)))))) != join(one,join(one,complement(join(one,one))))
| converse(join(one,join(one,complement(join(one,one))))) != converse(top)
| converse(converse(top)) = join(one,join(one,complement(join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(join(one,join(one,complement(join(one,one)))))),join(one,join(one,complement(join(one,one))))) ),[0,0],$fot(converse(top))]]) ).
cnf(refute_0_984,plain,
( converse(converse(join(one,join(one,complement(join(one,one)))))) != join(one,join(one,complement(join(one,one))))
| converse(converse(top)) = join(one,join(one,complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,complement(join(one,one))))),converse(top)) )],[refute_0_982,refute_0_983]) ).
cnf(refute_0_985,plain,
converse(converse(top)) = join(one,join(one,complement(join(one,one)))),
inference(resolve,[$cnf( $equal(converse(converse(join(one,join(one,complement(join(one,one)))))),join(one,join(one,complement(join(one,one))))) )],[refute_0_950,refute_0_984]) ).
cnf(refute_0_986,plain,
( converse(converse(top)) != join(one,join(one,complement(join(one,one))))
| converse(converse(top)) != top
| top = join(one,join(one,complement(join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(top)),join(one,join(one,complement(join(one,one))))) ),[0],$fot(top)]]) ).
cnf(refute_0_987,plain,
( converse(converse(top)) != join(one,join(one,complement(join(one,one))))
| top = join(one,join(one,complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(converse(converse(top)),top) )],[refute_0_496,refute_0_986]) ).
cnf(refute_0_988,plain,
top = join(one,join(one,complement(join(one,one)))),
inference(resolve,[$cnf( $equal(converse(converse(top)),join(one,join(one,complement(join(one,one))))) )],[refute_0_985,refute_0_987]) ).
cnf(refute_0_989,plain,
join(one,complement(one)) = top,
inference(subst,[],[refute_0_69:[bind(A,$fot(one))]]) ).
cnf(refute_0_990,plain,
complement(complement(X_60)) = X_60,
inference(subst,[],[refute_0_680:[bind(X_35,$fot(X_60))]]) ).
cnf(refute_0_991,plain,
join(X_60,complement(complement(X_60))) = join(X_60,complement(complement(X_60))),
introduced(tautology,[refl,[$fot(join(X_60,complement(complement(X_60))))]]) ).
cnf(refute_0_992,plain,
( complement(complement(X_60)) != X_60
| join(X_60,complement(complement(X_60))) != join(X_60,complement(complement(X_60)))
| join(X_60,complement(complement(X_60))) = join(X_60,X_60) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_60,complement(complement(X_60))),join(X_60,complement(complement(X_60)))) ),[1,1],$fot(X_60)]]) ).
cnf(refute_0_993,plain,
( complement(complement(X_60)) != X_60
| join(X_60,complement(complement(X_60))) = join(X_60,X_60) ),
inference(resolve,[$cnf( $equal(join(X_60,complement(complement(X_60))),join(X_60,complement(complement(X_60)))) )],[refute_0_991,refute_0_992]) ).
cnf(refute_0_994,plain,
join(X_60,complement(complement(X_60))) = join(X_60,X_60),
inference(resolve,[$cnf( $equal(complement(complement(X_60)),X_60) )],[refute_0_990,refute_0_993]) ).
cnf(refute_0_995,plain,
complement(join(X_60,complement(complement(X_60)))) = complement(join(X_60,complement(complement(X_60)))),
introduced(tautology,[refl,[$fot(complement(join(X_60,complement(complement(X_60)))))]]) ).
cnf(refute_0_996,plain,
( complement(join(X_60,complement(complement(X_60)))) != complement(join(X_60,complement(complement(X_60))))
| join(X_60,complement(complement(X_60))) != join(X_60,X_60)
| complement(join(X_60,complement(complement(X_60)))) = complement(join(X_60,X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(X_60,complement(complement(X_60)))),complement(join(X_60,complement(complement(X_60))))) ),[1,0],$fot(join(X_60,X_60))]]) ).
cnf(refute_0_997,plain,
( join(X_60,complement(complement(X_60))) != join(X_60,X_60)
| complement(join(X_60,complement(complement(X_60)))) = complement(join(X_60,X_60)) ),
inference(resolve,[$cnf( $equal(complement(join(X_60,complement(complement(X_60)))),complement(join(X_60,complement(complement(X_60))))) )],[refute_0_995,refute_0_996]) ).
cnf(refute_0_998,plain,
complement(join(X_60,complement(complement(X_60)))) = complement(join(X_60,X_60)),
inference(resolve,[$cnf( $equal(join(X_60,complement(complement(X_60))),join(X_60,X_60)) )],[refute_0_994,refute_0_997]) ).
cnf(refute_0_999,plain,
join(zero,complement(join(X_60,complement(complement(X_60))))) = complement(join(X_60,complement(complement(X_60)))),
inference(subst,[],[refute_0_701:[bind(X_35,$fot(complement(join(X_60,complement(complement(X_60))))))]]) ).
cnf(refute_0_1000,plain,
( complement(join(X_60,complement(complement(X_60)))) != complement(join(X_60,X_60))
| join(zero,complement(join(X_60,complement(complement(X_60))))) != complement(join(X_60,complement(complement(X_60))))
| join(zero,complement(join(X_60,complement(complement(X_60))))) = complement(join(X_60,X_60)) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(zero,complement(join(X_60,complement(complement(X_60))))))),bind(Y,$fot(complement(join(X_60,complement(complement(X_60)))))),bind(Z,$fot(complement(join(X_60,X_60))))]]) ).
cnf(refute_0_1001,plain,
( complement(join(X_60,complement(complement(X_60)))) != complement(join(X_60,X_60))
| join(zero,complement(join(X_60,complement(complement(X_60))))) = complement(join(X_60,X_60)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(X_60,complement(complement(X_60))))),complement(join(X_60,complement(complement(X_60))))) )],[refute_0_999,refute_0_1000]) ).
cnf(refute_0_1002,plain,
join(zero,complement(join(X_60,complement(complement(X_60))))) = complement(join(X_60,X_60)),
inference(resolve,[$cnf( $equal(complement(join(X_60,complement(complement(X_60)))),complement(join(X_60,X_60))) )],[refute_0_998,refute_0_1001]) ).
cnf(refute_0_1003,plain,
( complement(X_60) != join(zero,complement(join(X_60,complement(complement(X_60)))))
| join(zero,complement(join(X_60,complement(complement(X_60))))) != complement(join(X_60,X_60))
| complement(X_60) = complement(join(X_60,X_60)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_60),complement(join(X_60,X_60))) ),[0],$fot(join(zero,complement(join(X_60,complement(complement(X_60))))))]]) ).
cnf(refute_0_1004,plain,
( complement(X_60) != join(zero,complement(join(X_60,complement(complement(X_60)))))
| complement(X_60) = complement(join(X_60,X_60)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(X_60,complement(complement(X_60))))),complement(join(X_60,X_60))) )],[refute_0_1002,refute_0_1003]) ).
cnf(refute_0_1005,plain,
complement(X_60) = complement(join(X_60,X_60)),
inference(resolve,[$cnf( $equal(complement(X_60),join(zero,complement(join(X_60,complement(complement(X_60)))))) )],[refute_0_607,refute_0_1004]) ).
cnf(refute_0_1006,plain,
( complement(X_60) != complement(join(X_60,X_60))
| complement(join(X_60,X_60)) = complement(X_60) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_60))),bind(Y,$fot(complement(join(X_60,X_60))))]]) ).
cnf(refute_0_1007,plain,
complement(join(X_60,X_60)) = complement(X_60),
inference(resolve,[$cnf( $equal(complement(X_60),complement(join(X_60,X_60))) )],[refute_0_1005,refute_0_1006]) ).
cnf(refute_0_1008,plain,
complement(join(one,one)) = complement(one),
inference(subst,[],[refute_0_1007:[bind(X_60,$fot(one))]]) ).
cnf(refute_0_1009,plain,
join(one,complement(join(one,one))) = join(one,complement(join(one,one))),
introduced(tautology,[refl,[$fot(join(one,complement(join(one,one))))]]) ).
cnf(refute_0_1010,plain,
( complement(join(one,one)) != complement(one)
| join(one,complement(join(one,one))) != join(one,complement(join(one,one)))
| join(one,complement(join(one,one))) = join(one,complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(join(one,one))),join(one,complement(join(one,one)))) ),[1,1],$fot(complement(one))]]) ).
cnf(refute_0_1011,plain,
( complement(join(one,one)) != complement(one)
| join(one,complement(join(one,one))) = join(one,complement(one)) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,one))),join(one,complement(join(one,one)))) )],[refute_0_1009,refute_0_1010]) ).
cnf(refute_0_1012,plain,
join(one,complement(join(one,one))) = join(one,complement(one)),
inference(resolve,[$cnf( $equal(complement(join(one,one)),complement(one)) )],[refute_0_1008,refute_0_1011]) ).
cnf(refute_0_1013,plain,
( join(one,complement(join(one,one))) != join(one,complement(one))
| join(one,complement(one)) != top
| join(one,complement(join(one,one))) = top ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(one,complement(join(one,one))))),bind(Y,$fot(join(one,complement(one)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1014,plain,
( join(one,complement(one)) != top
| join(one,complement(join(one,one))) = top ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,one))),join(one,complement(one))) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
join(one,complement(join(one,one))) = top,
inference(resolve,[$cnf( $equal(join(one,complement(one)),top) )],[refute_0_989,refute_0_1014]) ).
cnf(refute_0_1016,plain,
join(one,join(one,complement(join(one,one)))) = join(one,join(one,complement(join(one,one)))),
introduced(tautology,[refl,[$fot(join(one,join(one,complement(join(one,one)))))]]) ).
cnf(refute_0_1017,plain,
( join(one,complement(join(one,one))) != top
| join(one,join(one,complement(join(one,one)))) != join(one,join(one,complement(join(one,one))))
| join(one,join(one,complement(join(one,one)))) = join(one,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,complement(join(one,one)))),join(one,join(one,complement(join(one,one))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1018,plain,
( join(one,complement(join(one,one))) != top
| join(one,join(one,complement(join(one,one)))) = join(one,top) ),
inference(resolve,[$cnf( $equal(join(one,join(one,complement(join(one,one)))),join(one,join(one,complement(join(one,one))))) )],[refute_0_1016,refute_0_1017]) ).
cnf(refute_0_1019,plain,
join(one,join(one,complement(join(one,one)))) = join(one,top),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,one))),top) )],[refute_0_1015,refute_0_1018]) ).
cnf(refute_0_1020,plain,
( join(one,join(one,complement(join(one,one)))) != join(one,top)
| top != join(one,join(one,complement(join(one,one))))
| top = join(one,top) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(one,join(one,complement(join(one,one))))) ),[1],$fot(join(one,top))]]) ).
cnf(refute_0_1021,plain,
( top != join(one,join(one,complement(join(one,one))))
| top = join(one,top) ),
inference(resolve,[$cnf( $equal(join(one,join(one,complement(join(one,one)))),join(one,top)) )],[refute_0_1019,refute_0_1020]) ).
cnf(refute_0_1022,plain,
top = join(one,top),
inference(resolve,[$cnf( $equal(top,join(one,join(one,complement(join(one,one))))) )],[refute_0_988,refute_0_1021]) ).
cnf(refute_0_1023,plain,
( top != join(one,top)
| join(one,top) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(one,top)))]]) ).
cnf(refute_0_1024,plain,
join(one,top) = top,
inference(resolve,[$cnf( $equal(top,join(one,top)) )],[refute_0_1022,refute_0_1023]) ).
cnf(refute_0_1025,plain,
converse(join(one,top)) = converse(join(one,top)),
introduced(tautology,[refl,[$fot(converse(join(one,top)))]]) ).
cnf(refute_0_1026,plain,
( converse(join(one,top)) != converse(join(one,top))
| join(one,top) != top
| converse(join(one,top)) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,top)),converse(join(one,top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1027,plain,
( join(one,top) != top
| converse(join(one,top)) = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(one,top)),converse(join(one,top))) )],[refute_0_1025,refute_0_1026]) ).
cnf(refute_0_1028,plain,
converse(join(one,top)) = converse(top),
inference(resolve,[$cnf( $equal(join(one,top),top) )],[refute_0_1024,refute_0_1027]) ).
cnf(refute_0_1029,plain,
( converse(join(one,top)) != converse(top)
| converse(top) != top
| converse(join(one,top)) = top ),
inference(subst,[],[refute_0_41:[bind(X,$fot(converse(join(one,top)))),bind(Y,$fot(converse(top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1030,plain,
( converse(top) != top
| converse(join(one,top)) = top ),
inference(resolve,[$cnf( $equal(converse(join(one,top)),converse(top)) )],[refute_0_1028,refute_0_1029]) ).
cnf(refute_0_1031,plain,
converse(join(one,top)) = top,
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_500,refute_0_1030]) ).
cnf(refute_0_1032,plain,
join(one,converse(top)) = converse(join(one,top)),
inference(subst,[],[refute_0_964:[bind(X_5,$fot(top))]]) ).
cnf(refute_0_1033,plain,
( converse(join(one,top)) != top
| join(one,converse(top)) != converse(join(one,top))
| join(one,converse(top)) = top ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(one,converse(top)))),bind(Y,$fot(converse(join(one,top)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1034,plain,
( converse(join(one,top)) != top
| join(one,converse(top)) = top ),
inference(resolve,[$cnf( $equal(join(one,converse(top)),converse(join(one,top))) )],[refute_0_1032,refute_0_1033]) ).
cnf(refute_0_1035,plain,
join(one,converse(top)) = top,
inference(resolve,[$cnf( $equal(converse(join(one,top)),top) )],[refute_0_1031,refute_0_1034]) ).
cnf(refute_0_1036,plain,
composition(join(one,converse(top)),complement(composition(top,X_124))) = composition(join(one,converse(top)),complement(composition(top,X_124))),
introduced(tautology,[refl,[$fot(composition(join(one,converse(top)),complement(composition(top,X_124))))]]) ).
cnf(refute_0_1037,plain,
( composition(join(one,converse(top)),complement(composition(top,X_124))) != composition(join(one,converse(top)),complement(composition(top,X_124)))
| join(one,converse(top)) != top
| composition(join(one,converse(top)),complement(composition(top,X_124))) = composition(top,complement(composition(top,X_124))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(top)),complement(composition(top,X_124))),composition(join(one,converse(top)),complement(composition(top,X_124)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1038,plain,
( join(one,converse(top)) != top
| composition(join(one,converse(top)),complement(composition(top,X_124))) = composition(top,complement(composition(top,X_124))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(top)),complement(composition(top,X_124))),composition(join(one,converse(top)),complement(composition(top,X_124)))) )],[refute_0_1036,refute_0_1037]) ).
cnf(refute_0_1039,plain,
composition(join(one,converse(top)),complement(composition(top,X_124))) = composition(top,complement(composition(top,X_124))),
inference(resolve,[$cnf( $equal(join(one,converse(top)),top) )],[refute_0_1035,refute_0_1038]) ).
cnf(refute_0_1040,plain,
composition(join(X_102,one),X_101) = join(X_101,composition(X_102,X_101)),
inference(subst,[],[refute_0_741:[bind(X_100,$fot(X_101)),bind(X_98,$fot(X_102))]]) ).
cnf(refute_0_1041,plain,
join(one,X_102) = join(X_102,one),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(one)),bind(B,$fot(X_102))]]) ).
cnf(refute_0_1042,plain,
( join(one,X_102) != join(X_102,one)
| join(X_102,one) = join(one,X_102) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,X_102))),bind(Y,$fot(join(X_102,one)))]]) ).
cnf(refute_0_1043,plain,
join(X_102,one) = join(one,X_102),
inference(resolve,[$cnf( $equal(join(one,X_102),join(X_102,one)) )],[refute_0_1041,refute_0_1042]) ).
cnf(refute_0_1044,plain,
( composition(join(X_102,one),X_101) != join(X_101,composition(X_102,X_101))
| join(X_102,one) != join(one,X_102)
| composition(join(one,X_102),X_101) = join(X_101,composition(X_102,X_101)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_102,one),X_101),join(X_101,composition(X_102,X_101))) ),[0,0],$fot(join(one,X_102))]]) ).
cnf(refute_0_1045,plain,
( composition(join(X_102,one),X_101) != join(X_101,composition(X_102,X_101))
| composition(join(one,X_102),X_101) = join(X_101,composition(X_102,X_101)) ),
inference(resolve,[$cnf( $equal(join(X_102,one),join(one,X_102)) )],[refute_0_1043,refute_0_1044]) ).
cnf(refute_0_1046,plain,
composition(join(one,X_102),X_101) = join(X_101,composition(X_102,X_101)),
inference(resolve,[$cnf( $equal(composition(join(X_102,one),X_101),join(X_101,composition(X_102,X_101))) )],[refute_0_1040,refute_0_1045]) ).
cnf(refute_0_1047,plain,
( composition(join(X_98,one),X_100) != join(X_100,composition(X_98,X_100))
| join(X_100,composition(X_98,X_100)) = composition(join(X_98,one),X_100) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_98,one),X_100))),bind(Y,$fot(join(X_100,composition(X_98,X_100))))]]) ).
cnf(refute_0_1048,plain,
join(X_100,composition(X_98,X_100)) = composition(join(X_98,one),X_100),
inference(resolve,[$cnf( $equal(composition(join(X_98,one),X_100),join(X_100,composition(X_98,X_100))) )],[refute_0_741,refute_0_1047]) ).
cnf(refute_0_1049,plain,
join(X_101,composition(X_102,X_101)) = composition(join(X_102,one),X_101),
inference(subst,[],[refute_0_1048:[bind(X_100,$fot(X_101)),bind(X_98,$fot(X_102))]]) ).
cnf(refute_0_1050,plain,
( composition(join(one,X_102),X_101) != join(X_101,composition(X_102,X_101))
| join(X_101,composition(X_102,X_101)) != composition(join(X_102,one),X_101)
| composition(join(one,X_102),X_101) = composition(join(X_102,one),X_101) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,X_102),X_101),composition(join(X_102,one),X_101)) ),[0],$fot(join(X_101,composition(X_102,X_101)))]]) ).
cnf(refute_0_1051,plain,
( composition(join(one,X_102),X_101) != join(X_101,composition(X_102,X_101))
| composition(join(one,X_102),X_101) = composition(join(X_102,one),X_101) ),
inference(resolve,[$cnf( $equal(join(X_101,composition(X_102,X_101)),composition(join(X_102,one),X_101)) )],[refute_0_1049,refute_0_1050]) ).
cnf(refute_0_1052,plain,
composition(join(one,X_102),X_101) = composition(join(X_102,one),X_101),
inference(resolve,[$cnf( $equal(composition(join(one,X_102),X_101),join(X_101,composition(X_102,X_101))) )],[refute_0_1046,refute_0_1051]) ).
cnf(refute_0_1053,plain,
( composition(join(one,X_102),X_101) != composition(join(X_102,one),X_101)
| composition(join(X_102,one),X_101) = composition(join(one,X_102),X_101) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,X_102),X_101))),bind(Y,$fot(composition(join(X_102,one),X_101)))]]) ).
cnf(refute_0_1054,plain,
composition(join(X_102,one),X_101) = composition(join(one,X_102),X_101),
inference(resolve,[$cnf( $equal(composition(join(one,X_102),X_101),composition(join(X_102,one),X_101)) )],[refute_0_1052,refute_0_1053]) ).
cnf(refute_0_1055,plain,
composition(join(converse(top),one),complement(composition(top,X_124))) = composition(join(one,converse(top)),complement(composition(top,X_124))),
inference(subst,[],[refute_0_1054:[bind(X_101,$fot(complement(composition(top,X_124)))),bind(X_102,$fot(converse(top)))]]) ).
cnf(refute_0_1056,plain,
join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) = composition(join(converse(top),one),complement(composition(top,X_124))),
inference(subst,[],[refute_0_1048:[bind(X_100,$fot(complement(composition(top,X_124)))),bind(X_98,$fot(converse(top)))]]) ).
cnf(refute_0_1057,plain,
( composition(join(converse(top),one),complement(composition(top,X_124))) != composition(join(one,converse(top)),complement(composition(top,X_124)))
| join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) != composition(join(converse(top),one),complement(composition(top,X_124)))
| join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) = composition(join(one,converse(top)),complement(composition(top,X_124))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))))),bind(Y,$fot(composition(join(converse(top),one),complement(composition(top,X_124))))),bind(Z,$fot(composition(join(one,converse(top)),complement(composition(top,X_124)))))]]) ).
cnf(refute_0_1058,plain,
( composition(join(converse(top),one),complement(composition(top,X_124))) != composition(join(one,converse(top)),complement(composition(top,X_124)))
| join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) = composition(join(one,converse(top)),complement(composition(top,X_124))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))),composition(join(converse(top),one),complement(composition(top,X_124)))) )],[refute_0_1056,refute_0_1057]) ).
cnf(refute_0_1059,plain,
join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) = composition(join(one,converse(top)),complement(composition(top,X_124))),
inference(resolve,[$cnf( $equal(composition(join(converse(top),one),complement(composition(top,X_124))),composition(join(one,converse(top)),complement(composition(top,X_124)))) )],[refute_0_1055,refute_0_1058]) ).
cnf(refute_0_1060,plain,
( composition(join(one,converse(top)),complement(composition(top,X_124))) != composition(top,complement(composition(top,X_124)))
| join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) != composition(join(one,converse(top)),complement(composition(top,X_124)))
| join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) = composition(top,complement(composition(top,X_124))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))))),bind(Y,$fot(composition(join(one,converse(top)),complement(composition(top,X_124))))),bind(Z,$fot(composition(top,complement(composition(top,X_124)))))]]) ).
cnf(refute_0_1061,plain,
( composition(join(one,converse(top)),complement(composition(top,X_124))) != composition(top,complement(composition(top,X_124)))
| join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) = composition(top,complement(composition(top,X_124))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))),composition(join(one,converse(top)),complement(composition(top,X_124)))) )],[refute_0_1059,refute_0_1060]) ).
cnf(refute_0_1062,plain,
join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) = composition(top,complement(composition(top,X_124))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(top)),complement(composition(top,X_124))),composition(top,complement(composition(top,X_124)))) )],[refute_0_1039,refute_0_1061]) ).
cnf(refute_0_1063,plain,
( join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) != complement(composition(top,X_124))
| join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) != composition(top,complement(composition(top,X_124)))
| composition(top,complement(composition(top,X_124))) = complement(composition(top,X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))),complement(composition(top,X_124))) ),[0],$fot(composition(top,complement(composition(top,X_124))))]]) ).
cnf(refute_0_1064,plain,
( join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))) != complement(composition(top,X_124))
| composition(top,complement(composition(top,X_124))) = complement(composition(top,X_124)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))),composition(top,complement(composition(top,X_124)))) )],[refute_0_1062,refute_0_1063]) ).
cnf(refute_0_1065,plain,
composition(top,complement(composition(top,X_124))) = complement(composition(top,X_124)),
inference(resolve,[$cnf( $equal(join(complement(composition(top,X_124)),composition(converse(top),complement(composition(top,X_124)))),complement(composition(top,X_124))) )],[refute_0_949,refute_0_1064]) ).
cnf(refute_0_1066,plain,
composition(top,complement(composition(top,converse(X_6)))) = complement(composition(top,converse(X_6))),
inference(subst,[],[refute_0_1065:[bind(X_124,$fot(converse(X_6)))]]) ).
cnf(refute_0_1067,plain,
converse(composition(X_6,converse(A))) = composition(converse(converse(A)),converse(X_6)),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(X_6)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_1068,plain,
( converse(composition(X_6,converse(A))) != composition(converse(converse(A)),converse(X_6))
| converse(converse(A)) != A
| converse(composition(X_6,converse(A))) = composition(A,converse(X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_6,converse(A))),composition(converse(converse(A)),converse(X_6))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_1069,plain,
( converse(composition(X_6,converse(A))) != composition(converse(converse(A)),converse(X_6))
| converse(composition(X_6,converse(A))) = composition(A,converse(X_6)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1068]) ).
cnf(refute_0_1070,plain,
converse(composition(X_6,converse(A))) = composition(A,converse(X_6)),
inference(resolve,[$cnf( $equal(converse(composition(X_6,converse(A))),composition(converse(converse(A)),converse(X_6))) )],[refute_0_1067,refute_0_1069]) ).
cnf(refute_0_1071,plain,
converse(composition(X_6,converse(top))) = composition(top,converse(X_6)),
inference(subst,[],[refute_0_1070:[bind(A,$fot(top))]]) ).
cnf(refute_0_1072,plain,
( converse(composition(X_6,converse(top))) != composition(top,converse(X_6))
| converse(top) != top
| converse(composition(X_6,top)) = composition(top,converse(X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_6,converse(top))),composition(top,converse(X_6))) ),[0,0,1],$fot(top)]]) ).
cnf(refute_0_1073,plain,
( converse(composition(X_6,converse(top))) != composition(top,converse(X_6))
| converse(composition(X_6,top)) = composition(top,converse(X_6)) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_500,refute_0_1072]) ).
cnf(refute_0_1074,plain,
converse(composition(X_6,top)) = composition(top,converse(X_6)),
inference(resolve,[$cnf( $equal(converse(composition(X_6,converse(top))),composition(top,converse(X_6))) )],[refute_0_1071,refute_0_1073]) ).
cnf(refute_0_1075,plain,
( converse(composition(X_6,top)) != composition(top,converse(X_6))
| composition(top,converse(X_6)) = converse(composition(X_6,top)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(X_6,top)))),bind(Y,$fot(composition(top,converse(X_6))))]]) ).
cnf(refute_0_1076,plain,
composition(top,converse(X_6)) = converse(composition(X_6,top)),
inference(resolve,[$cnf( $equal(converse(composition(X_6,top)),composition(top,converse(X_6))) )],[refute_0_1074,refute_0_1075]) ).
cnf(refute_0_1077,plain,
( composition(top,complement(composition(top,converse(X_6)))) != complement(composition(top,converse(X_6)))
| composition(top,converse(X_6)) != converse(composition(X_6,top))
| composition(top,complement(converse(composition(X_6,top)))) = complement(composition(top,converse(X_6))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(composition(top,converse(X_6)))),complement(composition(top,converse(X_6)))) ),[0,1,0],$fot(converse(composition(X_6,top)))]]) ).
cnf(refute_0_1078,plain,
( composition(top,complement(composition(top,converse(X_6)))) != complement(composition(top,converse(X_6)))
| composition(top,complement(converse(composition(X_6,top)))) = complement(composition(top,converse(X_6))) ),
inference(resolve,[$cnf( $equal(composition(top,converse(X_6)),converse(composition(X_6,top))) )],[refute_0_1076,refute_0_1077]) ).
cnf(refute_0_1079,plain,
composition(top,complement(converse(composition(X_6,top)))) = complement(composition(top,converse(X_6))),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,converse(X_6)))),complement(composition(top,converse(X_6)))) )],[refute_0_1066,refute_0_1078]) ).
cnf(refute_0_1080,plain,
complement(composition(top,converse(X_6))) = complement(composition(top,converse(X_6))),
introduced(tautology,[refl,[$fot(complement(composition(top,converse(X_6))))]]) ).
cnf(refute_0_1081,plain,
( complement(composition(top,converse(X_6))) != complement(composition(top,converse(X_6)))
| composition(top,converse(X_6)) != converse(composition(X_6,top))
| complement(composition(top,converse(X_6))) = complement(converse(composition(X_6,top))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(top,converse(X_6))),complement(composition(top,converse(X_6)))) ),[1,0],$fot(converse(composition(X_6,top)))]]) ).
cnf(refute_0_1082,plain,
( composition(top,converse(X_6)) != converse(composition(X_6,top))
| complement(composition(top,converse(X_6))) = complement(converse(composition(X_6,top))) ),
inference(resolve,[$cnf( $equal(complement(composition(top,converse(X_6))),complement(composition(top,converse(X_6)))) )],[refute_0_1080,refute_0_1081]) ).
cnf(refute_0_1083,plain,
complement(composition(top,converse(X_6))) = complement(converse(composition(X_6,top))),
inference(resolve,[$cnf( $equal(composition(top,converse(X_6)),converse(composition(X_6,top))) )],[refute_0_1076,refute_0_1082]) ).
cnf(refute_0_1084,plain,
( complement(composition(top,converse(X_6))) != complement(converse(composition(X_6,top)))
| composition(top,complement(converse(composition(X_6,top)))) != complement(composition(top,converse(X_6)))
| composition(top,complement(converse(composition(X_6,top)))) = complement(converse(composition(X_6,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(converse(composition(X_6,top)))),complement(composition(top,converse(X_6)))) ),[1],$fot(complement(converse(composition(X_6,top))))]]) ).
cnf(refute_0_1085,plain,
( composition(top,complement(converse(composition(X_6,top)))) != complement(composition(top,converse(X_6)))
| composition(top,complement(converse(composition(X_6,top)))) = complement(converse(composition(X_6,top))) ),
inference(resolve,[$cnf( $equal(complement(composition(top,converse(X_6))),complement(converse(composition(X_6,top)))) )],[refute_0_1083,refute_0_1084]) ).
cnf(refute_0_1086,plain,
composition(top,complement(converse(composition(X_6,top)))) = complement(converse(composition(X_6,top))),
inference(resolve,[$cnf( $equal(composition(top,complement(converse(composition(X_6,top)))),complement(composition(top,converse(X_6)))) )],[refute_0_1079,refute_0_1085]) ).
cnf(refute_0_1087,plain,
composition(top,complement(converse(composition(X_461,top)))) = complement(converse(composition(X_461,top))),
inference(subst,[],[refute_0_1086:[bind(X_6,$fot(X_461))]]) ).
cnf(refute_0_1088,plain,
( composition(complement(converse(composition(X_461,top))),complement(converse(composition(top,complement(converse(composition(X_461,top))))))) != zero
| composition(top,complement(converse(composition(X_461,top)))) != complement(converse(composition(X_461,top)))
| composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(converse(composition(X_461,top))),complement(converse(composition(top,complement(converse(composition(X_461,top))))))),zero) ),[0,1,0,0],$fot(complement(converse(composition(X_461,top))))]]) ).
cnf(refute_0_1089,plain,
( composition(complement(converse(composition(X_461,top))),complement(converse(composition(top,complement(converse(composition(X_461,top))))))) != zero
| composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))) = zero ),
inference(resolve,[$cnf( $equal(composition(top,complement(converse(composition(X_461,top)))),complement(converse(composition(X_461,top)))) )],[refute_0_1087,refute_0_1088]) ).
cnf(refute_0_1090,plain,
composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))) = zero,
inference(resolve,[$cnf( $equal(composition(complement(converse(composition(X_461,top))),complement(converse(composition(top,complement(converse(composition(X_461,top))))))),zero) )],[refute_0_728,refute_0_1089]) ).
cnf(refute_0_1091,plain,
converse(converse(composition(X_461,top))) = composition(X_461,top),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(X_461,top)))]]) ).
cnf(refute_0_1092,plain,
converse(converse(complement(converse(complement(X_370))))) = complement(converse(complement(X_370))),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(converse(complement(X_370)))))]]) ).
cnf(refute_0_1093,plain,
join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_36),complement(join(complement(join(zero,complement(B))),X_36))),
inference(subst,[],[refute_0_47:[bind(A,$fot(join(zero,complement(B)))),bind(B,$fot(X_36))]]) ).
cnf(refute_0_1094,plain,
( complement(join(zero,complement(B))) != meet(top,B)
| join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_36),complement(join(complement(join(zero,complement(B))),X_36)))
| join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_36),complement(join(meet(top,B),X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_36),complement(join(complement(join(zero,complement(B))),X_36)))) ),[1,1,0,0],$fot(meet(top,B))]]) ).
cnf(refute_0_1095,plain,
( join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_36),complement(join(complement(join(zero,complement(B))),X_36)))
| join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_36),complement(join(meet(top,B),X_36))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),meet(top,B)) )],[refute_0_96,refute_0_1094]) ).
cnf(refute_0_1096,plain,
join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_36),complement(join(meet(top,B),X_36))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_36),complement(join(complement(join(zero,complement(B))),X_36)))) )],[refute_0_1093,refute_0_1095]) ).
cnf(refute_0_1097,plain,
join(meet(join(zero,complement(B)),X_36),complement(join(meet(top,B),X_36))) = join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(meet(top,B),X_36)))),bind(B,$fot(meet(join(zero,complement(B)),X_36)))]]) ).
cnf(refute_0_1098,plain,
( join(meet(join(zero,complement(B)),X_36),complement(join(meet(top,B),X_36))) != join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36))
| join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_36),complement(join(meet(top,B),X_36)))
| join(zero,complement(B)) = join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_36),complement(join(meet(top,B),X_36)))) ),[1],$fot(join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)))]]) ).
cnf(refute_0_1099,plain,
( join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_36),complement(join(meet(top,B),X_36)))
| join(zero,complement(B)) = join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)) ),
inference(resolve,[$cnf( $equal(join(meet(join(zero,complement(B)),X_36),complement(join(meet(top,B),X_36))),join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36))) )],[refute_0_1097,refute_0_1098]) ).
cnf(refute_0_1100,plain,
join(zero,complement(B)) = join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_36),complement(join(meet(top,B),X_36)))) )],[refute_0_1096,refute_0_1099]) ).
