TSTP Solution File: REL050-2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL050-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:46:21 EDT 2022
% Result : Unsatisfiable 12.25s 12.69s
% Output : CNFRefutation 12.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 145
% Number of leaves : 485
% Syntax : Number of clauses : 2044 (1017 unt; 0 nHn;1191 RR)
% Number of literals : 3522 (3521 equ;1484 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 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 : 2506 ( 40 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,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,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( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_3]) ).
cnf(refute_0_5,plain,
join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) = join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(composition(sk1,top)))),bind(B,$fot(composition(complement(composition(sk1,top)),top)))]]) ).
cnf(refute_0_6,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top))
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) = composition(complement(composition(sk1,top)),top) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))))),bind(Y,$fot(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)))),bind(Z,$fot(composition(complement(composition(sk1,top)),top)))]]) ).
cnf(refute_0_9,plain,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) = composition(complement(composition(sk1,top)),top) ),
inference(resolve,[$cnf( $equal(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) = complement(composition(sk1,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),composition(complement(composition(sk1,top)),top)) ),[1],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_11,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) = complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),composition(complement(composition(sk1,top)),top)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
inference(resolve,[$cnf( $equal(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),complement(composition(sk1,top))) )],[refute_0_11,goals_14]) ).
cnf(refute_0_13,plain,
join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),
introduced(tautology,[refl,[$fot(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)))]]) ).
cnf(refute_0_14,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = join(complement(composition(sk1,top)),complement(composition(sk1,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top))) ),[1,1],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_15,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = join(complement(composition(sk1,top)),complement(composition(sk1,top))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( join(complement(composition(sk1,top)),complement(composition(sk1,top))) != composition(complement(composition(sk1,top)),top)
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != join(complement(composition(sk1,top)),complement(composition(sk1,top)))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = composition(complement(composition(sk1,top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),join(complement(composition(sk1,top)),complement(composition(sk1,top)))) ),[1],$fot(composition(complement(composition(sk1,top)),top))]]) ).
cnf(refute_0_17,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) != composition(complement(composition(sk1,top)),top)
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = composition(complement(composition(sk1,top)),top) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),join(complement(composition(sk1,top)),complement(composition(sk1,top)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) = composition(complement(composition(sk1,top)),top) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(composition(sk1,top)),complement(composition(sk1,top))),composition(complement(composition(sk1,top)),top)) ),[1],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_19,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = composition(complement(composition(sk1,top)),top) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),complement(composition(sk1,top))),composition(complement(composition(sk1,top)),top)) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) != complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),composition(complement(composition(sk1,top)),top)) )],[refute_0_19,refute_0_12]) ).
cnf(refute_0_21,plain,
meet(B,B) = complement(join(complement(B),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_22,plain,
composition(join(X_32,one),X_34) = join(composition(X_32,X_34),composition(one,X_34)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_32)),bind(B,$fot(one)),bind(C,$fot(X_34))]]) ).
cnf(refute_0_23,plain,
converse(composition(converse(A),X_23)) = composition(converse(X_23),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_23))]]) ).
cnf(refute_0_24,plain,
( converse(composition(converse(A),X_23)) != composition(converse(X_23),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_23)) = composition(converse(X_23),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_23)),composition(converse(X_23),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_25,plain,
( converse(composition(converse(A),X_23)) != composition(converse(X_23),converse(converse(A)))
| converse(composition(converse(A),X_23)) = composition(converse(X_23),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_24]) ).
cnf(refute_0_26,plain,
converse(composition(converse(A),X_23)) = composition(converse(X_23),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_23)),composition(converse(X_23),converse(converse(A)))) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
converse(composition(converse(X_24),one)) = composition(converse(one),X_24),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_24)),bind(X_23,$fot(one))]]) ).
cnf(refute_0_28,plain,
composition(converse(X_24),one) = converse(X_24),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_24)))]]) ).
cnf(refute_0_29,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_30,plain,
( converse(composition(converse(X_24),one)) != composition(converse(one),X_24)
| converse(converse(X_24)) = composition(converse(one),X_24) ),
inference(resolve,[$cnf( $equal(composition(converse(X_24),one),converse(X_24)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
converse(converse(X_24)) = composition(converse(one),X_24),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_24),one)),composition(converse(one),X_24)) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
converse(converse(X_24)) = X_24,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_24))]]) ).
cnf(refute_0_33,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_34,plain,
( converse(converse(X_24)) != composition(converse(one),X_24)
| X_24 = composition(converse(one),X_24) ),
inference(resolve,[$cnf( $equal(converse(converse(X_24)),X_24) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
X_24 = composition(converse(one),X_24),
inference(resolve,[$cnf( $equal(converse(converse(X_24)),composition(converse(one),X_24)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_37,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_35:[bind(X_24,$fot(one))]]) ).
cnf(refute_0_38,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_39,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_41,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_44,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
composition(converse(one),X_24) = composition(converse(one),X_24),
introduced(tautology,[refl,[$fot(composition(converse(one),X_24))]]) ).
cnf(refute_0_46,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_47,plain,
( converse(one) != one
| composition(converse(one),X_24) = composition(one,X_24) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_24),composition(converse(one),X_24)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
composition(converse(one),X_24) = composition(one,X_24),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
( X_24 != composition(converse(one),X_24)
| composition(converse(one),X_24) != composition(one,X_24)
| X_24 = composition(one,X_24) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_24,composition(one,X_24)) ),[0],$fot(composition(converse(one),X_24))]]) ).
cnf(refute_0_50,plain,
( X_24 != composition(converse(one),X_24)
| X_24 = composition(one,X_24) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_24),composition(one,X_24)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
X_24 = composition(one,X_24),
inference(resolve,[$cnf( $equal(X_24,composition(converse(one),X_24)) )],[refute_0_35,refute_0_50]) ).
cnf(refute_0_52,plain,
X_34 = composition(one,X_34),
inference(subst,[],[refute_0_51:[bind(X_24,$fot(X_34))]]) ).
cnf(refute_0_53,plain,
( X_34 != composition(one,X_34)
| composition(one,X_34) = X_34 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_34)),bind(Y,$fot(composition(one,X_34)))]]) ).
cnf(refute_0_54,plain,
composition(one,X_34) = X_34,
inference(resolve,[$cnf( $equal(X_34,composition(one,X_34)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( composition(join(X_32,one),X_34) != join(composition(X_32,X_34),composition(one,X_34))
| composition(one,X_34) != X_34
| composition(join(X_32,one),X_34) = join(composition(X_32,X_34),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_32,one),X_34),join(composition(X_32,X_34),composition(one,X_34))) ),[1,1],$fot(X_34)]]) ).
cnf(refute_0_56,plain,
( composition(join(X_32,one),X_34) != join(composition(X_32,X_34),composition(one,X_34))
| composition(join(X_32,one),X_34) = join(composition(X_32,X_34),X_34) ),
inference(resolve,[$cnf( $equal(composition(one,X_34),X_34) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
composition(join(X_32,one),X_34) = join(composition(X_32,X_34),X_34),
inference(resolve,[$cnf( $equal(composition(join(X_32,one),X_34),join(composition(X_32,X_34),composition(one,X_34))) )],[refute_0_22,refute_0_56]) ).
cnf(refute_0_58,plain,
join(composition(X_32,X_34),X_34) = join(X_34,composition(X_32,X_34)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_34)),bind(B,$fot(composition(X_32,X_34)))]]) ).
cnf(refute_0_59,plain,
( composition(join(X_32,one),X_34) != join(composition(X_32,X_34),X_34)
| join(composition(X_32,X_34),X_34) != join(X_34,composition(X_32,X_34))
| composition(join(X_32,one),X_34) = join(X_34,composition(X_32,X_34)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_32,one),X_34),join(X_34,composition(X_32,X_34))) ),[0],$fot(join(composition(X_32,X_34),X_34))]]) ).
cnf(refute_0_60,plain,
( composition(join(X_32,one),X_34) != join(composition(X_32,X_34),X_34)
| composition(join(X_32,one),X_34) = join(X_34,composition(X_32,X_34)) ),
inference(resolve,[$cnf( $equal(join(composition(X_32,X_34),X_34),join(X_34,composition(X_32,X_34))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
composition(join(X_32,one),X_34) = join(X_34,composition(X_32,X_34)),
inference(resolve,[$cnf( $equal(composition(join(X_32,one),X_34),join(composition(X_32,X_34),X_34)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
composition(join(one,one),X_47) = join(X_47,composition(one,X_47)),
inference(subst,[],[refute_0_61:[bind(X_32,$fot(one)),bind(X_34,$fot(X_47))]]) ).
cnf(refute_0_63,plain,
X_47 = composition(one,X_47),
inference(subst,[],[refute_0_51:[bind(X_24,$fot(X_47))]]) ).
cnf(refute_0_64,plain,
( X_47 != composition(one,X_47)
| composition(one,X_47) = X_47 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_47)),bind(Y,$fot(composition(one,X_47)))]]) ).
cnf(refute_0_65,plain,
composition(one,X_47) = X_47,
inference(resolve,[$cnf( $equal(X_47,composition(one,X_47)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( composition(join(one,one),X_47) != join(X_47,composition(one,X_47))
| composition(one,X_47) != X_47
| composition(join(one,one),X_47) = join(X_47,X_47) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),X_47),join(X_47,composition(one,X_47))) ),[1,1],$fot(X_47)]]) ).
cnf(refute_0_67,plain,
( composition(join(one,one),X_47) != join(X_47,composition(one,X_47))
| composition(join(one,one),X_47) = join(X_47,X_47) ),
inference(resolve,[$cnf( $equal(composition(one,X_47),X_47) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
composition(join(one,one),X_47) = join(X_47,X_47),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_47),join(X_47,composition(one,X_47))) )],[refute_0_62,refute_0_67]) ).
cnf(refute_0_69,plain,
composition(join(one,one),complement(B)) = join(complement(B),complement(B)),
inference(subst,[],[refute_0_68:[bind(X_47,$fot(complement(B)))]]) ).
cnf(refute_0_70,plain,
( composition(join(one,one),complement(B)) != join(complement(B),complement(B))
| join(complement(B),complement(B)) = composition(join(one,one),complement(B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),complement(B)))),bind(Y,$fot(join(complement(B),complement(B))))]]) ).
cnf(refute_0_71,plain,
join(complement(B),complement(B)) = composition(join(one,one),complement(B)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(B)),join(complement(B),complement(B))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( join(complement(B),complement(B)) != composition(join(one,one),complement(B))
| meet(B,B) != complement(join(complement(B),complement(B)))
| meet(B,B) = complement(composition(join(one,one),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(B,B),complement(join(complement(B),complement(B)))) ),[1,0],$fot(composition(join(one,one),complement(B)))]]) ).
cnf(refute_0_73,plain,
( meet(B,B) != complement(join(complement(B),complement(B)))
| meet(B,B) = complement(composition(join(one,one),complement(B))) ),
inference(resolve,[$cnf( $equal(join(complement(B),complement(B)),composition(join(one,one),complement(B))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
meet(B,B) = complement(composition(join(one,one),complement(B))),
inference(resolve,[$cnf( $equal(meet(B,B),complement(join(complement(B),complement(B)))) )],[refute_0_21,refute_0_73]) ).
cnf(refute_0_75,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_76,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
introduced(tautology,[equality,[$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_77,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( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_77]) ).
cnf(refute_0_79,plain,
join(complement(X_63),composition(converse(one),complement(composition(one,X_63)))) = complement(X_63),
inference(subst,[],[refute_0_78:[bind(A,$fot(one)),bind(B,$fot(X_63))]]) ).
cnf(refute_0_80,plain,
X_63 = composition(one,X_63),
inference(subst,[],[refute_0_51:[bind(X_24,$fot(X_63))]]) ).
cnf(refute_0_81,plain,
( X_63 != composition(one,X_63)
| composition(one,X_63) = X_63 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_63)),bind(Y,$fot(composition(one,X_63)))]]) ).
cnf(refute_0_82,plain,
composition(one,X_63) = X_63,
inference(resolve,[$cnf( $equal(X_63,composition(one,X_63)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
( composition(one,X_63) != X_63
| join(complement(X_63),composition(converse(one),complement(composition(one,X_63)))) != complement(X_63)
| join(complement(X_63),composition(converse(one),complement(X_63))) = complement(X_63) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_63),composition(converse(one),complement(composition(one,X_63)))),complement(X_63)) ),[0,1,1,0],$fot(X_63)]]) ).
cnf(refute_0_84,plain,
( join(complement(X_63),composition(converse(one),complement(composition(one,X_63)))) != complement(X_63)
| join(complement(X_63),composition(converse(one),complement(X_63))) = complement(X_63) ),
inference(resolve,[$cnf( $equal(composition(one,X_63),X_63) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
join(complement(X_63),composition(converse(one),complement(X_63))) = complement(X_63),
inference(resolve,[$cnf( $equal(join(complement(X_63),composition(converse(one),complement(composition(one,X_63)))),complement(X_63)) )],[refute_0_79,refute_0_84]) ).
cnf(refute_0_86,plain,
converse(join(converse(A),X_13)) = join(converse(converse(A)),converse(X_13)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(A))),bind(B,$fot(X_13))]]) ).
cnf(refute_0_87,plain,
( converse(converse(A)) != A
| converse(join(converse(A),X_13)) != join(converse(converse(A)),converse(X_13))
| converse(join(converse(A),X_13)) = join(A,converse(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),X_13)),join(converse(converse(A)),converse(X_13))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_88,plain,
( converse(join(converse(A),X_13)) != join(converse(converse(A)),converse(X_13))
| converse(join(converse(A),X_13)) = join(A,converse(X_13)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_87]) ).
cnf(refute_0_89,plain,
converse(join(converse(A),X_13)) = join(A,converse(X_13)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_13)),join(converse(converse(A)),converse(X_13))) )],[refute_0_86,refute_0_88]) ).
cnf(refute_0_90,plain,
converse(join(converse(one),X_13)) = join(one,converse(X_13)),
inference(subst,[],[refute_0_89:[bind(A,$fot(one))]]) ).
cnf(refute_0_91,plain,
( converse(join(converse(one),X_13)) != join(one,converse(X_13))
| converse(one) != one
| converse(join(one,X_13)) = join(one,converse(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(one),X_13)),join(one,converse(X_13))) ),[0,0,0],$fot(one)]]) ).
cnf(refute_0_92,plain,
( converse(join(converse(one),X_13)) != join(one,converse(X_13))
| converse(join(one,X_13)) = join(one,converse(X_13)) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_44,refute_0_91]) ).
cnf(refute_0_93,plain,
converse(join(one,X_13)) = join(one,converse(X_13)),
inference(resolve,[$cnf( $equal(converse(join(converse(one),X_13)),join(one,converse(X_13))) )],[refute_0_90,refute_0_92]) ).
cnf(refute_0_94,plain,
converse(join(one,one)) = join(one,converse(one)),
inference(subst,[],[refute_0_93:[bind(X_13,$fot(one))]]) ).
cnf(refute_0_95,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_96,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(join(one,one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_44,refute_0_95]) ).
cnf(refute_0_97,plain,
converse(join(one,one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) )],[refute_0_94,refute_0_96]) ).
cnf(refute_0_98,plain,
( converse(join(one,X_13)) != join(one,converse(X_13))
| join(one,converse(X_13)) = converse(join(one,X_13)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(one,X_13)))),bind(Y,$fot(join(one,converse(X_13))))]]) ).
cnf(refute_0_99,plain,
join(one,converse(X_13)) = converse(join(one,X_13)),
inference(resolve,[$cnf( $equal(converse(join(one,X_13)),join(one,converse(X_13))) )],[refute_0_93,refute_0_98]) ).
cnf(refute_0_100,plain,
join(one,converse(one)) = converse(join(one,one)),
inference(subst,[],[refute_0_99:[bind(X_13,$fot(one))]]) ).
cnf(refute_0_101,plain,
( converse(join(one,one)) != join(one,one)
| join(one,converse(one)) != converse(join(one,one))
| join(one,converse(one)) = join(one,one) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,converse(one)))),bind(Y,$fot(converse(join(one,one)))),bind(Z,$fot(join(one,one)))]]) ).
cnf(refute_0_102,plain,
( converse(join(one,one)) != join(one,one)
| join(one,converse(one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(join(one,converse(one)),converse(join(one,one))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
join(one,converse(one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_97,refute_0_102]) ).
cnf(refute_0_104,plain,
composition(join(one,converse(one)),complement(X_63)) = composition(join(one,converse(one)),complement(X_63)),
introduced(tautology,[refl,[$fot(composition(join(one,converse(one)),complement(X_63)))]]) ).
cnf(refute_0_105,plain,
( composition(join(one,converse(one)),complement(X_63)) != composition(join(one,converse(one)),complement(X_63))
| join(one,converse(one)) != join(one,one)
| composition(join(one,converse(one)),complement(X_63)) = composition(join(one,one),complement(X_63)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(one)),complement(X_63)),composition(join(one,converse(one)),complement(X_63))) ),[1,0],$fot(join(one,one))]]) ).
cnf(refute_0_106,plain,
( join(one,converse(one)) != join(one,one)
| composition(join(one,converse(one)),complement(X_63)) = composition(join(one,one),complement(X_63)) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(one)),complement(X_63)),composition(join(one,converse(one)),complement(X_63))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
composition(join(one,converse(one)),complement(X_63)) = composition(join(one,one),complement(X_63)),
inference(resolve,[$cnf( $equal(join(one,converse(one)),join(one,one)) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
composition(join(X_46,one),X_47) = join(X_47,composition(X_46,X_47)),
inference(subst,[],[refute_0_61:[bind(X_32,$fot(X_46)),bind(X_34,$fot(X_47))]]) ).
cnf(refute_0_109,plain,
join(one,X_46) = join(X_46,one),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(one)),bind(B,$fot(X_46))]]) ).
cnf(refute_0_110,plain,
( join(one,X_46) != join(X_46,one)
| join(X_46,one) = join(one,X_46) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,X_46))),bind(Y,$fot(join(X_46,one)))]]) ).
cnf(refute_0_111,plain,
join(X_46,one) = join(one,X_46),
inference(resolve,[$cnf( $equal(join(one,X_46),join(X_46,one)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( composition(join(X_46,one),X_47) != join(X_47,composition(X_46,X_47))
| join(X_46,one) != join(one,X_46)
| composition(join(one,X_46),X_47) = join(X_47,composition(X_46,X_47)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_46,one),X_47),join(X_47,composition(X_46,X_47))) ),[0,0],$fot(join(one,X_46))]]) ).
cnf(refute_0_113,plain,
( composition(join(X_46,one),X_47) != join(X_47,composition(X_46,X_47))
| composition(join(one,X_46),X_47) = join(X_47,composition(X_46,X_47)) ),
inference(resolve,[$cnf( $equal(join(X_46,one),join(one,X_46)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
composition(join(one,X_46),X_47) = join(X_47,composition(X_46,X_47)),
inference(resolve,[$cnf( $equal(composition(join(X_46,one),X_47),join(X_47,composition(X_46,X_47))) )],[refute_0_108,refute_0_113]) ).
cnf(refute_0_115,plain,
( composition(join(X_32,one),X_34) != join(X_34,composition(X_32,X_34))
| join(X_34,composition(X_32,X_34)) = composition(join(X_32,one),X_34) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_32,one),X_34))),bind(Y,$fot(join(X_34,composition(X_32,X_34))))]]) ).
cnf(refute_0_116,plain,
join(X_34,composition(X_32,X_34)) = composition(join(X_32,one),X_34),
inference(resolve,[$cnf( $equal(composition(join(X_32,one),X_34),join(X_34,composition(X_32,X_34))) )],[refute_0_61,refute_0_115]) ).
cnf(refute_0_117,plain,
join(X_47,composition(X_46,X_47)) = composition(join(X_46,one),X_47),
inference(subst,[],[refute_0_116:[bind(X_32,$fot(X_46)),bind(X_34,$fot(X_47))]]) ).
cnf(refute_0_118,plain,
( composition(join(one,X_46),X_47) != join(X_47,composition(X_46,X_47))
| join(X_47,composition(X_46,X_47)) != composition(join(X_46,one),X_47)
| composition(join(one,X_46),X_47) = composition(join(X_46,one),X_47) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,X_46),X_47),composition(join(X_46,one),X_47)) ),[0],$fot(join(X_47,composition(X_46,X_47)))]]) ).
cnf(refute_0_119,plain,
( composition(join(one,X_46),X_47) != join(X_47,composition(X_46,X_47))
| composition(join(one,X_46),X_47) = composition(join(X_46,one),X_47) ),
inference(resolve,[$cnf( $equal(join(X_47,composition(X_46,X_47)),composition(join(X_46,one),X_47)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
composition(join(one,X_46),X_47) = composition(join(X_46,one),X_47),
inference(resolve,[$cnf( $equal(composition(join(one,X_46),X_47),join(X_47,composition(X_46,X_47))) )],[refute_0_114,refute_0_119]) ).
cnf(refute_0_121,plain,
( composition(join(one,X_46),X_47) != composition(join(X_46,one),X_47)
| composition(join(X_46,one),X_47) = composition(join(one,X_46),X_47) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,X_46),X_47))),bind(Y,$fot(composition(join(X_46,one),X_47)))]]) ).
cnf(refute_0_122,plain,
composition(join(X_46,one),X_47) = composition(join(one,X_46),X_47),
inference(resolve,[$cnf( $equal(composition(join(one,X_46),X_47),composition(join(X_46,one),X_47)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
composition(join(converse(one),one),complement(X_63)) = composition(join(one,converse(one)),complement(X_63)),
inference(subst,[],[refute_0_122:[bind(X_46,$fot(converse(one))),bind(X_47,$fot(complement(X_63)))]]) ).
cnf(refute_0_124,plain,
join(complement(X_63),composition(converse(one),complement(X_63))) = composition(join(converse(one),one),complement(X_63)),
inference(subst,[],[refute_0_116:[bind(X_32,$fot(converse(one))),bind(X_34,$fot(complement(X_63)))]]) ).
cnf(refute_0_125,plain,
( composition(join(converse(one),one),complement(X_63)) != composition(join(one,converse(one)),complement(X_63))
| join(complement(X_63),composition(converse(one),complement(X_63))) != composition(join(converse(one),one),complement(X_63))
| join(complement(X_63),composition(converse(one),complement(X_63))) = composition(join(one,converse(one)),complement(X_63)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(X_63),composition(converse(one),complement(X_63))))),bind(Y,$fot(composition(join(converse(one),one),complement(X_63)))),bind(Z,$fot(composition(join(one,converse(one)),complement(X_63))))]]) ).
cnf(refute_0_126,plain,
( composition(join(converse(one),one),complement(X_63)) != composition(join(one,converse(one)),complement(X_63))
| join(complement(X_63),composition(converse(one),complement(X_63))) = composition(join(one,converse(one)),complement(X_63)) ),
inference(resolve,[$cnf( $equal(join(complement(X_63),composition(converse(one),complement(X_63))),composition(join(converse(one),one),complement(X_63))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
join(complement(X_63),composition(converse(one),complement(X_63))) = composition(join(one,converse(one)),complement(X_63)),
inference(resolve,[$cnf( $equal(composition(join(converse(one),one),complement(X_63)),composition(join(one,converse(one)),complement(X_63))) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
( composition(join(one,converse(one)),complement(X_63)) != composition(join(one,one),complement(X_63))
| join(complement(X_63),composition(converse(one),complement(X_63))) != composition(join(one,converse(one)),complement(X_63))
| join(complement(X_63),composition(converse(one),complement(X_63))) = composition(join(one,one),complement(X_63)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(X_63),composition(converse(one),complement(X_63))))),bind(Y,$fot(composition(join(one,converse(one)),complement(X_63)))),bind(Z,$fot(composition(join(one,one),complement(X_63))))]]) ).
cnf(refute_0_129,plain,
( composition(join(one,converse(one)),complement(X_63)) != composition(join(one,one),complement(X_63))
| join(complement(X_63),composition(converse(one),complement(X_63))) = composition(join(one,one),complement(X_63)) ),
inference(resolve,[$cnf( $equal(join(complement(X_63),composition(converse(one),complement(X_63))),composition(join(one,converse(one)),complement(X_63))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
join(complement(X_63),composition(converse(one),complement(X_63))) = composition(join(one,one),complement(X_63)),
inference(resolve,[$cnf( $equal(composition(join(one,converse(one)),complement(X_63)),composition(join(one,one),complement(X_63))) )],[refute_0_107,refute_0_129]) ).
cnf(refute_0_131,plain,
( join(complement(X_63),composition(converse(one),complement(X_63))) != complement(X_63)
| join(complement(X_63),composition(converse(one),complement(X_63))) != composition(join(one,one),complement(X_63))
| composition(join(one,one),complement(X_63)) = complement(X_63) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_63),composition(converse(one),complement(X_63))),complement(X_63)) ),[0],$fot(composition(join(one,one),complement(X_63)))]]) ).
cnf(refute_0_132,plain,
( join(complement(X_63),composition(converse(one),complement(X_63))) != complement(X_63)
| composition(join(one,one),complement(X_63)) = complement(X_63) ),
inference(resolve,[$cnf( $equal(join(complement(X_63),composition(converse(one),complement(X_63))),composition(join(one,one),complement(X_63))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
composition(join(one,one),complement(X_63)) = complement(X_63),
inference(resolve,[$cnf( $equal(join(complement(X_63),composition(converse(one),complement(X_63))),complement(X_63)) )],[refute_0_85,refute_0_132]) ).
cnf(refute_0_134,plain,
composition(join(one,one),complement(B)) = complement(B),
inference(subst,[],[refute_0_133:[bind(X_63,$fot(B))]]) ).
cnf(refute_0_135,plain,
complement(composition(join(one,one),complement(B))) = complement(composition(join(one,one),complement(B))),
introduced(tautology,[refl,[$fot(complement(composition(join(one,one),complement(B))))]]) ).
cnf(refute_0_136,plain,
( complement(composition(join(one,one),complement(B))) != complement(composition(join(one,one),complement(B)))
| composition(join(one,one),complement(B)) != complement(B)
| complement(composition(join(one,one),complement(B))) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(join(one,one),complement(B))),complement(composition(join(one,one),complement(B)))) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_137,plain,
( composition(join(one,one),complement(B)) != complement(B)
| complement(composition(join(one,one),complement(B))) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),complement(B))),complement(composition(join(one,one),complement(B)))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
complement(composition(join(one,one),complement(B))) = complement(complement(B)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(B)),complement(B)) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
( complement(composition(join(one,one),complement(B))) != complement(complement(B))
| meet(B,B) != complement(composition(join(one,one),complement(B)))
| meet(B,B) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(B,B),complement(composition(join(one,one),complement(B)))) ),[1],$fot(complement(complement(B)))]]) ).
cnf(refute_0_140,plain,
( meet(B,B) != complement(composition(join(one,one),complement(B)))
| meet(B,B) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),complement(B))),complement(complement(B))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
meet(B,B) = complement(complement(B)),
inference(resolve,[$cnf( $equal(meet(B,B),complement(composition(join(one,one),complement(B)))) )],[refute_0_74,refute_0_140]) ).
cnf(refute_0_142,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_143,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$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_144,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( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_144]) ).
cnf(refute_0_146,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_147,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_148,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_147]) ).
cnf(refute_0_149,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_150,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_151,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_7:[bind(X,$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_154,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_146,refute_0_154]) ).
cnf(refute_0_156,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$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_157,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_145,refute_0_157]) ).
cnf(refute_0_159,plain,
X_87 = join(meet(X_87,complement(X_87)),complement(join(complement(X_87),complement(X_87)))),
inference(subst,[],[refute_0_158:[bind(A,$fot(X_87)),bind(B,$fot(complement(X_87)))]]) ).
cnf(refute_0_160,plain,
converse(composition(X_22,converse(A))) = composition(converse(converse(A)),converse(X_22)),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(X_22)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_161,plain,
( converse(composition(X_22,converse(A))) != composition(converse(converse(A)),converse(X_22))
| converse(converse(A)) != A
| converse(composition(X_22,converse(A))) = composition(A,converse(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_22,converse(A))),composition(converse(converse(A)),converse(X_22))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_162,plain,
( converse(composition(X_22,converse(A))) != composition(converse(converse(A)),converse(X_22))
| converse(composition(X_22,converse(A))) = composition(A,converse(X_22)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_161]) ).
cnf(refute_0_163,plain,
converse(composition(X_22,converse(A))) = composition(A,converse(X_22)),
inference(resolve,[$cnf( $equal(converse(composition(X_22,converse(A))),composition(converse(converse(A)),converse(X_22))) )],[refute_0_160,refute_0_162]) ).
cnf(refute_0_164,plain,
converse(composition(join(one,one),converse(A))) = composition(A,converse(join(one,one))),
inference(subst,[],[refute_0_163:[bind(X_22,$fot(join(one,one)))]]) ).
cnf(refute_0_165,plain,
composition(join(one,one),converse(A)) = join(converse(A),converse(A)),
inference(subst,[],[refute_0_68:[bind(X_47,$fot(converse(A)))]]) ).
cnf(refute_0_166,plain,
( composition(join(one,one),converse(A)) != join(converse(A),converse(A))
| converse(composition(join(one,one),converse(A))) != composition(A,converse(join(one,one)))
| converse(join(converse(A),converse(A))) = composition(A,converse(join(one,one))) ),
introduced(tautology,[equality,[$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_167,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( $equal(composition(join(one,one),converse(A)),join(converse(A),converse(A))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
converse(join(converse(A),converse(A))) = composition(A,converse(join(one,one))),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),converse(A))),composition(A,converse(join(one,one)))) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
join(A,converse(converse(A))) = join(A,converse(converse(A))),
introduced(tautology,[refl,[$fot(join(A,converse(converse(A))))]]) ).
cnf(refute_0_170,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_171,plain,
( converse(converse(A)) != A
| join(A,converse(converse(A))) = join(A,A) ),
inference(resolve,[$cnf( $equal(join(A,converse(converse(A))),join(A,converse(converse(A)))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
join(A,converse(converse(A))) = join(A,A),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_171]) ).
cnf(refute_0_173,plain,
converse(join(converse(A),converse(A))) = join(A,converse(converse(A))),
inference(subst,[],[refute_0_89:[bind(X_13,$fot(converse(A)))]]) ).
cnf(refute_0_174,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_7:[bind(X,$fot(converse(join(converse(A),converse(A))))),bind(Y,$fot(join(A,converse(converse(A))))),bind(Z,$fot(join(A,A)))]]) ).
cnf(refute_0_175,plain,
( join(A,converse(converse(A))) != join(A,A)
| converse(join(converse(A),converse(A))) = join(A,A) ),
inference(resolve,[$cnf( $equal(converse(join(converse(A),converse(A))),join(A,converse(converse(A)))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
converse(join(converse(A),converse(A))) = join(A,A),
inference(resolve,[$cnf( $equal(join(A,converse(converse(A))),join(A,A)) )],[refute_0_172,refute_0_175]) ).
cnf(refute_0_177,plain,
( converse(join(converse(A),converse(A))) != composition(A,converse(join(one,one)))
| converse(join(converse(A),converse(A))) != join(A,A)
| join(A,A) = composition(A,converse(join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),converse(A))),composition(A,converse(join(one,one)))) ),[0],$fot(join(A,A))]]) ).