cnf(refute_0_1101,plain,
meet(join(zero,complement(X_17)),B) = complement(join(complement(join(zero,complement(X_17))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(zero,complement(X_17))))]]) ).
cnf(refute_0_1102,plain,
( complement(join(zero,complement(X_17))) != meet(top,X_17)
| meet(join(zero,complement(X_17)),B) != complement(join(complement(join(zero,complement(X_17))),complement(B)))
| meet(join(zero,complement(X_17)),B) = complement(join(meet(top,X_17),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_17)),B),complement(join(complement(join(zero,complement(X_17))),complement(B)))) ),[1,0,0],$fot(meet(top,X_17))]]) ).
cnf(refute_0_1103,plain,
( meet(join(zero,complement(X_17)),B) != complement(join(complement(join(zero,complement(X_17))),complement(B)))
| meet(join(zero,complement(X_17)),B) = complement(join(meet(top,X_17),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_17))),meet(top,X_17)) )],[refute_0_640,refute_0_1102]) ).
cnf(refute_0_1104,plain,
meet(join(zero,complement(X_17)),B) = complement(join(meet(top,X_17),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_17)),B),complement(join(complement(join(zero,complement(X_17))),complement(B)))) )],[refute_0_1101,refute_0_1103]) ).
cnf(refute_0_1105,plain,
meet(join(complement(X_14),complement(X_15)),B) = meet(join(complement(X_14),complement(X_15)),B),
introduced(tautology,[refl,[$fot(meet(join(complement(X_14),complement(X_15)),B))]]) ).
cnf(refute_0_1106,plain,
( join(complement(X_14),complement(X_15)) != complement(meet(X_14,X_15))
| meet(join(complement(X_14),complement(X_15)),B) != meet(join(complement(X_14),complement(X_15)),B)
| meet(join(complement(X_14),complement(X_15)),B) = meet(complement(meet(X_14,X_15)),B) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_14),complement(X_15)),B),meet(join(complement(X_14),complement(X_15)),B)) ),[1,0],$fot(complement(meet(X_14,X_15)))]]) ).
cnf(refute_0_1107,plain,
( join(complement(X_14),complement(X_15)) != complement(meet(X_14,X_15))
| meet(join(complement(X_14),complement(X_15)),B) = meet(complement(meet(X_14,X_15)),B) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_14),complement(X_15)),B),meet(join(complement(X_14),complement(X_15)),B)) )],[refute_0_1105,refute_0_1106]) ).
cnf(refute_0_1108,plain,
meet(join(complement(X_14),complement(X_15)),B) = meet(complement(meet(X_14,X_15)),B),
inference(resolve,[$cnf( $equal(join(complement(X_14),complement(X_15)),complement(meet(X_14,X_15))) )],[refute_0_644,refute_0_1107]) ).
cnf(refute_0_1109,plain,
( meet(join(complement(X_14),complement(X_15)),B) != complement(join(meet(X_14,X_15),complement(B)))
| meet(join(complement(X_14),complement(X_15)),B) != meet(complement(meet(X_14,X_15)),B)
| meet(complement(meet(X_14,X_15)),B) = complement(join(meet(X_14,X_15),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_14),complement(X_15)),B),complement(join(meet(X_14,X_15),complement(B)))) ),[0],$fot(meet(complement(meet(X_14,X_15)),B))]]) ).
cnf(refute_0_1110,plain,
( meet(join(complement(X_14),complement(X_15)),B) != complement(join(meet(X_14,X_15),complement(B)))
| meet(complement(meet(X_14,X_15)),B) = complement(join(meet(X_14,X_15),complement(B))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_14),complement(X_15)),B),meet(complement(meet(X_14,X_15)),B)) )],[refute_0_1108,refute_0_1109]) ).
cnf(refute_0_1111,plain,
meet(complement(meet(X_14,X_15)),B) = complement(join(meet(X_14,X_15),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_14),complement(X_15)),B),complement(join(meet(X_14,X_15),complement(B)))) )],[refute_0_78,refute_0_1110]) ).
cnf(refute_0_1112,plain,
( meet(complement(meet(X_14,X_15)),B) != complement(join(meet(X_14,X_15),complement(B)))
| complement(join(meet(X_14,X_15),complement(B))) = meet(complement(meet(X_14,X_15)),B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(meet(X_14,X_15)),B))),bind(Y,$fot(complement(join(meet(X_14,X_15),complement(B)))))]]) ).
cnf(refute_0_1113,plain,
complement(join(meet(X_14,X_15),complement(B))) = meet(complement(meet(X_14,X_15)),B),
inference(resolve,[$cnf( $equal(meet(complement(meet(X_14,X_15)),B),complement(join(meet(X_14,X_15),complement(B)))) )],[refute_0_1111,refute_0_1112]) ).
cnf(refute_0_1114,plain,
complement(join(meet(top,X_17),complement(B))) = meet(complement(meet(top,X_17)),B),
inference(subst,[],[refute_0_1113:[bind(X_14,$fot(top)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_1115,plain,
( complement(join(meet(top,X_17),complement(B))) != meet(complement(meet(top,X_17)),B)
| meet(join(zero,complement(X_17)),B) != complement(join(meet(top,X_17),complement(B)))
| meet(join(zero,complement(X_17)),B) = meet(complement(meet(top,X_17)),B) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_17)),B),complement(join(meet(top,X_17),complement(B)))) ),[1],$fot(meet(complement(meet(top,X_17)),B))]]) ).
cnf(refute_0_1116,plain,
( meet(join(zero,complement(X_17)),B) != complement(join(meet(top,X_17),complement(B)))
| meet(join(zero,complement(X_17)),B) = meet(complement(meet(top,X_17)),B) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,X_17),complement(B))),meet(complement(meet(top,X_17)),B)) )],[refute_0_1114,refute_0_1115]) ).
cnf(refute_0_1117,plain,
meet(join(zero,complement(X_17)),B) = meet(complement(meet(top,X_17)),B),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_17)),B),complement(join(meet(top,X_17),complement(B)))) )],[refute_0_1104,refute_0_1116]) ).
cnf(refute_0_1118,plain,
meet(join(zero,complement(B)),X_36) = meet(complement(meet(top,B)),X_36),
inference(subst,[],[refute_0_1117:[bind(B,$fot(X_36)),bind(X_17,$fot(B))]]) ).
cnf(refute_0_1119,plain,
join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)) = join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)),
introduced(tautology,[refl,[$fot(join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)))]]) ).
cnf(refute_0_1120,plain,
( join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)) != join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36))
| meet(join(zero,complement(B)),X_36) != meet(complement(meet(top,B)),X_36)
| join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)),join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36))) ),[1,1],$fot(meet(complement(meet(top,B)),X_36))]]) ).
cnf(refute_0_1121,plain,
( meet(join(zero,complement(B)),X_36) != meet(complement(meet(top,B)),X_36)
| join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)),join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36))) )],[refute_0_1119,refute_0_1120]) ).
cnf(refute_0_1122,plain,
join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(B)),X_36),meet(complement(meet(top,B)),X_36)) )],[refute_0_1118,refute_0_1121]) ).
cnf(refute_0_1123,plain,
( join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)) != join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))
| join(zero,complement(B)) != join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36))
| join(zero,complement(B)) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36))) ),[1],$fot(join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)))]]) ).
cnf(refute_0_1124,plain,
( join(zero,complement(B)) != join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36))
| join(zero,complement(B)) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36)),join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))) )],[refute_0_1122,refute_0_1123]) ).
cnf(refute_0_1125,plain,
join(zero,complement(B)) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(complement(join(meet(top,B),X_36)),meet(join(zero,complement(B)),X_36))) )],[refute_0_1100,refute_0_1124]) ).
cnf(refute_0_1126,plain,
( join(zero,complement(B)) != complement(meet(top,B))
| join(zero,complement(B)) != join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))
| complement(meet(top,B)) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))) ),[0],$fot(complement(meet(top,B)))]]) ).
cnf(refute_0_1127,plain,
( join(zero,complement(B)) != join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))
| complement(meet(top,B)) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(meet(top,B))) )],[refute_0_671,refute_0_1126]) ).
cnf(refute_0_1128,plain,
complement(meet(top,B)) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))) )],[refute_0_1125,refute_0_1127]) ).
cnf(refute_0_1129,plain,
( join(zero,complement(B)) != complement(B)
| join(zero,complement(B)) != complement(meet(top,B))
| complement(B) = complement(meet(top,B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),complement(meet(top,B))) ),[0],$fot(complement(B))]]) ).
cnf(refute_0_1130,plain,
( join(zero,complement(B)) != complement(meet(top,B))
| complement(B) = complement(meet(top,B)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(B)) )],[refute_0_852,refute_0_1129]) ).
cnf(refute_0_1131,plain,
complement(B) = complement(meet(top,B)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(meet(top,B))) )],[refute_0_671,refute_0_1130]) ).
cnf(refute_0_1132,plain,
( complement(B) != complement(meet(top,B))
| complement(meet(top,B)) = complement(B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(B))),bind(Y,$fot(complement(meet(top,B))))]]) ).
cnf(refute_0_1133,plain,
complement(meet(top,B)) = complement(B),
inference(resolve,[$cnf( $equal(complement(B),complement(meet(top,B))) )],[refute_0_1131,refute_0_1132]) ).
cnf(refute_0_1134,plain,
( complement(meet(top,B)) != complement(B)
| complement(meet(top,B)) != join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))
| complement(B) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,B)),join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))) ),[0],$fot(complement(B))]]) ).
cnf(refute_0_1135,plain,
( complement(meet(top,B)) != join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))
| complement(B) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) ),
inference(resolve,[$cnf( $equal(complement(meet(top,B)),complement(B)) )],[refute_0_1133,refute_0_1134]) ).
cnf(refute_0_1136,plain,
join(complement(join(meet(top,B),X_36)),meet(complement(B),X_36)) = join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(complement(B),X_36))),bind(B,$fot(complement(join(meet(top,B),X_36))))]]) ).
cnf(refute_0_1137,plain,
meet(complement(meet(top,B)),X_36) = meet(complement(meet(top,B)),X_36),
introduced(tautology,[refl,[$fot(meet(complement(meet(top,B)),X_36))]]) ).
cnf(refute_0_1138,plain,
( complement(meet(top,B)) != complement(B)
| meet(complement(meet(top,B)),X_36) != meet(complement(meet(top,B)),X_36)
| meet(complement(meet(top,B)),X_36) = meet(complement(B),X_36) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(top,B)),X_36),meet(complement(meet(top,B)),X_36)) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_1139,plain,
( complement(meet(top,B)) != complement(B)
| meet(complement(meet(top,B)),X_36) = meet(complement(B),X_36) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,B)),X_36),meet(complement(meet(top,B)),X_36)) )],[refute_0_1137,refute_0_1138]) ).
cnf(refute_0_1140,plain,
meet(complement(meet(top,B)),X_36) = meet(complement(B),X_36),
inference(resolve,[$cnf( $equal(complement(meet(top,B)),complement(B)) )],[refute_0_1133,refute_0_1139]) ).
cnf(refute_0_1141,plain,
join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) = join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)),
introduced(tautology,[refl,[$fot(join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)))]]) ).
cnf(refute_0_1142,plain,
( join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) != join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))
| meet(complement(meet(top,B)),X_36) != meet(complement(B),X_36)
| join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) = join(complement(join(meet(top,B),X_36)),meet(complement(B),X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)),join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))) ),[1,1],$fot(meet(complement(B),X_36))]]) ).
cnf(refute_0_1143,plain,
( meet(complement(meet(top,B)),X_36) != meet(complement(B),X_36)
| join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) = join(complement(join(meet(top,B),X_36)),meet(complement(B),X_36)) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)),join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))) )],[refute_0_1141,refute_0_1142]) ).
cnf(refute_0_1144,plain,
join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) = join(complement(join(meet(top,B),X_36)),meet(complement(B),X_36)),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,B)),X_36),meet(complement(B),X_36)) )],[refute_0_1140,refute_0_1143]) ).
cnf(refute_0_1145,plain,
( join(complement(join(meet(top,B),X_36)),meet(complement(B),X_36)) != join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))
| join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) != join(complement(join(meet(top,B),X_36)),meet(complement(B),X_36))
| join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) = join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)))),bind(Y,$fot(join(complement(join(meet(top,B),X_36)),meet(complement(B),X_36)))),bind(Z,$fot(join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))))]]) ).
cnf(refute_0_1146,plain,
( join(complement(join(meet(top,B),X_36)),meet(complement(B),X_36)) != join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))
| join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) = join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)),join(complement(join(meet(top,B),X_36)),meet(complement(B),X_36))) )],[refute_0_1144,refute_0_1145]) ).
cnf(refute_0_1147,plain,
join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) = join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_36)),meet(complement(B),X_36)),join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))) )],[refute_0_1136,refute_0_1146]) ).
cnf(refute_0_1148,plain,
( complement(B) != join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))
| join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)) != join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))
| complement(B) = join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(B),join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))) ),[0],$fot(join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)))]]) ).
cnf(refute_0_1149,plain,
( complement(B) != join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))
| complement(B) = join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36)),join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))) )],[refute_0_1147,refute_0_1148]) ).
cnf(refute_0_1150,plain,
( complement(meet(top,B)) != join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))
| complement(B) = join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) ),
inference(resolve,[$cnf( $equal(complement(B),join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))) )],[refute_0_1135,refute_0_1149]) ).
cnf(refute_0_1151,plain,
complement(B) = join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))),
inference(resolve,[$cnf( $equal(complement(meet(top,B)),join(complement(join(meet(top,B),X_36)),meet(complement(meet(top,B)),X_36))) )],[refute_0_1128,refute_0_1150]) ).
cnf(refute_0_1152,plain,
join(meet(complement(B),X_36),complement(join(B,X_36))) = join(complement(join(B,X_36)),meet(complement(B),X_36)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(B,X_36)))),bind(B,$fot(meet(complement(B),X_36)))]]) ).
cnf(refute_0_1153,plain,
join(meet(top,B),X_36) = join(meet(top,B),X_36),
introduced(tautology,[refl,[$fot(join(meet(top,B),X_36))]]) ).
cnf(refute_0_1154,plain,
( join(meet(top,B),X_36) != join(meet(top,B),X_36)
| meet(top,B) != B
| join(meet(top,B),X_36) = join(B,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,B),X_36),join(meet(top,B),X_36)) ),[1,0],$fot(B)]]) ).
cnf(refute_0_1155,plain,
( meet(top,B) != B
| join(meet(top,B),X_36) = join(B,X_36) ),
inference(resolve,[$cnf( $equal(join(meet(top,B),X_36),join(meet(top,B),X_36)) )],[refute_0_1153,refute_0_1154]) ).
cnf(refute_0_1156,plain,
join(meet(top,B),X_36) = join(B,X_36),
inference(resolve,[$cnf( $equal(meet(top,B),B) )],[refute_0_862,refute_0_1155]) ).
cnf(refute_0_1157,plain,
complement(join(meet(top,B),X_36)) = complement(join(meet(top,B),X_36)),
introduced(tautology,[refl,[$fot(complement(join(meet(top,B),X_36)))]]) ).
cnf(refute_0_1158,plain,
( complement(join(meet(top,B),X_36)) != complement(join(meet(top,B),X_36))
| join(meet(top,B),X_36) != join(B,X_36)
| complement(join(meet(top,B),X_36)) = complement(join(B,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(top,B),X_36)),complement(join(meet(top,B),X_36))) ),[1,0],$fot(join(B,X_36))]]) ).
cnf(refute_0_1159,plain,
( join(meet(top,B),X_36) != join(B,X_36)
| complement(join(meet(top,B),X_36)) = complement(join(B,X_36)) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,B),X_36)),complement(join(meet(top,B),X_36))) )],[refute_0_1157,refute_0_1158]) ).
cnf(refute_0_1160,plain,
complement(join(meet(top,B),X_36)) = complement(join(B,X_36)),
inference(resolve,[$cnf( $equal(join(meet(top,B),X_36),join(B,X_36)) )],[refute_0_1156,refute_0_1159]) ).
cnf(refute_0_1161,plain,
join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) = join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))),
introduced(tautology,[refl,[$fot(join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))))]]) ).
cnf(refute_0_1162,plain,
( complement(join(meet(top,B),X_36)) != complement(join(B,X_36))
| join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) != join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))
| join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) = join(meet(complement(B),X_36),complement(join(B,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))),join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))) ),[1,1],$fot(complement(join(B,X_36)))]]) ).
cnf(refute_0_1163,plain,
( complement(join(meet(top,B),X_36)) != complement(join(B,X_36))
| join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) = join(meet(complement(B),X_36),complement(join(B,X_36))) ),
inference(resolve,[$cnf( $equal(join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))),join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))) )],[refute_0_1161,refute_0_1162]) ).
cnf(refute_0_1164,plain,
join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) = join(meet(complement(B),X_36),complement(join(B,X_36))),
inference(resolve,[$cnf( $equal(complement(join(meet(top,B),X_36)),complement(join(B,X_36))) )],[refute_0_1160,refute_0_1163]) ).
cnf(refute_0_1165,plain,
( join(meet(complement(B),X_36),complement(join(B,X_36))) != join(complement(join(B,X_36)),meet(complement(B),X_36))
| join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) != join(meet(complement(B),X_36),complement(join(B,X_36)))
| join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) = join(complement(join(B,X_36)),meet(complement(B),X_36)) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))))),bind(Y,$fot(join(meet(complement(B),X_36),complement(join(B,X_36))))),bind(Z,$fot(join(complement(join(B,X_36)),meet(complement(B),X_36))))]]) ).
cnf(refute_0_1166,plain,
( join(meet(complement(B),X_36),complement(join(B,X_36))) != join(complement(join(B,X_36)),meet(complement(B),X_36))
| join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) = join(complement(join(B,X_36)),meet(complement(B),X_36)) ),
inference(resolve,[$cnf( $equal(join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))),join(meet(complement(B),X_36),complement(join(B,X_36)))) )],[refute_0_1164,refute_0_1165]) ).
cnf(refute_0_1167,plain,
join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) = join(complement(join(B,X_36)),meet(complement(B),X_36)),
inference(resolve,[$cnf( $equal(join(meet(complement(B),X_36),complement(join(B,X_36))),join(complement(join(B,X_36)),meet(complement(B),X_36))) )],[refute_0_1152,refute_0_1166]) ).
cnf(refute_0_1168,plain,
( complement(B) != join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))
| join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))) != join(complement(join(B,X_36)),meet(complement(B),X_36))
| complement(B) = join(complement(join(B,X_36)),meet(complement(B),X_36)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(B),join(complement(join(B,X_36)),meet(complement(B),X_36))) ),[0],$fot(join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))))]]) ).
cnf(refute_0_1169,plain,
( complement(B) != join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))
| complement(B) = join(complement(join(B,X_36)),meet(complement(B),X_36)) ),
inference(resolve,[$cnf( $equal(join(meet(complement(B),X_36),complement(join(meet(top,B),X_36))),join(complement(join(B,X_36)),meet(complement(B),X_36))) )],[refute_0_1167,refute_0_1168]) ).
cnf(refute_0_1170,plain,
complement(B) = join(complement(join(B,X_36)),meet(complement(B),X_36)),
inference(resolve,[$cnf( $equal(complement(B),join(meet(complement(B),X_36),complement(join(meet(top,B),X_36)))) )],[refute_0_1151,refute_0_1169]) ).
cnf(refute_0_1171,plain,
complement(complement(converse(X_204))) = join(complement(join(complement(converse(X_204)),converse(join(X_205,X_204)))),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),
inference(subst,[],[refute_0_1170:[bind(B,$fot(complement(converse(X_204)))),bind(X_36,$fot(converse(join(X_205,X_204))))]]) ).
cnf(refute_0_1172,plain,
converse(join(join(X_10,X_11),B)) = join(converse(join(X_10,X_11)),converse(B)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(join(X_10,X_11)))]]) ).
cnf(refute_0_1173,plain,
converse(join(X_10,X_11)) = converse(join(X_11,X_10)),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_10)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_1174,plain,
( converse(join(X_10,X_11)) != converse(join(X_11,X_10))
| converse(join(join(X_10,X_11),B)) != join(converse(join(X_10,X_11)),converse(B))
| converse(join(join(X_10,X_11),B)) = join(converse(join(X_11,X_10)),converse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_10,X_11),B)),join(converse(join(X_10,X_11)),converse(B))) ),[1,0],$fot(converse(join(X_11,X_10)))]]) ).
cnf(refute_0_1175,plain,
( converse(join(join(X_10,X_11),B)) != join(converse(join(X_10,X_11)),converse(B))
| converse(join(join(X_10,X_11),B)) = join(converse(join(X_11,X_10)),converse(B)) ),
inference(resolve,[$cnf( $equal(converse(join(X_10,X_11)),converse(join(X_11,X_10))) )],[refute_0_1173,refute_0_1174]) ).
cnf(refute_0_1176,plain,
converse(join(join(X_10,X_11),B)) = join(converse(join(X_11,X_10)),converse(B)),
inference(resolve,[$cnf( $equal(converse(join(join(X_10,X_11),B)),join(converse(join(X_10,X_11)),converse(B))) )],[refute_0_1172,refute_0_1175]) ).
cnf(refute_0_1177,plain,
join(join(X_10,X_11),B) = join(X_10,join(X_11,B)),
inference(subst,[],[refute_0_205:[bind(A,$fot(X_10)),bind(B,$fot(X_11)),bind(C,$fot(B))]]) ).
cnf(refute_0_1178,plain,
converse(join(join(X_10,X_11),B)) = converse(join(join(X_10,X_11),B)),
introduced(tautology,[refl,[$fot(converse(join(join(X_10,X_11),B)))]]) ).
cnf(refute_0_1179,plain,
( converse(join(join(X_10,X_11),B)) != converse(join(join(X_10,X_11),B))
| join(join(X_10,X_11),B) != join(X_10,join(X_11,B))
| converse(join(join(X_10,X_11),B)) = converse(join(X_10,join(X_11,B))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_10,X_11),B)),converse(join(join(X_10,X_11),B))) ),[1,0],$fot(join(X_10,join(X_11,B)))]]) ).
cnf(refute_0_1180,plain,
( join(join(X_10,X_11),B) != join(X_10,join(X_11,B))
| converse(join(join(X_10,X_11),B)) = converse(join(X_10,join(X_11,B))) ),
inference(resolve,[$cnf( $equal(converse(join(join(X_10,X_11),B)),converse(join(join(X_10,X_11),B))) )],[refute_0_1178,refute_0_1179]) ).
cnf(refute_0_1181,plain,
converse(join(join(X_10,X_11),B)) = converse(join(X_10,join(X_11,B))),
inference(resolve,[$cnf( $equal(join(join(X_10,X_11),B),join(X_10,join(X_11,B))) )],[refute_0_1177,refute_0_1180]) ).
cnf(refute_0_1182,plain,
( converse(join(join(X_10,X_11),B)) != converse(join(X_10,join(X_11,B)))
| converse(join(join(X_10,X_11),B)) != join(converse(join(X_11,X_10)),converse(B))
| converse(join(X_10,join(X_11,B))) = join(converse(join(X_11,X_10)),converse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_10,X_11),B)),join(converse(join(X_11,X_10)),converse(B))) ),[0],$fot(converse(join(X_10,join(X_11,B))))]]) ).
cnf(refute_0_1183,plain,
( converse(join(join(X_10,X_11),B)) != join(converse(join(X_11,X_10)),converse(B))
| converse(join(X_10,join(X_11,B))) = join(converse(join(X_11,X_10)),converse(B)) ),
inference(resolve,[$cnf( $equal(converse(join(join(X_10,X_11),B)),converse(join(X_10,join(X_11,B)))) )],[refute_0_1181,refute_0_1182]) ).
cnf(refute_0_1184,plain,
join(join(X_11,X_10),B) = join(X_11,join(X_10,B)),
inference(subst,[],[refute_0_205:[bind(A,$fot(X_11)),bind(B,$fot(X_10)),bind(C,$fot(B))]]) ).
cnf(refute_0_1185,plain,
converse(join(join(X_11,X_10),B)) = converse(join(join(X_11,X_10),B)),
introduced(tautology,[refl,[$fot(converse(join(join(X_11,X_10),B)))]]) ).
cnf(refute_0_1186,plain,
( converse(join(join(X_11,X_10),B)) != converse(join(join(X_11,X_10),B))
| join(join(X_11,X_10),B) != join(X_11,join(X_10,B))
| converse(join(join(X_11,X_10),B)) = converse(join(X_11,join(X_10,B))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_11,X_10),B)),converse(join(join(X_11,X_10),B))) ),[1,0],$fot(join(X_11,join(X_10,B)))]]) ).
cnf(refute_0_1187,plain,
( join(join(X_11,X_10),B) != join(X_11,join(X_10,B))
| converse(join(join(X_11,X_10),B)) = converse(join(X_11,join(X_10,B))) ),
inference(resolve,[$cnf( $equal(converse(join(join(X_11,X_10),B)),converse(join(join(X_11,X_10),B))) )],[refute_0_1185,refute_0_1186]) ).
cnf(refute_0_1188,plain,
converse(join(join(X_11,X_10),B)) = converse(join(X_11,join(X_10,B))),
inference(resolve,[$cnf( $equal(join(join(X_11,X_10),B),join(X_11,join(X_10,B))) )],[refute_0_1184,refute_0_1187]) ).
cnf(refute_0_1189,plain,
join(converse(join(X_11,X_10)),converse(B)) = converse(join(join(X_11,X_10),B)),
inference(subst,[],[refute_0_21:[bind(A,$fot(join(X_11,X_10)))]]) ).
cnf(refute_0_1190,plain,
( converse(join(join(X_11,X_10),B)) != converse(join(X_11,join(X_10,B)))
| join(converse(join(X_11,X_10)),converse(B)) != converse(join(join(X_11,X_10),B))
| join(converse(join(X_11,X_10)),converse(B)) = converse(join(X_11,join(X_10,B))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(converse(join(X_11,X_10)),converse(B)))),bind(Y,$fot(converse(join(join(X_11,X_10),B)))),bind(Z,$fot(converse(join(X_11,join(X_10,B)))))]]) ).
cnf(refute_0_1191,plain,
( converse(join(join(X_11,X_10),B)) != converse(join(X_11,join(X_10,B)))
| join(converse(join(X_11,X_10)),converse(B)) = converse(join(X_11,join(X_10,B))) ),
inference(resolve,[$cnf( $equal(join(converse(join(X_11,X_10)),converse(B)),converse(join(join(X_11,X_10),B))) )],[refute_0_1189,refute_0_1190]) ).
cnf(refute_0_1192,plain,
join(converse(join(X_11,X_10)),converse(B)) = converse(join(X_11,join(X_10,B))),
inference(resolve,[$cnf( $equal(converse(join(join(X_11,X_10),B)),converse(join(X_11,join(X_10,B)))) )],[refute_0_1188,refute_0_1191]) ).
cnf(refute_0_1193,plain,
( converse(join(X_10,join(X_11,B))) != join(converse(join(X_11,X_10)),converse(B))
| join(converse(join(X_11,X_10)),converse(B)) != converse(join(X_11,join(X_10,B)))
| converse(join(X_10,join(X_11,B))) = converse(join(X_11,join(X_10,B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X_10,join(X_11,B))),converse(join(X_11,join(X_10,B)))) ),[0],$fot(join(converse(join(X_11,X_10)),converse(B)))]]) ).
cnf(refute_0_1194,plain,
( converse(join(X_10,join(X_11,B))) != join(converse(join(X_11,X_10)),converse(B))
| converse(join(X_10,join(X_11,B))) = converse(join(X_11,join(X_10,B))) ),
inference(resolve,[$cnf( $equal(join(converse(join(X_11,X_10)),converse(B)),converse(join(X_11,join(X_10,B)))) )],[refute_0_1192,refute_0_1193]) ).
cnf(refute_0_1195,plain,
( converse(join(join(X_10,X_11),B)) != join(converse(join(X_11,X_10)),converse(B))
| converse(join(X_10,join(X_11,B))) = converse(join(X_11,join(X_10,B))) ),
inference(resolve,[$cnf( $equal(converse(join(X_10,join(X_11,B))),join(converse(join(X_11,X_10)),converse(B))) )],[refute_0_1183,refute_0_1194]) ).
cnf(refute_0_1196,plain,
converse(join(X_10,join(X_11,B))) = converse(join(X_11,join(X_10,B))),
inference(resolve,[$cnf( $equal(converse(join(join(X_10,X_11),B)),join(converse(join(X_11,X_10)),converse(B))) )],[refute_0_1176,refute_0_1195]) ).
cnf(refute_0_1197,plain,
converse(join(X_204,join(X_205,converse(complement(converse(X_204)))))) = converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))),
inference(subst,[],[refute_0_1196:[bind(B,$fot(converse(complement(converse(X_204))))),bind(X_10,$fot(X_204)),bind(X_11,$fot(X_205))]]) ).
cnf(refute_0_1198,plain,
join(X_79,join(converse(complement(converse(X_79))),X_81)) = join(join(X_79,converse(complement(converse(X_79)))),X_81),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_79)),bind(B,$fot(converse(complement(converse(X_79))))),bind(C,$fot(X_81))]]) ).
cnf(refute_0_1199,plain,
converse(top) = join(X_79,converse(complement(converse(X_79)))),
inference(subst,[],[refute_0_466:[bind(X_21,$fot(X_79))]]) ).
cnf(refute_0_1200,plain,
( converse(top) != join(X_79,converse(complement(converse(X_79))))
| join(X_79,converse(complement(converse(X_79)))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(X_79,converse(complement(converse(X_79))))))]]) ).
cnf(refute_0_1201,plain,
join(X_79,converse(complement(converse(X_79)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(X_79,converse(complement(converse(X_79))))) )],[refute_0_1199,refute_0_1200]) ).
cnf(refute_0_1202,plain,
( join(X_79,converse(complement(converse(X_79)))) != converse(top)
| join(X_79,join(converse(complement(converse(X_79))),X_81)) != join(join(X_79,converse(complement(converse(X_79)))),X_81)
| join(X_79,join(converse(complement(converse(X_79))),X_81)) = join(converse(top),X_81) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_79,join(converse(complement(converse(X_79))),X_81)),join(join(X_79,converse(complement(converse(X_79)))),X_81)) ),[1,0],$fot(converse(top))]]) ).
cnf(refute_0_1203,plain,
( join(X_79,join(converse(complement(converse(X_79))),X_81)) != join(join(X_79,converse(complement(converse(X_79)))),X_81)
| join(X_79,join(converse(complement(converse(X_79))),X_81)) = join(converse(top),X_81) ),
inference(resolve,[$cnf( $equal(join(X_79,converse(complement(converse(X_79)))),converse(top)) )],[refute_0_1201,refute_0_1202]) ).
cnf(refute_0_1204,plain,
join(X_79,join(converse(complement(converse(X_79))),X_81)) = join(converse(top),X_81),
inference(resolve,[$cnf( $equal(join(X_79,join(converse(complement(converse(X_79))),X_81)),join(join(X_79,converse(complement(converse(X_79)))),X_81)) )],[refute_0_1198,refute_0_1203]) ).
cnf(refute_0_1205,plain,
join(converse(top),X_81) = join(converse(top),X_81),
introduced(tautology,[refl,[$fot(join(converse(top),X_81))]]) ).
cnf(refute_0_1206,plain,
( converse(top) != top
| join(converse(top),X_81) != join(converse(top),X_81)
| join(converse(top),X_81) = join(top,X_81) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(top),X_81),join(converse(top),X_81)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1207,plain,
( converse(top) != top
| join(converse(top),X_81) = join(top,X_81) ),
inference(resolve,[$cnf( $equal(join(converse(top),X_81),join(converse(top),X_81)) )],[refute_0_1205,refute_0_1206]) ).
cnf(refute_0_1208,plain,
join(converse(top),X_81) = join(top,X_81),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_500,refute_0_1207]) ).
cnf(refute_0_1209,plain,
( join(X_79,join(converse(complement(converse(X_79))),X_81)) != join(converse(top),X_81)
| join(converse(top),X_81) != join(top,X_81)
| join(X_79,join(converse(complement(converse(X_79))),X_81)) = join(top,X_81) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_79,join(converse(complement(converse(X_79))),X_81)),join(top,X_81)) ),[0],$fot(join(converse(top),X_81))]]) ).
cnf(refute_0_1210,plain,
( join(X_79,join(converse(complement(converse(X_79))),X_81)) != join(converse(top),X_81)
| join(X_79,join(converse(complement(converse(X_79))),X_81)) = join(top,X_81) ),
inference(resolve,[$cnf( $equal(join(converse(top),X_81),join(top,X_81)) )],[refute_0_1208,refute_0_1209]) ).
cnf(refute_0_1211,plain,
join(X_79,join(converse(complement(converse(X_79))),X_81)) = join(top,X_81),
inference(resolve,[$cnf( $equal(join(X_79,join(converse(complement(converse(X_79))),X_81)),join(converse(top),X_81)) )],[refute_0_1204,refute_0_1210]) ).
cnf(refute_0_1212,plain,
( top != join(top,X_117)
| join(top,X_117) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,X_117)))]]) ).
cnf(refute_0_1213,plain,
join(top,X_117) = top,
inference(resolve,[$cnf( $equal(top,join(top,X_117)) )],[refute_0_929,refute_0_1212]) ).