cnf(refute_0_178,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( $equal(converse(join(converse(A),converse(A))),join(A,A)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
composition(A,converse(join(one,one))) = composition(A,converse(join(one,one))),
introduced(tautology,[refl,[$fot(composition(A,converse(join(one,one))))]]) ).
cnf(refute_0_180,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_181,plain,
( converse(join(one,one)) != join(one,one)
| composition(A,converse(join(one,one))) = composition(A,join(one,one)) ),
inference(resolve,[$cnf( $equal(composition(A,converse(join(one,one))),composition(A,converse(join(one,one)))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
composition(A,converse(join(one,one))) = composition(A,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_97,refute_0_181]) ).
cnf(refute_0_183,plain,
( composition(A,converse(join(one,one))) != composition(A,join(one,one))
| join(A,A) != composition(A,converse(join(one,one)))
| join(A,A) = composition(A,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,A),composition(A,converse(join(one,one)))) ),[1],$fot(composition(A,join(one,one)))]]) ).
cnf(refute_0_184,plain,
( join(A,A) != composition(A,converse(join(one,one)))
| join(A,A) = composition(A,join(one,one)) ),
inference(resolve,[$cnf( $equal(composition(A,converse(join(one,one))),composition(A,join(one,one))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
( converse(join(converse(A),converse(A))) != composition(A,converse(join(one,one)))
| join(A,A) = composition(A,join(one,one)) ),
inference(resolve,[$cnf( $equal(join(A,A),composition(A,converse(join(one,one)))) )],[refute_0_178,refute_0_184]) ).
cnf(refute_0_186,plain,
join(A,A) = composition(A,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),converse(A))),composition(A,converse(join(one,one)))) )],[refute_0_168,refute_0_185]) ).
cnf(refute_0_187,plain,
join(complement(X_87),complement(X_87)) = composition(complement(X_87),join(one,one)),
inference(subst,[],[refute_0_186:[bind(A,$fot(complement(X_87)))]]) ).
cnf(refute_0_188,plain,
( X_87 != join(meet(X_87,complement(X_87)),complement(join(complement(X_87),complement(X_87))))
| join(complement(X_87),complement(X_87)) != composition(complement(X_87),join(one,one))
| X_87 = join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_87,join(meet(X_87,complement(X_87)),complement(join(complement(X_87),complement(X_87))))) ),[1,1,0],$fot(composition(complement(X_87),join(one,one)))]]) ).
cnf(refute_0_189,plain,
( X_87 != join(meet(X_87,complement(X_87)),complement(join(complement(X_87),complement(X_87))))
| X_87 = join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_87),complement(X_87)),composition(complement(X_87),join(one,one))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
X_87 = join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,complement(X_87)),complement(join(complement(X_87),complement(X_87))))) )],[refute_0_159,refute_0_189]) ).
cnf(refute_0_191,plain,
composition(join(one,one),composition(X_55,X_56)) = composition(composition(join(one,one),X_55),X_56),
inference(subst,[],[composition_associativity_5:[bind(A,$fot(join(one,one))),bind(B,$fot(X_55)),bind(C,$fot(X_56))]]) ).
cnf(refute_0_192,plain,
composition(join(one,one),X_55) = join(X_55,X_55),
inference(subst,[],[refute_0_68:[bind(X_47,$fot(X_55))]]) ).
cnf(refute_0_193,plain,
( composition(join(one,one),X_55) != join(X_55,X_55)
| composition(join(one,one),composition(X_55,X_56)) != composition(composition(join(one,one),X_55),X_56)
| composition(join(one,one),composition(X_55,X_56)) = composition(join(X_55,X_55),X_56) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),composition(X_55,X_56)),composition(composition(join(one,one),X_55),X_56)) ),[1,0],$fot(join(X_55,X_55))]]) ).
cnf(refute_0_194,plain,
( composition(join(one,one),composition(X_55,X_56)) != composition(composition(join(one,one),X_55),X_56)
| composition(join(one,one),composition(X_55,X_56)) = composition(join(X_55,X_55),X_56) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_55),join(X_55,X_55)) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
composition(join(one,one),composition(X_55,X_56)) = composition(join(X_55,X_55),X_56),
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(X_55,X_56)),composition(composition(join(one,one),X_55),X_56)) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
composition(join(one,one),composition(join(one,one),complement(X_64))) = composition(join(join(one,one),join(one,one)),complement(X_64)),
inference(subst,[],[refute_0_195:[bind(X_55,$fot(join(one,one))),bind(X_56,$fot(complement(X_64)))]]) ).
cnf(refute_0_197,plain,
composition(join(one,one),complement(X_64)) = complement(X_64),
inference(subst,[],[refute_0_133:[bind(X_63,$fot(X_64))]]) ).
cnf(refute_0_198,plain,
( composition(join(one,one),complement(X_64)) != complement(X_64)
| composition(join(one,one),composition(join(one,one),complement(X_64))) != composition(join(join(one,one),join(one,one)),complement(X_64))
| composition(join(one,one),complement(X_64)) = composition(join(join(one,one),join(one,one)),complement(X_64)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),composition(join(one,one),complement(X_64))),composition(join(join(one,one),join(one,one)),complement(X_64))) ),[0,1],$fot(complement(X_64))]]) ).
cnf(refute_0_199,plain,
( composition(join(one,one),composition(join(one,one),complement(X_64))) != composition(join(join(one,one),join(one,one)),complement(X_64))
| composition(join(one,one),complement(X_64)) = composition(join(join(one,one),join(one,one)),complement(X_64)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_64)),complement(X_64)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
composition(join(one,one),complement(X_64)) = composition(join(join(one,one),join(one,one)),complement(X_64)),
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(join(one,one),complement(X_64))),composition(join(join(one,one),join(one,one)),complement(X_64))) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
( composition(join(one,one),complement(X_64)) != complement(X_64)
| composition(join(one,one),complement(X_64)) != composition(join(join(one,one),join(one,one)),complement(X_64))
| complement(X_64) = composition(join(join(one,one),join(one,one)),complement(X_64)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),complement(X_64)),composition(join(join(one,one),join(one,one)),complement(X_64))) ),[0],$fot(complement(X_64))]]) ).
cnf(refute_0_202,plain,
( composition(join(one,one),complement(X_64)) != composition(join(join(one,one),join(one,one)),complement(X_64))
| complement(X_64) = composition(join(join(one,one),join(one,one)),complement(X_64)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_64)),complement(X_64)) )],[refute_0_197,refute_0_201]) ).
cnf(refute_0_203,plain,
composition(join(one,one),composition(X_59,X_60)) = join(composition(X_59,X_60),composition(X_59,X_60)),
inference(subst,[],[refute_0_68:[bind(X_47,$fot(composition(X_59,X_60)))]]) ).
cnf(refute_0_204,plain,
composition(join(one,one),composition(X_59,X_60)) = composition(join(X_59,X_59),X_60),
inference(subst,[],[refute_0_195:[bind(X_55,$fot(X_59)),bind(X_56,$fot(X_60))]]) ).
cnf(refute_0_205,plain,
( composition(join(one,one),composition(X_59,X_60)) != composition(join(X_59,X_59),X_60)
| composition(join(one,one),composition(X_59,X_60)) != join(composition(X_59,X_60),composition(X_59,X_60))
| composition(join(X_59,X_59),X_60) = join(composition(X_59,X_60),composition(X_59,X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),composition(X_59,X_60)),join(composition(X_59,X_60),composition(X_59,X_60))) ),[0],$fot(composition(join(X_59,X_59),X_60))]]) ).
cnf(refute_0_206,plain,
( composition(join(one,one),composition(X_59,X_60)) != join(composition(X_59,X_60),composition(X_59,X_60))
| composition(join(X_59,X_59),X_60) = join(composition(X_59,X_60),composition(X_59,X_60)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(X_59,X_60)),composition(join(X_59,X_59),X_60)) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
composition(join(X_59,X_59),X_60) = join(composition(X_59,X_60),composition(X_59,X_60)),
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(X_59,X_60)),join(composition(X_59,X_60),composition(X_59,X_60))) )],[refute_0_203,refute_0_206]) ).
cnf(refute_0_208,plain,
( composition(A,composition(B,C)) != composition(composition(A,B),C)
| composition(composition(A,B),C) = composition(A,composition(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(A,composition(B,C)))),bind(Y,$fot(composition(composition(A,B),C)))]]) ).
cnf(refute_0_209,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(resolve,[$cnf( $equal(composition(A,composition(B,C)),composition(composition(A,B),C)) )],[composition_associativity_5,refute_0_208]) ).
cnf(refute_0_210,plain,
composition(composition(X_59,X_60),join(one,one)) = composition(X_59,composition(X_60,join(one,one))),
inference(subst,[],[refute_0_209:[bind(A,$fot(X_59)),bind(B,$fot(X_60)),bind(C,$fot(join(one,one)))]]) ).
cnf(refute_0_211,plain,
join(composition(X_59,X_60),composition(X_59,X_60)) = composition(composition(X_59,X_60),join(one,one)),
inference(subst,[],[refute_0_186:[bind(A,$fot(composition(X_59,X_60)))]]) ).
cnf(refute_0_212,plain,
( composition(composition(X_59,X_60),join(one,one)) != composition(X_59,composition(X_60,join(one,one)))
| join(composition(X_59,X_60),composition(X_59,X_60)) != composition(composition(X_59,X_60),join(one,one))
| join(composition(X_59,X_60),composition(X_59,X_60)) = composition(X_59,composition(X_60,join(one,one))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(composition(X_59,X_60),composition(X_59,X_60)))),bind(Y,$fot(composition(composition(X_59,X_60),join(one,one)))),bind(Z,$fot(composition(X_59,composition(X_60,join(one,one)))))]]) ).
cnf(refute_0_213,plain,
( composition(composition(X_59,X_60),join(one,one)) != composition(X_59,composition(X_60,join(one,one)))
| join(composition(X_59,X_60),composition(X_59,X_60)) = composition(X_59,composition(X_60,join(one,one))) ),
inference(resolve,[$cnf( $equal(join(composition(X_59,X_60),composition(X_59,X_60)),composition(composition(X_59,X_60),join(one,one))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
join(composition(X_59,X_60),composition(X_59,X_60)) = composition(X_59,composition(X_60,join(one,one))),
inference(resolve,[$cnf( $equal(composition(composition(X_59,X_60),join(one,one)),composition(X_59,composition(X_60,join(one,one)))) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
( composition(join(X_59,X_59),X_60) != join(composition(X_59,X_60),composition(X_59,X_60))
| join(composition(X_59,X_60),composition(X_59,X_60)) != composition(X_59,composition(X_60,join(one,one)))
| composition(join(X_59,X_59),X_60) = composition(X_59,composition(X_60,join(one,one))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_59,X_59),X_60),composition(X_59,composition(X_60,join(one,one)))) ),[0],$fot(join(composition(X_59,X_60),composition(X_59,X_60)))]]) ).
cnf(refute_0_216,plain,
( composition(join(X_59,X_59),X_60) != join(composition(X_59,X_60),composition(X_59,X_60))
| composition(join(X_59,X_59),X_60) = composition(X_59,composition(X_60,join(one,one))) ),
inference(resolve,[$cnf( $equal(join(composition(X_59,X_60),composition(X_59,X_60)),composition(X_59,composition(X_60,join(one,one)))) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
composition(join(X_59,X_59),X_60) = composition(X_59,composition(X_60,join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(X_59,X_59),X_60),join(composition(X_59,X_60),composition(X_59,X_60))) )],[refute_0_207,refute_0_216]) ).
cnf(refute_0_218,plain,
composition(join(join(one,one),join(one,one)),complement(X_64)) = composition(join(one,one),composition(complement(X_64),join(one,one))),
inference(subst,[],[refute_0_217:[bind(X_59,$fot(join(one,one))),bind(X_60,$fot(complement(X_64)))]]) ).
cnf(refute_0_219,plain,
( complement(X_64) != composition(join(join(one,one),join(one,one)),complement(X_64))
| composition(join(join(one,one),join(one,one)),complement(X_64)) != composition(join(one,one),composition(complement(X_64),join(one,one)))
| complement(X_64) = composition(join(one,one),composition(complement(X_64),join(one,one))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_64),composition(join(one,one),composition(complement(X_64),join(one,one)))) ),[0],$fot(composition(join(join(one,one),join(one,one)),complement(X_64)))]]) ).
cnf(refute_0_220,plain,
( complement(X_64) != composition(join(join(one,one),join(one,one)),complement(X_64))
| complement(X_64) = composition(join(one,one),composition(complement(X_64),join(one,one))) ),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),join(one,one)),complement(X_64)),composition(join(one,one),composition(complement(X_64),join(one,one)))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
( composition(join(one,one),complement(X_64)) != composition(join(join(one,one),join(one,one)),complement(X_64))
| complement(X_64) = composition(join(one,one),composition(complement(X_64),join(one,one))) ),
inference(resolve,[$cnf( $equal(complement(X_64),composition(join(join(one,one),join(one,one)),complement(X_64))) )],[refute_0_202,refute_0_220]) ).
cnf(refute_0_222,plain,
complement(X_64) = composition(join(one,one),composition(complement(X_64),join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_64)),composition(join(join(one,one),join(one,one)),complement(X_64))) )],[refute_0_200,refute_0_221]) ).
cnf(refute_0_223,plain,
composition(join(one,one),composition(complement(X_64),C)) = composition(composition(join(one,one),complement(X_64)),C),
inference(subst,[],[composition_associativity_5:[bind(A,$fot(join(one,one))),bind(B,$fot(complement(X_64)))]]) ).
cnf(refute_0_224,plain,
( composition(join(one,one),complement(X_64)) != complement(X_64)
| composition(join(one,one),composition(complement(X_64),C)) != composition(composition(join(one,one),complement(X_64)),C)
| composition(join(one,one),composition(complement(X_64),C)) = composition(complement(X_64),C) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),composition(complement(X_64),C)),composition(composition(join(one,one),complement(X_64)),C)) ),[1,0],$fot(complement(X_64))]]) ).
cnf(refute_0_225,plain,
( composition(join(one,one),composition(complement(X_64),C)) != composition(composition(join(one,one),complement(X_64)),C)
| composition(join(one,one),composition(complement(X_64),C)) = composition(complement(X_64),C) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_64)),complement(X_64)) )],[refute_0_197,refute_0_224]) ).
cnf(refute_0_226,plain,
composition(join(one,one),composition(complement(X_64),C)) = composition(complement(X_64),C),
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(complement(X_64),C)),composition(composition(join(one,one),complement(X_64)),C)) )],[refute_0_223,refute_0_225]) ).
cnf(refute_0_227,plain,
composition(join(one,one),composition(complement(X_64),join(one,one))) = composition(complement(X_64),join(one,one)),
inference(subst,[],[refute_0_226:[bind(C,$fot(join(one,one)))]]) ).
cnf(refute_0_228,plain,
( complement(X_64) != composition(join(one,one),composition(complement(X_64),join(one,one)))
| composition(join(one,one),composition(complement(X_64),join(one,one))) != composition(complement(X_64),join(one,one))
| complement(X_64) = composition(complement(X_64),join(one,one)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_64),composition(complement(X_64),join(one,one))) ),[0],$fot(composition(join(one,one),composition(complement(X_64),join(one,one))))]]) ).
cnf(refute_0_229,plain,
( complement(X_64) != composition(join(one,one),composition(complement(X_64),join(one,one)))
| complement(X_64) = composition(complement(X_64),join(one,one)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(complement(X_64),join(one,one))),composition(complement(X_64),join(one,one))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
complement(X_64) = composition(complement(X_64),join(one,one)),
inference(resolve,[$cnf( $equal(complement(X_64),composition(join(one,one),composition(complement(X_64),join(one,one)))) )],[refute_0_222,refute_0_229]) ).
cnf(refute_0_231,plain,
( complement(X_64) != composition(complement(X_64),join(one,one))
| composition(complement(X_64),join(one,one)) = complement(X_64) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_64))),bind(Y,$fot(composition(complement(X_64),join(one,one))))]]) ).