cnf(refute_0_1214,plain,
join(top,X_81) = top,
inference(subst,[],[refute_0_1213:[bind(X_117,$fot(X_81))]]) ).
cnf(refute_0_1215,plain,
( join(X_79,join(converse(complement(converse(X_79))),X_81)) != join(top,X_81)
| join(top,X_81) != top
| join(X_79,join(converse(complement(converse(X_79))),X_81)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_79,join(converse(complement(converse(X_79))),X_81)),top) ),[0],$fot(join(top,X_81))]]) ).
cnf(refute_0_1216,plain,
( join(X_79,join(converse(complement(converse(X_79))),X_81)) != join(top,X_81)
| join(X_79,join(converse(complement(converse(X_79))),X_81)) = top ),
inference(resolve,[$cnf( $equal(join(top,X_81),top) )],[refute_0_1214,refute_0_1215]) ).
cnf(refute_0_1217,plain,
join(X_79,join(converse(complement(converse(X_79))),X_81)) = top,
inference(resolve,[$cnf( $equal(join(X_79,join(converse(complement(converse(X_79))),X_81)),join(top,X_81)) )],[refute_0_1211,refute_0_1216]) ).
cnf(refute_0_1218,plain,
join(X_172,join(converse(complement(converse(X_172))),X_173)) = top,
inference(subst,[],[refute_0_1217:[bind(X_79,$fot(X_172)),bind(X_81,$fot(X_173))]]) ).
cnf(refute_0_1219,plain,
join(X_173,converse(complement(converse(X_172)))) = join(converse(complement(converse(X_172))),X_173),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_173)),bind(B,$fot(converse(complement(converse(X_172)))))]]) ).
cnf(refute_0_1220,plain,
( join(X_173,converse(complement(converse(X_172)))) != join(converse(complement(converse(X_172))),X_173)
| join(converse(complement(converse(X_172))),X_173) = join(X_173,converse(complement(converse(X_172)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_173,converse(complement(converse(X_172)))))),bind(Y,$fot(join(converse(complement(converse(X_172))),X_173)))]]) ).
cnf(refute_0_1221,plain,
join(converse(complement(converse(X_172))),X_173) = join(X_173,converse(complement(converse(X_172)))),
inference(resolve,[$cnf( $equal(join(X_173,converse(complement(converse(X_172)))),join(converse(complement(converse(X_172))),X_173)) )],[refute_0_1219,refute_0_1220]) ).
cnf(refute_0_1222,plain,
( join(X_172,join(converse(complement(converse(X_172))),X_173)) != top
| join(converse(complement(converse(X_172))),X_173) != join(X_173,converse(complement(converse(X_172))))
| join(X_172,join(X_173,converse(complement(converse(X_172))))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(X_172,join(converse(complement(converse(X_172))),X_173)),top) ),[0,1],$fot(join(X_173,converse(complement(converse(X_172)))))]]) ).
cnf(refute_0_1223,plain,
( join(X_172,join(converse(complement(converse(X_172))),X_173)) != top
| join(X_172,join(X_173,converse(complement(converse(X_172))))) = top ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(X_172))),X_173),join(X_173,converse(complement(converse(X_172))))) )],[refute_0_1221,refute_0_1222]) ).
cnf(refute_0_1224,plain,
join(X_172,join(X_173,converse(complement(converse(X_172))))) = top,
inference(resolve,[$cnf( $equal(join(X_172,join(converse(complement(converse(X_172))),X_173)),top) )],[refute_0_1218,refute_0_1223]) ).
cnf(refute_0_1225,plain,
join(X_204,join(X_205,converse(complement(converse(X_204))))) = top,
inference(subst,[],[refute_0_1224:[bind(X_172,$fot(X_204)),bind(X_173,$fot(X_205))]]) ).
cnf(refute_0_1226,plain,
( converse(join(X_204,join(X_205,converse(complement(converse(X_204)))))) != converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))
| join(X_204,join(X_205,converse(complement(converse(X_204))))) != top
| converse(top) = converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_204,join(X_205,converse(complement(converse(X_204)))))),converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_1227,plain,
( converse(join(X_204,join(X_205,converse(complement(converse(X_204)))))) != converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))
| converse(top) = converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))) ),
inference(resolve,[$cnf( $equal(join(X_204,join(X_205,converse(complement(converse(X_204))))),top) )],[refute_0_1225,refute_0_1226]) ).
cnf(refute_0_1228,plain,
converse(top) = converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))),
inference(resolve,[$cnf( $equal(converse(join(X_204,join(X_205,converse(complement(converse(X_204)))))),converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))) )],[refute_0_1197,refute_0_1227]) ).
cnf(refute_0_1229,plain,
( converse(top) != converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))
| converse(top) != top
| top = converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))) ),[0],$fot(top)]]) ).
cnf(refute_0_1230,plain,
( converse(top) != converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))
| top = converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_500,refute_0_1229]) ).
cnf(refute_0_1231,plain,
join(converse(join(X_205,X_204)),complement(converse(X_204))) = join(complement(converse(X_204)),converse(join(X_205,X_204))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(converse(X_204)))),bind(B,$fot(converse(join(X_205,X_204))))]]) ).
cnf(refute_0_1232,plain,
converse(join(join(X_79,X_80),converse(A))) = join(converse(join(X_79,X_80)),A),
inference(subst,[],[refute_0_486:[bind(X_4,$fot(join(X_79,X_80)))]]) ).
cnf(refute_0_1233,plain,
join(X_79,join(X_80,converse(A))) = join(join(X_79,X_80),converse(A)),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_79)),bind(B,$fot(X_80)),bind(C,$fot(converse(A)))]]) ).
cnf(refute_0_1234,plain,
( join(X_79,join(X_80,converse(A))) != join(join(X_79,X_80),converse(A))
| join(join(X_79,X_80),converse(A)) = join(X_79,join(X_80,converse(A))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_79,join(X_80,converse(A))))),bind(Y,$fot(join(join(X_79,X_80),converse(A))))]]) ).
cnf(refute_0_1235,plain,
join(join(X_79,X_80),converse(A)) = join(X_79,join(X_80,converse(A))),
inference(resolve,[$cnf( $equal(join(X_79,join(X_80,converse(A))),join(join(X_79,X_80),converse(A))) )],[refute_0_1233,refute_0_1234]) ).
cnf(refute_0_1236,plain,
( converse(join(join(X_79,X_80),converse(A))) != join(converse(join(X_79,X_80)),A)
| join(join(X_79,X_80),converse(A)) != join(X_79,join(X_80,converse(A)))
| converse(join(X_79,join(X_80,converse(A)))) = join(converse(join(X_79,X_80)),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_79,X_80),converse(A))),join(converse(join(X_79,X_80)),A)) ),[0,0],$fot(join(X_79,join(X_80,converse(A))))]]) ).
cnf(refute_0_1237,plain,
( converse(join(join(X_79,X_80),converse(A))) != join(converse(join(X_79,X_80)),A)
| converse(join(X_79,join(X_80,converse(A)))) = join(converse(join(X_79,X_80)),A) ),
inference(resolve,[$cnf( $equal(join(join(X_79,X_80),converse(A)),join(X_79,join(X_80,converse(A)))) )],[refute_0_1235,refute_0_1236]) ).
cnf(refute_0_1238,plain,
converse(join(X_79,join(X_80,converse(A)))) = join(converse(join(X_79,X_80)),A),
inference(resolve,[$cnf( $equal(converse(join(join(X_79,X_80),converse(A))),join(converse(join(X_79,X_80)),A)) )],[refute_0_1232,refute_0_1237]) ).
cnf(refute_0_1239,plain,
converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))) = join(converse(join(X_205,X_204)),complement(converse(X_204))),
inference(subst,[],[refute_0_1238:[bind(A,$fot(complement(converse(X_204)))),bind(X_79,$fot(X_205)),bind(X_80,$fot(X_204))]]) ).
cnf(refute_0_1240,plain,
( converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))) != join(converse(join(X_205,X_204)),complement(converse(X_204)))
| join(converse(join(X_205,X_204)),complement(converse(X_204))) != join(complement(converse(X_204)),converse(join(X_205,X_204)))
| converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))) = join(complement(converse(X_204)),converse(join(X_205,X_204))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))))),bind(Y,$fot(join(converse(join(X_205,X_204)),complement(converse(X_204))))),bind(Z,$fot(join(complement(converse(X_204)),converse(join(X_205,X_204)))))]]) ).
cnf(refute_0_1241,plain,
( join(converse(join(X_205,X_204)),complement(converse(X_204))) != join(complement(converse(X_204)),converse(join(X_205,X_204)))
| converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))) = join(complement(converse(X_204)),converse(join(X_205,X_204))) ),
inference(resolve,[$cnf( $equal(converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))),join(converse(join(X_205,X_204)),complement(converse(X_204)))) )],[refute_0_1239,refute_0_1240]) ).
cnf(refute_0_1242,plain,
converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))) = join(complement(converse(X_204)),converse(join(X_205,X_204))),
inference(resolve,[$cnf( $equal(join(converse(join(X_205,X_204)),complement(converse(X_204))),join(complement(converse(X_204)),converse(join(X_205,X_204)))) )],[refute_0_1231,refute_0_1241]) ).
cnf(refute_0_1243,plain,
( converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))) != join(complement(converse(X_204)),converse(join(X_205,X_204)))
| top != converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))
| top = join(complement(converse(X_204)),converse(join(X_205,X_204))) ),
introduced(tautology,[equality,[$cnf( $equal(top,converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))) ),[1],$fot(join(complement(converse(X_204)),converse(join(X_205,X_204))))]]) ).
cnf(refute_0_1244,plain,
( top != converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))
| top = join(complement(converse(X_204)),converse(join(X_205,X_204))) ),
inference(resolve,[$cnf( $equal(converse(join(X_205,join(X_204,converse(complement(converse(X_204)))))),join(complement(converse(X_204)),converse(join(X_205,X_204)))) )],[refute_0_1242,refute_0_1243]) ).
cnf(refute_0_1245,plain,
( converse(top) != converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))
| top = join(complement(converse(X_204)),converse(join(X_205,X_204))) ),
inference(resolve,[$cnf( $equal(top,converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))) )],[refute_0_1230,refute_0_1244]) ).
cnf(refute_0_1246,plain,
top = join(complement(converse(X_204)),converse(join(X_205,X_204))),
inference(resolve,[$cnf( $equal(converse(top),converse(join(X_205,join(X_204,converse(complement(converse(X_204))))))) )],[refute_0_1228,refute_0_1245]) ).
cnf(refute_0_1247,plain,
( top != join(complement(converse(X_204)),converse(join(X_205,X_204)))
| join(complement(converse(X_204)),converse(join(X_205,X_204))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(converse(X_204)),converse(join(X_205,X_204)))))]]) ).
cnf(refute_0_1248,plain,
join(complement(converse(X_204)),converse(join(X_205,X_204))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(converse(X_204)),converse(join(X_205,X_204)))) )],[refute_0_1246,refute_0_1247]) ).
cnf(refute_0_1249,plain,
( complement(complement(converse(X_204))) != join(complement(join(complement(converse(X_204)),converse(join(X_205,X_204)))),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))
| join(complement(converse(X_204)),converse(join(X_205,X_204))) != top
| complement(complement(converse(X_204))) = join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(converse(X_204))),join(complement(join(complement(converse(X_204)),converse(join(X_205,X_204)))),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))) ),[1,0,0],$fot(top)]]) ).
cnf(refute_0_1250,plain,
( complement(complement(converse(X_204))) != join(complement(join(complement(converse(X_204)),converse(join(X_205,X_204)))),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))
| complement(complement(converse(X_204))) = join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(X_204)),converse(join(X_205,X_204))),top) )],[refute_0_1248,refute_0_1249]) ).
cnf(refute_0_1251,plain,
complement(complement(converse(X_204))) = join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),
inference(resolve,[$cnf( $equal(complement(complement(converse(X_204))),join(complement(join(complement(converse(X_204)),converse(join(X_205,X_204)))),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))) )],[refute_0_1171,refute_0_1250]) ).
cnf(refute_0_1252,plain,
complement(complement(converse(X_204))) = converse(X_204),
inference(subst,[],[refute_0_680:[bind(X_35,$fot(converse(X_204)))]]) ).
cnf(refute_0_1253,plain,
( complement(complement(converse(X_204))) != converse(X_204)
| complement(complement(converse(X_204))) != join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))
| converse(X_204) = join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(converse(X_204))),join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))) ),[0],$fot(converse(X_204))]]) ).
cnf(refute_0_1254,plain,
( complement(complement(converse(X_204))) != join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))
| converse(X_204) = join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) ),
inference(resolve,[$cnf( $equal(complement(complement(converse(X_204))),converse(X_204)) )],[refute_0_1252,refute_0_1253]) ).
cnf(refute_0_1255,plain,
join(zero,meet(converse(X_204),converse(join(X_205,X_204)))) = meet(converse(X_204),converse(join(X_205,X_204))),
inference(subst,[],[refute_0_701:[bind(X_35,$fot(meet(converse(X_204),converse(join(X_205,X_204)))))]]) ).
cnf(refute_0_1256,plain,
meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))) = meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))),
introduced(tautology,[refl,[$fot(meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))]]) ).
cnf(refute_0_1257,plain,
( complement(complement(converse(X_204))) != converse(X_204)
| meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))) != meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))
| meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))) = meet(converse(X_204),converse(join(X_205,X_204))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) ),[1,0],$fot(converse(X_204))]]) ).
cnf(refute_0_1258,plain,
( complement(complement(converse(X_204))) != converse(X_204)
| meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))) = meet(converse(X_204),converse(join(X_205,X_204))) ),
inference(resolve,[$cnf( $equal(meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) )],[refute_0_1256,refute_0_1257]) ).
cnf(refute_0_1259,plain,
meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))) = meet(converse(X_204),converse(join(X_205,X_204))),
inference(resolve,[$cnf( $equal(complement(complement(converse(X_204))),converse(X_204)) )],[refute_0_1252,refute_0_1258]) ).
cnf(refute_0_1260,plain,
join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),
introduced(tautology,[refl,[$fot(join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))))]]) ).
cnf(refute_0_1261,plain,
( join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) != join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))
| meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))) != meet(converse(X_204),converse(join(X_205,X_204)))
| join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = join(zero,meet(converse(X_204),converse(join(X_205,X_204)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))) ),[1,1],$fot(meet(converse(X_204),converse(join(X_205,X_204))))]]) ).
cnf(refute_0_1262,plain,
( meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))) != meet(converse(X_204),converse(join(X_205,X_204)))
| join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = join(zero,meet(converse(X_204),converse(join(X_205,X_204)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))) )],[refute_0_1260,refute_0_1261]) ).
cnf(refute_0_1263,plain,
join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = join(zero,meet(converse(X_204),converse(join(X_205,X_204)))),
inference(resolve,[$cnf( $equal(meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))),meet(converse(X_204),converse(join(X_205,X_204)))) )],[refute_0_1259,refute_0_1262]) ).
cnf(refute_0_1264,plain,
join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))))]]) ).
cnf(refute_0_1265,plain,
( complement(top) != zero
| join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) != join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))
| join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1266,plain,
( complement(top) != zero
| join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))) )],[refute_0_1264,refute_0_1265]) ).
cnf(refute_0_1267,plain,
join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_1266]) ).
cnf(refute_0_1268,plain,
( join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) != join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))
| join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) != join(zero,meet(converse(X_204),converse(join(X_205,X_204))))
| join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = join(zero,meet(converse(X_204),converse(join(X_205,X_204)))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))))),bind(Y,$fot(join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))))),bind(Z,$fot(join(zero,meet(converse(X_204),converse(join(X_205,X_204))))))]]) ).
cnf(refute_0_1269,plain,
( join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) != join(zero,meet(converse(X_204),converse(join(X_205,X_204))))
| join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = join(zero,meet(converse(X_204),converse(join(X_205,X_204)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))) )],[refute_0_1267,refute_0_1268]) ).
cnf(refute_0_1270,plain,
join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = join(zero,meet(converse(X_204),converse(join(X_205,X_204)))),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),join(zero,meet(converse(X_204),converse(join(X_205,X_204))))) )],[refute_0_1263,refute_0_1269]) ).
cnf(refute_0_1271,plain,
( join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) != join(zero,meet(converse(X_204),converse(join(X_205,X_204))))
| join(zero,meet(converse(X_204),converse(join(X_205,X_204)))) != meet(converse(X_204),converse(join(X_205,X_204)))
| join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = meet(converse(X_204),converse(join(X_205,X_204))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))))),bind(Y,$fot(join(zero,meet(converse(X_204),converse(join(X_205,X_204)))))),bind(Z,$fot(meet(converse(X_204),converse(join(X_205,X_204)))))]]) ).
cnf(refute_0_1272,plain,
( join(zero,meet(converse(X_204),converse(join(X_205,X_204)))) != meet(converse(X_204),converse(join(X_205,X_204)))
| join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = meet(converse(X_204),converse(join(X_205,X_204))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),join(zero,meet(converse(X_204),converse(join(X_205,X_204))))) )],[refute_0_1270,refute_0_1271]) ).
cnf(refute_0_1273,plain,
join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) = meet(converse(X_204),converse(join(X_205,X_204))),
inference(resolve,[$cnf( $equal(join(zero,meet(converse(X_204),converse(join(X_205,X_204)))),meet(converse(X_204),converse(join(X_205,X_204)))) )],[refute_0_1255,refute_0_1272]) ).
cnf(refute_0_1274,plain,
( converse(X_204) != join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))
| join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))) != meet(converse(X_204),converse(join(X_205,X_204)))
| converse(X_204) = meet(converse(X_204),converse(join(X_205,X_204))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(X_204),meet(converse(X_204),converse(join(X_205,X_204)))) ),[0],$fot(join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))))]]) ).
cnf(refute_0_1275,plain,
( converse(X_204) != join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))
| converse(X_204) = meet(converse(X_204),converse(join(X_205,X_204))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204)))),meet(converse(X_204),converse(join(X_205,X_204)))) )],[refute_0_1273,refute_0_1274]) ).
cnf(refute_0_1276,plain,
( complement(complement(converse(X_204))) != join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))
| converse(X_204) = meet(converse(X_204),converse(join(X_205,X_204))) ),
inference(resolve,[$cnf( $equal(converse(X_204),join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))) )],[refute_0_1254,refute_0_1275]) ).
cnf(refute_0_1277,plain,
converse(X_204) = meet(converse(X_204),converse(join(X_205,X_204))),
inference(resolve,[$cnf( $equal(complement(complement(converse(X_204))),join(complement(top),meet(complement(complement(converse(X_204))),converse(join(X_205,X_204))))) )],[refute_0_1251,refute_0_1276]) ).
cnf(refute_0_1278,plain,
converse(complement(converse(complement(X_366)))) = meet(converse(complement(converse(complement(X_366)))),converse(join(converse(X_366),complement(converse(complement(X_366)))))),
inference(subst,[],[refute_0_1277:[bind(X_204,$fot(complement(converse(complement(X_366))))),bind(X_205,$fot(converse(X_366)))]]) ).
cnf(refute_0_1279,plain,
join(complement(complement(converse(A))),complement(converse(complement(A)))) = complement(meet(complement(converse(A)),converse(complement(A)))),
inference(subst,[],[refute_0_613:[bind(A,$fot(complement(converse(A)))),bind(B,$fot(converse(complement(A))))]]) ).
cnf(refute_0_1280,plain,
X_35 = join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(join(complement(X_35),converse(complement(converse(complement(X_35))))))),
inference(subst,[],[refute_0_47:[bind(A,$fot(X_35)),bind(B,$fot(converse(complement(converse(complement(X_35))))))]]) ).
cnf(refute_0_1281,plain,
converse(top) = join(complement(X_35),converse(complement(converse(complement(X_35))))),
inference(subst,[],[refute_0_466:[bind(X_21,$fot(complement(X_35)))]]) ).
cnf(refute_0_1282,plain,
( converse(top) != join(complement(X_35),converse(complement(converse(complement(X_35)))))
| join(complement(X_35),converse(complement(converse(complement(X_35))))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(complement(X_35),converse(complement(converse(complement(X_35)))))))]]) ).
cnf(refute_0_1283,plain,
join(complement(X_35),converse(complement(converse(complement(X_35))))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(complement(X_35),converse(complement(converse(complement(X_35)))))) )],[refute_0_1281,refute_0_1282]) ).
cnf(refute_0_1284,plain,
( X_35 != join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(join(complement(X_35),converse(complement(converse(complement(X_35)))))))
| join(complement(X_35),converse(complement(converse(complement(X_35))))) != converse(top)
| X_35 = join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_35,join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(join(complement(X_35),converse(complement(converse(complement(X_35)))))))) ),[1,1,0],$fot(converse(top))]]) ).
cnf(refute_0_1285,plain,
( X_35 != join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(join(complement(X_35),converse(complement(converse(complement(X_35)))))))
| X_35 = join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(converse(top))) ),
inference(resolve,[$cnf( $equal(join(complement(X_35),converse(complement(converse(complement(X_35))))),converse(top)) )],[refute_0_1283,refute_0_1284]) ).
cnf(refute_0_1286,plain,
X_35 = join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(converse(top))),
inference(resolve,[$cnf( $equal(X_35,join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(join(complement(X_35),converse(complement(converse(complement(X_35)))))))) )],[refute_0_1280,refute_0_1285]) ).
cnf(refute_0_1287,plain,
join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(converse(top))) = join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(converse(top)))),bind(B,$fot(meet(X_35,converse(complement(converse(complement(X_35)))))))]]) ).
cnf(refute_0_1288,plain,
( X_35 != join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(converse(top)))
| join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(converse(top))) != join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35))))))
| X_35 = join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_35,join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35))))))) ),[0],$fot(join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(converse(top))))]]) ).
cnf(refute_0_1289,plain,
( X_35 != join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(converse(top)))
| X_35 = join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(converse(top))),join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35))))))) )],[refute_0_1287,refute_0_1288]) ).
cnf(refute_0_1290,plain,
X_35 = join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))),
inference(resolve,[$cnf( $equal(X_35,join(meet(X_35,converse(complement(converse(complement(X_35))))),complement(converse(top)))) )],[refute_0_1286,refute_0_1289]) ).
cnf(refute_0_1291,plain,
join(zero,complement(B)) = join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(complement(join(zero,complement(B)))))))),
inference(subst,[],[refute_0_1290:[bind(X_35,$fot(join(zero,complement(B))))]]) ).
cnf(refute_0_1292,plain,
( complement(join(zero,complement(B))) != meet(top,B)
| join(zero,complement(B)) != join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(complement(join(zero,complement(B))))))))
| join(zero,complement(B)) = join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(complement(join(zero,complement(B))))))))) ),[1,1,1,0,0,0],$fot(meet(top,B))]]) ).
cnf(refute_0_1293,plain,
( join(zero,complement(B)) != join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(complement(join(zero,complement(B))))))))
| join(zero,complement(B)) = join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),meet(top,B)) )],[refute_0_96,refute_0_1292]) ).
cnf(refute_0_1294,plain,
join(zero,complement(B)) = join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(complement(join(zero,complement(B))))))))) )],[refute_0_1291,refute_0_1293]) ).
cnf(refute_0_1295,plain,
( join(zero,complement(B)) != complement(B)
| join(zero,complement(B)) != join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))
| complement(B) = join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))) ),[0],$fot(complement(B))]]) ).
cnf(refute_0_1296,plain,
( join(zero,complement(B)) != join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))
| complement(B) = join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(B)) )],[refute_0_852,refute_0_1295]) ).
cnf(refute_0_1297,plain,
meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))) = meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))),
introduced(tautology,[refl,[$fot(meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))]]) ).
cnf(refute_0_1298,plain,
( join(zero,complement(B)) != complement(B)
| meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))) != meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))
| meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))) = meet(complement(B),converse(complement(converse(meet(top,B))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_1299,plain,
( join(zero,complement(B)) != complement(B)
| meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))) = meet(complement(B),converse(complement(converse(meet(top,B))))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) )],[refute_0_1297,refute_0_1298]) ).
cnf(refute_0_1300,plain,
meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))) = meet(complement(B),converse(complement(converse(meet(top,B))))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(B)) )],[refute_0_852,refute_0_1299]) ).
cnf(refute_0_1301,plain,
join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) = join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))),
introduced(tautology,[refl,[$fot(join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))))]]) ).
cnf(refute_0_1302,plain,
( join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) != join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))
| meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))) != meet(complement(B),converse(complement(converse(meet(top,B)))))
| join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))),join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))) ),[1,1],$fot(meet(complement(B),converse(complement(converse(meet(top,B))))))]]) ).
cnf(refute_0_1303,plain,
( meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))) != meet(complement(B),converse(complement(converse(meet(top,B)))))
| join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))),join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))) )],[refute_0_1301,refute_0_1302]) ).
cnf(refute_0_1304,plain,
join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))),meet(complement(B),converse(complement(converse(meet(top,B)))))) )],[refute_0_1300,refute_0_1303]) ).
cnf(refute_0_1305,plain,
( complement(B) != join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))
| join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))) != join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B))))))
| complement(B) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(B),join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B))))))) ),[0],$fot(join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))))]]) ).
cnf(refute_0_1306,plain,
( complement(B) != join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))
| complement(B) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B)))))),join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B))))))) )],[refute_0_1304,refute_0_1305]) ).
cnf(refute_0_1307,plain,
( join(zero,complement(B)) != join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))
| complement(B) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))) ),
inference(resolve,[$cnf( $equal(complement(B),join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))) )],[refute_0_1296,refute_0_1306]) ).
cnf(refute_0_1308,plain,
complement(B) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(complement(converse(top)),meet(join(zero,complement(B)),converse(complement(converse(meet(top,B))))))) )],[refute_0_1294,refute_0_1307]) ).
cnf(refute_0_1309,plain,
converse(meet(top,B)) = converse(meet(top,B)),
introduced(tautology,[refl,[$fot(converse(meet(top,B)))]]) ).
cnf(refute_0_1310,plain,
( converse(meet(top,B)) != converse(meet(top,B))
| meet(top,B) != B
| converse(meet(top,B)) = converse(B) ),
introduced(tautology,[equality,[$cnf( $equal(converse(meet(top,B)),converse(meet(top,B))) ),[1,0],$fot(B)]]) ).
cnf(refute_0_1311,plain,
( meet(top,B) != B
| converse(meet(top,B)) = converse(B) ),
inference(resolve,[$cnf( $equal(converse(meet(top,B)),converse(meet(top,B))) )],[refute_0_1309,refute_0_1310]) ).
cnf(refute_0_1312,plain,
converse(meet(top,B)) = converse(B),
inference(resolve,[$cnf( $equal(meet(top,B),B) )],[refute_0_862,refute_0_1311]) ).
cnf(refute_0_1313,plain,
complement(converse(meet(top,B))) = complement(converse(meet(top,B))),
introduced(tautology,[refl,[$fot(complement(converse(meet(top,B))))]]) ).
cnf(refute_0_1314,plain,
( complement(converse(meet(top,B))) != complement(converse(meet(top,B)))
| converse(meet(top,B)) != converse(B)
| complement(converse(meet(top,B))) = complement(converse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(meet(top,B))),complement(converse(meet(top,B)))) ),[1,0],$fot(converse(B))]]) ).
cnf(refute_0_1315,plain,
( converse(meet(top,B)) != converse(B)
| complement(converse(meet(top,B))) = complement(converse(B)) ),
inference(resolve,[$cnf( $equal(complement(converse(meet(top,B))),complement(converse(meet(top,B)))) )],[refute_0_1313,refute_0_1314]) ).
cnf(refute_0_1316,plain,
complement(converse(meet(top,B))) = complement(converse(B)),
inference(resolve,[$cnf( $equal(converse(meet(top,B)),converse(B)) )],[refute_0_1312,refute_0_1315]) ).
cnf(refute_0_1317,plain,
converse(complement(converse(meet(top,B)))) = converse(complement(converse(meet(top,B)))),
introduced(tautology,[refl,[$fot(converse(complement(converse(meet(top,B)))))]]) ).
cnf(refute_0_1318,plain,
( complement(converse(meet(top,B))) != complement(converse(B))
| converse(complement(converse(meet(top,B)))) != converse(complement(converse(meet(top,B))))
| converse(complement(converse(meet(top,B)))) = converse(complement(converse(B))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(meet(top,B)))),converse(complement(converse(meet(top,B))))) ),[1,0],$fot(complement(converse(B)))]]) ).
cnf(refute_0_1319,plain,
( complement(converse(meet(top,B))) != complement(converse(B))
| converse(complement(converse(meet(top,B)))) = converse(complement(converse(B))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(meet(top,B)))),converse(complement(converse(meet(top,B))))) )],[refute_0_1317,refute_0_1318]) ).
cnf(refute_0_1320,plain,
converse(complement(converse(meet(top,B)))) = converse(complement(converse(B))),
inference(resolve,[$cnf( $equal(complement(converse(meet(top,B))),complement(converse(B))) )],[refute_0_1316,refute_0_1319]) ).
cnf(refute_0_1321,plain,
meet(complement(B),converse(complement(converse(meet(top,B))))) = meet(complement(B),converse(complement(converse(meet(top,B))))),
introduced(tautology,[refl,[$fot(meet(complement(B),converse(complement(converse(meet(top,B))))))]]) ).
cnf(refute_0_1322,plain,
( converse(complement(converse(meet(top,B)))) != converse(complement(converse(B)))
| meet(complement(B),converse(complement(converse(meet(top,B))))) != meet(complement(B),converse(complement(converse(meet(top,B)))))
| meet(complement(B),converse(complement(converse(meet(top,B))))) = meet(complement(B),converse(complement(converse(B)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(B),converse(complement(converse(meet(top,B))))),meet(complement(B),converse(complement(converse(meet(top,B)))))) ),[1,1],$fot(converse(complement(converse(B))))]]) ).
cnf(refute_0_1323,plain,
( converse(complement(converse(meet(top,B)))) != converse(complement(converse(B)))
| meet(complement(B),converse(complement(converse(meet(top,B))))) = meet(complement(B),converse(complement(converse(B)))) ),
inference(resolve,[$cnf( $equal(meet(complement(B),converse(complement(converse(meet(top,B))))),meet(complement(B),converse(complement(converse(meet(top,B)))))) )],[refute_0_1321,refute_0_1322]) ).
cnf(refute_0_1324,plain,
meet(complement(B),converse(complement(converse(meet(top,B))))) = meet(complement(B),converse(complement(converse(B)))),
inference(resolve,[$cnf( $equal(converse(complement(converse(meet(top,B)))),converse(complement(converse(B)))) )],[refute_0_1320,refute_0_1323]) ).
cnf(refute_0_1325,plain,
join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))),
introduced(tautology,[refl,[$fot(join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))))]]) ).
cnf(refute_0_1326,plain,
( join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))) != join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B))))))
| meet(complement(B),converse(complement(converse(meet(top,B))))) != meet(complement(B),converse(complement(converse(B))))
| join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))),join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B))))))) ),[1,1],$fot(meet(complement(B),converse(complement(converse(B)))))]]) ).
cnf(refute_0_1327,plain,
( meet(complement(B),converse(complement(converse(meet(top,B))))) != meet(complement(B),converse(complement(converse(B))))
| join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))),join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B))))))) )],[refute_0_1325,refute_0_1326]) ).
cnf(refute_0_1328,plain,
join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))),
inference(resolve,[$cnf( $equal(meet(complement(B),converse(complement(converse(meet(top,B))))),meet(complement(B),converse(complement(converse(B))))) )],[refute_0_1324,refute_0_1327]) ).
cnf(refute_0_1329,plain,
( complement(B) != join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B))))))
| join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))) != join(complement(converse(top)),meet(complement(B),converse(complement(converse(B)))))
| complement(B) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(B),join(complement(converse(top)),meet(complement(B),converse(complement(converse(B)))))) ),[0],$fot(join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))))]]) ).
cnf(refute_0_1330,plain,
( complement(B) != join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B))))))
| complement(B) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B)))))),join(complement(converse(top)),meet(complement(B),converse(complement(converse(B)))))) )],[refute_0_1328,refute_0_1329]) ).
cnf(refute_0_1331,plain,
complement(B) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))),
inference(resolve,[$cnf( $equal(complement(B),join(complement(converse(top)),meet(complement(B),converse(complement(converse(meet(top,B))))))) )],[refute_0_1308,refute_0_1330]) ).
cnf(refute_0_1332,plain,
join(zero,meet(complement(B),converse(complement(converse(B))))) = meet(complement(B),converse(complement(converse(B)))),
inference(subst,[],[refute_0_701:[bind(X_35,$fot(meet(complement(B),converse(complement(converse(B))))))]]) ).
cnf(refute_0_1333,plain,
complement(converse(top)) = complement(converse(top)),
introduced(tautology,[refl,[$fot(complement(converse(top)))]]) ).
cnf(refute_0_1334,plain,
( complement(converse(top)) != complement(converse(top))
| converse(top) != top
| complement(converse(top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(top)),complement(converse(top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1335,plain,
( converse(top) != top
| complement(converse(top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(converse(top)),complement(converse(top))) )],[refute_0_1333,refute_0_1334]) ).
cnf(refute_0_1336,plain,
complement(converse(top)) = complement(top),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_500,refute_0_1335]) ).