cnf(refute_0_232,plain,
composition(complement(X_64),join(one,one)) = complement(X_64),
inference(resolve,[$cnf( $equal(complement(X_64),composition(complement(X_64),join(one,one))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
composition(complement(X_87),join(one,one)) = complement(X_87),
inference(subst,[],[refute_0_232:[bind(X_64,$fot(X_87))]]) ).
cnf(refute_0_234,plain,
complement(composition(complement(X_87),join(one,one))) = complement(composition(complement(X_87),join(one,one))),
introduced(tautology,[refl,[$fot(complement(composition(complement(X_87),join(one,one))))]]) ).
cnf(refute_0_235,plain,
( complement(composition(complement(X_87),join(one,one))) != complement(composition(complement(X_87),join(one,one)))
| composition(complement(X_87),join(one,one)) != complement(X_87)
| complement(composition(complement(X_87),join(one,one))) = complement(complement(X_87)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(complement(X_87),join(one,one))),complement(composition(complement(X_87),join(one,one)))) ),[1,0],$fot(complement(X_87))]]) ).
cnf(refute_0_236,plain,
( composition(complement(X_87),join(one,one)) != complement(X_87)
| complement(composition(complement(X_87),join(one,one))) = complement(complement(X_87)) ),
inference(resolve,[$cnf( $equal(complement(composition(complement(X_87),join(one,one))),complement(composition(complement(X_87),join(one,one)))) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
complement(composition(complement(X_87),join(one,one))) = complement(complement(X_87)),
inference(resolve,[$cnf( $equal(composition(complement(X_87),join(one,one)),complement(X_87)) )],[refute_0_233,refute_0_236]) ).
cnf(refute_0_238,plain,
join(zero,complement(composition(complement(X_87),join(one,one)))) = join(zero,complement(composition(complement(X_87),join(one,one)))),
introduced(tautology,[refl,[$fot(join(zero,complement(composition(complement(X_87),join(one,one)))))]]) ).
cnf(refute_0_239,plain,
( complement(composition(complement(X_87),join(one,one))) != complement(complement(X_87))
| join(zero,complement(composition(complement(X_87),join(one,one)))) != join(zero,complement(composition(complement(X_87),join(one,one))))
| join(zero,complement(composition(complement(X_87),join(one,one)))) = join(zero,complement(complement(X_87))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(composition(complement(X_87),join(one,one)))),join(zero,complement(composition(complement(X_87),join(one,one))))) ),[1,1],$fot(complement(complement(X_87)))]]) ).
cnf(refute_0_240,plain,
( complement(composition(complement(X_87),join(one,one))) != complement(complement(X_87))
| join(zero,complement(composition(complement(X_87),join(one,one)))) = join(zero,complement(complement(X_87))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(complement(X_87),join(one,one)))),join(zero,complement(composition(complement(X_87),join(one,one))))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
join(zero,complement(composition(complement(X_87),join(one,one)))) = join(zero,complement(complement(X_87))),
inference(resolve,[$cnf( $equal(complement(composition(complement(X_87),join(one,one))),complement(complement(X_87))) )],[refute_0_237,refute_0_240]) ).
cnf(refute_0_242,plain,
( zero != meet(A,complement(A))
| meet(A,complement(A)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(A,complement(A))))]]) ).
cnf(refute_0_243,plain,
meet(A,complement(A)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(A,complement(A))) )],[def_zero_13,refute_0_242]) ).
cnf(refute_0_244,plain,
meet(X_87,complement(X_87)) = zero,
inference(subst,[],[refute_0_243:[bind(A,$fot(X_87))]]) ).
cnf(refute_0_245,plain,
join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) = join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))),
introduced(tautology,[refl,[$fot(join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))))]]) ).
cnf(refute_0_246,plain,
( join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) != join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one))))
| meet(X_87,complement(X_87)) != zero
| join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) = join(zero,complement(composition(complement(X_87),join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))),join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_247,plain,
( meet(X_87,complement(X_87)) != zero
| join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) = join(zero,complement(composition(complement(X_87),join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))),join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one))))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) = join(zero,complement(composition(complement(X_87),join(one,one)))),
inference(resolve,[$cnf( $equal(meet(X_87,complement(X_87)),zero) )],[refute_0_244,refute_0_247]) ).
cnf(refute_0_249,plain,
( join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) != join(zero,complement(composition(complement(X_87),join(one,one))))
| join(zero,complement(composition(complement(X_87),join(one,one)))) != join(zero,complement(complement(X_87)))
| join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) = join(zero,complement(complement(X_87))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))))),bind(Y,$fot(join(zero,complement(composition(complement(X_87),join(one,one)))))),bind(Z,$fot(join(zero,complement(complement(X_87)))))]]) ).
cnf(refute_0_250,plain,
( join(zero,complement(composition(complement(X_87),join(one,one)))) != join(zero,complement(complement(X_87)))
| join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) = join(zero,complement(complement(X_87))) ),
inference(resolve,[$cnf( $equal(join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))),join(zero,complement(composition(complement(X_87),join(one,one))))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) = join(zero,complement(complement(X_87))),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(complement(X_87),join(one,one)))),join(zero,complement(complement(X_87)))) )],[refute_0_241,refute_0_250]) ).
cnf(refute_0_252,plain,
( X_87 != join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one))))
| join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))) != join(zero,complement(complement(X_87)))
| X_87 = join(zero,complement(complement(X_87))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_87,join(zero,complement(complement(X_87)))) ),[0],$fot(join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))))]]) ).
cnf(refute_0_253,plain,
( X_87 != join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one))))
| X_87 = join(zero,complement(complement(X_87))) ),
inference(resolve,[$cnf( $equal(join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one)))),join(zero,complement(complement(X_87)))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
X_87 = join(zero,complement(complement(X_87))),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,complement(X_87)),complement(composition(complement(X_87),join(one,one))))) )],[refute_0_190,refute_0_253]) ).
cnf(refute_0_255,plain,
X_87 = join(meet(X_87,top),complement(join(complement(X_87),top))),
inference(subst,[],[refute_0_158:[bind(A,$fot(X_87)),bind(B,$fot(top))]]) ).
cnf(refute_0_256,plain,
meet(A,top) = complement(join(complement(A),complement(top))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(top))]]) ).
cnf(refute_0_257,plain,
zero = meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_258,plain,
meet(X_6,X_7) = complement(join(complement(X_6),complement(X_7))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_6)),bind(B,$fot(X_7))]]) ).
cnf(refute_0_259,plain,
( meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| complement(join(complement(X_6),complement(X_7))) = meet(X_6,X_7) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_6,X_7))),bind(Y,$fot(complement(join(complement(X_6),complement(X_7)))))]]) ).
cnf(refute_0_260,plain,
complement(join(complement(X_6),complement(X_7))) = meet(X_6,X_7),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| zero != meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) ),[1,1],$fot(meet(X_6,X_7))]]) ).
cnf(refute_0_262,plain,
( zero != meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
zero = meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) )],[refute_0_257,refute_0_262]) ).
cnf(refute_0_264,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_265,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_264]) ).
cnf(refute_0_266,plain,
join(meet(X_6,X_7),complement(meet(X_6,X_7))) = top,
inference(subst,[],[refute_0_265:[bind(A,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_267,plain,
complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))))]]) ).
cnf(refute_0_268,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))
| join(meet(X_6,X_7),complement(meet(X_6,X_7))) != top
| complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_269,plain,
( join(meet(X_6,X_7),complement(meet(X_6,X_7))) != top
| complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_6,X_7),complement(meet(X_6,X_7))),top) )],[refute_0_266,refute_0_269]) ).
cnf(refute_0_271,plain,
meet(join(complement(X_6),complement(X_7)),B) = complement(join(complement(join(complement(X_6),complement(X_7))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_272,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| meet(join(complement(X_6),complement(X_7)),B) != complement(join(complement(join(complement(X_6),complement(X_7))),complement(B)))
| meet(join(complement(X_6),complement(X_7)),B) = complement(join(meet(X_6,X_7),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),B),complement(join(complement(join(complement(X_6),complement(X_7))),complement(B)))) ),[1,0,0],$fot(meet(X_6,X_7))]]) ).
cnf(refute_0_273,plain,
( meet(join(complement(X_6),complement(X_7)),B) != complement(join(complement(join(complement(X_6),complement(X_7))),complement(B)))
| meet(join(complement(X_6),complement(X_7)),B) = complement(join(meet(X_6,X_7),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_260,refute_0_272]) ).
cnf(refute_0_274,plain,
meet(join(complement(X_6),complement(X_7)),B) = complement(join(meet(X_6,X_7),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),B),complement(join(complement(join(complement(X_6),complement(X_7))),complement(B)))) )],[refute_0_271,refute_0_273]) ).
cnf(refute_0_275,plain,
meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),
inference(subst,[],[refute_0_274:[bind(B,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_276,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(top)
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) != complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)))),bind(Y,$fot(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_277,plain,
( complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))) != complement(top)
| meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),complement(join(meet(X_6,X_7),complement(meet(X_6,X_7))))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_6,X_7),complement(meet(X_6,X_7)))),complement(top)) )],[refute_0_270,refute_0_277]) ).
cnf(refute_0_279,plain,
( meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) != complement(top)
| zero != meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_280,plain,
( zero != meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),complement(top)) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) )],[refute_0_263,refute_0_280]) ).
cnf(refute_0_282,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_283,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
( complement(top) != zero
| meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_285,plain,
( meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
meet(A,top) = complement(join(complement(A),zero)),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) )],[refute_0_256,refute_0_285]) ).
cnf(refute_0_287,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_288,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_289,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_288]) ).
cnf(refute_0_290,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_287,refute_0_289]) ).
cnf(refute_0_291,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) = meet(top,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,B))),bind(Y,$fot(complement(join(zero,complement(B)))))]]) ).
cnf(refute_0_292,plain,
complement(join(zero,complement(B))) = meet(top,B),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
complement(join(zero,complement(A))) = meet(top,A),
inference(subst,[],[refute_0_292:[bind(B,$fot(A))]]) ).
cnf(refute_0_294,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_295,plain,
complement(join(complement(A),zero)) = complement(join(complement(A),zero)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),zero)))]]) ).
cnf(refute_0_296,plain,
( complement(join(complement(A),zero)) != complement(join(complement(A),zero))
| join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) ),[1,0],$fot(join(zero,complement(A)))]]) ).
cnf(refute_0_297,plain,
( join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
complement(join(complement(A),zero)) = complement(join(zero,complement(A))),
inference(resolve,[$cnf( $equal(join(complement(A),zero),join(zero,complement(A))) )],[refute_0_294,refute_0_297]) ).
cnf(refute_0_299,plain,
( complement(join(complement(A),zero)) != complement(join(zero,complement(A)))
| complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(complement(join(complement(A),zero)))),bind(Y,$fot(complement(join(zero,complement(A))))),bind(Z,$fot(meet(top,A)))]]) ).
cnf(refute_0_300,plain,
( complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(zero,complement(A)))) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
complement(join(complement(A),zero)) = meet(top,A),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(A))),meet(top,A)) )],[refute_0_293,refute_0_300]) ).
cnf(refute_0_302,plain,
( complement(join(complement(A),zero)) != meet(top,A)
| meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) ),[1],$fot(meet(top,A))]]) ).
cnf(refute_0_303,plain,
( meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),meet(top,A)) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
meet(A,top) = meet(top,A),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) )],[refute_0_286,refute_0_303]) ).
cnf(refute_0_305,plain,
meet(X_87,top) = meet(top,X_87),
inference(subst,[],[refute_0_304:[bind(A,$fot(X_87))]]) ).
cnf(refute_0_306,plain,
( X_87 != join(meet(X_87,top),complement(join(complement(X_87),top)))
| meet(X_87,top) != meet(top,X_87)
| X_87 = join(meet(top,X_87),complement(join(complement(X_87),top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_87,join(meet(X_87,top),complement(join(complement(X_87),top)))) ),[1,0],$fot(meet(top,X_87))]]) ).
cnf(refute_0_307,plain,
( X_87 != join(meet(X_87,top),complement(join(complement(X_87),top)))
| X_87 = join(meet(top,X_87),complement(join(complement(X_87),top))) ),
inference(resolve,[$cnf( $equal(meet(X_87,top),meet(top,X_87)) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
X_87 = join(meet(top,X_87),complement(join(complement(X_87),top))),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,top),complement(join(complement(X_87),top)))) )],[refute_0_255,refute_0_307]) ).
cnf(refute_0_309,plain,
join(meet(top,X_87),zero) = join(zero,meet(top,X_87)),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(meet(top,X_87)))]]) ).
cnf(refute_0_310,plain,
join(X_35,join(complement(X_35),X_37)) = join(join(X_35,complement(X_35)),X_37),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_35)),bind(B,$fot(complement(X_35))),bind(C,$fot(X_37))]]) ).
cnf(refute_0_311,plain,
top = join(X_35,complement(X_35)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_35))]]) ).
cnf(refute_0_312,plain,
( top != join(X_35,complement(X_35))
| join(X_35,complement(X_35)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(X_35,complement(X_35))))]]) ).
cnf(refute_0_313,plain,
join(X_35,complement(X_35)) = top,
inference(resolve,[$cnf( $equal(top,join(X_35,complement(X_35))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
( join(X_35,complement(X_35)) != top
| join(X_35,join(complement(X_35),X_37)) != join(join(X_35,complement(X_35)),X_37)
| join(X_35,join(complement(X_35),X_37)) = join(top,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,join(complement(X_35),X_37)),join(join(X_35,complement(X_35)),X_37)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_315,plain,
( join(X_35,join(complement(X_35),X_37)) != join(join(X_35,complement(X_35)),X_37)
| join(X_35,join(complement(X_35),X_37)) = join(top,X_37) ),
inference(resolve,[$cnf( $equal(join(X_35,complement(X_35)),top) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
join(X_35,join(complement(X_35),X_37)) = join(top,X_37),
inference(resolve,[$cnf( $equal(join(X_35,join(complement(X_35),X_37)),join(join(X_35,complement(X_35)),X_37)) )],[refute_0_310,refute_0_315]) ).
cnf(refute_0_317,plain,
join(X_41,join(complement(X_41),complement(complement(X_41)))) = join(top,complement(complement(X_41))),
inference(subst,[],[refute_0_316:[bind(X_35,$fot(X_41)),bind(X_37,$fot(complement(complement(X_41))))]]) ).
cnf(refute_0_318,plain,
top = join(complement(X_41),complement(complement(X_41))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_41)))]]) ).
cnf(refute_0_319,plain,
( top != join(complement(X_41),complement(complement(X_41)))
| join(complement(X_41),complement(complement(X_41))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_41),complement(complement(X_41)))))]]) ).
cnf(refute_0_320,plain,
join(complement(X_41),complement(complement(X_41))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_41),complement(complement(X_41)))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
( join(X_41,join(complement(X_41),complement(complement(X_41)))) != join(top,complement(complement(X_41)))
| join(complement(X_41),complement(complement(X_41))) != top
| join(X_41,top) = join(top,complement(complement(X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,join(complement(X_41),complement(complement(X_41)))),join(top,complement(complement(X_41)))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_322,plain,
( join(X_41,join(complement(X_41),complement(complement(X_41)))) != join(top,complement(complement(X_41)))
| join(X_41,top) = join(top,complement(complement(X_41))) ),
inference(resolve,[$cnf( $equal(join(complement(X_41),complement(complement(X_41))),top) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
join(X_41,top) = join(top,complement(complement(X_41))),
inference(resolve,[$cnf( $equal(join(X_41,join(complement(X_41),complement(complement(X_41)))),join(top,complement(complement(X_41)))) )],[refute_0_317,refute_0_322]) ).