cnf(refute_0_1337,plain,
( complement(converse(top)) != complement(top)
| complement(top) != zero
| complement(converse(top)) = zero ),
inference(subst,[],[refute_0_41:[bind(X,$fot(complement(converse(top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1338,plain,
( complement(top) != zero
| complement(converse(top)) = zero ),
inference(resolve,[$cnf( $equal(complement(converse(top)),complement(top)) )],[refute_0_1336,refute_0_1337]) ).
cnf(refute_0_1339,plain,
complement(converse(top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_87,refute_0_1338]) ).
cnf(refute_0_1340,plain,
join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) = join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))),
introduced(tautology,[refl,[$fot(join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))))]]) ).
cnf(refute_0_1341,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) != join(complement(converse(top)),meet(complement(B),converse(complement(converse(B)))))
| join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) = join(zero,meet(complement(B),converse(complement(converse(B))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))),join(complement(converse(top)),meet(complement(B),converse(complement(converse(B)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1342,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) = join(zero,meet(complement(B),converse(complement(converse(B))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))),join(complement(converse(top)),meet(complement(B),converse(complement(converse(B)))))) )],[refute_0_1340,refute_0_1341]) ).
cnf(refute_0_1343,plain,
join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) = join(zero,meet(complement(B),converse(complement(converse(B))))),
inference(resolve,[$cnf( $equal(complement(converse(top)),zero) )],[refute_0_1339,refute_0_1342]) ).
cnf(refute_0_1344,plain,
( join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) != join(zero,meet(complement(B),converse(complement(converse(B)))))
| join(zero,meet(complement(B),converse(complement(converse(B))))) != meet(complement(B),converse(complement(converse(B))))
| join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) = meet(complement(B),converse(complement(converse(B)))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))))),bind(Y,$fot(join(zero,meet(complement(B),converse(complement(converse(B))))))),bind(Z,$fot(meet(complement(B),converse(complement(converse(B))))))]]) ).
cnf(refute_0_1345,plain,
( join(zero,meet(complement(B),converse(complement(converse(B))))) != meet(complement(B),converse(complement(converse(B))))
| join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) = meet(complement(B),converse(complement(converse(B)))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))),join(zero,meet(complement(B),converse(complement(converse(B)))))) )],[refute_0_1343,refute_0_1344]) ).
cnf(refute_0_1346,plain,
join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) = meet(complement(B),converse(complement(converse(B)))),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(B),converse(complement(converse(B))))),meet(complement(B),converse(complement(converse(B))))) )],[refute_0_1332,refute_0_1345]) ).
cnf(refute_0_1347,plain,
( complement(B) != join(complement(converse(top)),meet(complement(B),converse(complement(converse(B)))))
| join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))) != meet(complement(B),converse(complement(converse(B))))
| complement(B) = meet(complement(B),converse(complement(converse(B)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(B),meet(complement(B),converse(complement(converse(B))))) ),[0],$fot(join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))))]]) ).
cnf(refute_0_1348,plain,
( complement(B) != join(complement(converse(top)),meet(complement(B),converse(complement(converse(B)))))
| complement(B) = meet(complement(B),converse(complement(converse(B)))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(complement(B),converse(complement(converse(B))))),meet(complement(B),converse(complement(converse(B))))) )],[refute_0_1346,refute_0_1347]) ).
cnf(refute_0_1349,plain,
complement(B) = meet(complement(B),converse(complement(converse(B)))),
inference(resolve,[$cnf( $equal(complement(B),join(complement(converse(top)),meet(complement(B),converse(complement(converse(B)))))) )],[refute_0_1331,refute_0_1348]) ).
cnf(refute_0_1350,plain,
complement(converse(A)) = meet(complement(converse(A)),converse(complement(converse(converse(A))))),
inference(subst,[],[refute_0_1349:[bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_1351,plain,
( complement(converse(A)) != meet(complement(converse(A)),converse(complement(converse(converse(A)))))
| converse(converse(A)) != A
| complement(converse(A)) = meet(complement(converse(A)),converse(complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(A)),meet(complement(converse(A)),converse(complement(converse(converse(A)))))) ),[1,1,0,0],$fot(A)]]) ).
cnf(refute_0_1352,plain,
( complement(converse(A)) != meet(complement(converse(A)),converse(complement(converse(converse(A)))))
| complement(converse(A)) = meet(complement(converse(A)),converse(complement(A))) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1351]) ).
cnf(refute_0_1353,plain,
complement(converse(A)) = meet(complement(converse(A)),converse(complement(A))),
inference(resolve,[$cnf( $equal(complement(converse(A)),meet(complement(converse(A)),converse(complement(converse(converse(A)))))) )],[refute_0_1350,refute_0_1352]) ).
cnf(refute_0_1354,plain,
( complement(converse(A)) != meet(complement(converse(A)),converse(complement(A)))
| meet(complement(converse(A)),converse(complement(A))) = complement(converse(A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(converse(A)))),bind(Y,$fot(meet(complement(converse(A)),converse(complement(A)))))]]) ).
cnf(refute_0_1355,plain,
meet(complement(converse(A)),converse(complement(A))) = complement(converse(A)),
inference(resolve,[$cnf( $equal(complement(converse(A)),meet(complement(converse(A)),converse(complement(A)))) )],[refute_0_1353,refute_0_1354]) ).
cnf(refute_0_1356,plain,
( join(complement(complement(converse(A))),complement(converse(complement(A)))) != complement(meet(complement(converse(A)),converse(complement(A))))
| meet(complement(converse(A)),converse(complement(A))) != complement(converse(A))
| join(complement(complement(converse(A))),complement(converse(complement(A)))) = complement(complement(converse(A))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(converse(A))),complement(converse(complement(A)))),complement(meet(complement(converse(A)),converse(complement(A))))) ),[1,0],$fot(complement(converse(A)))]]) ).
cnf(refute_0_1357,plain,
( join(complement(complement(converse(A))),complement(converse(complement(A)))) != complement(meet(complement(converse(A)),converse(complement(A))))
| join(complement(complement(converse(A))),complement(converse(complement(A)))) = complement(complement(converse(A))) ),
inference(resolve,[$cnf( $equal(meet(complement(converse(A)),converse(complement(A))),complement(converse(A))) )],[refute_0_1355,refute_0_1356]) ).
cnf(refute_0_1358,plain,
join(complement(complement(converse(A))),complement(converse(complement(A)))) = complement(complement(converse(A))),
inference(resolve,[$cnf( $equal(join(complement(complement(converse(A))),complement(converse(complement(A)))),complement(meet(complement(converse(A)),converse(complement(A))))) )],[refute_0_1279,refute_0_1357]) ).
cnf(refute_0_1359,plain,
join(complement(complement(X_35)),complement(X_329)) = complement(meet(complement(X_35),X_329)),
inference(subst,[],[refute_0_613:[bind(A,$fot(complement(X_35))),bind(B,$fot(X_329))]]) ).
cnf(refute_0_1360,plain,
( complement(complement(X_35)) != X_35
| join(complement(complement(X_35)),complement(X_329)) != complement(meet(complement(X_35),X_329))
| join(X_35,complement(X_329)) = complement(meet(complement(X_35),X_329)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_35)),complement(X_329)),complement(meet(complement(X_35),X_329))) ),[0,0],$fot(X_35)]]) ).
cnf(refute_0_1361,plain,
( join(complement(complement(X_35)),complement(X_329)) != complement(meet(complement(X_35),X_329))
| join(X_35,complement(X_329)) = complement(meet(complement(X_35),X_329)) ),
inference(resolve,[$cnf( $equal(complement(complement(X_35)),X_35) )],[refute_0_680,refute_0_1360]) ).
cnf(refute_0_1362,plain,
join(X_35,complement(X_329)) = complement(meet(complement(X_35),X_329)),
inference(resolve,[$cnf( $equal(join(complement(complement(X_35)),complement(X_329)),complement(meet(complement(X_35),X_329))) )],[refute_0_1359,refute_0_1361]) ).
cnf(refute_0_1363,plain,
( join(X_35,complement(X_329)) != complement(meet(complement(X_35),X_329))
| complement(meet(complement(X_35),X_329)) = join(X_35,complement(X_329)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_35,complement(X_329)))),bind(Y,$fot(complement(meet(complement(X_35),X_329))))]]) ).
cnf(refute_0_1364,plain,
complement(meet(complement(X_35),X_329)) = join(X_35,complement(X_329)),
inference(resolve,[$cnf( $equal(join(X_35,complement(X_329)),complement(meet(complement(X_35),X_329))) )],[refute_0_1362,refute_0_1363]) ).
cnf(refute_0_1365,plain,
complement(meet(complement(converse(A)),converse(complement(A)))) = join(converse(A),complement(converse(complement(A)))),
inference(subst,[],[refute_0_1364:[bind(X_329,$fot(converse(complement(A)))),bind(X_35,$fot(converse(A)))]]) ).
cnf(refute_0_1366,plain,
( complement(meet(complement(converse(A)),converse(complement(A)))) != join(converse(A),complement(converse(complement(A))))
| join(complement(complement(converse(A))),complement(converse(complement(A)))) != complement(meet(complement(converse(A)),converse(complement(A))))
| join(complement(complement(converse(A))),complement(converse(complement(A)))) = join(converse(A),complement(converse(complement(A)))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(complement(converse(A))),complement(converse(complement(A)))))),bind(Y,$fot(complement(meet(complement(converse(A)),converse(complement(A)))))),bind(Z,$fot(join(converse(A),complement(converse(complement(A))))))]]) ).
cnf(refute_0_1367,plain,
( complement(meet(complement(converse(A)),converse(complement(A)))) != join(converse(A),complement(converse(complement(A))))
| join(complement(complement(converse(A))),complement(converse(complement(A)))) = join(converse(A),complement(converse(complement(A)))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(converse(A))),complement(converse(complement(A)))),complement(meet(complement(converse(A)),converse(complement(A))))) )],[refute_0_1279,refute_0_1366]) ).
cnf(refute_0_1368,plain,
join(complement(complement(converse(A))),complement(converse(complement(A)))) = join(converse(A),complement(converse(complement(A)))),
inference(resolve,[$cnf( $equal(complement(meet(complement(converse(A)),converse(complement(A)))),join(converse(A),complement(converse(complement(A))))) )],[refute_0_1365,refute_0_1367]) ).
cnf(refute_0_1369,plain,
( join(complement(complement(converse(A))),complement(converse(complement(A)))) != complement(complement(converse(A)))
| join(complement(complement(converse(A))),complement(converse(complement(A)))) != join(converse(A),complement(converse(complement(A))))
| join(converse(A),complement(converse(complement(A)))) = complement(complement(converse(A))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(converse(A))),complement(converse(complement(A)))),complement(complement(converse(A)))) ),[0],$fot(join(converse(A),complement(converse(complement(A)))))]]) ).
cnf(refute_0_1370,plain,
( join(complement(complement(converse(A))),complement(converse(complement(A)))) != complement(complement(converse(A)))
| join(converse(A),complement(converse(complement(A)))) = complement(complement(converse(A))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(converse(A))),complement(converse(complement(A)))),join(converse(A),complement(converse(complement(A))))) )],[refute_0_1368,refute_0_1369]) ).
cnf(refute_0_1371,plain,
complement(complement(converse(A))) = converse(A),
inference(subst,[],[refute_0_680:[bind(X_35,$fot(converse(A)))]]) ).
cnf(refute_0_1372,plain,
( complement(complement(converse(A))) != converse(A)
| join(converse(A),complement(converse(complement(A)))) != complement(complement(converse(A)))
| join(converse(A),complement(converse(complement(A)))) = converse(A) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(A),complement(converse(complement(A)))),complement(complement(converse(A)))) ),[1],$fot(converse(A))]]) ).
cnf(refute_0_1373,plain,
( join(converse(A),complement(converse(complement(A)))) != complement(complement(converse(A)))
| join(converse(A),complement(converse(complement(A)))) = converse(A) ),
inference(resolve,[$cnf( $equal(complement(complement(converse(A))),converse(A)) )],[refute_0_1371,refute_0_1372]) ).
cnf(refute_0_1374,plain,
( join(complement(complement(converse(A))),complement(converse(complement(A)))) != complement(complement(converse(A)))
| join(converse(A),complement(converse(complement(A)))) = converse(A) ),
inference(resolve,[$cnf( $equal(join(converse(A),complement(converse(complement(A)))),complement(complement(converse(A)))) )],[refute_0_1370,refute_0_1373]) ).
cnf(refute_0_1375,plain,
join(converse(A),complement(converse(complement(A)))) = converse(A),
inference(resolve,[$cnf( $equal(join(complement(complement(converse(A))),complement(converse(complement(A)))),complement(complement(converse(A)))) )],[refute_0_1358,refute_0_1374]) ).
cnf(refute_0_1376,plain,
join(converse(X_366),complement(converse(complement(X_366)))) = converse(X_366),
inference(subst,[],[refute_0_1375:[bind(A,$fot(X_366))]]) ).
cnf(refute_0_1377,plain,
( converse(complement(converse(complement(X_366)))) != meet(converse(complement(converse(complement(X_366)))),converse(join(converse(X_366),complement(converse(complement(X_366))))))
| join(converse(X_366),complement(converse(complement(X_366)))) != converse(X_366)
| converse(complement(converse(complement(X_366)))) = meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(X_366)))),meet(converse(complement(converse(complement(X_366)))),converse(join(converse(X_366),complement(converse(complement(X_366))))))) ),[1,1,0],$fot(converse(X_366))]]) ).
cnf(refute_0_1378,plain,
( converse(complement(converse(complement(X_366)))) != meet(converse(complement(converse(complement(X_366)))),converse(join(converse(X_366),complement(converse(complement(X_366))))))
| converse(complement(converse(complement(X_366)))) = meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))) ),
inference(resolve,[$cnf( $equal(join(converse(X_366),complement(converse(complement(X_366)))),converse(X_366)) )],[refute_0_1376,refute_0_1377]) ).
cnf(refute_0_1379,plain,
converse(complement(converse(complement(X_366)))) = meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(X_366)))),meet(converse(complement(converse(complement(X_366)))),converse(join(converse(X_366),complement(converse(complement(X_366))))))) )],[refute_0_1278,refute_0_1378]) ).
cnf(refute_0_1380,plain,
join(zero,meet(X_35,converse(complement(converse(complement(X_35)))))) = meet(X_35,converse(complement(converse(complement(X_35))))),
inference(subst,[],[refute_0_701:[bind(X_35,$fot(meet(X_35,converse(complement(converse(complement(X_35)))))))]]) ).
cnf(refute_0_1381,plain,
join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) = join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))),
introduced(tautology,[refl,[$fot(join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))))]]) ).
cnf(refute_0_1382,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) != join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35))))))
| join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) = join(zero,meet(X_35,converse(complement(converse(complement(X_35)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))),join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1383,plain,
( complement(converse(top)) != zero
| join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) = join(zero,meet(X_35,converse(complement(converse(complement(X_35)))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))),join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35))))))) )],[refute_0_1381,refute_0_1382]) ).
cnf(refute_0_1384,plain,
join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) = join(zero,meet(X_35,converse(complement(converse(complement(X_35)))))),
inference(resolve,[$cnf( $equal(complement(converse(top)),zero) )],[refute_0_1339,refute_0_1383]) ).
cnf(refute_0_1385,plain,
( join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) != join(zero,meet(X_35,converse(complement(converse(complement(X_35))))))
| join(zero,meet(X_35,converse(complement(converse(complement(X_35)))))) != meet(X_35,converse(complement(converse(complement(X_35)))))
| join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) = meet(X_35,converse(complement(converse(complement(X_35))))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))))),bind(Y,$fot(join(zero,meet(X_35,converse(complement(converse(complement(X_35)))))))),bind(Z,$fot(meet(X_35,converse(complement(converse(complement(X_35)))))))]]) ).
cnf(refute_0_1386,plain,
( join(zero,meet(X_35,converse(complement(converse(complement(X_35)))))) != meet(X_35,converse(complement(converse(complement(X_35)))))
| join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) = meet(X_35,converse(complement(converse(complement(X_35))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))),join(zero,meet(X_35,converse(complement(converse(complement(X_35))))))) )],[refute_0_1384,refute_0_1385]) ).
cnf(refute_0_1387,plain,
join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) = meet(X_35,converse(complement(converse(complement(X_35))))),
inference(resolve,[$cnf( $equal(join(zero,meet(X_35,converse(complement(converse(complement(X_35)))))),meet(X_35,converse(complement(converse(complement(X_35)))))) )],[refute_0_1380,refute_0_1386]) ).
cnf(refute_0_1388,plain,
( X_35 != join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35))))))
| join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))) != meet(X_35,converse(complement(converse(complement(X_35)))))
| X_35 = meet(X_35,converse(complement(converse(complement(X_35))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_35,meet(X_35,converse(complement(converse(complement(X_35)))))) ),[0],$fot(join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))))]]) ).
cnf(refute_0_1389,plain,
( X_35 != join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35))))))
| X_35 = meet(X_35,converse(complement(converse(complement(X_35))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35)))))),meet(X_35,converse(complement(converse(complement(X_35)))))) )],[refute_0_1387,refute_0_1388]) ).
cnf(refute_0_1390,plain,
X_35 = meet(X_35,converse(complement(converse(complement(X_35))))),
inference(resolve,[$cnf( $equal(X_35,join(complement(converse(top)),meet(X_35,converse(complement(converse(complement(X_35))))))) )],[refute_0_1290,refute_0_1389]) ).
cnf(refute_0_1391,plain,
( X_35 != meet(X_35,converse(complement(converse(complement(X_35)))))
| meet(X_35,converse(complement(converse(complement(X_35))))) = X_35 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_35)),bind(Y,$fot(meet(X_35,converse(complement(converse(complement(X_35)))))))]]) ).
cnf(refute_0_1392,plain,
meet(X_35,converse(complement(converse(complement(X_35))))) = X_35,
inference(resolve,[$cnf( $equal(X_35,meet(X_35,converse(complement(converse(complement(X_35)))))) )],[refute_0_1390,refute_0_1391]) ).
cnf(refute_0_1393,plain,
meet(X_366,converse(complement(converse(complement(X_366))))) = X_366,
inference(subst,[],[refute_0_1392:[bind(X_35,$fot(X_366))]]) ).
cnf(refute_0_1394,plain,
converse(converse(X_366)) = X_366,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_366))]]) ).
cnf(refute_0_1395,plain,
meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))) = meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))),
introduced(tautology,[refl,[$fot(meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))))]]) ).
cnf(refute_0_1396,plain,
( converse(converse(X_366)) != X_366
| meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))) != meet(converse(converse(X_366)),converse(complement(converse(complement(X_366)))))
| meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))) = meet(X_366,converse(complement(converse(complement(X_366))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))),meet(converse(converse(X_366)),converse(complement(converse(complement(X_366)))))) ),[1,0],$fot(X_366)]]) ).
cnf(refute_0_1397,plain,
( converse(converse(X_366)) != X_366
| meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))) = meet(X_366,converse(complement(converse(complement(X_366))))) ),
inference(resolve,[$cnf( $equal(meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))),meet(converse(converse(X_366)),converse(complement(converse(complement(X_366)))))) )],[refute_0_1395,refute_0_1396]) ).
cnf(refute_0_1398,plain,
meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))) = meet(X_366,converse(complement(converse(complement(X_366))))),
inference(resolve,[$cnf( $equal(converse(converse(X_366)),X_366) )],[refute_0_1394,refute_0_1397]) ).
cnf(refute_0_1399,plain,
( meet(X_366,converse(complement(converse(complement(X_366))))) != X_366
| meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))) != meet(X_366,converse(complement(converse(complement(X_366)))))
| meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))) = X_366 ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))))),bind(Y,$fot(meet(X_366,converse(complement(converse(complement(X_366))))))),bind(Z,$fot(X_366))]]) ).
cnf(refute_0_1400,plain,
( meet(X_366,converse(complement(converse(complement(X_366))))) != X_366
| meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))) = X_366 ),
inference(resolve,[$cnf( $equal(meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))),meet(X_366,converse(complement(converse(complement(X_366)))))) )],[refute_0_1398,refute_0_1399]) ).
cnf(refute_0_1401,plain,
meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))) = X_366,
inference(resolve,[$cnf( $equal(meet(X_366,converse(complement(converse(complement(X_366))))),X_366) )],[refute_0_1393,refute_0_1400]) ).
cnf(refute_0_1402,plain,
meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))) = meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))),
inference(subst,[],[refute_0_355:[bind(X_14,$fot(converse(converse(X_366)))),bind(X_15,$fot(converse(complement(converse(complement(X_366))))))]]) ).
cnf(refute_0_1403,plain,
( meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))) != meet(converse(converse(X_366)),converse(complement(converse(complement(X_366)))))
| meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))) != X_366
| meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))) = X_366 ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))))),bind(Y,$fot(meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))))),bind(Z,$fot(X_366))]]) ).
cnf(refute_0_1404,plain,
( meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))) != X_366
| meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))) = X_366 ),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))),meet(converse(converse(X_366)),converse(complement(converse(complement(X_366)))))) )],[refute_0_1402,refute_0_1403]) ).
cnf(refute_0_1405,plain,
meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))) = X_366,
inference(resolve,[$cnf( $equal(meet(converse(converse(X_366)),converse(complement(converse(complement(X_366))))),X_366) )],[refute_0_1401,refute_0_1404]) ).
cnf(refute_0_1406,plain,
( converse(complement(converse(complement(X_366)))) != meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366)))
| meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))) != X_366
| converse(complement(converse(complement(X_366)))) = X_366 ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(converse(complement(X_366)))),X_366) ),[0],$fot(meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))))]]) ).
cnf(refute_0_1407,plain,
( converse(complement(converse(complement(X_366)))) != meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366)))
| converse(complement(converse(complement(X_366)))) = X_366 ),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366))),X_366) )],[refute_0_1405,refute_0_1406]) ).
cnf(refute_0_1408,plain,
converse(complement(converse(complement(X_366)))) = X_366,
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(X_366)))),meet(converse(complement(converse(complement(X_366)))),converse(converse(X_366)))) )],[refute_0_1379,refute_0_1407]) ).
cnf(refute_0_1409,plain,
converse(complement(converse(complement(X_370)))) = X_370,
inference(subst,[],[refute_0_1408:[bind(X_366,$fot(X_370))]]) ).
cnf(refute_0_1410,plain,
( converse(complement(converse(complement(X_370)))) != X_370
| converse(converse(complement(converse(complement(X_370))))) != complement(converse(complement(X_370)))
| converse(X_370) = complement(converse(complement(X_370))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(complement(converse(complement(X_370))))),complement(converse(complement(X_370)))) ),[0,0],$fot(X_370)]]) ).
cnf(refute_0_1411,plain,
( converse(converse(complement(converse(complement(X_370))))) != complement(converse(complement(X_370)))
| converse(X_370) = complement(converse(complement(X_370))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(X_370)))),X_370) )],[refute_0_1409,refute_0_1410]) ).
cnf(refute_0_1412,plain,
converse(X_370) = complement(converse(complement(X_370))),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(complement(X_370))))),complement(converse(complement(X_370)))) )],[refute_0_1092,refute_0_1411]) ).
cnf(refute_0_1413,plain,
( converse(X_370) != complement(converse(complement(X_370)))
| complement(converse(complement(X_370))) = converse(X_370) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(X_370))),bind(Y,$fot(complement(converse(complement(X_370)))))]]) ).
cnf(refute_0_1414,plain,
complement(converse(complement(X_370))) = converse(X_370),
inference(resolve,[$cnf( $equal(converse(X_370),complement(converse(complement(X_370)))) )],[refute_0_1412,refute_0_1413]) ).
cnf(refute_0_1415,plain,
complement(converse(complement(converse(composition(X_461,top))))) = converse(converse(composition(X_461,top))),
inference(subst,[],[refute_0_1414:[bind(X_370,$fot(converse(composition(X_461,top))))]]) ).
cnf(refute_0_1416,plain,
( complement(converse(complement(converse(composition(X_461,top))))) != converse(converse(composition(X_461,top)))
| converse(converse(composition(X_461,top))) != composition(X_461,top)
| complement(converse(complement(converse(composition(X_461,top))))) = composition(X_461,top) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(complement(converse(complement(converse(composition(X_461,top))))))),bind(Y,$fot(converse(converse(composition(X_461,top))))),bind(Z,$fot(composition(X_461,top)))]]) ).
cnf(refute_0_1417,plain,
( converse(converse(composition(X_461,top))) != composition(X_461,top)
| complement(converse(complement(converse(composition(X_461,top))))) = composition(X_461,top) ),
inference(resolve,[$cnf( $equal(complement(converse(complement(converse(composition(X_461,top))))),converse(converse(composition(X_461,top)))) )],[refute_0_1415,refute_0_1416]) ).
cnf(refute_0_1418,plain,
complement(converse(complement(converse(composition(X_461,top))))) = composition(X_461,top),
inference(resolve,[$cnf( $equal(converse(converse(composition(X_461,top))),composition(X_461,top)) )],[refute_0_1091,refute_0_1417]) ).
cnf(refute_0_1419,plain,
composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))) = composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))),
introduced(tautology,[refl,[$fot(composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))))]]) ).
cnf(refute_0_1420,plain,
( complement(converse(complement(converse(composition(X_461,top))))) != composition(X_461,top)
| composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))) != composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top))))))
| composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))) = composition(complement(converse(composition(X_461,top))),composition(X_461,top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))),composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top))))))) ),[1,1],$fot(composition(X_461,top))]]) ).
cnf(refute_0_1421,plain,
( complement(converse(complement(converse(composition(X_461,top))))) != composition(X_461,top)
| composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))) = composition(complement(converse(composition(X_461,top))),composition(X_461,top)) ),
inference(resolve,[$cnf( $equal(composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))),composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top))))))) )],[refute_0_1419,refute_0_1420]) ).
cnf(refute_0_1422,plain,
composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))) = composition(complement(converse(composition(X_461,top))),composition(X_461,top)),
inference(resolve,[$cnf( $equal(complement(converse(complement(converse(composition(X_461,top))))),composition(X_461,top)) )],[refute_0_1418,refute_0_1421]) ).
cnf(refute_0_1423,plain,
( composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))) != composition(complement(converse(composition(X_461,top))),composition(X_461,top))
| composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))) != zero
| composition(complement(converse(composition(X_461,top))),composition(X_461,top)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))),zero) ),[0],$fot(composition(complement(converse(composition(X_461,top))),composition(X_461,top)))]]) ).
cnf(refute_0_1424,plain,
( composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))) != zero
| composition(complement(converse(composition(X_461,top))),composition(X_461,top)) = zero ),
inference(resolve,[$cnf( $equal(composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))),composition(complement(converse(composition(X_461,top))),composition(X_461,top))) )],[refute_0_1422,refute_0_1423]) ).
cnf(refute_0_1425,plain,
composition(complement(converse(composition(X_461,top))),composition(X_461,top)) = zero,
inference(resolve,[$cnf( $equal(composition(complement(converse(composition(X_461,top))),complement(converse(complement(converse(composition(X_461,top)))))),zero) )],[refute_0_1090,refute_0_1424]) ).
cnf(refute_0_1426,plain,
composition(complement(converse(composition(X_670,top))),composition(X_670,top)) = zero,
inference(subst,[],[refute_0_1425:[bind(X_461,$fot(X_670))]]) ).
cnf(refute_0_1427,plain,
( composition(complement(converse(composition(X_670,top))),composition(X_670,top)) != zero
| join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(composition(complement(converse(composition(X_670,top))),composition(X_670,top))))) != complement(composition(X_670,top))
| join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) = complement(composition(X_670,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(composition(complement(converse(composition(X_670,top))),composition(X_670,top))))),complement(composition(X_670,top))) ),[0,1,1,0],$fot(zero)]]) ).
cnf(refute_0_1428,plain,
( join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(composition(complement(converse(composition(X_670,top))),composition(X_670,top))))) != complement(composition(X_670,top))
| join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) = complement(composition(X_670,top)) ),
inference(resolve,[$cnf( $equal(composition(complement(converse(composition(X_670,top))),composition(X_670,top)),zero) )],[refute_0_1426,refute_0_1427]) ).
cnf(refute_0_1429,plain,
join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) = complement(composition(X_670,top)),
inference(resolve,[$cnf( $equal(join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(composition(complement(converse(composition(X_670,top))),composition(X_670,top))))),complement(composition(X_670,top))) )],[refute_0_9,refute_0_1428]) ).
cnf(refute_0_1430,plain,
composition(join(join(one,one),one),X_100) = join(X_100,composition(join(one,one),X_100)),
inference(subst,[],[refute_0_741:[bind(X_98,$fot(join(one,one)))]]) ).
cnf(refute_0_1431,plain,
composition(join(one,one),X_101) = join(X_101,composition(one,X_101)),
inference(subst,[],[refute_0_741:[bind(X_100,$fot(X_101)),bind(X_98,$fot(one))]]) ).
cnf(refute_0_1432,plain,
X_101 = composition(one,X_101),
inference(subst,[],[refute_0_272:[bind(X_24,$fot(X_101))]]) ).
cnf(refute_0_1433,plain,
( X_101 != composition(one,X_101)
| composition(one,X_101) = X_101 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_101)),bind(Y,$fot(composition(one,X_101)))]]) ).
cnf(refute_0_1434,plain,
composition(one,X_101) = X_101,
inference(resolve,[$cnf( $equal(X_101,composition(one,X_101)) )],[refute_0_1432,refute_0_1433]) ).
cnf(refute_0_1435,plain,
( composition(join(one,one),X_101) != join(X_101,composition(one,X_101))
| composition(one,X_101) != X_101
| composition(join(one,one),X_101) = join(X_101,X_101) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),X_101),join(X_101,composition(one,X_101))) ),[1,1],$fot(X_101)]]) ).
cnf(refute_0_1436,plain,
( composition(join(one,one),X_101) != join(X_101,composition(one,X_101))
| composition(join(one,one),X_101) = join(X_101,X_101) ),
inference(resolve,[$cnf( $equal(composition(one,X_101),X_101) )],[refute_0_1434,refute_0_1435]) ).
cnf(refute_0_1437,plain,
composition(join(one,one),X_101) = join(X_101,X_101),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_101),join(X_101,composition(one,X_101))) )],[refute_0_1431,refute_0_1436]) ).
cnf(refute_0_1438,plain,
composition(join(one,one),X_100) = join(X_100,X_100),
inference(subst,[],[refute_0_1437:[bind(X_101,$fot(X_100))]]) ).
cnf(refute_0_1439,plain,
( composition(join(join(one,one),one),X_100) != join(X_100,composition(join(one,one),X_100))
| composition(join(one,one),X_100) != join(X_100,X_100)
| composition(join(join(one,one),one),X_100) = join(X_100,join(X_100,X_100)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(one,one),one),X_100),join(X_100,composition(join(one,one),X_100))) ),[1,1],$fot(join(X_100,X_100))]]) ).
cnf(refute_0_1440,plain,
( composition(join(join(one,one),one),X_100) != join(X_100,composition(join(one,one),X_100))
| composition(join(join(one,one),one),X_100) = join(X_100,join(X_100,X_100)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_100),join(X_100,X_100)) )],[refute_0_1438,refute_0_1439]) ).
cnf(refute_0_1441,plain,
composition(join(join(one,one),one),X_100) = join(X_100,join(X_100,X_100)),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),X_100),join(X_100,composition(join(one,one),X_100))) )],[refute_0_1430,refute_0_1440]) ).
cnf(refute_0_1442,plain,
composition(join(join(one,one),one),X_100) = composition(join(one,join(one,one)),X_100),
inference(subst,[],[refute_0_1054:[bind(X_101,$fot(X_100)),bind(X_102,$fot(join(one,one)))]]) ).
cnf(refute_0_1443,plain,
( composition(join(join(one,one),one),X_100) != composition(join(one,join(one,one)),X_100)
| composition(join(join(one,one),one),X_100) != join(X_100,join(X_100,X_100))
| composition(join(one,join(one,one)),X_100) = join(X_100,join(X_100,X_100)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(one,one),one),X_100),join(X_100,join(X_100,X_100))) ),[0],$fot(composition(join(one,join(one,one)),X_100))]]) ).
cnf(refute_0_1444,plain,
( composition(join(join(one,one),one),X_100) != join(X_100,join(X_100,X_100))
| composition(join(one,join(one,one)),X_100) = join(X_100,join(X_100,X_100)) ),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),X_100),composition(join(one,join(one,one)),X_100)) )],[refute_0_1442,refute_0_1443]) ).
cnf(refute_0_1445,plain,
composition(join(one,join(one,one)),X_100) = join(X_100,join(X_100,X_100)),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),X_100),join(X_100,join(X_100,X_100))) )],[refute_0_1441,refute_0_1444]) ).
cnf(refute_0_1446,plain,
join(complement(complement(X_138)),composition(converse(join(one,one)),complement(composition(join(one,one),complement(X_138))))) = complement(complement(X_138)),
inference(subst,[],[refute_0_8:[bind(A,$fot(join(one,one))),bind(B,$fot(complement(X_138)))]]) ).
cnf(refute_0_1447,plain,
X_35 = join(meet(complement(X_35),X_35),complement(join(complement(X_35),complement(X_35)))),
inference(subst,[],[refute_0_588:[bind(X_36,$fot(complement(X_35)))]]) ).
cnf(refute_0_1448,plain,
composition(join(one,one),complement(X_35)) = join(complement(X_35),complement(X_35)),
inference(subst,[],[refute_0_1437:[bind(X_101,$fot(complement(X_35)))]]) ).
cnf(refute_0_1449,plain,
( composition(join(one,one),complement(X_35)) != join(complement(X_35),complement(X_35))
| join(complement(X_35),complement(X_35)) = composition(join(one,one),complement(X_35)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),complement(X_35)))),bind(Y,$fot(join(complement(X_35),complement(X_35))))]]) ).
cnf(refute_0_1450,plain,
join(complement(X_35),complement(X_35)) = composition(join(one,one),complement(X_35)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_35)),join(complement(X_35),complement(X_35))) )],[refute_0_1448,refute_0_1449]) ).
cnf(refute_0_1451,plain,
( X_35 != join(meet(complement(X_35),X_35),complement(join(complement(X_35),complement(X_35))))
| join(complement(X_35),complement(X_35)) != composition(join(one,one),complement(X_35))
| X_35 = join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_35,join(meet(complement(X_35),X_35),complement(join(complement(X_35),complement(X_35))))) ),[1,1,0],$fot(composition(join(one,one),complement(X_35)))]]) ).
cnf(refute_0_1452,plain,
( X_35 != join(meet(complement(X_35),X_35),complement(join(complement(X_35),complement(X_35))))
| X_35 = join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_35),complement(X_35)),composition(join(one,one),complement(X_35))) )],[refute_0_1450,refute_0_1451]) ).
cnf(refute_0_1453,plain,
X_35 = join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))),
inference(resolve,[$cnf( $equal(X_35,join(meet(complement(X_35),X_35),complement(join(complement(X_35),complement(X_35))))) )],[refute_0_1447,refute_0_1452]) ).
cnf(refute_0_1454,plain,
join(zero,complement(composition(join(one,one),complement(X_35)))) = complement(composition(join(one,one),complement(X_35))),
inference(subst,[],[refute_0_701:[bind(X_35,$fot(complement(composition(join(one,one),complement(X_35)))))]]) ).
cnf(refute_0_1455,plain,
meet(complement(X_35),X_35) = meet(X_35,complement(X_35)),
inference(subst,[],[refute_0_355:[bind(X_14,$fot(X_35)),bind(X_15,$fot(complement(X_35)))]]) ).
cnf(refute_0_1456,plain,
( meet(X_35,complement(X_35)) != zero
| meet(complement(X_35),X_35) != meet(X_35,complement(X_35))
| meet(complement(X_35),X_35) = zero ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(complement(X_35),X_35))),bind(Y,$fot(meet(X_35,complement(X_35)))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1457,plain,
( meet(X_35,complement(X_35)) != zero
| meet(complement(X_35),X_35) = zero ),
inference(resolve,[$cnf( $equal(meet(complement(X_35),X_35),meet(X_35,complement(X_35))) )],[refute_0_1455,refute_0_1456]) ).
cnf(refute_0_1458,plain,
meet(complement(X_35),X_35) = zero,
inference(resolve,[$cnf( $equal(meet(X_35,complement(X_35)),zero) )],[refute_0_303,refute_0_1457]) ).
cnf(refute_0_1459,plain,
join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) = join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))),
introduced(tautology,[refl,[$fot(join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))))]]) ).
cnf(refute_0_1460,plain,
( join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) != join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35))))
| meet(complement(X_35),X_35) != zero
| join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) = join(zero,complement(composition(join(one,one),complement(X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))),join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1461,plain,
( meet(complement(X_35),X_35) != zero
| join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) = join(zero,complement(composition(join(one,one),complement(X_35)))) ),
inference(resolve,[$cnf( $equal(join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))),join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35))))) )],[refute_0_1459,refute_0_1460]) ).
cnf(refute_0_1462,plain,
join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) = join(zero,complement(composition(join(one,one),complement(X_35)))),
inference(resolve,[$cnf( $equal(meet(complement(X_35),X_35),zero) )],[refute_0_1458,refute_0_1461]) ).
cnf(refute_0_1463,plain,
( join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) != join(zero,complement(composition(join(one,one),complement(X_35))))
| join(zero,complement(composition(join(one,one),complement(X_35)))) != complement(composition(join(one,one),complement(X_35)))
| join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) = complement(composition(join(one,one),complement(X_35))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))))),bind(Y,$fot(join(zero,complement(composition(join(one,one),complement(X_35)))))),bind(Z,$fot(complement(composition(join(one,one),complement(X_35)))))]]) ).
cnf(refute_0_1464,plain,
( join(zero,complement(composition(join(one,one),complement(X_35)))) != complement(composition(join(one,one),complement(X_35)))
| join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) = complement(composition(join(one,one),complement(X_35))) ),
inference(resolve,[$cnf( $equal(join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))),join(zero,complement(composition(join(one,one),complement(X_35))))) )],[refute_0_1462,refute_0_1463]) ).
cnf(refute_0_1465,plain,
join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) = complement(composition(join(one,one),complement(X_35))),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(join(one,one),complement(X_35)))),complement(composition(join(one,one),complement(X_35)))) )],[refute_0_1454,refute_0_1464]) ).
cnf(refute_0_1466,plain,
( X_35 != join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35))))
| join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))) != complement(composition(join(one,one),complement(X_35)))
| X_35 = complement(composition(join(one,one),complement(X_35))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_35,complement(composition(join(one,one),complement(X_35)))) ),[0],$fot(join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))))]]) ).
cnf(refute_0_1467,plain,
( X_35 != join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35))))
| X_35 = complement(composition(join(one,one),complement(X_35))) ),
inference(resolve,[$cnf( $equal(join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35)))),complement(composition(join(one,one),complement(X_35)))) )],[refute_0_1465,refute_0_1466]) ).
cnf(refute_0_1468,plain,
X_35 = complement(composition(join(one,one),complement(X_35))),
inference(resolve,[$cnf( $equal(X_35,join(meet(complement(X_35),X_35),complement(composition(join(one,one),complement(X_35))))) )],[refute_0_1453,refute_0_1467]) ).
cnf(refute_0_1469,plain,
X_138 = complement(composition(join(one,one),complement(X_138))),
inference(subst,[],[refute_0_1468:[bind(X_35,$fot(X_138))]]) ).
cnf(refute_0_1470,plain,
( X_138 != complement(composition(join(one,one),complement(X_138)))
| complement(composition(join(one,one),complement(X_138))) = X_138 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_138)),bind(Y,$fot(complement(composition(join(one,one),complement(X_138)))))]]) ).
cnf(refute_0_1471,plain,
complement(composition(join(one,one),complement(X_138))) = X_138,
inference(resolve,[$cnf( $equal(X_138,complement(composition(join(one,one),complement(X_138)))) )],[refute_0_1469,refute_0_1470]) ).
cnf(refute_0_1472,plain,
( complement(composition(join(one,one),complement(X_138))) != X_138
| join(complement(complement(X_138)),composition(converse(join(one,one)),complement(composition(join(one,one),complement(X_138))))) != complement(complement(X_138))
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = complement(complement(X_138)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_138)),composition(converse(join(one,one)),complement(composition(join(one,one),complement(X_138))))),complement(complement(X_138))) ),[0,1,1],$fot(X_138)]]) ).
cnf(refute_0_1473,plain,
( join(complement(complement(X_138)),composition(converse(join(one,one)),complement(composition(join(one,one),complement(X_138))))) != complement(complement(X_138))
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = complement(complement(X_138)) ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),complement(X_138))),X_138) )],[refute_0_1471,refute_0_1472]) ).
cnf(refute_0_1474,plain,
join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = complement(complement(X_138)),
inference(resolve,[$cnf( $equal(join(complement(complement(X_138)),composition(converse(join(one,one)),complement(composition(join(one,one),complement(X_138))))),complement(complement(X_138))) )],[refute_0_1446,refute_0_1473]) ).
cnf(refute_0_1475,plain,
composition(join(join(one,one),one),X_138) = composition(join(one,join(one,one)),X_138),
inference(subst,[],[refute_0_1054:[bind(X_101,$fot(X_138)),bind(X_102,$fot(join(one,one)))]]) ).
cnf(refute_0_1476,plain,
join(X_138,composition(join(one,one),X_138)) = composition(join(join(one,one),one),X_138),
inference(subst,[],[refute_0_1048:[bind(X_100,$fot(X_138)),bind(X_98,$fot(join(one,one)))]]) ).
cnf(refute_0_1477,plain,
( composition(join(join(one,one),one),X_138) != composition(join(one,join(one,one)),X_138)
| join(X_138,composition(join(one,one),X_138)) != composition(join(join(one,one),one),X_138)
| join(X_138,composition(join(one,one),X_138)) = composition(join(one,join(one,one)),X_138) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(X_138,composition(join(one,one),X_138)))),bind(Y,$fot(composition(join(join(one,one),one),X_138))),bind(Z,$fot(composition(join(one,join(one,one)),X_138)))]]) ).
cnf(refute_0_1478,plain,
( composition(join(join(one,one),one),X_138) != composition(join(one,join(one,one)),X_138)
| join(X_138,composition(join(one,one),X_138)) = composition(join(one,join(one,one)),X_138) ),
inference(resolve,[$cnf( $equal(join(X_138,composition(join(one,one),X_138)),composition(join(join(one,one),one),X_138)) )],[refute_0_1476,refute_0_1477]) ).
cnf(refute_0_1479,plain,
join(X_138,composition(join(one,one),X_138)) = composition(join(one,join(one,one)),X_138),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),X_138),composition(join(one,join(one,one)),X_138)) )],[refute_0_1475,refute_0_1478]) ).
cnf(refute_0_1480,plain,
composition(converse(join(one,one)),X_138) = composition(converse(join(one,one)),X_138),
introduced(tautology,[refl,[$fot(composition(converse(join(one,one)),X_138))]]) ).
cnf(refute_0_1481,plain,
( composition(converse(join(one,one)),X_138) != composition(converse(join(one,one)),X_138)
| converse(join(one,one)) != join(one,one)
| composition(converse(join(one,one)),X_138) = composition(join(one,one),X_138) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(one,one)),X_138),composition(converse(join(one,one)),X_138)) ),[1,0],$fot(join(one,one))]]) ).
cnf(refute_0_1482,plain,
( converse(join(one,one)) != join(one,one)
| composition(converse(join(one,one)),X_138) = composition(join(one,one),X_138) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,one)),X_138),composition(converse(join(one,one)),X_138)) )],[refute_0_1480,refute_0_1481]) ).
cnf(refute_0_1483,plain,
composition(converse(join(one,one)),X_138) = composition(join(one,one),X_138),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_959,refute_0_1482]) ).
cnf(refute_0_1484,plain,
join(X_138,composition(converse(join(one,one)),X_138)) = join(X_138,composition(converse(join(one,one)),X_138)),
introduced(tautology,[refl,[$fot(join(X_138,composition(converse(join(one,one)),X_138)))]]) ).
cnf(refute_0_1485,plain,
( composition(converse(join(one,one)),X_138) != composition(join(one,one),X_138)
| join(X_138,composition(converse(join(one,one)),X_138)) != join(X_138,composition(converse(join(one,one)),X_138))
| join(X_138,composition(converse(join(one,one)),X_138)) = join(X_138,composition(join(one,one),X_138)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_138,composition(converse(join(one,one)),X_138)),join(X_138,composition(converse(join(one,one)),X_138))) ),[1,1],$fot(composition(join(one,one),X_138))]]) ).
cnf(refute_0_1486,plain,
( composition(converse(join(one,one)),X_138) != composition(join(one,one),X_138)
| join(X_138,composition(converse(join(one,one)),X_138)) = join(X_138,composition(join(one,one),X_138)) ),
inference(resolve,[$cnf( $equal(join(X_138,composition(converse(join(one,one)),X_138)),join(X_138,composition(converse(join(one,one)),X_138))) )],[refute_0_1484,refute_0_1485]) ).
cnf(refute_0_1487,plain,
join(X_138,composition(converse(join(one,one)),X_138)) = join(X_138,composition(join(one,one),X_138)),
inference(resolve,[$cnf( $equal(composition(converse(join(one,one)),X_138),composition(join(one,one),X_138)) )],[refute_0_1483,refute_0_1486]) ).
cnf(refute_0_1488,plain,
complement(complement(X_138)) = X_138,
inference(subst,[],[refute_0_680:[bind(X_35,$fot(X_138))]]) ).
cnf(refute_0_1489,plain,
join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)),
introduced(tautology,[refl,[$fot(join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)))]]) ).
cnf(refute_0_1490,plain,
( complement(complement(X_138)) != X_138
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) != join(complement(complement(X_138)),composition(converse(join(one,one)),X_138))
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = join(X_138,composition(converse(join(one,one)),X_138)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)),join(complement(complement(X_138)),composition(converse(join(one,one)),X_138))) ),[1,0],$fot(X_138)]]) ).
cnf(refute_0_1491,plain,
( complement(complement(X_138)) != X_138
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = join(X_138,composition(converse(join(one,one)),X_138)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)),join(complement(complement(X_138)),composition(converse(join(one,one)),X_138))) )],[refute_0_1489,refute_0_1490]) ).
cnf(refute_0_1492,plain,
join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = join(X_138,composition(converse(join(one,one)),X_138)),
inference(resolve,[$cnf( $equal(complement(complement(X_138)),X_138) )],[refute_0_1488,refute_0_1491]) ).
cnf(refute_0_1493,plain,
( join(X_138,composition(converse(join(one,one)),X_138)) != join(X_138,composition(join(one,one),X_138))
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) != join(X_138,composition(converse(join(one,one)),X_138))
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = join(X_138,composition(join(one,one),X_138)) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)))),bind(Y,$fot(join(X_138,composition(converse(join(one,one)),X_138)))),bind(Z,$fot(join(X_138,composition(join(one,one),X_138))))]]) ).
cnf(refute_0_1494,plain,
( join(X_138,composition(converse(join(one,one)),X_138)) != join(X_138,composition(join(one,one),X_138))
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = join(X_138,composition(join(one,one),X_138)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)),join(X_138,composition(converse(join(one,one)),X_138))) )],[refute_0_1492,refute_0_1493]) ).
cnf(refute_0_1495,plain,
join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = join(X_138,composition(join(one,one),X_138)),
inference(resolve,[$cnf( $equal(join(X_138,composition(converse(join(one,one)),X_138)),join(X_138,composition(join(one,one),X_138))) )],[refute_0_1487,refute_0_1494]) ).
cnf(refute_0_1496,plain,
( join(X_138,composition(join(one,one),X_138)) != composition(join(one,join(one,one)),X_138)
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) != join(X_138,composition(join(one,one),X_138))
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = composition(join(one,join(one,one)),X_138) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)))),bind(Y,$fot(join(X_138,composition(join(one,one),X_138)))),bind(Z,$fot(composition(join(one,join(one,one)),X_138)))]]) ).
cnf(refute_0_1497,plain,
( join(X_138,composition(join(one,one),X_138)) != composition(join(one,join(one,one)),X_138)
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = composition(join(one,join(one,one)),X_138) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)),join(X_138,composition(join(one,one),X_138))) )],[refute_0_1495,refute_0_1496]) ).
cnf(refute_0_1498,plain,
join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) = composition(join(one,join(one,one)),X_138),
inference(resolve,[$cnf( $equal(join(X_138,composition(join(one,one),X_138)),composition(join(one,join(one,one)),X_138)) )],[refute_0_1479,refute_0_1497]) ).
cnf(refute_0_1499,plain,
( join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) != complement(complement(X_138))
| join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) != composition(join(one,join(one,one)),X_138)
| composition(join(one,join(one,one)),X_138) = complement(complement(X_138)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)),complement(complement(X_138))) ),[0],$fot(composition(join(one,join(one,one)),X_138))]]) ).
cnf(refute_0_1500,plain,
( join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) != complement(complement(X_138))
| composition(join(one,join(one,one)),X_138) = complement(complement(X_138)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)),composition(join(one,join(one,one)),X_138)) )],[refute_0_1498,refute_0_1499]) ).
cnf(refute_0_1501,plain,
( complement(complement(X_138)) != X_138
| composition(join(one,join(one,one)),X_138) != complement(complement(X_138))
| composition(join(one,join(one,one)),X_138) = X_138 ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(one,one)),X_138),complement(complement(X_138))) ),[1],$fot(X_138)]]) ).
cnf(refute_0_1502,plain,
( composition(join(one,join(one,one)),X_138) != complement(complement(X_138))
| composition(join(one,join(one,one)),X_138) = X_138 ),
inference(resolve,[$cnf( $equal(complement(complement(X_138)),X_138) )],[refute_0_1488,refute_0_1501]) ).
cnf(refute_0_1503,plain,
( join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)) != complement(complement(X_138))
| composition(join(one,join(one,one)),X_138) = X_138 ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),X_138),complement(complement(X_138))) )],[refute_0_1500,refute_0_1502]) ).
cnf(refute_0_1504,plain,
composition(join(one,join(one,one)),X_138) = X_138,
inference(resolve,[$cnf( $equal(join(complement(complement(X_138)),composition(converse(join(one,one)),X_138)),complement(complement(X_138))) )],[refute_0_1474,refute_0_1503]) ).
cnf(refute_0_1505,plain,
composition(join(one,join(one,one)),X_100) = X_100,
inference(subst,[],[refute_0_1504:[bind(X_138,$fot(X_100))]]) ).
cnf(refute_0_1506,plain,
( composition(join(one,join(one,one)),X_100) != X_100
| composition(join(one,join(one,one)),X_100) != join(X_100,join(X_100,X_100))
| X_100 = join(X_100,join(X_100,X_100)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(one,one)),X_100),join(X_100,join(X_100,X_100))) ),[0],$fot(X_100)]]) ).
cnf(refute_0_1507,plain,
( composition(join(one,join(one,one)),X_100) != join(X_100,join(X_100,X_100))
| X_100 = join(X_100,join(X_100,X_100)) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),X_100),X_100) )],[refute_0_1505,refute_0_1506]) ).
cnf(refute_0_1508,plain,
X_100 = join(X_100,join(X_100,X_100)),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),X_100),join(X_100,join(X_100,X_100))) )],[refute_0_1445,refute_0_1507]) ).
cnf(refute_0_1509,plain,
composition(join(A,B),join(one,one)) = join(composition(A,join(one,one)),composition(B,join(one,one))),
inference(subst,[],[composition_distributivity_7:[bind(C,$fot(join(one,one)))]]) ).
cnf(refute_0_1510,plain,
converse(composition(join(one,one),converse(A))) = composition(A,converse(join(one,one))),
inference(subst,[],[refute_0_1070:[bind(X_6,$fot(join(one,one)))]]) ).
cnf(refute_0_1511,plain,
composition(join(one,one),converse(A)) = join(converse(A),converse(A)),
inference(subst,[],[refute_0_1437:[bind(X_101,$fot(converse(A)))]]) ).
cnf(refute_0_1512,plain,
( composition(join(one,one),converse(A)) != join(converse(A),converse(A))
| converse(composition(join(one,one),converse(A))) != composition(A,converse(join(one,one)))
| converse(join(converse(A),converse(A))) = composition(A,converse(join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(one,one),converse(A))),composition(A,converse(join(one,one)))) ),[0,0],$fot(join(converse(A),converse(A)))]]) ).
cnf(refute_0_1513,plain,
( converse(composition(join(one,one),converse(A))) != composition(A,converse(join(one,one)))
| converse(join(converse(A),converse(A))) = composition(A,converse(join(one,one))) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),converse(A)),join(converse(A),converse(A))) )],[refute_0_1511,refute_0_1512]) ).
cnf(refute_0_1514,plain,
converse(join(converse(A),converse(A))) = composition(A,converse(join(one,one))),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),converse(A))),composition(A,converse(join(one,one)))) )],[refute_0_1510,refute_0_1513]) ).
cnf(refute_0_1515,plain,
join(A,converse(converse(A))) = join(A,converse(converse(A))),
introduced(tautology,[refl,[$fot(join(A,converse(converse(A))))]]) ).
cnf(refute_0_1516,plain,
( converse(converse(A)) != A
| join(A,converse(converse(A))) != join(A,converse(converse(A)))
| join(A,converse(converse(A))) = join(A,A) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,converse(converse(A))),join(A,converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_1517,plain,
( converse(converse(A)) != A
| join(A,converse(converse(A))) = join(A,A) ),
inference(resolve,[$cnf( $equal(join(A,converse(converse(A))),join(A,converse(converse(A)))) )],[refute_0_1515,refute_0_1516]) ).
cnf(refute_0_1518,plain,
join(A,converse(converse(A))) = join(A,A),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1517]) ).
cnf(refute_0_1519,plain,
converse(join(converse(A),converse(A))) = join(A,converse(converse(A))),
inference(subst,[],[refute_0_459:[bind(X_5,$fot(converse(A)))]]) ).
cnf(refute_0_1520,plain,
( converse(join(converse(A),converse(A))) != join(A,converse(converse(A)))
| join(A,converse(converse(A))) != join(A,A)
| converse(join(converse(A),converse(A))) = join(A,A) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(converse(join(converse(A),converse(A))))),bind(Y,$fot(join(A,converse(converse(A))))),bind(Z,$fot(join(A,A)))]]) ).
cnf(refute_0_1521,plain,
( join(A,converse(converse(A))) != join(A,A)
| converse(join(converse(A),converse(A))) = join(A,A) ),
inference(resolve,[$cnf( $equal(converse(join(converse(A),converse(A))),join(A,converse(converse(A)))) )],[refute_0_1519,refute_0_1520]) ).
cnf(refute_0_1522,plain,
converse(join(converse(A),converse(A))) = join(A,A),
inference(resolve,[$cnf( $equal(join(A,converse(converse(A))),join(A,A)) )],[refute_0_1518,refute_0_1521]) ).
cnf(refute_0_1523,plain,
( converse(join(converse(A),converse(A))) != composition(A,converse(join(one,one)))
| converse(join(converse(A),converse(A))) != join(A,A)
| join(A,A) = composition(A,converse(join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),converse(A))),composition(A,converse(join(one,one)))) ),[0],$fot(join(A,A))]]) ).
cnf(refute_0_1524,plain,
( converse(join(converse(A),converse(A))) != composition(A,converse(join(one,one)))
| join(A,A) = composition(A,converse(join(one,one))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(A),converse(A))),join(A,A)) )],[refute_0_1522,refute_0_1523]) ).
cnf(refute_0_1525,plain,
composition(A,converse(join(one,one))) = composition(A,converse(join(one,one))),
introduced(tautology,[refl,[$fot(composition(A,converse(join(one,one))))]]) ).
cnf(refute_0_1526,plain,
( composition(A,converse(join(one,one))) != composition(A,converse(join(one,one)))
| converse(join(one,one)) != join(one,one)
| composition(A,converse(join(one,one))) = composition(A,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(A,converse(join(one,one))),composition(A,converse(join(one,one)))) ),[1,1],$fot(join(one,one))]]) ).
cnf(refute_0_1527,plain,
( converse(join(one,one)) != join(one,one)
| composition(A,converse(join(one,one))) = composition(A,join(one,one)) ),
inference(resolve,[$cnf( $equal(composition(A,converse(join(one,one))),composition(A,converse(join(one,one)))) )],[refute_0_1525,refute_0_1526]) ).
cnf(refute_0_1528,plain,
composition(A,converse(join(one,one))) = composition(A,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_959,refute_0_1527]) ).
cnf(refute_0_1529,plain,
( composition(A,converse(join(one,one))) != composition(A,join(one,one))
| join(A,A) != composition(A,converse(join(one,one)))
| join(A,A) = composition(A,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,A),composition(A,converse(join(one,one)))) ),[1],$fot(composition(A,join(one,one)))]]) ).
cnf(refute_0_1530,plain,
( join(A,A) != composition(A,converse(join(one,one)))
| join(A,A) = composition(A,join(one,one)) ),
inference(resolve,[$cnf( $equal(composition(A,converse(join(one,one))),composition(A,join(one,one))) )],[refute_0_1528,refute_0_1529]) ).
cnf(refute_0_1531,plain,
( converse(join(converse(A),converse(A))) != composition(A,converse(join(one,one)))
| join(A,A) = composition(A,join(one,one)) ),
inference(resolve,[$cnf( $equal(join(A,A),composition(A,converse(join(one,one)))) )],[refute_0_1524,refute_0_1530]) ).
cnf(refute_0_1532,plain,
join(A,A) = composition(A,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),converse(A))),composition(A,converse(join(one,one)))) )],[refute_0_1514,refute_0_1531]) ).
cnf(refute_0_1533,plain,
( join(A,A) != composition(A,join(one,one))
| composition(A,join(one,one)) = join(A,A) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,A))),bind(Y,$fot(composition(A,join(one,one))))]]) ).
cnf(refute_0_1534,plain,
composition(A,join(one,one)) = join(A,A),
inference(resolve,[$cnf( $equal(join(A,A),composition(A,join(one,one))) )],[refute_0_1532,refute_0_1533]) ).
cnf(refute_0_1535,plain,
( composition(A,join(one,one)) != join(A,A)
| composition(join(A,B),join(one,one)) != join(composition(A,join(one,one)),composition(B,join(one,one)))
| composition(join(A,B),join(one,one)) = join(join(A,A),composition(B,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(A,B),join(one,one)),join(composition(A,join(one,one)),composition(B,join(one,one)))) ),[1,0],$fot(join(A,A))]]) ).
cnf(refute_0_1536,plain,
( composition(join(A,B),join(one,one)) != join(composition(A,join(one,one)),composition(B,join(one,one)))
| composition(join(A,B),join(one,one)) = join(join(A,A),composition(B,join(one,one))) ),
inference(resolve,[$cnf( $equal(composition(A,join(one,one)),join(A,A)) )],[refute_0_1534,refute_0_1535]) ).
cnf(refute_0_1537,plain,
composition(join(A,B),join(one,one)) = join(join(A,A),composition(B,join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),join(composition(A,join(one,one)),composition(B,join(one,one)))) )],[refute_0_1509,refute_0_1536]) ).
cnf(refute_0_1538,plain,
join(join(A,A),composition(B,join(one,one))) = join(A,join(A,composition(B,join(one,one)))),
inference(subst,[],[refute_0_205:[bind(B,$fot(A)),bind(C,$fot(composition(B,join(one,one))))]]) ).
cnf(refute_0_1539,plain,
( composition(join(A,B),join(one,one)) != join(join(A,A),composition(B,join(one,one)))
| join(join(A,A),composition(B,join(one,one))) != join(A,join(A,composition(B,join(one,one))))
| composition(join(A,B),join(one,one)) = join(A,join(A,composition(B,join(one,one)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(A,B),join(one,one)),join(A,join(A,composition(B,join(one,one))))) ),[0],$fot(join(join(A,A),composition(B,join(one,one))))]]) ).
cnf(refute_0_1540,plain,
( composition(join(A,B),join(one,one)) != join(join(A,A),composition(B,join(one,one)))
| composition(join(A,B),join(one,one)) = join(A,join(A,composition(B,join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(join(A,A),composition(B,join(one,one))),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_1538,refute_0_1539]) ).
cnf(refute_0_1541,plain,
composition(join(A,B),join(one,one)) = join(A,join(A,composition(B,join(one,one)))),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),join(join(A,A),composition(B,join(one,one)))) )],[refute_0_1537,refute_0_1540]) ).
cnf(refute_0_1542,plain,
composition(join(A,B),one) = join(A,B),
inference(subst,[],[composition_identity_6:[bind(A,$fot(join(A,B)))]]) ).
cnf(refute_0_1543,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_1544,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_8:[bind(A,$fot(join(one,join(one,one)))),bind(B,$fot(complement(one)))]]) ).
cnf(refute_0_1545,plain,
join(complement(one),composition(converse(X_31),complement(composition(X_31,one)))) = complement(one),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_31)),bind(B,$fot(one))]]) ).
cnf(refute_0_1546,plain,
composition(X_31,one) = X_31,
inference(subst,[],[composition_identity_6:[bind(A,$fot(X_31))]]) ).
cnf(refute_0_1547,plain,
( composition(X_31,one) != X_31
| join(complement(one),composition(converse(X_31),complement(composition(X_31,one)))) != complement(one)
| join(complement(one),composition(converse(X_31),complement(X_31))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(X_31),complement(composition(X_31,one)))),complement(one)) ),[0,1,1,0],$fot(X_31)]]) ).
cnf(refute_0_1548,plain,
( join(complement(one),composition(converse(X_31),complement(composition(X_31,one)))) != complement(one)
| join(complement(one),composition(converse(X_31),complement(X_31))) = complement(one) ),
inference(resolve,[$cnf( $equal(composition(X_31,one),X_31) )],[refute_0_1546,refute_0_1547]) ).
cnf(refute_0_1549,plain,
join(complement(one),composition(converse(X_31),complement(X_31))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(X_31),complement(composition(X_31,one)))),complement(one)) )],[refute_0_1545,refute_0_1548]) ).
cnf(refute_0_1550,plain,
join(complement(one),composition(converse(join(one,one)),complement(join(one,one)))) = complement(one),
inference(subst,[],[refute_0_1549:[bind(X_31,$fot(join(one,one)))]]) ).
cnf(refute_0_1551,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_1552,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( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_959,refute_0_1551]) ).
cnf(refute_0_1553,plain,
join(complement(one),composition(join(one,one),complement(join(one,one)))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(join(one,one)),complement(join(one,one)))),complement(one)) )],[refute_0_1550,refute_0_1552]) ).
cnf(refute_0_1554,plain,
composition(join(one,one),complement(join(one,one))) = composition(join(one,one),complement(join(one,one))),
introduced(tautology,[refl,[$fot(composition(join(one,one),complement(join(one,one))))]]) ).
cnf(refute_0_1555,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_1556,plain,
( complement(join(one,one)) != complement(one)
| composition(join(one,one),complement(join(one,one))) = composition(join(one,one),complement(one)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(join(one,one))),composition(join(one,one),complement(join(one,one)))) )],[refute_0_1554,refute_0_1555]) ).
cnf(refute_0_1557,plain,
composition(join(one,one),complement(join(one,one))) = composition(join(one,one),complement(one)),
inference(resolve,[$cnf( $equal(complement(join(one,one)),complement(one)) )],[refute_0_1008,refute_0_1556]) ).
cnf(refute_0_1558,plain,
join(complement(one),composition(join(one,one),complement(join(one,one)))) = join(complement(one),composition(join(one,one),complement(join(one,one)))),
introduced(tautology,[refl,[$fot(join(complement(one),composition(join(one,one),complement(join(one,one)))))]]) ).
cnf(refute_0_1559,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_1560,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( $equal(join(complement(one),composition(join(one,one),complement(join(one,one)))),join(complement(one),composition(join(one,one),complement(join(one,one))))) )],[refute_0_1558,refute_0_1559]) ).
cnf(refute_0_1561,plain,
join(complement(one),composition(join(one,one),complement(join(one,one)))) = join(complement(one),composition(join(one,one),complement(one))),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(join(one,one))),composition(join(one,one),complement(one))) )],[refute_0_1557,refute_0_1560]) ).
cnf(refute_0_1562,plain,
( join(complement(one),composition(join(one,one),complement(join(one,one)))) != complement(one)
| join(complement(one),composition(join(one,one),complement(join(one,one)))) != join(complement(one),composition(join(one,one),complement(one)))
| join(complement(one),composition(join(one,one),complement(one))) = complement(one) ),
introduced(tautology,[equality,[$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_1563,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( $equal(join(complement(one),composition(join(one,one),complement(join(one,one)))),join(complement(one),composition(join(one,one),complement(one)))) )],[refute_0_1561,refute_0_1562]) ).
cnf(refute_0_1564,plain,
join(complement(one),composition(join(one,one),complement(one))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(join(one,one)))),complement(one)) )],[refute_0_1553,refute_0_1563]) ).
cnf(refute_0_1565,plain,
join(composition(X_99,X_100),composition(X_98,X_100)) = join(composition(X_98,X_100),composition(X_99,X_100)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(composition(X_99,X_100))),bind(B,$fot(composition(X_98,X_100)))]]) ).
cnf(refute_0_1566,plain,
composition(join(X_98,X_99),X_100) = join(composition(X_98,X_100),composition(X_99,X_100)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_98)),bind(B,$fot(X_99)),bind(C,$fot(X_100))]]) ).
cnf(refute_0_1567,plain,
( composition(join(X_98,X_99),X_100) != join(composition(X_98,X_100),composition(X_99,X_100))
| join(composition(X_98,X_100),composition(X_99,X_100)) = composition(join(X_98,X_99),X_100) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_98,X_99),X_100))),bind(Y,$fot(join(composition(X_98,X_100),composition(X_99,X_100))))]]) ).
cnf(refute_0_1568,plain,
join(composition(X_98,X_100),composition(X_99,X_100)) = composition(join(X_98,X_99),X_100),
inference(resolve,[$cnf( $equal(composition(join(X_98,X_99),X_100),join(composition(X_98,X_100),composition(X_99,X_100))) )],[refute_0_1566,refute_0_1567]) ).