cnf(refute_0_324,plain,
join(X_35,join(complement(X_35),complement(X_35))) = join(top,complement(X_35)),
inference(subst,[],[refute_0_316:[bind(X_37,$fot(complement(X_35)))]]) ).
cnf(refute_0_325,plain,
join(complement(X_35),complement(X_35)) = composition(complement(X_35),join(one,one)),
inference(subst,[],[refute_0_186:[bind(A,$fot(complement(X_35)))]]) ).
cnf(refute_0_326,plain,
( join(X_35,join(complement(X_35),complement(X_35))) != join(top,complement(X_35))
| join(complement(X_35),complement(X_35)) != composition(complement(X_35),join(one,one))
| join(X_35,composition(complement(X_35),join(one,one))) = join(top,complement(X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,join(complement(X_35),complement(X_35))),join(top,complement(X_35))) ),[0,1],$fot(composition(complement(X_35),join(one,one)))]]) ).
cnf(refute_0_327,plain,
( join(X_35,join(complement(X_35),complement(X_35))) != join(top,complement(X_35))
| join(X_35,composition(complement(X_35),join(one,one))) = join(top,complement(X_35)) ),
inference(resolve,[$cnf( $equal(join(complement(X_35),complement(X_35)),composition(complement(X_35),join(one,one))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
join(X_35,composition(complement(X_35),join(one,one))) = join(top,complement(X_35)),
inference(resolve,[$cnf( $equal(join(X_35,join(complement(X_35),complement(X_35))),join(top,complement(X_35))) )],[refute_0_324,refute_0_327]) ).
cnf(refute_0_329,plain,
composition(complement(X_35),join(one,one)) = complement(X_35),
inference(subst,[],[refute_0_232:[bind(X_64,$fot(X_35))]]) ).
cnf(refute_0_330,plain,
join(X_35,composition(complement(X_35),join(one,one))) = join(X_35,composition(complement(X_35),join(one,one))),
introduced(tautology,[refl,[$fot(join(X_35,composition(complement(X_35),join(one,one))))]]) ).
cnf(refute_0_331,plain,
( composition(complement(X_35),join(one,one)) != complement(X_35)
| join(X_35,composition(complement(X_35),join(one,one))) != join(X_35,composition(complement(X_35),join(one,one)))
| join(X_35,composition(complement(X_35),join(one,one))) = join(X_35,complement(X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,composition(complement(X_35),join(one,one))),join(X_35,composition(complement(X_35),join(one,one)))) ),[1,1],$fot(complement(X_35))]]) ).
cnf(refute_0_332,plain,
( composition(complement(X_35),join(one,one)) != complement(X_35)
| join(X_35,composition(complement(X_35),join(one,one))) = join(X_35,complement(X_35)) ),
inference(resolve,[$cnf( $equal(join(X_35,composition(complement(X_35),join(one,one))),join(X_35,composition(complement(X_35),join(one,one)))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
join(X_35,composition(complement(X_35),join(one,one))) = join(X_35,complement(X_35)),
inference(resolve,[$cnf( $equal(composition(complement(X_35),join(one,one)),complement(X_35)) )],[refute_0_329,refute_0_332]) ).
cnf(refute_0_334,plain,
( join(X_35,complement(X_35)) != top
| join(X_35,composition(complement(X_35),join(one,one))) != join(X_35,complement(X_35))
| join(X_35,composition(complement(X_35),join(one,one))) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X_35,composition(complement(X_35),join(one,one))))),bind(Y,$fot(join(X_35,complement(X_35)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_335,plain,
( join(X_35,complement(X_35)) != top
| join(X_35,composition(complement(X_35),join(one,one))) = top ),
inference(resolve,[$cnf( $equal(join(X_35,composition(complement(X_35),join(one,one))),join(X_35,complement(X_35))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
join(X_35,composition(complement(X_35),join(one,one))) = top,
inference(resolve,[$cnf( $equal(join(X_35,complement(X_35)),top) )],[refute_0_313,refute_0_335]) ).
cnf(refute_0_337,plain,
( join(X_35,composition(complement(X_35),join(one,one))) != join(top,complement(X_35))
| join(X_35,composition(complement(X_35),join(one,one))) != top
| top = join(top,complement(X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,composition(complement(X_35),join(one,one))),join(top,complement(X_35))) ),[0],$fot(top)]]) ).
cnf(refute_0_338,plain,
( join(X_35,composition(complement(X_35),join(one,one))) != join(top,complement(X_35))
| top = join(top,complement(X_35)) ),
inference(resolve,[$cnf( $equal(join(X_35,composition(complement(X_35),join(one,one))),top) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
top = join(top,complement(X_35)),
inference(resolve,[$cnf( $equal(join(X_35,composition(complement(X_35),join(one,one))),join(top,complement(X_35))) )],[refute_0_328,refute_0_338]) ).
cnf(refute_0_340,plain,
( top != join(top,complement(X_35))
| join(top,complement(X_35)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(X_35))))]]) ).
cnf(refute_0_341,plain,
join(top,complement(X_35)) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(X_35))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
join(top,complement(complement(X_41))) = top,
inference(subst,[],[refute_0_341:[bind(X_35,$fot(complement(X_41)))]]) ).
cnf(refute_0_343,plain,
( join(X_41,top) != join(top,complement(complement(X_41)))
| join(top,complement(complement(X_41))) != top
| join(X_41,top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_41,top),top) ),[0],$fot(join(top,complement(complement(X_41))))]]) ).
cnf(refute_0_344,plain,
( join(X_41,top) != join(top,complement(complement(X_41)))
| join(X_41,top) = top ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(X_41))),top) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
join(X_41,top) = top,
inference(resolve,[$cnf( $equal(join(X_41,top),join(top,complement(complement(X_41)))) )],[refute_0_323,refute_0_344]) ).
cnf(refute_0_346,plain,
join(complement(X_87),top) = top,
inference(subst,[],[refute_0_345:[bind(X_41,$fot(complement(X_87)))]]) ).
cnf(refute_0_347,plain,
complement(join(complement(X_87),top)) = complement(join(complement(X_87),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(X_87),top)))]]) ).
cnf(refute_0_348,plain,
( complement(join(complement(X_87),top)) != complement(join(complement(X_87),top))
| join(complement(X_87),top) != top
| complement(join(complement(X_87),top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X_87),top)),complement(join(complement(X_87),top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_349,plain,
( join(complement(X_87),top) != top
| complement(join(complement(X_87),top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_87),top)),complement(join(complement(X_87),top))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
complement(join(complement(X_87),top)) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(X_87),top),top) )],[refute_0_346,refute_0_349]) ).
cnf(refute_0_351,plain,
( complement(join(complement(X_87),top)) != complement(top)
| complement(top) != zero
| complement(join(complement(X_87),top)) = zero ),
inference(subst,[],[refute_0_7:[bind(X,$fot(complement(join(complement(X_87),top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_352,plain,
( complement(top) != zero
| complement(join(complement(X_87),top)) = zero ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_87),top)),complement(top)) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
complement(join(complement(X_87),top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_352]) ).
cnf(refute_0_354,plain,
join(meet(top,X_87),complement(join(complement(X_87),top))) = join(meet(top,X_87),complement(join(complement(X_87),top))),
introduced(tautology,[refl,[$fot(join(meet(top,X_87),complement(join(complement(X_87),top))))]]) ).
cnf(refute_0_355,plain,
( complement(join(complement(X_87),top)) != zero
| join(meet(top,X_87),complement(join(complement(X_87),top))) != join(meet(top,X_87),complement(join(complement(X_87),top)))
| join(meet(top,X_87),complement(join(complement(X_87),top))) = join(meet(top,X_87),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_87),complement(join(complement(X_87),top))),join(meet(top,X_87),complement(join(complement(X_87),top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_356,plain,
( complement(join(complement(X_87),top)) != zero
| join(meet(top,X_87),complement(join(complement(X_87),top))) = join(meet(top,X_87),zero) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_87),complement(join(complement(X_87),top))),join(meet(top,X_87),complement(join(complement(X_87),top)))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
join(meet(top,X_87),complement(join(complement(X_87),top))) = join(meet(top,X_87),zero),
inference(resolve,[$cnf( $equal(complement(join(complement(X_87),top)),zero) )],[refute_0_353,refute_0_356]) ).
cnf(refute_0_358,plain,
( join(meet(top,X_87),complement(join(complement(X_87),top))) != join(meet(top,X_87),zero)
| join(meet(top,X_87),zero) != join(zero,meet(top,X_87))
| join(meet(top,X_87),complement(join(complement(X_87),top))) = join(zero,meet(top,X_87)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(meet(top,X_87),complement(join(complement(X_87),top))))),bind(Y,$fot(join(meet(top,X_87),zero))),bind(Z,$fot(join(zero,meet(top,X_87))))]]) ).
cnf(refute_0_359,plain,
( join(meet(top,X_87),zero) != join(zero,meet(top,X_87))
| join(meet(top,X_87),complement(join(complement(X_87),top))) = join(zero,meet(top,X_87)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_87),complement(join(complement(X_87),top))),join(meet(top,X_87),zero)) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
join(meet(top,X_87),complement(join(complement(X_87),top))) = join(zero,meet(top,X_87)),
inference(resolve,[$cnf( $equal(join(meet(top,X_87),zero),join(zero,meet(top,X_87))) )],[refute_0_309,refute_0_359]) ).
cnf(refute_0_361,plain,
( X_87 != join(meet(top,X_87),complement(join(complement(X_87),top)))
| join(meet(top,X_87),complement(join(complement(X_87),top))) != join(zero,meet(top,X_87))
| X_87 = join(zero,meet(top,X_87)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_87,join(zero,meet(top,X_87))) ),[0],$fot(join(meet(top,X_87),complement(join(complement(X_87),top))))]]) ).
cnf(refute_0_362,plain,
( X_87 != join(meet(top,X_87),complement(join(complement(X_87),top)))
| X_87 = join(zero,meet(top,X_87)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_87),complement(join(complement(X_87),top))),join(zero,meet(top,X_87))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
X_87 = join(zero,meet(top,X_87)),
inference(resolve,[$cnf( $equal(X_87,join(meet(top,X_87),complement(join(complement(X_87),top)))) )],[refute_0_308,refute_0_362]) ).
cnf(refute_0_364,plain,
complement(X_92) = join(zero,meet(top,complement(X_92))),
inference(subst,[],[refute_0_363:[bind(X_87,$fot(complement(X_92)))]]) ).
cnf(refute_0_365,plain,
meet(top,complement(X_90)) = complement(join(zero,complement(complement(X_90)))),
inference(subst,[],[refute_0_290:[bind(B,$fot(complement(X_90)))]]) ).
cnf(refute_0_366,plain,
X_90 = join(zero,complement(complement(X_90))),
inference(subst,[],[refute_0_254:[bind(X_87,$fot(X_90))]]) ).
cnf(refute_0_367,plain,
( X_90 != join(zero,complement(complement(X_90)))
| join(zero,complement(complement(X_90))) = X_90 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_90)),bind(Y,$fot(join(zero,complement(complement(X_90)))))]]) ).
cnf(refute_0_368,plain,
join(zero,complement(complement(X_90))) = X_90,
inference(resolve,[$cnf( $equal(X_90,join(zero,complement(complement(X_90)))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
( join(zero,complement(complement(X_90))) != X_90
| meet(top,complement(X_90)) != complement(join(zero,complement(complement(X_90))))
| meet(top,complement(X_90)) = complement(X_90) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(X_90)),complement(join(zero,complement(complement(X_90))))) ),[1,0],$fot(X_90)]]) ).
cnf(refute_0_370,plain,
( meet(top,complement(X_90)) != complement(join(zero,complement(complement(X_90))))
| meet(top,complement(X_90)) = complement(X_90) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_90))),X_90) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
meet(top,complement(X_90)) = complement(X_90),
inference(resolve,[$cnf( $equal(meet(top,complement(X_90)),complement(join(zero,complement(complement(X_90))))) )],[refute_0_365,refute_0_370]) ).
cnf(refute_0_372,plain,
meet(top,complement(X_92)) = complement(X_92),
inference(subst,[],[refute_0_371:[bind(X_90,$fot(X_92))]]) ).
cnf(refute_0_373,plain,
( complement(X_92) != join(zero,meet(top,complement(X_92)))
| meet(top,complement(X_92)) != complement(X_92)
| complement(X_92) = join(zero,complement(X_92)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_92),join(zero,meet(top,complement(X_92)))) ),[1,1],$fot(complement(X_92))]]) ).
cnf(refute_0_374,plain,
( complement(X_92) != join(zero,meet(top,complement(X_92)))
| complement(X_92) = join(zero,complement(X_92)) ),
inference(resolve,[$cnf( $equal(meet(top,complement(X_92)),complement(X_92)) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
complement(X_92) = join(zero,complement(X_92)),
inference(resolve,[$cnf( $equal(complement(X_92),join(zero,meet(top,complement(X_92)))) )],[refute_0_364,refute_0_374]) ).
cnf(refute_0_376,plain,
( complement(X_92) != join(zero,complement(X_92))
| join(zero,complement(X_92)) = complement(X_92) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_92))),bind(Y,$fot(join(zero,complement(X_92))))]]) ).
cnf(refute_0_377,plain,
join(zero,complement(X_92)) = complement(X_92),
inference(resolve,[$cnf( $equal(complement(X_92),join(zero,complement(X_92))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
join(zero,complement(complement(X_87))) = complement(complement(X_87)),
inference(subst,[],[refute_0_377:[bind(X_92,$fot(complement(X_87)))]]) ).
cnf(refute_0_379,plain,
( X_87 != join(zero,complement(complement(X_87)))
| join(zero,complement(complement(X_87))) != complement(complement(X_87))
| X_87 = complement(complement(X_87)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_87,complement(complement(X_87))) ),[0],$fot(join(zero,complement(complement(X_87))))]]) ).
cnf(refute_0_380,plain,
( X_87 != join(zero,complement(complement(X_87)))
| X_87 = complement(complement(X_87)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_87))),complement(complement(X_87))) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
X_87 = complement(complement(X_87)),
inference(resolve,[$cnf( $equal(X_87,join(zero,complement(complement(X_87)))) )],[refute_0_254,refute_0_380]) ).
cnf(refute_0_382,plain,
( X_87 != complement(complement(X_87))
| complement(complement(X_87)) = X_87 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_87)),bind(Y,$fot(complement(complement(X_87))))]]) ).
cnf(refute_0_383,plain,
complement(complement(X_87)) = X_87,
inference(resolve,[$cnf( $equal(X_87,complement(complement(X_87))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
complement(complement(B)) = B,
inference(subst,[],[refute_0_383:[bind(X_87,$fot(B))]]) ).
cnf(refute_0_385,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_386,plain,
( meet(B,B) != complement(complement(B))
| meet(B,B) = B ),
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
meet(B,B) = B,
inference(resolve,[$cnf( $equal(meet(B,B),complement(complement(B))) )],[refute_0_141,refute_0_386]) ).
cnf(refute_0_388,plain,
meet(composition(sk1,top),composition(sk1,top)) = composition(sk1,top),
inference(subst,[],[refute_0_387:[bind(B,$fot(composition(sk1,top)))]]) ).
cnf(refute_0_389,plain,
complement(meet(composition(sk1,top),composition(sk1,top))) = complement(meet(composition(sk1,top),composition(sk1,top))),
introduced(tautology,[refl,[$fot(complement(meet(composition(sk1,top),composition(sk1,top))))]]) ).
cnf(refute_0_390,plain,
( complement(meet(composition(sk1,top),composition(sk1,top))) != complement(meet(composition(sk1,top),composition(sk1,top)))
| meet(composition(sk1,top),composition(sk1,top)) != composition(sk1,top)
| complement(meet(composition(sk1,top),composition(sk1,top))) = complement(composition(sk1,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(composition(sk1,top),composition(sk1,top))),complement(meet(composition(sk1,top),composition(sk1,top)))) ),[1,0],$fot(composition(sk1,top))]]) ).