cnf(refute_0_1569,plain,
( join(composition(X_98,X_100),composition(X_99,X_100)) != composition(join(X_98,X_99),X_100)
| join(composition(X_99,X_100),composition(X_98,X_100)) != join(composition(X_98,X_100),composition(X_99,X_100))
| join(composition(X_99,X_100),composition(X_98,X_100)) = composition(join(X_98,X_99),X_100) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_99,X_100),composition(X_98,X_100)),join(composition(X_98,X_100),composition(X_99,X_100))) ),[1],$fot(composition(join(X_98,X_99),X_100))]]) ).
cnf(refute_0_1570,plain,
( join(composition(X_99,X_100),composition(X_98,X_100)) != join(composition(X_98,X_100),composition(X_99,X_100))
| join(composition(X_99,X_100),composition(X_98,X_100)) = composition(join(X_98,X_99),X_100) ),
inference(resolve,[$cnf( $equal(join(composition(X_98,X_100),composition(X_99,X_100)),composition(join(X_98,X_99),X_100)) )],[refute_0_1568,refute_0_1569]) ).
cnf(refute_0_1571,plain,
join(composition(X_99,X_100),composition(X_98,X_100)) = composition(join(X_98,X_99),X_100),
inference(resolve,[$cnf( $equal(join(composition(X_99,X_100),composition(X_98,X_100)),join(composition(X_98,X_100),composition(X_99,X_100))) )],[refute_0_1565,refute_0_1570]) ).
cnf(refute_0_1572,plain,
( composition(join(A,B),C) != join(composition(A,C),composition(B,C))
| join(composition(A,C),composition(B,C)) = composition(join(A,B),C) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(A,B),C))),bind(Y,$fot(join(composition(A,C),composition(B,C))))]]) ).
cnf(refute_0_1573,plain,
join(composition(A,C),composition(B,C)) = composition(join(A,B),C),
inference(resolve,[$cnf( $equal(composition(join(A,B),C),join(composition(A,C),composition(B,C))) )],[composition_distributivity_7,refute_0_1572]) ).
cnf(refute_0_1574,plain,
join(composition(X_99,X_100),composition(X_98,X_100)) = composition(join(X_99,X_98),X_100),
inference(subst,[],[refute_0_1573:[bind(A,$fot(X_99)),bind(B,$fot(X_98)),bind(C,$fot(X_100))]]) ).
cnf(refute_0_1575,plain,
( join(composition(X_99,X_100),composition(X_98,X_100)) != composition(join(X_98,X_99),X_100)
| join(composition(X_99,X_100),composition(X_98,X_100)) != composition(join(X_99,X_98),X_100)
| composition(join(X_99,X_98),X_100) = composition(join(X_98,X_99),X_100) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_99,X_100),composition(X_98,X_100)),composition(join(X_98,X_99),X_100)) ),[0],$fot(composition(join(X_99,X_98),X_100))]]) ).
cnf(refute_0_1576,plain,
( join(composition(X_99,X_100),composition(X_98,X_100)) != composition(join(X_98,X_99),X_100)
| composition(join(X_99,X_98),X_100) = composition(join(X_98,X_99),X_100) ),
inference(resolve,[$cnf( $equal(join(composition(X_99,X_100),composition(X_98,X_100)),composition(join(X_99,X_98),X_100)) )],[refute_0_1574,refute_0_1575]) ).
cnf(refute_0_1577,plain,
composition(join(X_99,X_98),X_100) = composition(join(X_98,X_99),X_100),
inference(resolve,[$cnf( $equal(join(composition(X_99,X_100),composition(X_98,X_100)),composition(join(X_98,X_99),X_100)) )],[refute_0_1571,refute_0_1576]) ).
cnf(refute_0_1578,plain,
( composition(join(X_99,X_98),X_100) != composition(join(X_98,X_99),X_100)
| composition(join(X_98,X_99),X_100) = composition(join(X_99,X_98),X_100) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_99,X_98),X_100))),bind(Y,$fot(composition(join(X_98,X_99),X_100)))]]) ).
cnf(refute_0_1579,plain,
composition(join(X_98,X_99),X_100) = composition(join(X_99,X_98),X_100),
inference(resolve,[$cnf( $equal(composition(join(X_99,X_98),X_100),composition(join(X_98,X_99),X_100)) )],[refute_0_1577,refute_0_1578]) ).
cnf(refute_0_1580,plain,
composition(join(join(one,one),one),complement(one)) = composition(join(one,join(one,one)),complement(one)),
inference(subst,[],[refute_0_1579:[bind(X_100,$fot(complement(one))),bind(X_98,$fot(join(one,one))),bind(X_99,$fot(one))]]) ).
cnf(refute_0_1581,plain,
join(complement(one),composition(join(one,one),complement(one))) = composition(join(join(one,one),one),complement(one)),
inference(subst,[],[refute_0_1048:[bind(X_100,$fot(complement(one))),bind(X_98,$fot(join(one,one)))]]) ).
cnf(refute_0_1582,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_41:[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,$fot(composition(join(one,join(one,one)),complement(one))))]]) ).
cnf(refute_0_1583,plain,
( composition(join(join(one,one),one),complement(one)) != composition(join(one,join(one,one)),complement(one))
| join(complement(one),composition(join(one,one),complement(one))) = composition(join(one,join(one,one)),complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(one))),composition(join(join(one,one),one),complement(one))) )],[refute_0_1581,refute_0_1582]) ).
cnf(refute_0_1584,plain,
join(complement(one),composition(join(one,one),complement(one))) = composition(join(one,join(one,one)),complement(one)),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),complement(one)),composition(join(one,join(one,one)),complement(one))) )],[refute_0_1580,refute_0_1583]) ).
cnf(refute_0_1585,plain,
( join(complement(one),composition(join(one,one),complement(one))) != complement(one)
| join(complement(one),composition(join(one,one),complement(one))) != composition(join(one,join(one,one)),complement(one))
| composition(join(one,join(one,one)),complement(one)) = complement(one) ),
introduced(tautology,[equality,[$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_1586,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( $equal(join(complement(one),composition(join(one,one),complement(one))),composition(join(one,join(one,one)),complement(one))) )],[refute_0_1584,refute_0_1585]) ).
cnf(refute_0_1587,plain,
composition(join(one,join(one,one)),complement(one)) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,one),complement(one))),complement(one)) )],[refute_0_1564,refute_0_1586]) ).
cnf(refute_0_1588,plain,
( composition(join(one,join(one,one)),complement(one)) != complement(one)
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(composition(join(one,join(one,one)),complement(one))))) != complement(complement(one))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = complement(complement(one)) ),
introduced(tautology,[equality,[$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_1589,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( $equal(composition(join(one,join(one,one)),complement(one)),complement(one)) )],[refute_0_1587,refute_0_1588]) ).
cnf(refute_0_1590,plain,
join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = complement(complement(one)),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(composition(join(one,join(one,one)),complement(one))))),complement(complement(one))) )],[refute_0_1544,refute_0_1589]) ).
cnf(refute_0_1591,plain,
composition(join(one,join(one,join(one,one))),one) = join(one,join(one,join(one,one))),
inference(subst,[],[composition_identity_6:[bind(A,$fot(join(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_1592,plain,
complement(complement(one)) = one,
inference(subst,[],[refute_0_680:[bind(X_35,$fot(one))]]) ).
cnf(refute_0_1593,plain,
composition(join(one,join(one,join(one,one))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),complement(complement(one))),
introduced(tautology,[refl,[$fot(composition(join(one,join(one,join(one,one))),complement(complement(one))))]]) ).
cnf(refute_0_1594,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_1595,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( $equal(composition(join(one,join(one,join(one,one))),complement(complement(one))),composition(join(one,join(one,join(one,one))),complement(complement(one)))) )],[refute_0_1593,refute_0_1594]) ).
cnf(refute_0_1596,plain,
composition(join(one,join(one,join(one,one))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),one),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_1592,refute_0_1595]) ).
cnf(refute_0_1597,plain,
converse(join(one,join(one,join(one,one)))) = join(one,converse(join(one,join(one,one)))),
inference(subst,[],[refute_0_955:[bind(X_5,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_1598,plain,
converse(join(one,join(one,one))) = join(one,converse(join(one,one))),
inference(subst,[],[refute_0_955:[bind(X_5,$fot(join(one,one)))]]) ).
cnf(refute_0_1599,plain,
( converse(join(one,join(one,one))) != join(one,converse(join(one,one)))
| converse(join(one,one)) != join(one,one)
| converse(join(one,join(one,one))) = join(one,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,one))),join(one,converse(join(one,one)))) ),[1,1],$fot(join(one,one))]]) ).
cnf(refute_0_1600,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( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_959,refute_0_1599]) ).
cnf(refute_0_1601,plain,
converse(join(one,join(one,one))) = join(one,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,one))),join(one,converse(join(one,one)))) )],[refute_0_1598,refute_0_1600]) ).
cnf(refute_0_1602,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,converse(join(one,join(one,one))))
| converse(join(one,join(one,one))) != join(one,join(one,one))
| converse(join(one,join(one,join(one,one)))) = join(one,join(one,join(one,one))) ),
introduced(tautology,[equality,[$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_1603,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( $equal(converse(join(one,join(one,one))),join(one,join(one,one))) )],[refute_0_1601,refute_0_1602]) ).
cnf(refute_0_1604,plain,
converse(join(one,join(one,join(one,one)))) = join(one,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),join(one,converse(join(one,join(one,one))))) )],[refute_0_1597,refute_0_1603]) ).
cnf(refute_0_1605,plain,
join(one,converse(join(one,join(one,one)))) = converse(join(one,join(one,join(one,one)))),
inference(subst,[],[refute_0_964:[bind(X_5,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_1606,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_41:[bind(X,$fot(join(one,converse(join(one,join(one,one)))))),bind(Y,$fot(converse(join(one,join(one,join(one,one)))))),bind(Z,$fot(join(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_1607,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| join(one,converse(join(one,join(one,one)))) = join(one,join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(one,one)))),converse(join(one,join(one,join(one,one))))) )],[refute_0_1605,refute_0_1606]) ).
cnf(refute_0_1608,plain,
join(one,converse(join(one,join(one,one)))) = join(one,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),join(one,join(one,join(one,one)))) )],[refute_0_1604,refute_0_1607]) ).
cnf(refute_0_1609,plain,
composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),
introduced(tautology,[refl,[$fot(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))))]]) ).
cnf(refute_0_1610,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_1611,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( $equal(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))) )],[refute_0_1609,refute_0_1610]) ).
cnf(refute_0_1612,plain,
composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),complement(complement(one))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(one,one)))),join(one,join(one,join(one,one)))) )],[refute_0_1608,refute_0_1611]) ).
cnf(refute_0_1613,plain,
( composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) != composition(join(one,join(one,join(one,one))),complement(complement(one)))
| composition(join(one,join(one,join(one,one))),complement(complement(one))) != composition(join(one,join(one,join(one,one))),one)
| composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),one) ),
inference(subst,[],[refute_0_41:[bind(X,$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_1614,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( $equal(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),composition(join(one,join(one,join(one,one))),complement(complement(one)))) )],[refute_0_1612,refute_0_1613]) ).
cnf(refute_0_1615,plain,
composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = composition(join(one,join(one,join(one,one))),one),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,join(one,one))),complement(complement(one))),composition(join(one,join(one,join(one,one))),one)) )],[refute_0_1596,refute_0_1614]) ).
cnf(refute_0_1616,plain,
( composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) != composition(join(one,join(one,join(one,one))),one)
| composition(join(one,join(one,join(one,one))),one) != join(one,join(one,join(one,one)))
| composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = join(one,join(one,join(one,one))) ),
inference(subst,[],[refute_0_41:[bind(X,$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_1617,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( $equal(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),composition(join(one,join(one,join(one,one))),one)) )],[refute_0_1615,refute_0_1616]) ).
cnf(refute_0_1618,plain,
composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) = join(one,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,join(one,one))),one),join(one,join(one,join(one,one)))) )],[refute_0_1591,refute_0_1617]) ).
cnf(refute_0_1619,plain,
composition(join(converse(join(one,join(one,one))),one),complement(complement(one))) = composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),
inference(subst,[],[refute_0_1579:[bind(X_100,$fot(complement(complement(one)))),bind(X_98,$fot(converse(join(one,join(one,one))))),bind(X_99,$fot(one))]]) ).
cnf(refute_0_1620,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_1048:[bind(X_100,$fot(complement(complement(one)))),bind(X_98,$fot(converse(join(one,join(one,one)))))]]) ).
cnf(refute_0_1621,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_41:[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,$fot(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))))]]) ).
cnf(refute_0_1622,plain,
( composition(join(converse(join(one,join(one,one))),one),complement(complement(one))) != composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))),composition(join(converse(join(one,join(one,one))),one),complement(complement(one)))) )],[refute_0_1620,refute_0_1621]) ).
cnf(refute_0_1623,plain,
join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),
inference(resolve,[$cnf( $equal(composition(join(converse(join(one,join(one,one))),one),complement(complement(one))),composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))) )],[refute_0_1619,refute_0_1622]) ).
cnf(refute_0_1624,plain,
( composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))) != join(one,join(one,join(one,one)))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) != composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = join(one,join(one,join(one,one))) ),
inference(subst,[],[refute_0_41:[bind(X,$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_1625,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( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))),composition(join(one,converse(join(one,join(one,one)))),complement(complement(one)))) )],[refute_0_1623,refute_0_1624]) ).
cnf(refute_0_1626,plain,
join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) = join(one,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(join(one,join(one,one)))),complement(complement(one))),join(one,join(one,join(one,one)))) )],[refute_0_1618,refute_0_1625]) ).
cnf(refute_0_1627,plain,
( join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) != complement(complement(one))
| join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) != join(one,join(one,join(one,one)))
| join(one,join(one,join(one,one))) = complement(complement(one)) ),
introduced(tautology,[equality,[$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_1628,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( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))),join(one,join(one,join(one,one)))) )],[refute_0_1626,refute_0_1627]) ).
cnf(refute_0_1629,plain,
( complement(complement(one)) != one
| join(one,join(one,join(one,one))) != complement(complement(one))
| join(one,join(one,join(one,one))) = one ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(one,one))),complement(complement(one))) ),[1],$fot(one)]]) ).
cnf(refute_0_1630,plain,
( join(one,join(one,join(one,one))) != complement(complement(one))
| join(one,join(one,join(one,one))) = one ),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_1592,refute_0_1629]) ).
cnf(refute_0_1631,plain,
( join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))) != complement(complement(one))
| join(one,join(one,join(one,one))) = one ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,one))),complement(complement(one))) )],[refute_0_1628,refute_0_1630]) ).
cnf(refute_0_1632,plain,
join(one,join(one,join(one,one))) = one,
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,join(one,one))),complement(complement(one)))),complement(complement(one))) )],[refute_0_1590,refute_0_1631]) ).
cnf(refute_0_1633,plain,
( join(A,join(one,join(one,join(one,one)))) != join(join(A,one),join(one,join(one,one)))
| join(one,join(one,join(one,one))) != one
| join(A,one) = join(join(A,one),join(one,join(one,one))) ),
introduced(tautology,[equality,[$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_1634,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( $equal(join(one,join(one,join(one,one))),one) )],[refute_0_1632,refute_0_1633]) ).
cnf(refute_0_1635,plain,
join(A,one) = join(join(A,one),join(one,join(one,one))),
inference(resolve,[$cnf( $equal(join(A,join(one,join(one,join(one,one)))),join(join(A,one),join(one,join(one,one)))) )],[refute_0_1543,refute_0_1634]) ).
cnf(refute_0_1636,plain,
join(X_79,join(X_80,X_81)) = join(join(X_79,X_80),X_81),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_79)),bind(B,$fot(X_80)),bind(C,$fot(X_81))]]) ).
cnf(refute_0_1637,plain,
join(X_81,X_80) = join(X_80,X_81),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_81)),bind(B,$fot(X_80))]]) ).
cnf(refute_0_1638,plain,
( join(X_81,X_80) != join(X_80,X_81)
| join(X_80,X_81) = join(X_81,X_80) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_81,X_80))),bind(Y,$fot(join(X_80,X_81)))]]) ).
cnf(refute_0_1639,plain,
join(X_80,X_81) = join(X_81,X_80),
inference(resolve,[$cnf( $equal(join(X_81,X_80),join(X_80,X_81)) )],[refute_0_1637,refute_0_1638]) ).
cnf(refute_0_1640,plain,
( join(X_79,join(X_80,X_81)) != join(join(X_79,X_80),X_81)
| join(X_80,X_81) != join(X_81,X_80)
| join(X_79,join(X_81,X_80)) = join(join(X_79,X_80),X_81) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_79,join(X_80,X_81)),join(join(X_79,X_80),X_81)) ),[0,1],$fot(join(X_81,X_80))]]) ).
cnf(refute_0_1641,plain,
( join(X_79,join(X_80,X_81)) != join(join(X_79,X_80),X_81)
| join(X_79,join(X_81,X_80)) = join(join(X_79,X_80),X_81) ),
inference(resolve,[$cnf( $equal(join(X_80,X_81),join(X_81,X_80)) )],[refute_0_1639,refute_0_1640]) ).
cnf(refute_0_1642,plain,
join(X_79,join(X_81,X_80)) = join(join(X_79,X_80),X_81),
inference(resolve,[$cnf( $equal(join(X_79,join(X_80,X_81)),join(join(X_79,X_80),X_81)) )],[refute_0_1636,refute_0_1641]) ).
cnf(refute_0_1643,plain,
join(join(X_79,X_80),X_81) = join(X_79,join(X_80,X_81)),
inference(subst,[],[refute_0_205:[bind(A,$fot(X_79)),bind(B,$fot(X_80)),bind(C,$fot(X_81))]]) ).
cnf(refute_0_1644,plain,
( join(X_79,join(X_81,X_80)) != join(join(X_79,X_80),X_81)
| join(join(X_79,X_80),X_81) != join(X_79,join(X_80,X_81))
| join(X_79,join(X_81,X_80)) = join(X_79,join(X_80,X_81)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_79,join(X_81,X_80)),join(X_79,join(X_80,X_81))) ),[0],$fot(join(join(X_79,X_80),X_81))]]) ).
cnf(refute_0_1645,plain,
( join(X_79,join(X_81,X_80)) != join(join(X_79,X_80),X_81)
| join(X_79,join(X_81,X_80)) = join(X_79,join(X_80,X_81)) ),
inference(resolve,[$cnf( $equal(join(join(X_79,X_80),X_81),join(X_79,join(X_80,X_81))) )],[refute_0_1643,refute_0_1644]) ).
cnf(refute_0_1646,plain,
join(X_79,join(X_81,X_80)) = join(X_79,join(X_80,X_81)),
inference(resolve,[$cnf( $equal(join(X_79,join(X_81,X_80)),join(join(X_79,X_80),X_81)) )],[refute_0_1642,refute_0_1645]) ).
cnf(refute_0_1647,plain,
( join(X_79,join(X_81,X_80)) != join(X_79,join(X_80,X_81))
| join(X_79,join(X_80,X_81)) = join(X_79,join(X_81,X_80)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_79,join(X_81,X_80)))),bind(Y,$fot(join(X_79,join(X_80,X_81))))]]) ).
cnf(refute_0_1648,plain,
join(X_79,join(X_80,X_81)) = join(X_79,join(X_81,X_80)),
inference(resolve,[$cnf( $equal(join(X_79,join(X_81,X_80)),join(X_79,join(X_80,X_81))) )],[refute_0_1646,refute_0_1647]) ).
cnf(refute_0_1649,plain,
join(one,join(join(A,one),one)) = join(one,join(one,join(A,one))),
inference(subst,[],[refute_0_1648:[bind(X_79,$fot(one)),bind(X_80,$fot(join(A,one))),bind(X_81,$fot(one))]]) ).
cnf(refute_0_1650,plain,
join(X_80,X_79) = join(X_79,X_80),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_80)),bind(B,$fot(X_79))]]) ).
cnf(refute_0_1651,plain,
( join(X_80,X_79) != join(X_79,X_80)
| join(X_79,X_80) = join(X_80,X_79) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_80,X_79))),bind(Y,$fot(join(X_79,X_80)))]]) ).
cnf(refute_0_1652,plain,
join(X_79,X_80) = join(X_80,X_79),
inference(resolve,[$cnf( $equal(join(X_80,X_79),join(X_79,X_80)) )],[refute_0_1650,refute_0_1651]) ).
cnf(refute_0_1653,plain,
( join(X_79,X_80) != join(X_80,X_79)
| join(X_79,join(X_80,X_81)) != join(join(X_79,X_80),X_81)
| join(X_79,join(X_80,X_81)) = join(join(X_80,X_79),X_81) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_79,join(X_80,X_81)),join(join(X_79,X_80),X_81)) ),[1,0],$fot(join(X_80,X_79))]]) ).
cnf(refute_0_1654,plain,
( join(X_79,join(X_80,X_81)) != join(join(X_79,X_80),X_81)
| join(X_79,join(X_80,X_81)) = join(join(X_80,X_79),X_81) ),
inference(resolve,[$cnf( $equal(join(X_79,X_80),join(X_80,X_79)) )],[refute_0_1652,refute_0_1653]) ).
cnf(refute_0_1655,plain,
join(X_79,join(X_80,X_81)) = join(join(X_80,X_79),X_81),
inference(resolve,[$cnf( $equal(join(X_79,join(X_80,X_81)),join(join(X_79,X_80),X_81)) )],[refute_0_1636,refute_0_1654]) ).
cnf(refute_0_1656,plain,
join(join(X_80,X_79),X_81) = join(X_80,join(X_79,X_81)),
inference(subst,[],[refute_0_205:[bind(A,$fot(X_80)),bind(B,$fot(X_79)),bind(C,$fot(X_81))]]) ).
cnf(refute_0_1657,plain,
( join(X_79,join(X_80,X_81)) != join(join(X_80,X_79),X_81)
| join(join(X_80,X_79),X_81) != join(X_80,join(X_79,X_81))
| join(X_79,join(X_80,X_81)) = join(X_80,join(X_79,X_81)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_79,join(X_80,X_81)),join(X_80,join(X_79,X_81))) ),[0],$fot(join(join(X_80,X_79),X_81))]]) ).
cnf(refute_0_1658,plain,
( join(X_79,join(X_80,X_81)) != join(join(X_80,X_79),X_81)
| join(X_79,join(X_80,X_81)) = join(X_80,join(X_79,X_81)) ),
inference(resolve,[$cnf( $equal(join(join(X_80,X_79),X_81),join(X_80,join(X_79,X_81))) )],[refute_0_1656,refute_0_1657]) ).
cnf(refute_0_1659,plain,
join(X_79,join(X_80,X_81)) = join(X_80,join(X_79,X_81)),
inference(resolve,[$cnf( $equal(join(X_79,join(X_80,X_81)),join(join(X_80,X_79),X_81)) )],[refute_0_1655,refute_0_1658]) ).
cnf(refute_0_1660,plain,
( join(X_79,join(X_80,X_81)) != join(X_80,join(X_79,X_81))
| join(X_80,join(X_79,X_81)) = join(X_79,join(X_80,X_81)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_79,join(X_80,X_81)))),bind(Y,$fot(join(X_80,join(X_79,X_81))))]]) ).
cnf(refute_0_1661,plain,
join(X_80,join(X_79,X_81)) = join(X_79,join(X_80,X_81)),
inference(resolve,[$cnf( $equal(join(X_79,join(X_80,X_81)),join(X_80,join(X_79,X_81))) )],[refute_0_1659,refute_0_1660]) ).
cnf(refute_0_1662,plain,
join(join(A,one),join(one,one)) = join(one,join(join(A,one),one)),
inference(subst,[],[refute_0_1661:[bind(X_79,$fot(one)),bind(X_80,$fot(join(A,one))),bind(X_81,$fot(one))]]) ).
cnf(refute_0_1663,plain,
( join(join(A,one),join(one,one)) != join(one,join(join(A,one),one))
| join(one,join(join(A,one),one)) != join(one,join(one,join(A,one)))
| join(join(A,one),join(one,one)) = join(one,join(one,join(A,one))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(join(A,one),join(one,one)))),bind(Y,$fot(join(one,join(join(A,one),one)))),bind(Z,$fot(join(one,join(one,join(A,one)))))]]) ).
cnf(refute_0_1664,plain,
( join(one,join(join(A,one),one)) != join(one,join(one,join(A,one)))
| join(join(A,one),join(one,one)) = join(one,join(one,join(A,one))) ),
inference(resolve,[$cnf( $equal(join(join(A,one),join(one,one)),join(one,join(join(A,one),one))) )],[refute_0_1662,refute_0_1663]) ).
cnf(refute_0_1665,plain,
join(join(A,one),join(one,one)) = join(one,join(one,join(A,one))),
inference(resolve,[$cnf( $equal(join(one,join(join(A,one),one)),join(one,join(one,join(A,one)))) )],[refute_0_1649,refute_0_1664]) ).
cnf(refute_0_1666,plain,
join(one,join(join(A,one),join(one,one))) = join(one,join(join(A,one),join(one,one))),
introduced(tautology,[refl,[$fot(join(one,join(join(A,one),join(one,one))))]]) ).
cnf(refute_0_1667,plain,
( join(join(A,one),join(one,one)) != join(one,join(one,join(A,one)))
| join(one,join(join(A,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)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(A,one),join(one,one))),join(one,join(join(A,one),join(one,one)))) ),[1,1],$fot(join(one,join(one,join(A,one))))]]) ).
cnf(refute_0_1668,plain,
( join(join(A,one),join(one,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( $equal(join(one,join(join(A,one),join(one,one))),join(one,join(join(A,one),join(one,one)))) )],[refute_0_1666,refute_0_1667]) ).
cnf(refute_0_1669,plain,
join(one,join(join(A,one),join(one,one))) = join(one,join(one,join(one,join(A,one)))),
inference(resolve,[$cnf( $equal(join(join(A,one),join(one,one)),join(one,join(one,join(A,one)))) )],[refute_0_1665,refute_0_1668]) ).
cnf(refute_0_1670,plain,
join(join(A,one),join(one,join(one,one))) = join(one,join(join(A,one),join(one,one))),
inference(subst,[],[refute_0_1661:[bind(X_79,$fot(one)),bind(X_80,$fot(join(A,one))),bind(X_81,$fot(join(one,one)))]]) ).
cnf(refute_0_1671,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_41:[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,$fot(join(one,join(one,join(one,join(A,one))))))]]) ).
cnf(refute_0_1672,plain,
( join(one,join(join(A,one),join(one,one))) != join(one,join(one,join(one,join(A,one))))
| join(join(A,one),join(one,join(one,one))) = join(one,join(one,join(one,join(A,one)))) ),
inference(resolve,[$cnf( $equal(join(join(A,one),join(one,join(one,one))),join(one,join(join(A,one),join(one,one)))) )],[refute_0_1670,refute_0_1671]) ).
cnf(refute_0_1673,plain,
join(join(A,one),join(one,join(one,one))) = join(one,join(one,join(one,join(A,one)))),
inference(resolve,[$cnf( $equal(join(one,join(join(A,one),join(one,one))),join(one,join(one,join(one,join(A,one))))) )],[refute_0_1669,refute_0_1672]) ).
cnf(refute_0_1674,plain,
( join(A,one) != join(join(A,one),join(one,join(one,one)))
| join(join(A,one),join(one,join(one,one))) != join(one,join(one,join(one,join(A,one))))
| join(A,one) = join(one,join(one,join(one,join(A,one)))) ),
introduced(tautology,[equality,[$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_1675,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( $equal(join(join(A,one),join(one,join(one,one))),join(one,join(one,join(one,join(A,one))))) )],[refute_0_1673,refute_0_1674]) ).
cnf(refute_0_1676,plain,
join(A,one) = join(one,join(one,join(one,join(A,one)))),
inference(resolve,[$cnf( $equal(join(A,one),join(join(A,one),join(one,join(one,one)))) )],[refute_0_1635,refute_0_1675]) ).
cnf(refute_0_1677,plain,
join(one,join(meet(complement(one),join(one,join(one,one))),C)) = join(join(one,meet(complement(one),join(one,join(one,one)))),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(one)),bind(B,$fot(meet(complement(one),join(one,join(one,one)))))]]) ).
cnf(refute_0_1678,plain,
X_50 = join(meet(X_50,X_49),meet(X_50,complement(X_49))),
inference(subst,[],[refute_0_58:[bind(B,$fot(X_49)),bind(X_35,$fot(X_50))]]) ).
cnf(refute_0_1679,plain,
meet(X_49,X_50) = meet(X_50,X_49),
inference(subst,[],[refute_0_353:[bind(X_14,$fot(X_49)),bind(X_15,$fot(X_50))]]) ).
cnf(refute_0_1680,plain,
( meet(X_49,X_50) != meet(X_50,X_49)
| meet(X_50,X_49) = meet(X_49,X_50) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_49,X_50))),bind(Y,$fot(meet(X_50,X_49)))]]) ).
cnf(refute_0_1681,plain,
meet(X_50,X_49) = meet(X_49,X_50),
inference(resolve,[$cnf( $equal(meet(X_49,X_50),meet(X_50,X_49)) )],[refute_0_1679,refute_0_1680]) ).
cnf(refute_0_1682,plain,
( X_50 != join(meet(X_50,X_49),meet(X_50,complement(X_49)))
| meet(X_50,X_49) != meet(X_49,X_50)
| X_50 = join(meet(X_49,X_50),meet(X_50,complement(X_49))) ),
introduced(tautology,[equality,[$cnf( $equal(X_50,join(meet(X_50,X_49),meet(X_50,complement(X_49)))) ),[1,0],$fot(meet(X_49,X_50))]]) ).
cnf(refute_0_1683,plain,
( X_50 != join(meet(X_50,X_49),meet(X_50,complement(X_49)))
| X_50 = join(meet(X_49,X_50),meet(X_50,complement(X_49))) ),
inference(resolve,[$cnf( $equal(meet(X_50,X_49),meet(X_49,X_50)) )],[refute_0_1681,refute_0_1682]) ).
cnf(refute_0_1684,plain,
X_50 = join(meet(X_49,X_50),meet(X_50,complement(X_49))),
inference(resolve,[$cnf( $equal(X_50,join(meet(X_50,X_49),meet(X_50,complement(X_49)))) )],[refute_0_1678,refute_0_1683]) ).
cnf(refute_0_1685,plain,
X_76 = join(meet(X_75,X_76),meet(X_76,complement(X_75))),
inference(subst,[],[refute_0_1684:[bind(X_49,$fot(X_75)),bind(X_50,$fot(X_76))]]) ).
cnf(refute_0_1686,plain,
meet(complement(X_75),X_76) = meet(X_76,complement(X_75)),
inference(subst,[],[refute_0_353:[bind(X_14,$fot(complement(X_75))),bind(X_15,$fot(X_76))]]) ).
cnf(refute_0_1687,plain,
( meet(complement(X_75),X_76) != meet(X_76,complement(X_75))
| meet(X_76,complement(X_75)) = meet(complement(X_75),X_76) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_75),X_76))),bind(Y,$fot(meet(X_76,complement(X_75))))]]) ).
cnf(refute_0_1688,plain,
meet(X_76,complement(X_75)) = meet(complement(X_75),X_76),
inference(resolve,[$cnf( $equal(meet(complement(X_75),X_76),meet(X_76,complement(X_75))) )],[refute_0_1686,refute_0_1687]) ).
cnf(refute_0_1689,plain,
( X_76 != join(meet(X_75,X_76),meet(X_76,complement(X_75)))
| meet(X_76,complement(X_75)) != meet(complement(X_75),X_76)
| X_76 = join(meet(X_75,X_76),meet(complement(X_75),X_76)) ),
introduced(tautology,[equality,[$cnf( $equal(X_76,join(meet(X_75,X_76),meet(X_76,complement(X_75)))) ),[1,1],$fot(meet(complement(X_75),X_76))]]) ).
cnf(refute_0_1690,plain,
( X_76 != join(meet(X_75,X_76),meet(X_76,complement(X_75)))
| X_76 = join(meet(X_75,X_76),meet(complement(X_75),X_76)) ),
inference(resolve,[$cnf( $equal(meet(X_76,complement(X_75)),meet(complement(X_75),X_76)) )],[refute_0_1688,refute_0_1689]) ).
cnf(refute_0_1691,plain,
X_76 = join(meet(X_75,X_76),meet(complement(X_75),X_76)),
inference(resolve,[$cnf( $equal(X_76,join(meet(X_75,X_76),meet(X_76,complement(X_75)))) )],[refute_0_1685,refute_0_1690]) ).
cnf(refute_0_1692,plain,
join(one,join(one,one)) = join(meet(one,join(one,join(one,one))),meet(complement(one),join(one,join(one,one)))),
inference(subst,[],[refute_0_1691:[bind(X_75,$fot(one)),bind(X_76,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_1693,plain,
meet(one,join(one,join(one,one))) = complement(complement(meet(one,join(one,join(one,one))))),
inference(subst,[],[refute_0_678:[bind(X_35,$fot(meet(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_1694,plain,
join(complement(one),composition(converse(join(one,join(one,one))),complement(join(one,join(one,one))))) = complement(one),
inference(subst,[],[refute_0_1549:[bind(X_31,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_1695,plain,
( converse(join(one,join(one,one))) != join(one,join(one,one))
| join(complement(one),composition(converse(join(one,join(one,one))),complement(join(one,join(one,one))))) != complement(one)
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(join(one,join(one,one))),complement(join(one,join(one,one))))),complement(one)) ),[0,1,0],$fot(join(one,join(one,one)))]]) ).
cnf(refute_0_1696,plain,
( join(complement(one),composition(converse(join(one,join(one,one))),complement(join(one,join(one,one))))) != complement(one)
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = complement(one) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,one))),join(one,join(one,one))) )],[refute_0_1601,refute_0_1695]) ).
cnf(refute_0_1697,plain,
join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(join(one,join(one,one))),complement(join(one,join(one,one))))),complement(one)) )],[refute_0_1694,refute_0_1696]) ).
cnf(refute_0_1698,plain,
join(complement(one),complement(join(one,join(one,one)))) = complement(meet(one,join(one,join(one,one)))),
inference(subst,[],[refute_0_613:[bind(A,$fot(one)),bind(B,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_1699,plain,
join(complement(B),composition(converse(join(one,one)),complement(composition(join(one,one),B)))) = complement(B),
inference(subst,[],[refute_0_8:[bind(A,$fot(join(one,one)))]]) ).
cnf(refute_0_1700,plain,
composition(join(one,one),B) = join(B,B),
inference(subst,[],[refute_0_1437:[bind(X_101,$fot(B))]]) ).
cnf(refute_0_1701,plain,
( composition(join(one,one),B) != join(B,B)
| join(complement(B),composition(converse(join(one,one)),complement(composition(join(one,one),B)))) != complement(B)
| join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) = complement(B) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(B),composition(converse(join(one,one)),complement(composition(join(one,one),B)))),complement(B)) ),[0,1,1,0],$fot(join(B,B))]]) ).
cnf(refute_0_1702,plain,
( join(complement(B),composition(converse(join(one,one)),complement(composition(join(one,one),B)))) != complement(B)
| join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) = complement(B) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),B),join(B,B)) )],[refute_0_1700,refute_0_1701]) ).
cnf(refute_0_1703,plain,
join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(complement(B),composition(converse(join(one,one)),complement(composition(join(one,one),B)))),complement(B)) )],[refute_0_1699,refute_0_1702]) ).
cnf(refute_0_1704,plain,
composition(join(join(one,one),one),complement(B)) = composition(join(one,join(one,one)),complement(B)),
inference(subst,[],[refute_0_1054:[bind(X_101,$fot(complement(B))),bind(X_102,$fot(join(one,one)))]]) ).
cnf(refute_0_1705,plain,
join(complement(B),composition(join(one,one),complement(B))) = composition(join(join(one,one),one),complement(B)),
inference(subst,[],[refute_0_1048:[bind(X_100,$fot(complement(B))),bind(X_98,$fot(join(one,one)))]]) ).
cnf(refute_0_1706,plain,
( composition(join(join(one,one),one),complement(B)) != composition(join(one,join(one,one)),complement(B))
| join(complement(B),composition(join(one,one),complement(B))) != composition(join(join(one,one),one),complement(B))
| join(complement(B),composition(join(one,one),complement(B))) = composition(join(one,join(one,one)),complement(B)) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(B),composition(join(one,one),complement(B))))),bind(Y,$fot(composition(join(join(one,one),one),complement(B)))),bind(Z,$fot(composition(join(one,join(one,one)),complement(B))))]]) ).
cnf(refute_0_1707,plain,
( composition(join(join(one,one),one),complement(B)) != composition(join(one,join(one,one)),complement(B))
| join(complement(B),composition(join(one,one),complement(B))) = composition(join(one,join(one,one)),complement(B)) ),
inference(resolve,[$cnf( $equal(join(complement(B),composition(join(one,one),complement(B))),composition(join(join(one,one),one),complement(B))) )],[refute_0_1705,refute_0_1706]) ).
cnf(refute_0_1708,plain,
join(complement(B),composition(join(one,one),complement(B))) = composition(join(one,join(one,one)),complement(B)),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),complement(B)),composition(join(one,join(one,one)),complement(B))) )],[refute_0_1704,refute_0_1707]) ).
cnf(refute_0_1709,plain,
complement(join(B,B)) = complement(B),
inference(subst,[],[refute_0_1007:[bind(X_60,$fot(B))]]) ).
cnf(refute_0_1710,plain,
composition(join(one,one),complement(join(B,B))) = composition(join(one,one),complement(join(B,B))),
introduced(tautology,[refl,[$fot(composition(join(one,one),complement(join(B,B))))]]) ).
cnf(refute_0_1711,plain,
( complement(join(B,B)) != complement(B)
| composition(join(one,one),complement(join(B,B))) != composition(join(one,one),complement(join(B,B)))
| composition(join(one,one),complement(join(B,B))) = composition(join(one,one),complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),complement(join(B,B))),composition(join(one,one),complement(join(B,B)))) ),[1,1],$fot(complement(B))]]) ).
cnf(refute_0_1712,plain,
( complement(join(B,B)) != complement(B)
| composition(join(one,one),complement(join(B,B))) = composition(join(one,one),complement(B)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(join(B,B))),composition(join(one,one),complement(join(B,B)))) )],[refute_0_1710,refute_0_1711]) ).
cnf(refute_0_1713,plain,
composition(join(one,one),complement(join(B,B))) = composition(join(one,one),complement(B)),
inference(resolve,[$cnf( $equal(complement(join(B,B)),complement(B)) )],[refute_0_1709,refute_0_1712]) ).
cnf(refute_0_1714,plain,
composition(converse(join(one,one)),complement(join(B,B))) = composition(converse(join(one,one)),complement(join(B,B))),
introduced(tautology,[refl,[$fot(composition(converse(join(one,one)),complement(join(B,B))))]]) ).
cnf(refute_0_1715,plain,
( composition(converse(join(one,one)),complement(join(B,B))) != composition(converse(join(one,one)),complement(join(B,B)))
| converse(join(one,one)) != join(one,one)
| composition(converse(join(one,one)),complement(join(B,B))) = composition(join(one,one),complement(join(B,B))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(one,one)),complement(join(B,B))),composition(converse(join(one,one)),complement(join(B,B)))) ),[1,0],$fot(join(one,one))]]) ).
cnf(refute_0_1716,plain,
( converse(join(one,one)) != join(one,one)
| composition(converse(join(one,one)),complement(join(B,B))) = composition(join(one,one),complement(join(B,B))) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,one)),complement(join(B,B))),composition(converse(join(one,one)),complement(join(B,B)))) )],[refute_0_1714,refute_0_1715]) ).
cnf(refute_0_1717,plain,
composition(converse(join(one,one)),complement(join(B,B))) = composition(join(one,one),complement(join(B,B))),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_959,refute_0_1716]) ).
cnf(refute_0_1718,plain,
( composition(converse(join(one,one)),complement(join(B,B))) != composition(join(one,one),complement(join(B,B)))
| composition(join(one,one),complement(join(B,B))) != composition(join(one,one),complement(B))
| composition(converse(join(one,one)),complement(join(B,B))) = composition(join(one,one),complement(B)) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(composition(converse(join(one,one)),complement(join(B,B))))),bind(Y,$fot(composition(join(one,one),complement(join(B,B))))),bind(Z,$fot(composition(join(one,one),complement(B))))]]) ).
cnf(refute_0_1719,plain,
( composition(join(one,one),complement(join(B,B))) != composition(join(one,one),complement(B))
| composition(converse(join(one,one)),complement(join(B,B))) = composition(join(one,one),complement(B)) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,one)),complement(join(B,B))),composition(join(one,one),complement(join(B,B)))) )],[refute_0_1717,refute_0_1718]) ).
cnf(refute_0_1720,plain,
composition(converse(join(one,one)),complement(join(B,B))) = composition(join(one,one),complement(B)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(join(B,B))),composition(join(one,one),complement(B))) )],[refute_0_1713,refute_0_1719]) ).
cnf(refute_0_1721,plain,
join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) = join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))),
introduced(tautology,[refl,[$fot(join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))))]]) ).
cnf(refute_0_1722,plain,
( composition(converse(join(one,one)),complement(join(B,B))) != composition(join(one,one),complement(B))
| join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) != join(complement(B),composition(converse(join(one,one)),complement(join(B,B))))
| join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) = join(complement(B),composition(join(one,one),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))),join(complement(B),composition(converse(join(one,one)),complement(join(B,B))))) ),[1,1],$fot(composition(join(one,one),complement(B)))]]) ).
cnf(refute_0_1723,plain,
( composition(converse(join(one,one)),complement(join(B,B))) != composition(join(one,one),complement(B))
| join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) = join(complement(B),composition(join(one,one),complement(B))) ),
inference(resolve,[$cnf( $equal(join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))),join(complement(B),composition(converse(join(one,one)),complement(join(B,B))))) )],[refute_0_1721,refute_0_1722]) ).
cnf(refute_0_1724,plain,
join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) = join(complement(B),composition(join(one,one),complement(B))),
inference(resolve,[$cnf( $equal(composition(converse(join(one,one)),complement(join(B,B))),composition(join(one,one),complement(B))) )],[refute_0_1720,refute_0_1723]) ).
cnf(refute_0_1725,plain,
( join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) != join(complement(B),composition(join(one,one),complement(B)))
| join(complement(B),composition(join(one,one),complement(B))) != composition(join(one,join(one,one)),complement(B))
| join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) = composition(join(one,join(one,one)),complement(B)) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))))),bind(Y,$fot(join(complement(B),composition(join(one,one),complement(B))))),bind(Z,$fot(composition(join(one,join(one,one)),complement(B))))]]) ).
cnf(refute_0_1726,plain,
( join(complement(B),composition(join(one,one),complement(B))) != composition(join(one,join(one,one)),complement(B))
| join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) = composition(join(one,join(one,one)),complement(B)) ),
inference(resolve,[$cnf( $equal(join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))),join(complement(B),composition(join(one,one),complement(B)))) )],[refute_0_1724,refute_0_1725]) ).
cnf(refute_0_1727,plain,
join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) = composition(join(one,join(one,one)),complement(B)),
inference(resolve,[$cnf( $equal(join(complement(B),composition(join(one,one),complement(B))),composition(join(one,join(one,one)),complement(B))) )],[refute_0_1708,refute_0_1726]) ).
cnf(refute_0_1728,plain,
( join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) != complement(B)
| join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) != composition(join(one,join(one,one)),complement(B))
| composition(join(one,join(one,one)),complement(B)) = complement(B) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))),complement(B)) ),[0],$fot(composition(join(one,join(one,one)),complement(B)))]]) ).
cnf(refute_0_1729,plain,
( join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))) != complement(B)
| composition(join(one,join(one,one)),complement(B)) = complement(B) ),
inference(resolve,[$cnf( $equal(join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))),composition(join(one,join(one,one)),complement(B))) )],[refute_0_1727,refute_0_1728]) ).
cnf(refute_0_1730,plain,
composition(join(one,join(one,one)),complement(B)) = complement(B),
inference(resolve,[$cnf( $equal(join(complement(B),composition(converse(join(one,one)),complement(join(B,B)))),complement(B)) )],[refute_0_1703,refute_0_1729]) ).
cnf(refute_0_1731,plain,
composition(join(one,join(one,one)),complement(join(one,join(one,one)))) = complement(join(one,join(one,one))),
inference(subst,[],[refute_0_1730:[bind(B,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_1732,plain,
join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),
introduced(tautology,[refl,[$fot(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))))]]) ).
cnf(refute_0_1733,plain,
( composition(join(one,join(one,one)),complement(join(one,join(one,one)))) != complement(join(one,join(one,one)))
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) != join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one)))))
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = join(complement(one),complement(join(one,join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one)))))) ),[1,1],$fot(complement(join(one,join(one,one))))]]) ).
cnf(refute_0_1734,plain,
( composition(join(one,join(one,one)),complement(join(one,join(one,one)))) != complement(join(one,join(one,one)))
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = join(complement(one),complement(join(one,join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one)))))) )],[refute_0_1732,refute_0_1733]) ).
cnf(refute_0_1735,plain,
join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = join(complement(one),complement(join(one,join(one,one)))),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),complement(join(one,join(one,one)))),complement(join(one,join(one,one)))) )],[refute_0_1731,refute_0_1734]) ).
cnf(refute_0_1736,plain,
( join(complement(one),complement(join(one,join(one,one)))) != complement(meet(one,join(one,join(one,one))))
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) != join(complement(one),complement(join(one,join(one,one))))
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = complement(meet(one,join(one,join(one,one)))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))))),bind(Y,$fot(join(complement(one),complement(join(one,join(one,one)))))),bind(Z,$fot(complement(meet(one,join(one,join(one,one))))))]]) ).
cnf(refute_0_1737,plain,
( join(complement(one),complement(join(one,join(one,one)))) != complement(meet(one,join(one,join(one,one))))
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = complement(meet(one,join(one,join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),join(complement(one),complement(join(one,join(one,one))))) )],[refute_0_1735,refute_0_1736]) ).
cnf(refute_0_1738,plain,
join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = complement(meet(one,join(one,join(one,one)))),
inference(resolve,[$cnf( $equal(join(complement(one),complement(join(one,join(one,one)))),complement(meet(one,join(one,join(one,one))))) )],[refute_0_1698,refute_0_1737]) ).
cnf(refute_0_1739,plain,
( join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) != complement(meet(one,join(one,join(one,one))))
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) != complement(one)
| complement(meet(one,join(one,join(one,one)))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),complement(one)) ),[0],$fot(complement(meet(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_1740,plain,
( join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) != complement(one)
| complement(meet(one,join(one,join(one,one)))) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),complement(meet(one,join(one,join(one,one))))) )],[refute_0_1738,refute_0_1739]) ).
cnf(refute_0_1741,plain,
complement(meet(one,join(one,join(one,one)))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),complement(one)) )],[refute_0_1697,refute_0_1740]) ).
cnf(refute_0_1742,plain,
( complement(meet(one,join(one,join(one,one)))) != complement(one)
| meet(one,join(one,join(one,one))) != complement(complement(meet(one,join(one,join(one,one)))))
| meet(one,join(one,join(one,one))) = complement(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,join(one,join(one,one))),complement(complement(meet(one,join(one,join(one,one)))))) ),[1,0],$fot(complement(one))]]) ).
cnf(refute_0_1743,plain,
( meet(one,join(one,join(one,one))) != complement(complement(meet(one,join(one,join(one,one)))))
| meet(one,join(one,join(one,one))) = complement(complement(one)) ),
inference(resolve,[$cnf( $equal(complement(meet(one,join(one,join(one,one)))),complement(one)) )],[refute_0_1741,refute_0_1742]) ).
cnf(refute_0_1744,plain,
meet(one,join(one,join(one,one))) = complement(complement(one)),
inference(resolve,[$cnf( $equal(meet(one,join(one,join(one,one))),complement(complement(meet(one,join(one,join(one,one)))))) )],[refute_0_1693,refute_0_1743]) ).
cnf(refute_0_1745,plain,
( complement(complement(one)) != one
| meet(one,join(one,join(one,one))) != complement(complement(one))
| meet(one,join(one,join(one,one))) = one ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,join(one,join(one,one))),complement(complement(one))) ),[1],$fot(one)]]) ).
cnf(refute_0_1746,plain,
( meet(one,join(one,join(one,one))) != complement(complement(one))
| meet(one,join(one,join(one,one))) = one ),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_1592,refute_0_1745]) ).
cnf(refute_0_1747,plain,
meet(one,join(one,join(one,one))) = one,
inference(resolve,[$cnf( $equal(meet(one,join(one,join(one,one))),complement(complement(one))) )],[refute_0_1744,refute_0_1746]) ).
cnf(refute_0_1748,plain,
( join(one,join(one,one)) != join(meet(one,join(one,join(one,one))),meet(complement(one),join(one,join(one,one))))
| meet(one,join(one,join(one,one))) != one
| join(one,join(one,one)) = join(one,meet(complement(one),join(one,join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,one)),join(meet(one,join(one,join(one,one))),meet(complement(one),join(one,join(one,one))))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1749,plain,
( join(one,join(one,one)) != join(meet(one,join(one,join(one,one))),meet(complement(one),join(one,join(one,one))))
| join(one,join(one,one)) = join(one,meet(complement(one),join(one,join(one,one)))) ),
inference(resolve,[$cnf( $equal(meet(one,join(one,join(one,one))),one) )],[refute_0_1747,refute_0_1748]) ).
cnf(refute_0_1750,plain,
join(one,join(one,one)) = join(one,meet(complement(one),join(one,join(one,one)))),
inference(resolve,[$cnf( $equal(join(one,join(one,one)),join(meet(one,join(one,join(one,one))),meet(complement(one),join(one,join(one,one))))) )],[refute_0_1692,refute_0_1749]) ).
cnf(refute_0_1751,plain,
( join(one,join(one,one)) != join(one,meet(complement(one),join(one,join(one,one))))
| join(one,meet(complement(one),join(one,join(one,one)))) = join(one,join(one,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,join(one,one)))),bind(Y,$fot(join(one,meet(complement(one),join(one,join(one,one))))))]]) ).
cnf(refute_0_1752,plain,
join(one,meet(complement(one),join(one,join(one,one)))) = join(one,join(one,one)),
inference(resolve,[$cnf( $equal(join(one,join(one,one)),join(one,meet(complement(one),join(one,join(one,one))))) )],[refute_0_1750,refute_0_1751]) ).
cnf(refute_0_1753,plain,
( join(one,join(meet(complement(one),join(one,join(one,one))),C)) != join(join(one,meet(complement(one),join(one,join(one,one)))),C)
| join(one,meet(complement(one),join(one,join(one,one)))) != join(one,join(one,one))
| join(one,join(meet(complement(one),join(one,join(one,one))),C)) = join(join(one,join(one,one)),C) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(meet(complement(one),join(one,join(one,one))),C)),join(join(one,meet(complement(one),join(one,join(one,one)))),C)) ),[1,0],$fot(join(one,join(one,one)))]]) ).
cnf(refute_0_1754,plain,
( join(one,join(meet(complement(one),join(one,join(one,one))),C)) != join(join(one,meet(complement(one),join(one,join(one,one)))),C)
| join(one,join(meet(complement(one),join(one,join(one,one))),C)) = join(join(one,join(one,one)),C) ),
inference(resolve,[$cnf( $equal(join(one,meet(complement(one),join(one,join(one,one)))),join(one,join(one,one))) )],[refute_0_1752,refute_0_1753]) ).
cnf(refute_0_1755,plain,
join(one,join(meet(complement(one),join(one,join(one,one))),C)) = join(join(one,join(one,one)),C),
inference(resolve,[$cnf( $equal(join(one,join(meet(complement(one),join(one,join(one,one))),C)),join(join(one,meet(complement(one),join(one,join(one,one)))),C)) )],[refute_0_1677,refute_0_1754]) ).
cnf(refute_0_1756,plain,
join(join(one,one),C) = join(one,join(one,C)),
inference(subst,[],[refute_0_205:[bind(A,$fot(one)),bind(B,$fot(one))]]) ).
cnf(refute_0_1757,plain,
join(one,join(join(one,one),C)) = join(one,join(join(one,one),C)),
introduced(tautology,[refl,[$fot(join(one,join(join(one,one),C)))]]) ).
cnf(refute_0_1758,plain,
( join(join(one,one),C) != join(one,join(one,C))
| join(one,join(join(one,one),C)) != join(one,join(join(one,one),C))
| join(one,join(join(one,one),C)) = join(one,join(one,join(one,C))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,one),C)),join(one,join(join(one,one),C))) ),[1,1],$fot(join(one,join(one,C)))]]) ).
cnf(refute_0_1759,plain,
( join(join(one,one),C) != join(one,join(one,C))
| join(one,join(join(one,one),C)) = join(one,join(one,join(one,C))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,one),C)),join(one,join(join(one,one),C))) )],[refute_0_1757,refute_0_1758]) ).
cnf(refute_0_1760,plain,
join(one,join(join(one,one),C)) = join(one,join(one,join(one,C))),
inference(resolve,[$cnf( $equal(join(join(one,one),C),join(one,join(one,C))) )],[refute_0_1756,refute_0_1759]) ).
cnf(refute_0_1761,plain,
join(join(one,join(one,one)),C) = join(one,join(join(one,one),C)),
inference(subst,[],[refute_0_205:[bind(A,$fot(one)),bind(B,$fot(join(one,one)))]]) ).
cnf(refute_0_1762,plain,
( join(join(one,join(one,one)),C) != join(one,join(join(one,one),C))
| join(one,join(join(one,one),C)) != join(one,join(one,join(one,C)))
| join(join(one,join(one,one)),C) = join(one,join(one,join(one,C))) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(join(one,join(one,one)),C))),bind(Y,$fot(join(one,join(join(one,one),C)))),bind(Z,$fot(join(one,join(one,join(one,C)))))]]) ).
cnf(refute_0_1763,plain,
( join(one,join(join(one,one),C)) != join(one,join(one,join(one,C)))
| join(join(one,join(one,one)),C) = join(one,join(one,join(one,C))) ),
inference(resolve,[$cnf( $equal(join(join(one,join(one,one)),C),join(one,join(join(one,one),C))) )],[refute_0_1761,refute_0_1762]) ).
cnf(refute_0_1764,plain,
join(join(one,join(one,one)),C) = join(one,join(one,join(one,C))),
inference(resolve,[$cnf( $equal(join(one,join(join(one,one),C)),join(one,join(one,join(one,C)))) )],[refute_0_1760,refute_0_1763]) ).
cnf(refute_0_1765,plain,
( join(join(one,join(one,one)),C) != join(one,join(one,join(one,C)))
| join(one,join(meet(complement(one),join(one,join(one,one))),C)) != join(join(one,join(one,one)),C)
| join(one,join(meet(complement(one),join(one,join(one,one))),C)) = join(one,join(one,join(one,C))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(meet(complement(one),join(one,join(one,one))),C)),join(join(one,join(one,one)),C)) ),[1],$fot(join(one,join(one,join(one,C))))]]) ).
cnf(refute_0_1766,plain,
( join(one,join(meet(complement(one),join(one,join(one,one))),C)) != join(join(one,join(one,one)),C)
| join(one,join(meet(complement(one),join(one,join(one,one))),C)) = join(one,join(one,join(one,C))) ),
inference(resolve,[$cnf( $equal(join(join(one,join(one,one)),C),join(one,join(one,join(one,C)))) )],[refute_0_1764,refute_0_1765]) ).
cnf(refute_0_1767,plain,
join(one,join(meet(complement(one),join(one,join(one,one))),C)) = join(one,join(one,join(one,C))),
inference(resolve,[$cnf( $equal(join(one,join(meet(complement(one),join(one,join(one,one))),C)),join(join(one,join(one,one)),C)) )],[refute_0_1755,refute_0_1766]) ).
cnf(refute_0_1768,plain,
join(zero,C) = C,
inference(subst,[],[refute_0_701:[bind(X_35,$fot(C))]]) ).
cnf(refute_0_1769,plain,
meet(one,complement(one)) = zero,
inference(subst,[],[refute_0_302:[bind(A,$fot(one))]]) ).
cnf(refute_0_1770,plain,
meet(complement(one),one) = meet(one,complement(one)),
inference(subst,[],[refute_0_355:[bind(X_14,$fot(one)),bind(X_15,$fot(complement(one)))]]) ).
cnf(refute_0_1771,plain,
( meet(complement(one),one) != meet(one,complement(one))
| meet(one,complement(one)) != zero
| meet(complement(one),one) = zero ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(complement(one),one))),bind(Y,$fot(meet(one,complement(one)))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1772,plain,
( meet(one,complement(one)) != zero
| meet(complement(one),one) = zero ),
inference(resolve,[$cnf( $equal(meet(complement(one),one),meet(one,complement(one))) )],[refute_0_1770,refute_0_1771]) ).
cnf(refute_0_1773,plain,
meet(complement(one),one) = zero,
inference(resolve,[$cnf( $equal(meet(one,complement(one)),zero) )],[refute_0_1769,refute_0_1772]) ).
cnf(refute_0_1774,plain,
( X_100 != join(X_100,join(X_100,X_100))
| join(X_100,join(X_100,X_100)) = X_100 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_100)),bind(Y,$fot(join(X_100,join(X_100,X_100))))]]) ).
cnf(refute_0_1775,plain,
join(X_100,join(X_100,X_100)) = X_100,
inference(resolve,[$cnf( $equal(X_100,join(X_100,join(X_100,X_100))) )],[refute_0_1508,refute_0_1774]) ).
cnf(refute_0_1776,plain,
join(one,join(one,one)) = one,
inference(subst,[],[refute_0_1775:[bind(X_100,$fot(one))]]) ).
cnf(refute_0_1777,plain,
meet(complement(one),join(one,join(one,one))) = meet(complement(one),join(one,join(one,one))),
introduced(tautology,[refl,[$fot(meet(complement(one),join(one,join(one,one))))]]) ).
cnf(refute_0_1778,plain,
( join(one,join(one,one)) != one
| meet(complement(one),join(one,join(one,one))) != meet(complement(one),join(one,join(one,one)))
| meet(complement(one),join(one,join(one,one))) = meet(complement(one),one) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(one),join(one,join(one,one))),meet(complement(one),join(one,join(one,one)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1779,plain,
( join(one,join(one,one)) != one
| meet(complement(one),join(one,join(one,one))) = meet(complement(one),one) ),
inference(resolve,[$cnf( $equal(meet(complement(one),join(one,join(one,one))),meet(complement(one),join(one,join(one,one)))) )],[refute_0_1777,refute_0_1778]) ).
cnf(refute_0_1780,plain,
meet(complement(one),join(one,join(one,one))) = meet(complement(one),one),
inference(resolve,[$cnf( $equal(join(one,join(one,one)),one) )],[refute_0_1776,refute_0_1779]) ).
cnf(refute_0_1781,plain,
( meet(complement(one),join(one,join(one,one))) != meet(complement(one),one)
| meet(complement(one),one) != zero
| meet(complement(one),join(one,join(one,one))) = zero ),
inference(subst,[],[refute_0_41:[bind(X,$fot(meet(complement(one),join(one,join(one,one))))),bind(Y,$fot(meet(complement(one),one))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1782,plain,
( meet(complement(one),one) != zero
| meet(complement(one),join(one,join(one,one))) = zero ),
inference(resolve,[$cnf( $equal(meet(complement(one),join(one,join(one,one))),meet(complement(one),one)) )],[refute_0_1780,refute_0_1781]) ).
cnf(refute_0_1783,plain,
meet(complement(one),join(one,join(one,one))) = zero,
inference(resolve,[$cnf( $equal(meet(complement(one),one),zero) )],[refute_0_1773,refute_0_1782]) ).
cnf(refute_0_1784,plain,
join(meet(complement(one),join(one,join(one,one))),C) = join(meet(complement(one),join(one,join(one,one))),C),
introduced(tautology,[refl,[$fot(join(meet(complement(one),join(one,join(one,one))),C))]]) ).
cnf(refute_0_1785,plain,
( join(meet(complement(one),join(one,join(one,one))),C) != join(meet(complement(one),join(one,join(one,one))),C)
| meet(complement(one),join(one,join(one,one))) != zero
| join(meet(complement(one),join(one,join(one,one))),C) = join(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(complement(one),join(one,join(one,one))),C),join(meet(complement(one),join(one,join(one,one))),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1786,plain,
( meet(complement(one),join(one,join(one,one))) != zero
| join(meet(complement(one),join(one,join(one,one))),C) = join(zero,C) ),
inference(resolve,[$cnf( $equal(join(meet(complement(one),join(one,join(one,one))),C),join(meet(complement(one),join(one,join(one,one))),C)) )],[refute_0_1784,refute_0_1785]) ).
cnf(refute_0_1787,plain,
join(meet(complement(one),join(one,join(one,one))),C) = join(zero,C),
inference(resolve,[$cnf( $equal(meet(complement(one),join(one,join(one,one))),zero) )],[refute_0_1783,refute_0_1786]) ).
cnf(refute_0_1788,plain,
( join(meet(complement(one),join(one,join(one,one))),C) != join(zero,C)
| join(zero,C) != C
| join(meet(complement(one),join(one,join(one,one))),C) = C ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(meet(complement(one),join(one,join(one,one))),C))),bind(Y,$fot(join(zero,C))),bind(Z,$fot(C))]]) ).
cnf(refute_0_1789,plain,
( join(zero,C) != C
| join(meet(complement(one),join(one,join(one,one))),C) = C ),
inference(resolve,[$cnf( $equal(join(meet(complement(one),join(one,join(one,one))),C),join(zero,C)) )],[refute_0_1787,refute_0_1788]) ).
cnf(refute_0_1790,plain,
join(meet(complement(one),join(one,join(one,one))),C) = C,
inference(resolve,[$cnf( $equal(join(zero,C),C) )],[refute_0_1768,refute_0_1789]) ).
cnf(refute_0_1791,plain,
join(one,join(meet(complement(one),join(one,join(one,one))),C)) = join(one,join(meet(complement(one),join(one,join(one,one))),C)),
introduced(tautology,[refl,[$fot(join(one,join(meet(complement(one),join(one,join(one,one))),C)))]]) ).
cnf(refute_0_1792,plain,
( join(meet(complement(one),join(one,join(one,one))),C) != C
| join(one,join(meet(complement(one),join(one,join(one,one))),C)) != join(one,join(meet(complement(one),join(one,join(one,one))),C))
| join(one,join(meet(complement(one),join(one,join(one,one))),C)) = join(one,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(meet(complement(one),join(one,join(one,one))),C)),join(one,join(meet(complement(one),join(one,join(one,one))),C))) ),[1,1],$fot(C)]]) ).
cnf(refute_0_1793,plain,
( join(meet(complement(one),join(one,join(one,one))),C) != C
| join(one,join(meet(complement(one),join(one,join(one,one))),C)) = join(one,C) ),
inference(resolve,[$cnf( $equal(join(one,join(meet(complement(one),join(one,join(one,one))),C)),join(one,join(meet(complement(one),join(one,join(one,one))),C))) )],[refute_0_1791,refute_0_1792]) ).
cnf(refute_0_1794,plain,
join(one,join(meet(complement(one),join(one,join(one,one))),C)) = join(one,C),
inference(resolve,[$cnf( $equal(join(meet(complement(one),join(one,join(one,one))),C),C) )],[refute_0_1790,refute_0_1793]) ).
cnf(refute_0_1795,plain,
( join(one,join(meet(complement(one),join(one,join(one,one))),C)) != join(one,C)
| join(one,join(meet(complement(one),join(one,join(one,one))),C)) != join(one,join(one,join(one,C)))
| join(one,C) = join(one,join(one,join(one,C))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(meet(complement(one),join(one,join(one,one))),C)),join(one,join(one,join(one,C)))) ),[0],$fot(join(one,C))]]) ).
cnf(refute_0_1796,plain,
( join(one,join(meet(complement(one),join(one,join(one,one))),C)) != join(one,join(one,join(one,C)))
| join(one,C) = join(one,join(one,join(one,C))) ),
inference(resolve,[$cnf( $equal(join(one,join(meet(complement(one),join(one,join(one,one))),C)),join(one,C)) )],[refute_0_1794,refute_0_1795]) ).
cnf(refute_0_1797,plain,
join(one,C) = join(one,join(one,join(one,C))),
inference(resolve,[$cnf( $equal(join(one,join(meet(complement(one),join(one,join(one,one))),C)),join(one,join(one,join(one,C)))) )],[refute_0_1767,refute_0_1796]) ).
cnf(refute_0_1798,plain,
( join(one,C) != join(one,join(one,join(one,C)))
| join(one,join(one,join(one,C))) = join(one,C) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,C))),bind(Y,$fot(join(one,join(one,join(one,C)))))]]) ).
cnf(refute_0_1799,plain,
join(one,join(one,join(one,C))) = join(one,C),
inference(resolve,[$cnf( $equal(join(one,C),join(one,join(one,join(one,C)))) )],[refute_0_1797,refute_0_1798]) ).
cnf(refute_0_1800,plain,
join(one,join(one,join(one,join(A,one)))) = join(one,join(A,one)),
inference(subst,[],[refute_0_1799:[bind(C,$fot(join(A,one)))]]) ).
cnf(refute_0_1801,plain,
( join(A,one) != join(one,join(one,join(one,join(A,one))))
| join(one,join(one,join(one,join(A,one)))) != join(one,join(A,one))
| join(A,one) = join(one,join(A,one)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,one),join(one,join(A,one))) ),[0],$fot(join(one,join(one,join(one,join(A,one)))))]]) ).
cnf(refute_0_1802,plain,
( join(A,one) != join(one,join(one,join(one,join(A,one))))
| join(A,one) = join(one,join(A,one)) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,join(A,one)))),join(one,join(A,one))) )],[refute_0_1800,refute_0_1801]) ).
cnf(refute_0_1803,plain,
join(A,one) = join(one,join(A,one)),
inference(resolve,[$cnf( $equal(join(A,one),join(one,join(one,join(one,join(A,one))))) )],[refute_0_1676,refute_0_1802]) ).
cnf(refute_0_1804,plain,
join(zero,one) = join(one,join(zero,one)),
inference(subst,[],[refute_0_1803:[bind(A,$fot(zero))]]) ).
cnf(refute_0_1805,plain,
one = join(zero,one),
inference(subst,[],[refute_0_699:[bind(X_35,$fot(one))]]) ).
cnf(refute_0_1806,plain,
( one != join(zero,one)
| join(zero,one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(join(zero,one)))]]) ).