cnf(refute_0_391,plain,
( meet(composition(sk1,top),composition(sk1,top)) != composition(sk1,top)
| complement(meet(composition(sk1,top),composition(sk1,top))) = complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(complement(meet(composition(sk1,top),composition(sk1,top))),complement(meet(composition(sk1,top),composition(sk1,top)))) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
complement(meet(composition(sk1,top),composition(sk1,top))) = complement(composition(sk1,top)),
inference(resolve,[$cnf( $equal(meet(composition(sk1,top),composition(sk1,top)),composition(sk1,top)) )],[refute_0_388,refute_0_391]) ).
cnf(refute_0_393,plain,
join(complement(A),complement(B)) = join(zero,complement(complement(join(complement(A),complement(B))))),
inference(subst,[],[refute_0_254:[bind(X_87,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_394,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_395,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( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_148,refute_0_394]) ).
cnf(refute_0_396,plain,
join(complement(A),complement(B)) = join(zero,complement(meet(A,B))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(complement(join(complement(A),complement(B)))))) )],[refute_0_393,refute_0_395]) ).
cnf(refute_0_397,plain,
join(zero,complement(meet(A,B))) = complement(meet(A,B)),
inference(subst,[],[refute_0_377:[bind(X_92,$fot(meet(A,B)))]]) ).
cnf(refute_0_398,plain,
( join(complement(A),complement(B)) != join(zero,complement(meet(A,B)))
| join(zero,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(meet(A,B))))]]) ).
cnf(refute_0_399,plain,
( join(complement(A),complement(B)) != join(zero,complement(meet(A,B)))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(meet(A,B))),complement(meet(A,B))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
join(complement(A),complement(B)) = complement(meet(A,B)),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(meet(A,B)))) )],[refute_0_396,refute_0_399]) ).
cnf(refute_0_401,plain,
join(complement(composition(sk1,top)),complement(composition(sk1,top))) = complement(meet(composition(sk1,top),composition(sk1,top))),
inference(subst,[],[refute_0_400:[bind(A,$fot(composition(sk1,top))),bind(B,$fot(composition(sk1,top)))]]) ).
cnf(refute_0_402,plain,
( complement(meet(composition(sk1,top),composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) != complement(meet(composition(sk1,top),composition(sk1,top)))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) = complement(composition(sk1,top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(composition(sk1,top)),complement(composition(sk1,top))))),bind(Y,$fot(complement(meet(composition(sk1,top),composition(sk1,top))))),bind(Z,$fot(complement(composition(sk1,top))))]]) ).
cnf(refute_0_403,plain,
( complement(meet(composition(sk1,top),composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) = complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),complement(composition(sk1,top))),complement(meet(composition(sk1,top),composition(sk1,top)))) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
join(complement(composition(sk1,top)),complement(composition(sk1,top))) = complement(composition(sk1,top)),
inference(resolve,[$cnf( $equal(complement(meet(composition(sk1,top),composition(sk1,top))),complement(composition(sk1,top))) )],[refute_0_392,refute_0_403]) ).
cnf(refute_0_405,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) = complement(composition(sk1,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(sk1,top)),complement(composition(sk1,top))),complement(composition(sk1,top))) ),[0,0],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_406,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) = complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),complement(composition(sk1,top))),complement(composition(sk1,top))) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),complement(composition(sk1,top))),complement(composition(sk1,top))) )],[refute_0_406,refute_0_20]) ).
cnf(refute_0_408,plain,
complement(composition(sk1,top)) = complement(composition(sk1,top)),
introduced(tautology,[refl,[$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_409,plain,
composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top)),
inference(resolve,[$cnf( $equal(complement(composition(sk1,top)),complement(composition(sk1,top))) )],[refute_0_408,refute_0_407]) ).
cnf(refute_0_410,plain,
converse(converse(composition(complement(composition(X_512,top)),top))) = composition(complement(composition(X_512,top)),top),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(complement(composition(X_512,top)),top)))]]) ).
cnf(refute_0_411,plain,
join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top)))))) = complement(converse(composition(X_475,top))),
inference(subst,[],[refute_0_78:[bind(A,$fot(complement(meet(one,composition(top,complement(one)))))),bind(B,$fot(converse(composition(X_475,top))))]]) ).
cnf(refute_0_412,plain,
converse(composition(X_22,converse(composition(complement(meet(one,composition(complement(one),top))),top)))) = composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)),
inference(subst,[],[refute_0_163:[bind(A,$fot(composition(complement(meet(one,composition(complement(one),top))),top)))]]) ).
cnf(refute_0_413,plain,
converse(composition(join(converse(A),X_13),X_23)) = composition(converse(X_23),converse(join(converse(A),X_13))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(join(converse(A),X_13))),bind(B,$fot(X_23))]]) ).
cnf(refute_0_414,plain,
( converse(composition(join(converse(A),X_13),X_23)) != composition(converse(X_23),converse(join(converse(A),X_13)))
| converse(join(converse(A),X_13)) != join(A,converse(X_13))
| converse(composition(join(converse(A),X_13),X_23)) = composition(converse(X_23),join(A,converse(X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(converse(A),X_13),X_23)),composition(converse(X_23),converse(join(converse(A),X_13)))) ),[1,1],$fot(join(A,converse(X_13)))]]) ).
cnf(refute_0_415,plain,
( converse(composition(join(converse(A),X_13),X_23)) != composition(converse(X_23),converse(join(converse(A),X_13)))
| converse(composition(join(converse(A),X_13),X_23)) = composition(converse(X_23),join(A,converse(X_13))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_13)),join(A,converse(X_13))) )],[refute_0_89,refute_0_414]) ).
cnf(refute_0_416,plain,
converse(composition(join(converse(A),X_13),X_23)) = composition(converse(X_23),join(A,converse(X_13))),
inference(resolve,[$cnf( $equal(converse(composition(join(converse(A),X_13),X_23)),composition(converse(X_23),converse(join(converse(A),X_13)))) )],[refute_0_413,refute_0_415]) ).
cnf(refute_0_417,plain,
converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top)) = composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))),
inference(subst,[],[refute_0_416:[bind(A,$fot(X_194)),bind(X_13,$fot(complement(composition(converse(X_194),top)))),bind(X_23,$fot(top))]]) ).
cnf(refute_0_418,plain,
composition(join(A,complement(composition(A,top))),top) = join(composition(A,top),composition(complement(composition(A,top)),top)),
inference(subst,[],[composition_distributivity_7:[bind(B,$fot(complement(composition(A,top)))),bind(C,$fot(top))]]) ).
cnf(refute_0_419,plain,
converse(join(converse(A),converse(composition(complement(converse(converse(A))),top)))) = join(A,converse(converse(composition(complement(converse(converse(A))),top)))),
inference(subst,[],[refute_0_89:[bind(X_13,$fot(converse(composition(complement(converse(converse(A))),top))))]]) ).
cnf(refute_0_420,plain,
join(X_35,join(converse(complement(converse(X_35))),X_37)) = join(join(X_35,converse(complement(converse(X_35)))),X_37),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_35)),bind(B,$fot(converse(complement(converse(X_35))))),bind(C,$fot(X_37))]]) ).
cnf(refute_0_421,plain,
converse(join(converse(X_16),complement(converse(X_16)))) = join(X_16,converse(complement(converse(X_16)))),
inference(subst,[],[refute_0_89:[bind(A,$fot(X_16)),bind(X_13,$fot(complement(converse(X_16))))]]) ).
cnf(refute_0_422,plain,
top = join(converse(X_16),complement(converse(X_16))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_16)))]]) ).
cnf(refute_0_423,plain,
( top != join(converse(X_16),complement(converse(X_16)))
| join(converse(X_16),complement(converse(X_16))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_16),complement(converse(X_16)))))]]) ).
cnf(refute_0_424,plain,
join(converse(X_16),complement(converse(X_16))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_16),complement(converse(X_16)))) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
( converse(join(converse(X_16),complement(converse(X_16)))) != join(X_16,converse(complement(converse(X_16))))
| join(converse(X_16),complement(converse(X_16))) != top
| converse(top) = join(X_16,converse(complement(converse(X_16)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_16),complement(converse(X_16)))),join(X_16,converse(complement(converse(X_16))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_426,plain,
( converse(join(converse(X_16),complement(converse(X_16)))) != join(X_16,converse(complement(converse(X_16))))
| converse(top) = join(X_16,converse(complement(converse(X_16)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_16),complement(converse(X_16))),top) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
converse(top) = join(X_16,converse(complement(converse(X_16)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_16),complement(converse(X_16)))),join(X_16,converse(complement(converse(X_16))))) )],[refute_0_421,refute_0_426]) ).
cnf(refute_0_428,plain,
converse(top) = join(X_35,converse(complement(converse(X_35)))),
inference(subst,[],[refute_0_427:[bind(X_16,$fot(X_35))]]) ).
cnf(refute_0_429,plain,
( converse(top) != join(X_35,converse(complement(converse(X_35))))
| join(X_35,converse(complement(converse(X_35)))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(X_35,converse(complement(converse(X_35))))))]]) ).
cnf(refute_0_430,plain,
join(X_35,converse(complement(converse(X_35)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(X_35,converse(complement(converse(X_35))))) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
( join(X_35,converse(complement(converse(X_35)))) != converse(top)
| join(X_35,join(converse(complement(converse(X_35))),X_37)) != join(join(X_35,converse(complement(converse(X_35)))),X_37)
| join(X_35,join(converse(complement(converse(X_35))),X_37)) = join(converse(top),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,join(converse(complement(converse(X_35))),X_37)),join(join(X_35,converse(complement(converse(X_35)))),X_37)) ),[1,0],$fot(converse(top))]]) ).
cnf(refute_0_432,plain,
( join(X_35,join(converse(complement(converse(X_35))),X_37)) != join(join(X_35,converse(complement(converse(X_35)))),X_37)
| join(X_35,join(converse(complement(converse(X_35))),X_37)) = join(converse(top),X_37) ),
inference(resolve,[$cnf( $equal(join(X_35,converse(complement(converse(X_35)))),converse(top)) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
join(X_35,join(converse(complement(converse(X_35))),X_37)) = join(converse(top),X_37),
inference(resolve,[$cnf( $equal(join(X_35,join(converse(complement(converse(X_35))),X_37)),join(join(X_35,converse(complement(converse(X_35)))),X_37)) )],[refute_0_420,refute_0_432]) ).
cnf(refute_0_434,plain,
join(X_35,join(complement(X_19),join(zero,complement(complement(X_19))))) = join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_35)),bind(B,$fot(complement(X_19))),bind(C,$fot(join(zero,complement(complement(X_19)))))]]) ).
cnf(refute_0_435,plain,
top = join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_436,plain,
( complement(join(complement(X_6),complement(X_7))) != meet(X_6,X_7)
| top != join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| top = join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) ),[1,1],$fot(meet(X_6,X_7))]]) ).
cnf(refute_0_437,plain,
( top != join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))
| top = join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_6),complement(X_7))),meet(X_6,X_7)) )],[refute_0_260,refute_0_436]) ).
cnf(refute_0_438,plain,
top = join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_6),complement(X_7)),complement(join(complement(X_6),complement(X_7))))) )],[refute_0_435,refute_0_437]) ).
cnf(refute_0_439,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_440,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_439]) ).
cnf(refute_0_441,plain,
join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) = join(complement(X_6),join(complement(X_7),meet(X_6,X_7))),
inference(subst,[],[refute_0_440:[bind(A,$fot(complement(X_6))),bind(B,$fot(complement(X_7))),bind(C,$fot(meet(X_6,X_7)))]]) ).
cnf(refute_0_442,plain,
( join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)) != join(complement(X_6),join(complement(X_7),meet(X_6,X_7)))
| top != join(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| top = join(complement(X_6),join(complement(X_7),meet(X_6,X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) ),[1],$fot(join(complement(X_6),join(complement(X_7),meet(X_6,X_7))))]]) ).
cnf(refute_0_443,plain,
( top != join(join(complement(X_6),complement(X_7)),meet(X_6,X_7))
| top = join(complement(X_6),join(complement(X_7),meet(X_6,X_7))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_6),complement(X_7)),meet(X_6,X_7)),join(complement(X_6),join(complement(X_7),meet(X_6,X_7)))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
top = join(complement(X_6),join(complement(X_7),meet(X_6,X_7))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_6),complement(X_7)),meet(X_6,X_7))) )],[refute_0_438,refute_0_443]) ).
cnf(refute_0_445,plain,
top = join(complement(X_19),join(complement(complement(X_19)),meet(X_19,complement(X_19)))),
inference(subst,[],[refute_0_444:[bind(X_6,$fot(X_19)),bind(X_7,$fot(complement(X_19)))]]) ).
cnf(refute_0_446,plain,
zero = meet(X_19,complement(X_19)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_19))]]) ).
cnf(refute_0_447,plain,
( zero != meet(X_19,complement(X_19))
| meet(X_19,complement(X_19)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_19,complement(X_19))))]]) ).
cnf(refute_0_448,plain,
meet(X_19,complement(X_19)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_19,complement(X_19))) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
( meet(X_19,complement(X_19)) != zero
| top != join(complement(X_19),join(complement(complement(X_19)),meet(X_19,complement(X_19))))
| top = join(complement(X_19),join(complement(complement(X_19)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_19),join(complement(complement(X_19)),meet(X_19,complement(X_19))))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_450,plain,
( top != join(complement(X_19),join(complement(complement(X_19)),meet(X_19,complement(X_19))))
| top = join(complement(X_19),join(complement(complement(X_19)),zero)) ),
inference(resolve,[$cnf( $equal(meet(X_19,complement(X_19)),zero) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
top = join(complement(X_19),join(complement(complement(X_19)),zero)),
inference(resolve,[$cnf( $equal(top,join(complement(X_19),join(complement(complement(X_19)),meet(X_19,complement(X_19))))) )],[refute_0_445,refute_0_450]) ).
cnf(refute_0_452,plain,
join(complement(complement(X_19)),zero) = join(zero,complement(complement(X_19))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(complement(X_19))))]]) ).
cnf(refute_0_453,plain,
join(complement(X_19),join(complement(complement(X_19)),zero)) = join(complement(X_19),join(complement(complement(X_19)),zero)),
introduced(tautology,[refl,[$fot(join(complement(X_19),join(complement(complement(X_19)),zero)))]]) ).
cnf(refute_0_454,plain,
( join(complement(X_19),join(complement(complement(X_19)),zero)) != join(complement(X_19),join(complement(complement(X_19)),zero))
| join(complement(complement(X_19)),zero) != join(zero,complement(complement(X_19)))
| join(complement(X_19),join(complement(complement(X_19)),zero)) = join(complement(X_19),join(zero,complement(complement(X_19)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_19),join(complement(complement(X_19)),zero)),join(complement(X_19),join(complement(complement(X_19)),zero))) ),[1,1],$fot(join(zero,complement(complement(X_19))))]]) ).
cnf(refute_0_455,plain,
( join(complement(complement(X_19)),zero) != join(zero,complement(complement(X_19)))
| join(complement(X_19),join(complement(complement(X_19)),zero)) = join(complement(X_19),join(zero,complement(complement(X_19)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_19),join(complement(complement(X_19)),zero)),join(complement(X_19),join(complement(complement(X_19)),zero))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
join(complement(X_19),join(complement(complement(X_19)),zero)) = join(complement(X_19),join(zero,complement(complement(X_19)))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_19)),zero),join(zero,complement(complement(X_19)))) )],[refute_0_452,refute_0_455]) ).