cnf(refute_0_1807,plain,
join(zero,one) = one,
inference(resolve,[$cnf( $equal(one,join(zero,one)) )],[refute_0_1805,refute_0_1806]) ).
cnf(refute_0_1808,plain,
( join(zero,one) != join(one,join(zero,one))
| join(zero,one) != one
| join(zero,one) = join(one,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,one),join(one,join(zero,one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1809,plain,
( join(zero,one) != join(one,join(zero,one))
| join(zero,one) = join(one,one) ),
inference(resolve,[$cnf( $equal(join(zero,one),one) )],[refute_0_1807,refute_0_1808]) ).
cnf(refute_0_1810,plain,
join(zero,one) = join(one,one),
inference(resolve,[$cnf( $equal(join(zero,one),join(one,join(zero,one))) )],[refute_0_1804,refute_0_1809]) ).
cnf(refute_0_1811,plain,
( join(zero,one) != join(one,one)
| join(zero,one) != one
| one = join(one,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,one),join(one,one)) ),[0],$fot(one)]]) ).
cnf(refute_0_1812,plain,
( join(zero,one) != join(one,one)
| one = join(one,one) ),
inference(resolve,[$cnf( $equal(join(zero,one),one) )],[refute_0_1807,refute_0_1811]) ).
cnf(refute_0_1813,plain,
one = join(one,one),
inference(resolve,[$cnf( $equal(join(zero,one),join(one,one)) )],[refute_0_1810,refute_0_1812]) ).
cnf(refute_0_1814,plain,
( one != join(one,one)
| join(one,one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(join(one,one)))]]) ).
cnf(refute_0_1815,plain,
join(one,one) = one,
inference(resolve,[$cnf( $equal(one,join(one,one)) )],[refute_0_1813,refute_0_1814]) ).
cnf(refute_0_1816,plain,
composition(join(A,B),join(one,one)) = composition(join(A,B),join(one,one)),
introduced(tautology,[refl,[$fot(composition(join(A,B),join(one,one)))]]) ).
cnf(refute_0_1817,plain,
( composition(join(A,B),join(one,one)) != composition(join(A,B),join(one,one))
| join(one,one) != one
| composition(join(A,B),join(one,one)) = composition(join(A,B),one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(A,B),join(one,one)),composition(join(A,B),join(one,one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1818,plain,
( join(one,one) != one
| composition(join(A,B),join(one,one)) = composition(join(A,B),one) ),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),composition(join(A,B),join(one,one))) )],[refute_0_1816,refute_0_1817]) ).
cnf(refute_0_1819,plain,
composition(join(A,B),join(one,one)) = composition(join(A,B),one),
inference(resolve,[$cnf( $equal(join(one,one),one) )],[refute_0_1815,refute_0_1818]) ).
cnf(refute_0_1820,plain,
( composition(join(A,B),join(one,one)) != composition(join(A,B),one)
| composition(join(A,B),one) != join(A,B)
| composition(join(A,B),join(one,one)) = join(A,B) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(composition(join(A,B),join(one,one)))),bind(Y,$fot(composition(join(A,B),one))),bind(Z,$fot(join(A,B)))]]) ).
cnf(refute_0_1821,plain,
( composition(join(A,B),one) != join(A,B)
| composition(join(A,B),join(one,one)) = join(A,B) ),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),composition(join(A,B),one)) )],[refute_0_1819,refute_0_1820]) ).
cnf(refute_0_1822,plain,
composition(join(A,B),join(one,one)) = join(A,B),
inference(resolve,[$cnf( $equal(composition(join(A,B),one),join(A,B)) )],[refute_0_1542,refute_0_1821]) ).
cnf(refute_0_1823,plain,
( composition(join(A,B),join(one,one)) != join(A,B)
| composition(join(A,B),join(one,one)) != join(A,join(A,composition(B,join(one,one))))
| join(A,B) = join(A,join(A,composition(B,join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(A,B),join(one,one)),join(A,join(A,composition(B,join(one,one))))) ),[0],$fot(join(A,B))]]) ).
cnf(refute_0_1824,plain,
( composition(join(A,B),join(one,one)) != join(A,join(A,composition(B,join(one,one))))
| join(A,B) = join(A,join(A,composition(B,join(one,one)))) ),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),join(A,B)) )],[refute_0_1822,refute_0_1823]) ).
cnf(refute_0_1825,plain,
composition(B,one) = B,
inference(subst,[],[composition_identity_6:[bind(A,$fot(B))]]) ).
cnf(refute_0_1826,plain,
composition(B,join(one,one)) = composition(B,join(one,one)),
introduced(tautology,[refl,[$fot(composition(B,join(one,one)))]]) ).
cnf(refute_0_1827,plain,
( composition(B,join(one,one)) != composition(B,join(one,one))
| join(one,one) != one
| composition(B,join(one,one)) = composition(B,one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(B,join(one,one)),composition(B,join(one,one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1828,plain,
( join(one,one) != one
| composition(B,join(one,one)) = composition(B,one) ),
inference(resolve,[$cnf( $equal(composition(B,join(one,one)),composition(B,join(one,one))) )],[refute_0_1826,refute_0_1827]) ).
cnf(refute_0_1829,plain,
composition(B,join(one,one)) = composition(B,one),
inference(resolve,[$cnf( $equal(join(one,one),one) )],[refute_0_1815,refute_0_1828]) ).
cnf(refute_0_1830,plain,
( composition(B,join(one,one)) != composition(B,one)
| composition(B,one) != B
| composition(B,join(one,one)) = B ),
inference(subst,[],[refute_0_41:[bind(X,$fot(composition(B,join(one,one)))),bind(Y,$fot(composition(B,one))),bind(Z,$fot(B))]]) ).
cnf(refute_0_1831,plain,
( composition(B,one) != B
| composition(B,join(one,one)) = B ),
inference(resolve,[$cnf( $equal(composition(B,join(one,one)),composition(B,one)) )],[refute_0_1829,refute_0_1830]) ).
cnf(refute_0_1832,plain,
composition(B,join(one,one)) = B,
inference(resolve,[$cnf( $equal(composition(B,one),B) )],[refute_0_1825,refute_0_1831]) ).
cnf(refute_0_1833,plain,
join(A,composition(B,join(one,one))) = join(A,composition(B,join(one,one))),
introduced(tautology,[refl,[$fot(join(A,composition(B,join(one,one))))]]) ).
cnf(refute_0_1834,plain,
( composition(B,join(one,one)) != B
| join(A,composition(B,join(one,one))) != join(A,composition(B,join(one,one)))
| join(A,composition(B,join(one,one))) = join(A,B) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,composition(B,join(one,one))),join(A,composition(B,join(one,one)))) ),[1,1],$fot(B)]]) ).
cnf(refute_0_1835,plain,
( composition(B,join(one,one)) != B
| join(A,composition(B,join(one,one))) = join(A,B) ),
inference(resolve,[$cnf( $equal(join(A,composition(B,join(one,one))),join(A,composition(B,join(one,one)))) )],[refute_0_1833,refute_0_1834]) ).
cnf(refute_0_1836,plain,
join(A,composition(B,join(one,one))) = join(A,B),
inference(resolve,[$cnf( $equal(composition(B,join(one,one)),B) )],[refute_0_1832,refute_0_1835]) ).
cnf(refute_0_1837,plain,
join(A,join(A,composition(B,join(one,one)))) = join(A,join(A,composition(B,join(one,one)))),
introduced(tautology,[refl,[$fot(join(A,join(A,composition(B,join(one,one)))))]]) ).
cnf(refute_0_1838,plain,
( join(A,composition(B,join(one,one))) != join(A,B)
| join(A,join(A,composition(B,join(one,one)))) != join(A,join(A,composition(B,join(one,one))))
| join(A,join(A,composition(B,join(one,one)))) = join(A,join(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(A,composition(B,join(one,one)))),join(A,join(A,composition(B,join(one,one))))) ),[1,1],$fot(join(A,B))]]) ).
cnf(refute_0_1839,plain,
( join(A,composition(B,join(one,one))) != join(A,B)
| join(A,join(A,composition(B,join(one,one)))) = join(A,join(A,B)) ),
inference(resolve,[$cnf( $equal(join(A,join(A,composition(B,join(one,one)))),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_1837,refute_0_1838]) ).
cnf(refute_0_1840,plain,
join(A,join(A,composition(B,join(one,one)))) = join(A,join(A,B)),
inference(resolve,[$cnf( $equal(join(A,composition(B,join(one,one))),join(A,B)) )],[refute_0_1836,refute_0_1839]) ).
cnf(refute_0_1841,plain,
( join(A,B) != join(A,join(A,composition(B,join(one,one))))
| join(A,join(A,composition(B,join(one,one)))) != join(A,join(A,B))
| join(A,B) = join(A,join(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,B),join(A,join(A,B))) ),[0],$fot(join(A,join(A,composition(B,join(one,one)))))]]) ).
cnf(refute_0_1842,plain,
( join(A,B) != join(A,join(A,composition(B,join(one,one))))
| join(A,B) = join(A,join(A,B)) ),
inference(resolve,[$cnf( $equal(join(A,join(A,composition(B,join(one,one)))),join(A,join(A,B))) )],[refute_0_1840,refute_0_1841]) ).
cnf(refute_0_1843,plain,
( composition(join(A,B),join(one,one)) != join(A,join(A,composition(B,join(one,one))))
| join(A,B) = join(A,join(A,B)) ),
inference(resolve,[$cnf( $equal(join(A,B),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_1824,refute_0_1842]) ).
cnf(refute_0_1844,plain,
join(A,B) = join(A,join(A,B)),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_1541,refute_0_1843]) ).
cnf(refute_0_1845,plain,
( join(A,B) != join(A,join(A,B))
| join(A,join(A,B)) = join(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(A,join(A,B))))]]) ).
cnf(refute_0_1846,plain,
join(A,join(A,B)) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(A,join(A,B))) )],[refute_0_1844,refute_0_1845]) ).
cnf(refute_0_1847,plain,
join(X_100,join(X_100,X_100)) = join(X_100,X_100),
inference(subst,[],[refute_0_1846:[bind(A,$fot(X_100)),bind(B,$fot(X_100))]]) ).
cnf(refute_0_1848,plain,
( X_100 != join(X_100,join(X_100,X_100))
| join(X_100,join(X_100,X_100)) != join(X_100,X_100)
| X_100 = join(X_100,X_100) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_100,join(X_100,X_100)) ),[0],$fot(join(X_100,join(X_100,X_100)))]]) ).
cnf(refute_0_1849,plain,
( X_100 != join(X_100,join(X_100,X_100))
| X_100 = join(X_100,X_100) ),
inference(resolve,[$cnf( $equal(join(X_100,join(X_100,X_100)),join(X_100,X_100)) )],[refute_0_1847,refute_0_1848]) ).
cnf(refute_0_1850,plain,
X_100 = join(X_100,X_100),
inference(resolve,[$cnf( $equal(X_100,join(X_100,join(X_100,X_100))) )],[refute_0_1508,refute_0_1849]) ).
cnf(refute_0_1851,plain,
( X_100 != join(X_100,X_100)
| join(X_100,X_100) = X_100 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_100)),bind(Y,$fot(join(X_100,X_100)))]]) ).
cnf(refute_0_1852,plain,
join(X_100,X_100) = X_100,
inference(resolve,[$cnf( $equal(X_100,join(X_100,X_100)) )],[refute_0_1850,refute_0_1851]) ).
cnf(refute_0_1853,plain,
join(complement(composition(X_670,top)),complement(composition(X_670,top))) = complement(composition(X_670,top)),
inference(subst,[],[refute_0_1852:[bind(X_100,$fot(complement(composition(X_670,top))))]]) ).
cnf(refute_0_1854,plain,
composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top) = composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top),
introduced(tautology,[refl,[$fot(composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top))]]) ).
cnf(refute_0_1855,plain,
( composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top) != composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top)
| join(complement(composition(X_670,top)),complement(composition(X_670,top))) != complement(composition(X_670,top))
| composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top) = composition(complement(composition(X_670,top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top),composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top)) ),[1,0],$fot(complement(composition(X_670,top)))]]) ).
cnf(refute_0_1856,plain,
( join(complement(composition(X_670,top)),complement(composition(X_670,top))) != complement(composition(X_670,top))
| composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top) = composition(complement(composition(X_670,top)),top) ),
inference(resolve,[$cnf( $equal(composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top),composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top)) )],[refute_0_1854,refute_0_1855]) ).
cnf(refute_0_1857,plain,
composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top) = composition(complement(composition(X_670,top)),top),
inference(resolve,[$cnf( $equal(join(complement(composition(X_670,top)),complement(composition(X_670,top))),complement(composition(X_670,top))) )],[refute_0_1853,refute_0_1856]) ).
cnf(refute_0_1858,plain,
composition(join(converse(X_7),X_99),top) = join(composition(converse(X_7),top),composition(X_99,top)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(converse(X_7))),bind(B,$fot(X_99)),bind(C,$fot(top))]]) ).
cnf(refute_0_1859,plain,
( converse(composition(top,X_7)) != composition(converse(X_7),top)
| composition(converse(X_7),top) = converse(composition(top,X_7)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(top,X_7)))),bind(Y,$fot(composition(converse(X_7),top)))]]) ).
cnf(refute_0_1860,plain,
composition(converse(X_7),top) = converse(composition(top,X_7)),
inference(resolve,[$cnf( $equal(converse(composition(top,X_7)),composition(converse(X_7),top)) )],[refute_0_503,refute_0_1859]) ).
cnf(refute_0_1861,plain,
( composition(converse(X_7),top) != converse(composition(top,X_7))
| composition(join(converse(X_7),X_99),top) != join(composition(converse(X_7),top),composition(X_99,top))
| composition(join(converse(X_7),X_99),top) = join(converse(composition(top,X_7)),composition(X_99,top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(X_7),X_99),top),join(composition(converse(X_7),top),composition(X_99,top))) ),[1,0],$fot(converse(composition(top,X_7)))]]) ).
cnf(refute_0_1862,plain,
( composition(join(converse(X_7),X_99),top) != join(composition(converse(X_7),top),composition(X_99,top))
| composition(join(converse(X_7),X_99),top) = join(converse(composition(top,X_7)),composition(X_99,top)) ),
inference(resolve,[$cnf( $equal(composition(converse(X_7),top),converse(composition(top,X_7))) )],[refute_0_1860,refute_0_1861]) ).
cnf(refute_0_1863,plain,
composition(join(converse(X_7),X_99),top) = join(converse(composition(top,X_7)),composition(X_99,top)),
inference(resolve,[$cnf( $equal(composition(join(converse(X_7),X_99),top),join(composition(converse(X_7),top),composition(X_99,top))) )],[refute_0_1858,refute_0_1862]) ).
cnf(refute_0_1864,plain,
composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) = join(converse(composition(top,complement(converse(composition(X_461,top))))),composition(X_99,top)),
inference(subst,[],[refute_0_1863:[bind(X_7,$fot(complement(converse(composition(X_461,top)))))]]) ).
cnf(refute_0_1865,plain,
( composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) != join(converse(composition(top,complement(converse(composition(X_461,top))))),composition(X_99,top))
| composition(top,complement(converse(composition(X_461,top)))) != complement(converse(composition(X_461,top)))
| composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) = join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top),join(converse(composition(top,complement(converse(composition(X_461,top))))),composition(X_99,top))) ),[1,0,0],$fot(complement(converse(composition(X_461,top))))]]) ).
cnf(refute_0_1866,plain,
( composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) != join(converse(composition(top,complement(converse(composition(X_461,top))))),composition(X_99,top))
| composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) = join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)) ),
inference(resolve,[$cnf( $equal(composition(top,complement(converse(composition(X_461,top)))),complement(converse(composition(X_461,top)))) )],[refute_0_1087,refute_0_1865]) ).
cnf(refute_0_1867,plain,
composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) = join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)),
inference(resolve,[$cnf( $equal(composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top),join(converse(composition(top,complement(converse(composition(X_461,top))))),composition(X_99,top))) )],[refute_0_1864,refute_0_1866]) ).
cnf(refute_0_1868,plain,
converse(complement(converse(complement(complement(X_35))))) = complement(X_35),
inference(subst,[],[refute_0_1408:[bind(X_366,$fot(complement(X_35)))]]) ).
cnf(refute_0_1869,plain,
( complement(complement(X_35)) != X_35
| converse(complement(converse(complement(complement(X_35))))) != complement(X_35)
| converse(complement(converse(X_35))) = complement(X_35) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_35))))),complement(X_35)) ),[0,0,0,0],$fot(X_35)]]) ).
cnf(refute_0_1870,plain,
( converse(complement(converse(complement(complement(X_35))))) != complement(X_35)
| converse(complement(converse(X_35))) = complement(X_35) ),
inference(resolve,[$cnf( $equal(complement(complement(X_35)),X_35) )],[refute_0_680,refute_0_1869]) ).
cnf(refute_0_1871,plain,
converse(complement(converse(X_35))) = complement(X_35),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_35))))),complement(X_35)) )],[refute_0_1868,refute_0_1870]) ).
cnf(refute_0_1872,plain,
converse(complement(converse(composition(X_461,top)))) = complement(composition(X_461,top)),
inference(subst,[],[refute_0_1871:[bind(X_35,$fot(composition(X_461,top)))]]) ).
cnf(refute_0_1873,plain,
join(converse(complement(converse(composition(X_461,top)))),X_99) = join(converse(complement(converse(composition(X_461,top)))),X_99),
introduced(tautology,[refl,[$fot(join(converse(complement(converse(composition(X_461,top)))),X_99))]]) ).
cnf(refute_0_1874,plain,
( converse(complement(converse(composition(X_461,top)))) != complement(composition(X_461,top))
| join(converse(complement(converse(composition(X_461,top)))),X_99) != join(converse(complement(converse(composition(X_461,top)))),X_99)
| join(converse(complement(converse(composition(X_461,top)))),X_99) = join(complement(composition(X_461,top)),X_99) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(complement(converse(composition(X_461,top)))),X_99),join(converse(complement(converse(composition(X_461,top)))),X_99)) ),[1,0],$fot(complement(composition(X_461,top)))]]) ).
cnf(refute_0_1875,plain,
( converse(complement(converse(composition(X_461,top)))) != complement(composition(X_461,top))
| join(converse(complement(converse(composition(X_461,top)))),X_99) = join(complement(composition(X_461,top)),X_99) ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(composition(X_461,top)))),X_99),join(converse(complement(converse(composition(X_461,top)))),X_99)) )],[refute_0_1873,refute_0_1874]) ).
cnf(refute_0_1876,plain,
join(converse(complement(converse(composition(X_461,top)))),X_99) = join(complement(composition(X_461,top)),X_99),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(X_461,top)))),complement(composition(X_461,top))) )],[refute_0_1872,refute_0_1875]) ).
cnf(refute_0_1877,plain,
composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) = composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top),
introduced(tautology,[refl,[$fot(composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top))]]) ).
cnf(refute_0_1878,plain,
( composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) != composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top)
| join(converse(complement(converse(composition(X_461,top)))),X_99) != join(complement(composition(X_461,top)),X_99)
| composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) = composition(join(complement(composition(X_461,top)),X_99),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top),composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top)) ),[1,0],$fot(join(complement(composition(X_461,top)),X_99))]]) ).
cnf(refute_0_1879,plain,
( join(converse(complement(converse(composition(X_461,top)))),X_99) != join(complement(composition(X_461,top)),X_99)
| composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) = composition(join(complement(composition(X_461,top)),X_99),top) ),
inference(resolve,[$cnf( $equal(composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top),composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top)) )],[refute_0_1877,refute_0_1878]) ).
cnf(refute_0_1880,plain,
composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) = composition(join(complement(composition(X_461,top)),X_99),top),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(composition(X_461,top)))),X_99),join(complement(composition(X_461,top)),X_99)) )],[refute_0_1876,refute_0_1879]) ).
cnf(refute_0_1881,plain,
( composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) != composition(join(complement(composition(X_461,top)),X_99),top)
| composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) != join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top))
| composition(join(complement(composition(X_461,top)),X_99),top) = join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top),join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top))) ),[0],$fot(composition(join(complement(composition(X_461,top)),X_99),top))]]) ).
cnf(refute_0_1882,plain,
( composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) != join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top))
| composition(join(complement(composition(X_461,top)),X_99),top) = join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)) ),
inference(resolve,[$cnf( $equal(composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top),composition(join(complement(composition(X_461,top)),X_99),top)) )],[refute_0_1880,refute_0_1881]) ).
cnf(refute_0_1883,plain,
join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)) = join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)),
introduced(tautology,[refl,[$fot(join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)))]]) ).
cnf(refute_0_1884,plain,
( converse(complement(converse(composition(X_461,top)))) != complement(composition(X_461,top))
| join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)) != join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top))
| join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)) = join(complement(composition(X_461,top)),composition(X_99,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)),join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top))) ),[1,0],$fot(complement(composition(X_461,top)))]]) ).
cnf(refute_0_1885,plain,
( converse(complement(converse(composition(X_461,top)))) != complement(composition(X_461,top))
| join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)) = join(complement(composition(X_461,top)),composition(X_99,top)) ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)),join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top))) )],[refute_0_1883,refute_0_1884]) ).
cnf(refute_0_1886,plain,
join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)) = join(complement(composition(X_461,top)),composition(X_99,top)),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(X_461,top)))),complement(composition(X_461,top))) )],[refute_0_1872,refute_0_1885]) ).
cnf(refute_0_1887,plain,
( composition(join(complement(composition(X_461,top)),X_99),top) != join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top))
| join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)) != join(complement(composition(X_461,top)),composition(X_99,top))
| composition(join(complement(composition(X_461,top)),X_99),top) = join(complement(composition(X_461,top)),composition(X_99,top)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(complement(composition(X_461,top)),X_99),top),join(complement(composition(X_461,top)),composition(X_99,top))) ),[0],$fot(join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)))]]) ).
cnf(refute_0_1888,plain,
( composition(join(complement(composition(X_461,top)),X_99),top) != join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top))
| composition(join(complement(composition(X_461,top)),X_99),top) = join(complement(composition(X_461,top)),composition(X_99,top)) ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top)),join(complement(composition(X_461,top)),composition(X_99,top))) )],[refute_0_1886,refute_0_1887]) ).
cnf(refute_0_1889,plain,
( composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top) != join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top))
| composition(join(complement(composition(X_461,top)),X_99),top) = join(complement(composition(X_461,top)),composition(X_99,top)) ),
inference(resolve,[$cnf( $equal(composition(join(complement(composition(X_461,top)),X_99),top),join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top))) )],[refute_0_1882,refute_0_1888]) ).
cnf(refute_0_1890,plain,
composition(join(complement(composition(X_461,top)),X_99),top) = join(complement(composition(X_461,top)),composition(X_99,top)),
inference(resolve,[$cnf( $equal(composition(join(converse(complement(converse(composition(X_461,top)))),X_99),top),join(converse(complement(converse(composition(X_461,top)))),composition(X_99,top))) )],[refute_0_1867,refute_0_1889]) ).
cnf(refute_0_1891,plain,
( composition(join(complement(composition(X_461,top)),X_99),top) != join(complement(composition(X_461,top)),composition(X_99,top))
| join(complement(composition(X_461,top)),composition(X_99,top)) = composition(join(complement(composition(X_461,top)),X_99),top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(complement(composition(X_461,top)),X_99),top))),bind(Y,$fot(join(complement(composition(X_461,top)),composition(X_99,top))))]]) ).
cnf(refute_0_1892,plain,
join(complement(composition(X_461,top)),composition(X_99,top)) = composition(join(complement(composition(X_461,top)),X_99),top),
inference(resolve,[$cnf( $equal(composition(join(complement(composition(X_461,top)),X_99),top),join(complement(composition(X_461,top)),composition(X_99,top))) )],[refute_0_1890,refute_0_1891]) ).
cnf(refute_0_1893,plain,
join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)) = composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top),
inference(subst,[],[refute_0_1892:[bind(X_461,$fot(X_670)),bind(X_99,$fot(complement(composition(X_670,top))))]]) ).
cnf(refute_0_1894,plain,
( composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top) != composition(complement(composition(X_670,top)),top)
| join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)) != composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top)
| join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)) = composition(complement(composition(X_670,top)),top) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)))),bind(Y,$fot(composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top))),bind(Z,$fot(composition(complement(composition(X_670,top)),top)))]]) ).
cnf(refute_0_1895,plain,
( composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top) != composition(complement(composition(X_670,top)),top)
| join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)) = composition(complement(composition(X_670,top)),top) ),
inference(resolve,[$cnf( $equal(join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)),composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top)) )],[refute_0_1893,refute_0_1894]) ).
cnf(refute_0_1896,plain,
join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)) = composition(complement(composition(X_670,top)),top),
inference(resolve,[$cnf( $equal(composition(join(complement(composition(X_670,top)),complement(composition(X_670,top))),top),composition(complement(composition(X_670,top)),top)) )],[refute_0_1857,refute_0_1895]) ).
cnf(refute_0_1897,plain,
composition(complement(composition(X_670,top)),complement(zero)) = composition(complement(composition(X_670,top)),complement(zero)),
introduced(tautology,[refl,[$fot(composition(complement(composition(X_670,top)),complement(zero)))]]) ).
cnf(refute_0_1898,plain,
( complement(zero) != top
| composition(complement(composition(X_670,top)),complement(zero)) != composition(complement(composition(X_670,top)),complement(zero))
| composition(complement(composition(X_670,top)),complement(zero)) = composition(complement(composition(X_670,top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(X_670,top)),complement(zero)),composition(complement(composition(X_670,top)),complement(zero))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1899,plain,
( complement(zero) != top
| composition(complement(composition(X_670,top)),complement(zero)) = composition(complement(composition(X_670,top)),top) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(X_670,top)),complement(zero)),composition(complement(composition(X_670,top)),complement(zero))) )],[refute_0_1897,refute_0_1898]) ).
cnf(refute_0_1900,plain,
composition(complement(composition(X_670,top)),complement(zero)) = composition(complement(composition(X_670,top)),top),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_791,refute_0_1899]) ).
cnf(refute_0_1901,plain,
converse(complement(converse(composition(X_670,top)))) = complement(composition(X_670,top)),
inference(subst,[],[refute_0_1871:[bind(X_35,$fot(composition(X_670,top)))]]) ).
cnf(refute_0_1902,plain,
composition(converse(complement(converse(composition(X_670,top)))),complement(zero)) = composition(converse(complement(converse(composition(X_670,top)))),complement(zero)),
introduced(tautology,[refl,[$fot(composition(converse(complement(converse(composition(X_670,top)))),complement(zero)))]]) ).
cnf(refute_0_1903,plain,
( composition(converse(complement(converse(composition(X_670,top)))),complement(zero)) != composition(converse(complement(converse(composition(X_670,top)))),complement(zero))
| converse(complement(converse(composition(X_670,top)))) != complement(composition(X_670,top))
| composition(converse(complement(converse(composition(X_670,top)))),complement(zero)) = composition(complement(composition(X_670,top)),complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(converse(composition(X_670,top)))),complement(zero)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) ),[1,0],$fot(complement(composition(X_670,top)))]]) ).
cnf(refute_0_1904,plain,
( converse(complement(converse(composition(X_670,top)))) != complement(composition(X_670,top))
| composition(converse(complement(converse(composition(X_670,top)))),complement(zero)) = composition(complement(composition(X_670,top)),complement(zero)) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(converse(composition(X_670,top)))),complement(zero)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) )],[refute_0_1902,refute_0_1903]) ).
cnf(refute_0_1905,plain,
composition(converse(complement(converse(composition(X_670,top)))),complement(zero)) = composition(complement(composition(X_670,top)),complement(zero)),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(X_670,top)))),complement(composition(X_670,top))) )],[refute_0_1901,refute_0_1904]) ).
cnf(refute_0_1906,plain,
( composition(complement(composition(X_670,top)),complement(zero)) != composition(complement(composition(X_670,top)),top)
| composition(converse(complement(converse(composition(X_670,top)))),complement(zero)) != composition(complement(composition(X_670,top)),complement(zero))
| composition(converse(complement(converse(composition(X_670,top)))),complement(zero)) = composition(complement(composition(X_670,top)),top) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(composition(converse(complement(converse(composition(X_670,top)))),complement(zero)))),bind(Y,$fot(composition(complement(composition(X_670,top)),complement(zero)))),bind(Z,$fot(composition(complement(composition(X_670,top)),top)))]]) ).
cnf(refute_0_1907,plain,
( composition(complement(composition(X_670,top)),complement(zero)) != composition(complement(composition(X_670,top)),top)
| composition(converse(complement(converse(composition(X_670,top)))),complement(zero)) = composition(complement(composition(X_670,top)),top) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(converse(composition(X_670,top)))),complement(zero)),composition(complement(composition(X_670,top)),complement(zero))) )],[refute_0_1905,refute_0_1906]) ).
cnf(refute_0_1908,plain,
composition(converse(complement(converse(composition(X_670,top)))),complement(zero)) = composition(complement(composition(X_670,top)),top),
inference(resolve,[$cnf( $equal(composition(complement(composition(X_670,top)),complement(zero)),composition(complement(composition(X_670,top)),top)) )],[refute_0_1900,refute_0_1907]) ).
cnf(refute_0_1909,plain,
join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) = join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))),
introduced(tautology,[refl,[$fot(join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))))]]) ).
cnf(refute_0_1910,plain,
( composition(converse(complement(converse(composition(X_670,top)))),complement(zero)) != composition(complement(composition(X_670,top)),top)
| join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) != join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero)))
| join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) = join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))),join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero)))) ),[1,1],$fot(composition(complement(composition(X_670,top)),top))]]) ).
cnf(refute_0_1911,plain,
( composition(converse(complement(converse(composition(X_670,top)))),complement(zero)) != composition(complement(composition(X_670,top)),top)
| join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) = join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))),join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero)))) )],[refute_0_1909,refute_0_1910]) ).
cnf(refute_0_1912,plain,
join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) = join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)),
inference(resolve,[$cnf( $equal(composition(converse(complement(converse(composition(X_670,top)))),complement(zero)),composition(complement(composition(X_670,top)),top)) )],[refute_0_1908,refute_0_1911]) ).
cnf(refute_0_1913,plain,
( join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)) != composition(complement(composition(X_670,top)),top)
| join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) != join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top))
| join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) = composition(complement(composition(X_670,top)),top) ),
inference(subst,[],[refute_0_41:[bind(X,$fot(join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))))),bind(Y,$fot(join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)))),bind(Z,$fot(composition(complement(composition(X_670,top)),top)))]]) ).
cnf(refute_0_1914,plain,
( join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)) != composition(complement(composition(X_670,top)),top)
| join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) = composition(complement(composition(X_670,top)),top) ),
inference(resolve,[$cnf( $equal(join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))),join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top))) )],[refute_0_1912,refute_0_1913]) ).
cnf(refute_0_1915,plain,
join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) = composition(complement(composition(X_670,top)),top),
inference(resolve,[$cnf( $equal(join(complement(composition(X_670,top)),composition(complement(composition(X_670,top)),top)),composition(complement(composition(X_670,top)),top)) )],[refute_0_1896,refute_0_1914]) ).
cnf(refute_0_1916,plain,
( join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) != complement(composition(X_670,top))
| join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) != composition(complement(composition(X_670,top)),top)
| composition(complement(composition(X_670,top)),top) = complement(composition(X_670,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))),complement(composition(X_670,top))) ),[0],$fot(composition(complement(composition(X_670,top)),top))]]) ).
cnf(refute_0_1917,plain,
( join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))) != complement(composition(X_670,top))
| composition(complement(composition(X_670,top)),top) = complement(composition(X_670,top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))),composition(complement(composition(X_670,top)),top)) )],[refute_0_1915,refute_0_1916]) ).
cnf(refute_0_1918,plain,
composition(complement(composition(X_670,top)),top) = complement(composition(X_670,top)),
inference(resolve,[$cnf( $equal(join(complement(composition(X_670,top)),composition(converse(complement(converse(composition(X_670,top)))),complement(zero))),complement(composition(X_670,top))) )],[refute_0_1429,refute_0_1917]) ).
cnf(refute_0_1919,plain,
composition(complement(composition(sk1,top)),top) = complement(composition(sk1,top)),
inference(subst,[],[refute_0_1918:[bind(X_670,$fot(sk1))]]) ).
cnf(refute_0_1920,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| complement(composition(sk1,top)) = composition(complement(composition(sk1,top)),top) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) ),[1],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_1921,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| complement(composition(sk1,top)) = composition(complement(composition(sk1,top)),top) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) )],[refute_0_1919,refute_0_1920]) ).
cnf(refute_0_1922,plain,
complement(composition(sk1,top)) != complement(composition(sk1,top)),
inference(resolve,[$cnf( $equal(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) )],[refute_0_1921,goals_14]) ).
cnf(refute_0_1923,plain,
complement(composition(sk1,top)) = complement(composition(sk1,top)),
introduced(tautology,[refl,[$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_1924,plain,
$false,
inference(resolve,[$cnf( $equal(complement(composition(sk1,top)),complement(composition(sk1,top))) )],[refute_0_1923,refute_0_1922]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL050-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 15:35:31 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 25.40/25.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.40/25.56
% 25.40/25.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.58/25.77
%------------------------------------------------------------------------------