cnf(refute_0_457,plain,
( join(complement(X_19),join(complement(complement(X_19)),zero)) != join(complement(X_19),join(zero,complement(complement(X_19))))
| top != join(complement(X_19),join(complement(complement(X_19)),zero))
| top = join(complement(X_19),join(zero,complement(complement(X_19)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_19),join(complement(complement(X_19)),zero))) ),[1],$fot(join(complement(X_19),join(zero,complement(complement(X_19)))))]]) ).
cnf(refute_0_458,plain,
( top != join(complement(X_19),join(complement(complement(X_19)),zero))
| top = join(complement(X_19),join(zero,complement(complement(X_19)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_19),join(complement(complement(X_19)),zero)),join(complement(X_19),join(zero,complement(complement(X_19))))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
top = join(complement(X_19),join(zero,complement(complement(X_19)))),
inference(resolve,[$cnf( $equal(top,join(complement(X_19),join(complement(complement(X_19)),zero))) )],[refute_0_451,refute_0_458]) ).
cnf(refute_0_460,plain,
( top != join(complement(X_19),join(zero,complement(complement(X_19))))
| join(complement(X_19),join(zero,complement(complement(X_19)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_19),join(zero,complement(complement(X_19))))))]]) ).
cnf(refute_0_461,plain,
join(complement(X_19),join(zero,complement(complement(X_19)))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_19),join(zero,complement(complement(X_19))))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
( join(X_35,join(complement(X_19),join(zero,complement(complement(X_19))))) != join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19))))
| join(complement(X_19),join(zero,complement(complement(X_19)))) != top
| join(X_35,top) = join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,join(complement(X_19),join(zero,complement(complement(X_19))))),join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_463,plain,
( join(X_35,join(complement(X_19),join(zero,complement(complement(X_19))))) != join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19))))
| join(X_35,top) = join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_19),join(zero,complement(complement(X_19)))),top) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
join(X_35,top) = join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))),
inference(resolve,[$cnf( $equal(join(X_35,join(complement(X_19),join(zero,complement(complement(X_19))))),join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19))))) )],[refute_0_434,refute_0_463]) ).
cnf(refute_0_465,plain,
join(A,join(X_35,X_36)) = join(join(X_35,X_36),A),
inference(subst,[],[maddux1_join_commutativity_1:[bind(B,$fot(join(X_35,X_36)))]]) ).
cnf(refute_0_466,plain,
join(X_35,join(X_36,A)) = join(join(X_35,X_36),A),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_35)),bind(B,$fot(X_36)),bind(C,$fot(A))]]) ).
cnf(refute_0_467,plain,
( join(X_35,join(X_36,A)) != join(join(X_35,X_36),A)
| join(join(X_35,X_36),A) = join(X_35,join(X_36,A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_35,join(X_36,A)))),bind(Y,$fot(join(join(X_35,X_36),A)))]]) ).
cnf(refute_0_468,plain,
join(join(X_35,X_36),A) = join(X_35,join(X_36,A)),
inference(resolve,[$cnf( $equal(join(X_35,join(X_36,A)),join(join(X_35,X_36),A)) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
( join(A,join(X_35,X_36)) != join(join(X_35,X_36),A)
| join(join(X_35,X_36),A) != join(X_35,join(X_36,A))
| join(A,join(X_35,X_36)) = join(X_35,join(X_36,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_35,X_36)),join(X_35,join(X_36,A))) ),[0],$fot(join(join(X_35,X_36),A))]]) ).
cnf(refute_0_470,plain,
( join(A,join(X_35,X_36)) != join(join(X_35,X_36),A)
| join(A,join(X_35,X_36)) = join(X_35,join(X_36,A)) ),
inference(resolve,[$cnf( $equal(join(join(X_35,X_36),A),join(X_35,join(X_36,A))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
join(A,join(X_35,X_36)) = join(X_35,join(X_36,A)),
inference(resolve,[$cnf( $equal(join(A,join(X_35,X_36)),join(join(X_35,X_36),A)) )],[refute_0_465,refute_0_470]) ).
cnf(refute_0_472,plain,
( join(A,join(X_35,X_36)) != join(X_35,join(X_36,A))
| join(X_35,join(X_36,A)) = join(A,join(X_35,X_36)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(X_35,X_36)))),bind(Y,$fot(join(X_35,join(X_36,A))))]]) ).
cnf(refute_0_473,plain,
join(X_35,join(X_36,A)) = join(A,join(X_35,X_36)),
inference(resolve,[$cnf( $equal(join(A,join(X_35,X_36)),join(X_35,join(X_36,A))) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
join(complement(complement(X_19)),join(X_35,complement(X_19))) = join(complement(X_19),join(complement(complement(X_19)),X_35)),
inference(subst,[],[refute_0_473:[bind(A,$fot(complement(X_19))),bind(X_35,$fot(complement(complement(X_19)))),bind(X_36,$fot(X_35))]]) ).
cnf(refute_0_475,plain,
join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))) = join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))),
introduced(tautology,[refl,[$fot(join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))))]]) ).
cnf(refute_0_476,plain,
( join(complement(complement(X_19)),join(X_35,complement(X_19))) != join(complement(X_19),join(complement(complement(X_19)),X_35))
| join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))) != join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19))))
| join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))) = join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))),join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19))))) ),[1,1],$fot(join(complement(X_19),join(complement(complement(X_19)),X_35)))]]) ).
cnf(refute_0_477,plain,
( join(complement(complement(X_19)),join(X_35,complement(X_19))) != join(complement(X_19),join(complement(complement(X_19)),X_35))
| join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))) = join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))),join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19))))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))) = join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_19)),join(X_35,complement(X_19))),join(complement(X_19),join(complement(complement(X_19)),X_35))) )],[refute_0_474,refute_0_477]) ).
cnf(refute_0_479,plain,
join(complement(complement(X_19)),join(join(X_35,complement(X_19)),zero)) = join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))),
inference(subst,[],[refute_0_473:[bind(A,$fot(zero)),bind(X_35,$fot(complement(complement(X_19)))),bind(X_36,$fot(join(X_35,complement(X_19))))]]) ).
cnf(refute_0_480,plain,
join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) = join(complement(complement(X_19)),join(join(X_35,complement(X_19)),zero)),
inference(subst,[],[refute_0_473:[bind(A,$fot(complement(complement(X_19)))),bind(X_35,$fot(join(X_35,complement(X_19)))),bind(X_36,$fot(zero))]]) ).
cnf(refute_0_481,plain,
( join(complement(complement(X_19)),join(join(X_35,complement(X_19)),zero)) != join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19))))
| join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) != join(complement(complement(X_19)),join(join(X_35,complement(X_19)),zero))
| join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) = join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))))),bind(Y,$fot(join(complement(complement(X_19)),join(join(X_35,complement(X_19)),zero)))),bind(Z,$fot(join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19))))))]]) ).
cnf(refute_0_482,plain,
( join(complement(complement(X_19)),join(join(X_35,complement(X_19)),zero)) != join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19))))
| join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) = join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))) ),
inference(resolve,[$cnf( $equal(join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))),join(complement(complement(X_19)),join(join(X_35,complement(X_19)),zero))) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) = join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_19)),join(join(X_35,complement(X_19)),zero)),join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19))))) )],[refute_0_479,refute_0_482]) ).
cnf(refute_0_484,plain,
( join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) != join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19))))
| join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))) != join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))
| join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) = join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))))),bind(Y,$fot(join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))))),bind(Z,$fot(join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))))]]) ).
cnf(refute_0_485,plain,
( join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))) != join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))
| join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) = join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) ),
inference(resolve,[$cnf( $equal(join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))),join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19))))) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) = join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))),
inference(resolve,[$cnf( $equal(join(zero,join(complement(complement(X_19)),join(X_35,complement(X_19)))),join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))) )],[refute_0_478,refute_0_485]) ).
cnf(refute_0_487,plain,
( join(X_35,top) != join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19))))
| join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))) != join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))
| join(X_35,top) = join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_35,top),join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))) ),[0],$fot(join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))))]]) ).
cnf(refute_0_488,plain,
( join(X_35,top) != join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19))))
| join(X_35,top) = join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) ),
inference(resolve,[$cnf( $equal(join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19)))),join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
join(X_35,top) = join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))),
inference(resolve,[$cnf( $equal(join(X_35,top),join(join(X_35,complement(X_19)),join(zero,complement(complement(X_19))))) )],[refute_0_464,refute_0_488]) ).
cnf(refute_0_490,plain,
join(top,join(zero,X_37)) = join(join(top,zero),X_37),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(top)),bind(B,$fot(zero)),bind(C,$fot(X_37))]]) ).
cnf(refute_0_491,plain,
top = join(top,complement(top)),
inference(subst,[],[def_top_12:[bind(A,$fot(top))]]) ).
cnf(refute_0_492,plain,
( complement(top) != zero
| top != join(top,complement(top))
| top = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_493,plain,
( top != join(top,complement(top))
| top = join(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_492]) ).
cnf(refute_0_494,plain,
top = join(top,zero),
inference(resolve,[$cnf( $equal(top,join(top,complement(top))) )],[refute_0_491,refute_0_493]) ).
cnf(refute_0_495,plain,
( top != join(top,zero)
| join(top,zero) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,zero)))]]) ).
cnf(refute_0_496,plain,
join(top,zero) = top,
inference(resolve,[$cnf( $equal(top,join(top,zero)) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
( join(top,join(zero,X_37)) != join(join(top,zero),X_37)
| join(top,zero) != top
| join(top,join(zero,X_37)) = join(top,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,X_37)),join(join(top,zero),X_37)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_498,plain,
( join(top,join(zero,X_37)) != join(join(top,zero),X_37)
| join(top,join(zero,X_37)) = join(top,X_37) ),
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
join(top,join(zero,X_37)) = join(top,X_37),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_37)),join(join(top,zero),X_37)) )],[refute_0_490,refute_0_498]) ).
cnf(refute_0_500,plain,
join(top,join(zero,X_35)) = join(top,X_35),
inference(subst,[],[refute_0_499:[bind(X_37,$fot(X_35))]]) ).
cnf(refute_0_501,plain,
join(X_35,join(X_36,X_37)) = join(join(X_35,X_36),X_37),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_35)),bind(B,$fot(X_36)),bind(C,$fot(X_37))]]) ).
cnf(refute_0_502,plain,
join(X_36,X_35) = join(X_35,X_36),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_36)),bind(B,$fot(X_35))]]) ).
cnf(refute_0_503,plain,
( join(X_36,X_35) != join(X_35,X_36)
| join(X_35,X_36) = join(X_36,X_35) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_36,X_35))),bind(Y,$fot(join(X_35,X_36)))]]) ).
cnf(refute_0_504,plain,
join(X_35,X_36) = join(X_36,X_35),
inference(resolve,[$cnf( $equal(join(X_36,X_35),join(X_35,X_36)) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
( join(X_35,X_36) != join(X_36,X_35)
| join(X_35,join(X_36,X_37)) != join(join(X_35,X_36),X_37)
| join(X_35,join(X_36,X_37)) = join(join(X_36,X_35),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,join(X_36,X_37)),join(join(X_35,X_36),X_37)) ),[1,0],$fot(join(X_36,X_35))]]) ).
cnf(refute_0_506,plain,
( join(X_35,join(X_36,X_37)) != join(join(X_35,X_36),X_37)
| join(X_35,join(X_36,X_37)) = join(join(X_36,X_35),X_37) ),
inference(resolve,[$cnf( $equal(join(X_35,X_36),join(X_36,X_35)) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
join(X_35,join(X_36,X_37)) = join(join(X_36,X_35),X_37),
inference(resolve,[$cnf( $equal(join(X_35,join(X_36,X_37)),join(join(X_35,X_36),X_37)) )],[refute_0_501,refute_0_506]) ).
cnf(refute_0_508,plain,
join(join(X_36,X_35),X_37) = join(X_36,join(X_35,X_37)),
inference(subst,[],[refute_0_440:[bind(A,$fot(X_36)),bind(B,$fot(X_35)),bind(C,$fot(X_37))]]) ).
cnf(refute_0_509,plain,
( join(X_35,join(X_36,X_37)) != join(join(X_36,X_35),X_37)
| join(join(X_36,X_35),X_37) != join(X_36,join(X_35,X_37))
| join(X_35,join(X_36,X_37)) = join(X_36,join(X_35,X_37)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_35,join(X_36,X_37)),join(X_36,join(X_35,X_37))) ),[0],$fot(join(join(X_36,X_35),X_37))]]) ).
cnf(refute_0_510,plain,
( join(X_35,join(X_36,X_37)) != join(join(X_36,X_35),X_37)
| join(X_35,join(X_36,X_37)) = join(X_36,join(X_35,X_37)) ),
inference(resolve,[$cnf( $equal(join(join(X_36,X_35),X_37),join(X_36,join(X_35,X_37))) )],[refute_0_508,refute_0_509]) ).
cnf(refute_0_511,plain,
join(X_35,join(X_36,X_37)) = join(X_36,join(X_35,X_37)),
inference(resolve,[$cnf( $equal(join(X_35,join(X_36,X_37)),join(join(X_36,X_35),X_37)) )],[refute_0_507,refute_0_510]) ).
cnf(refute_0_512,plain,
( join(X_35,join(X_36,X_37)) != join(X_36,join(X_35,X_37))
| join(X_36,join(X_35,X_37)) = join(X_35,join(X_36,X_37)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_35,join(X_36,X_37)))),bind(Y,$fot(join(X_36,join(X_35,X_37))))]]) ).
cnf(refute_0_513,plain,
join(X_36,join(X_35,X_37)) = join(X_35,join(X_36,X_37)),
inference(resolve,[$cnf( $equal(join(X_35,join(X_36,X_37)),join(X_36,join(X_35,X_37))) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
join(zero,join(top,X_35)) = join(top,join(zero,X_35)),
inference(subst,[],[refute_0_513:[bind(X_35,$fot(top)),bind(X_36,$fot(zero)),bind(X_37,$fot(X_35))]]) ).
cnf(refute_0_515,plain,
( join(top,join(zero,X_35)) != join(top,X_35)
| join(zero,join(top,X_35)) != join(top,join(zero,X_35))
| join(zero,join(top,X_35)) = join(top,X_35) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(zero,join(top,X_35)))),bind(Y,$fot(join(top,join(zero,X_35)))),bind(Z,$fot(join(top,X_35)))]]) ).
cnf(refute_0_516,plain,
( join(top,join(zero,X_35)) != join(top,X_35)
| join(zero,join(top,X_35)) = join(top,X_35) ),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_35)),join(top,join(zero,X_35))) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
join(zero,join(top,X_35)) = join(top,X_35),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_35)),join(top,X_35)) )],[refute_0_500,refute_0_516]) ).
cnf(refute_0_518,plain,
join(complement(X_19),join(complement(complement(X_19)),X_35)) = join(top,X_35),
inference(subst,[],[refute_0_316:[bind(X_35,$fot(complement(X_19))),bind(X_37,$fot(X_35))]]) ).
cnf(refute_0_519,plain,
join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) = join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))),
introduced(tautology,[refl,[$fot(join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))))]]) ).
cnf(refute_0_520,plain,
( join(complement(X_19),join(complement(complement(X_19)),X_35)) != join(top,X_35)
| join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) != join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))
| join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) = join(zero,join(top,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))),join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))) ),[1,1],$fot(join(top,X_35))]]) ).
cnf(refute_0_521,plain,
( join(complement(X_19),join(complement(complement(X_19)),X_35)) != join(top,X_35)
| join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) = join(zero,join(top,X_35)) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))),join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) = join(zero,join(top,X_35)),
inference(resolve,[$cnf( $equal(join(complement(X_19),join(complement(complement(X_19)),X_35)),join(top,X_35)) )],[refute_0_518,refute_0_521]) ).
cnf(refute_0_523,plain,
( join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) != join(zero,join(top,X_35))
| join(zero,join(top,X_35)) != join(top,X_35)
| join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) = join(top,X_35) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))))),bind(Y,$fot(join(zero,join(top,X_35)))),bind(Z,$fot(join(top,X_35)))]]) ).
cnf(refute_0_524,plain,
( join(zero,join(top,X_35)) != join(top,X_35)
| join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) = join(top,X_35) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))),join(zero,join(top,X_35))) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) = join(top,X_35),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_35)),join(top,X_35)) )],[refute_0_517,refute_0_524]) ).
cnf(refute_0_526,plain,
( join(X_35,top) != join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))
| join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))) != join(top,X_35)
| join(X_35,top) = join(top,X_35) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_35,top),join(top,X_35)) ),[0],$fot(join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))))]]) ).
cnf(refute_0_527,plain,
( join(X_35,top) != join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))
| join(X_35,top) = join(top,X_35) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35))),join(top,X_35)) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
join(X_35,top) = join(top,X_35),
inference(resolve,[$cnf( $equal(join(X_35,top),join(zero,join(complement(X_19),join(complement(complement(X_19)),X_35)))) )],[refute_0_489,refute_0_527]) ).
cnf(refute_0_529,plain,
join(X_35,top) = top,
inference(subst,[],[refute_0_345:[bind(X_41,$fot(X_35))]]) ).
cnf(refute_0_530,plain,
( join(X_35,top) != join(top,X_35)
| join(X_35,top) != top
| top = join(top,X_35) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,top),join(top,X_35)) ),[0],$fot(top)]]) ).
cnf(refute_0_531,plain,
( join(X_35,top) != join(top,X_35)
| top = join(top,X_35) ),
inference(resolve,[$cnf( $equal(join(X_35,top),top) )],[refute_0_529,refute_0_530]) ).
cnf(refute_0_532,plain,
top = join(top,X_35),
inference(resolve,[$cnf( $equal(join(X_35,top),join(top,X_35)) )],[refute_0_528,refute_0_531]) ).
cnf(refute_0_533,plain,
( top != join(top,X_35)
| join(top,X_35) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,X_35)))]]) ).
cnf(refute_0_534,plain,
join(top,X_35) = top,
inference(resolve,[$cnf( $equal(top,join(top,X_35)) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
join(top,X_37) = top,
inference(subst,[],[refute_0_534:[bind(X_35,$fot(X_37))]]) ).
cnf(refute_0_536,plain,
join(converse(X_13),converse(X_12)) = join(converse(X_12),converse(X_13)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(converse(X_13))),bind(B,$fot(converse(X_12)))]]) ).
cnf(refute_0_537,plain,
converse(join(X_12,X_13)) = join(converse(X_12),converse(X_13)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_12)),bind(B,$fot(X_13))]]) ).
cnf(refute_0_538,plain,
( converse(join(X_12,X_13)) != join(converse(X_12),converse(X_13))
| join(converse(X_12),converse(X_13)) = converse(join(X_12,X_13)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_12,X_13)))),bind(Y,$fot(join(converse(X_12),converse(X_13))))]]) ).
cnf(refute_0_539,plain,
join(converse(X_12),converse(X_13)) = converse(join(X_12,X_13)),
inference(resolve,[$cnf( $equal(converse(join(X_12,X_13)),join(converse(X_12),converse(X_13))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
( join(converse(X_12),converse(X_13)) != converse(join(X_12,X_13))
| join(converse(X_13),converse(X_12)) != join(converse(X_12),converse(X_13))
| join(converse(X_13),converse(X_12)) = converse(join(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(X_13),converse(X_12)),join(converse(X_12),converse(X_13))) ),[1],$fot(converse(join(X_12,X_13)))]]) ).
cnf(refute_0_541,plain,
( join(converse(X_13),converse(X_12)) != join(converse(X_12),converse(X_13))
| join(converse(X_13),converse(X_12)) = converse(join(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(join(converse(X_12),converse(X_13)),converse(join(X_12,X_13))) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
join(converse(X_13),converse(X_12)) = converse(join(X_12,X_13)),
inference(resolve,[$cnf( $equal(join(converse(X_13),converse(X_12)),join(converse(X_12),converse(X_13))) )],[refute_0_536,refute_0_541]) ).
cnf(refute_0_543,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(join(converse(A),converse(B))))]]) ).
cnf(refute_0_544,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_543]) ).
cnf(refute_0_545,plain,
join(converse(X_13),converse(X_12)) = converse(join(X_13,X_12)),
inference(subst,[],[refute_0_544:[bind(A,$fot(X_13)),bind(B,$fot(X_12))]]) ).
cnf(refute_0_546,plain,
( join(converse(X_13),converse(X_12)) != converse(join(X_12,X_13))
| join(converse(X_13),converse(X_12)) != converse(join(X_13,X_12))
| converse(join(X_13,X_12)) = converse(join(X_12,X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(X_13),converse(X_12)),converse(join(X_12,X_13))) ),[0],$fot(converse(join(X_13,X_12)))]]) ).
cnf(refute_0_547,plain,
( join(converse(X_13),converse(X_12)) != converse(join(X_12,X_13))
| converse(join(X_13,X_12)) = converse(join(X_12,X_13)) ),
inference(resolve,[$cnf( $equal(join(converse(X_13),converse(X_12)),converse(join(X_13,X_12))) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
converse(join(X_13,X_12)) = converse(join(X_12,X_13)),
inference(resolve,[$cnf( $equal(join(converse(X_13),converse(X_12)),converse(join(X_12,X_13))) )],[refute_0_542,refute_0_547]) ).
cnf(refute_0_549,plain,
converse(join(complement(converse(zero)),converse(top))) = converse(join(converse(top),complement(converse(zero)))),
inference(subst,[],[refute_0_548:[bind(X_12,$fot(converse(top))),bind(X_13,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_550,plain,
converse(join(top,converse(complement(converse(zero))))) = join(converse(top),converse(converse(complement(converse(zero))))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(top)),bind(B,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_551,plain,
join(top,join(zero,converse(complement(converse(zero))))) = join(top,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_499:[bind(X_37,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_552,plain,
converse(top) = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_427:[bind(X_16,$fot(zero))]]) ).
cnf(refute_0_553,plain,
( converse(top) != join(zero,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(zero,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_554,plain,
join(zero,converse(complement(converse(zero)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(zero,converse(complement(converse(zero))))) )],[refute_0_552,refute_0_553]) ).
cnf(refute_0_555,plain,
( join(top,join(zero,converse(complement(converse(zero))))) != join(top,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) != converse(top)
| join(top,converse(top)) = join(top,converse(complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,converse(complement(converse(zero))))),join(top,converse(complement(converse(zero))))) ),[0,1],$fot(converse(top))]]) ).
cnf(refute_0_556,plain,
( join(top,join(zero,converse(complement(converse(zero))))) != join(top,converse(complement(converse(zero))))
| join(top,converse(top)) = join(top,converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,converse(complement(converse(zero)))),converse(top)) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
join(top,converse(top)) = join(top,converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(join(top,join(zero,converse(complement(converse(zero))))),join(top,converse(complement(converse(zero))))) )],[refute_0_551,refute_0_556]) ).
cnf(refute_0_558,plain,
( join(top,converse(top)) != join(top,converse(complement(converse(zero))))
| join(top,converse(complement(converse(zero)))) = join(top,converse(top)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(top,converse(top)))),bind(Y,$fot(join(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_559,plain,
join(top,converse(complement(converse(zero)))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(top,converse(complement(converse(zero))))) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(complement(converse(zero)))) != join(top,converse(top))
| converse(join(top,converse(top))) = join(converse(top),converse(converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(top,converse(complement(converse(zero))))),join(converse(top),converse(converse(complement(converse(zero)))))) ),[0,0],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_561,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),converse(converse(complement(converse(zero)))))
| converse(join(top,converse(top))) = join(converse(top),converse(converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(zero)))),join(top,converse(top))) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
converse(join(top,converse(top))) = join(converse(top),converse(converse(complement(converse(zero))))),
inference(resolve,[$cnf( $equal(converse(join(top,converse(complement(converse(zero))))),join(converse(top),converse(converse(complement(converse(zero)))))) )],[refute_0_550,refute_0_561]) ).
cnf(refute_0_563,plain,
join(converse(top),top) = join(top,converse(top)),
inference(subst,[],[refute_0_528:[bind(X_35,$fot(converse(top)))]]) ).
cnf(refute_0_564,plain,
converse(join(X_12,converse(A))) = join(converse(X_12),converse(converse(A))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_12)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_565,plain,
( converse(converse(A)) != A
| converse(join(X_12,converse(A))) != join(converse(X_12),converse(converse(A)))
| converse(join(X_12,converse(A))) = join(converse(X_12),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_12,converse(A))),join(converse(X_12),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_566,plain,
( converse(join(X_12,converse(A))) != join(converse(X_12),converse(converse(A)))
| converse(join(X_12,converse(A))) = join(converse(X_12),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_565]) ).
cnf(refute_0_567,plain,
converse(join(X_12,converse(A))) = join(converse(X_12),A),
inference(resolve,[$cnf( $equal(converse(join(X_12,converse(A))),join(converse(X_12),converse(converse(A)))) )],[refute_0_564,refute_0_566]) ).
cnf(refute_0_568,plain,
converse(join(top,converse(top))) = join(converse(top),top),
inference(subst,[],[refute_0_567:[bind(A,$fot(top)),bind(X_12,$fot(top))]]) ).
cnf(refute_0_569,plain,
( converse(join(top,converse(top))) != join(converse(top),top)
| join(converse(top),top) != join(top,converse(top))
| converse(join(top,converse(top))) = join(top,converse(top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(top,converse(top))))),bind(Y,$fot(join(converse(top),top))),bind(Z,$fot(join(top,converse(top))))]]) ).
cnf(refute_0_570,plain,
( join(converse(top),top) != join(top,converse(top))
| converse(join(top,converse(top))) = join(top,converse(top)) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),top)) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
converse(join(top,converse(top))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(join(converse(top),top),join(top,converse(top))) )],[refute_0_563,refute_0_570]) ).
cnf(refute_0_572,plain,
( converse(join(top,converse(top))) != join(converse(top),converse(converse(complement(converse(zero)))))
| converse(join(top,converse(top))) != join(top,converse(top))
| join(top,converse(top)) = join(converse(top),converse(converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),converse(converse(complement(converse(zero)))))) ),[0],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_573,plain,
( converse(join(top,converse(top))) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),converse(converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(top,converse(top))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
converse(join(top,converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))),
inference(subst,[],[refute_0_567:[bind(A,$fot(complement(converse(zero)))),bind(X_12,$fot(top))]]) ).
cnf(refute_0_575,plain,
join(converse(top),converse(converse(complement(converse(zero))))) = converse(join(top,converse(complement(converse(zero))))),
inference(subst,[],[refute_0_544:[bind(A,$fot(top)),bind(B,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_576,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),complement(converse(zero)))
| join(converse(top),converse(converse(complement(converse(zero))))) != converse(join(top,converse(complement(converse(zero)))))
| join(converse(top),converse(converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(converse(top),converse(converse(complement(converse(zero))))))),bind(Y,$fot(converse(join(top,converse(complement(converse(zero))))))),bind(Z,$fot(join(converse(top),complement(converse(zero)))))]]) ).
cnf(refute_0_577,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),complement(converse(zero)))
| join(converse(top),converse(converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(converse(top),converse(converse(complement(converse(zero))))),converse(join(top,converse(complement(converse(zero)))))) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
join(converse(top),converse(converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))),
inference(resolve,[$cnf( $equal(converse(join(top,converse(complement(converse(zero))))),join(converse(top),complement(converse(zero)))) )],[refute_0_574,refute_0_577]) ).
cnf(refute_0_579,plain,
( join(converse(top),converse(converse(complement(converse(zero))))) != join(converse(top),complement(converse(zero)))
| join(top,converse(top)) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,converse(top)),join(converse(top),converse(converse(complement(converse(zero)))))) ),[1],$fot(join(converse(top),complement(converse(zero))))]]) ).
cnf(refute_0_580,plain,
( join(top,converse(top)) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(converse(top),converse(converse(complement(converse(zero))))),join(converse(top),complement(converse(zero)))) )],[refute_0_578,refute_0_579]) ).
cnf(refute_0_581,plain,
( converse(join(top,converse(top))) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(converse(top),converse(converse(complement(converse(zero)))))) )],[refute_0_573,refute_0_580]) ).
cnf(refute_0_582,plain,
join(top,converse(top)) = join(converse(top),complement(converse(zero))),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),converse(converse(complement(converse(zero)))))) )],[refute_0_562,refute_0_581]) ).
cnf(refute_0_583,plain,
join(top,converse(top)) = top,
inference(subst,[],[refute_0_534:[bind(X_35,$fot(converse(top)))]]) ).
cnf(refute_0_584,plain,
( join(top,converse(top)) != join(converse(top),complement(converse(zero)))
| join(top,converse(top)) != top
| top = join(converse(top),complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,converse(top)),join(converse(top),complement(converse(zero)))) ),[0],$fot(top)]]) ).
cnf(refute_0_585,plain,
( join(top,converse(top)) != join(converse(top),complement(converse(zero)))
| top = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(top,converse(top)),top) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
top = join(converse(top),complement(converse(zero))),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(converse(top),complement(converse(zero)))) )],[refute_0_582,refute_0_585]) ).
cnf(refute_0_587,plain,
( top != join(converse(top),complement(converse(zero)))
| join(converse(top),complement(converse(zero))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(converse(top),complement(converse(zero)))))]]) ).
cnf(refute_0_588,plain,
join(converse(top),complement(converse(zero))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(top),complement(converse(zero)))) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(join(converse(top),complement(converse(zero))))
| join(converse(top),complement(converse(zero))) != top
| converse(join(complement(converse(zero)),converse(top))) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(join(converse(top),complement(converse(zero))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_590,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(join(converse(top),complement(converse(zero))))
| converse(join(complement(converse(zero)),converse(top))) = converse(top) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(zero))),top) )],[refute_0_588,refute_0_589]) ).
cnf(refute_0_591,plain,
converse(join(complement(converse(zero)),converse(top))) = converse(top),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(join(converse(top),complement(converse(zero))))) )],[refute_0_549,refute_0_590]) ).
cnf(refute_0_592,plain,
join(converse(complement(converse(zero))),top) = top,
inference(subst,[],[refute_0_345:[bind(X_41,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_593,plain,
converse(join(complement(converse(zero)),converse(top))) = join(converse(complement(converse(zero))),top),
inference(subst,[],[refute_0_567:[bind(A,$fot(top)),bind(X_12,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_594,plain,
( converse(join(complement(converse(zero)),converse(top))) != join(converse(complement(converse(zero))),top)
| join(converse(complement(converse(zero))),top) != top
| converse(join(complement(converse(zero)),converse(top))) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(complement(converse(zero)),converse(top))))),bind(Y,$fot(join(converse(complement(converse(zero))),top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_595,plain,
( join(converse(complement(converse(zero))),top) != top
| converse(join(complement(converse(zero)),converse(top))) = top ),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),join(converse(complement(converse(zero))),top)) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
converse(join(complement(converse(zero)),converse(top))) = top,
inference(resolve,[$cnf( $equal(join(converse(complement(converse(zero))),top),top) )],[refute_0_592,refute_0_595]) ).
cnf(refute_0_597,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(top)
| converse(join(complement(converse(zero)),converse(top))) != top
| top = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(top)) ),[0],$fot(top)]]) ).
cnf(refute_0_598,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(top)
| top = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),top) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
top = converse(top),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(top)) )],[refute_0_591,refute_0_598]) ).
cnf(refute_0_600,plain,
( top != converse(top)
| converse(top) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(converse(top)))]]) ).
cnf(refute_0_601,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(top,converse(top)) )],[refute_0_599,refute_0_600]) ).
cnf(refute_0_602,plain,
join(converse(top),X_37) = join(converse(top),X_37),
introduced(tautology,[refl,[$fot(join(converse(top),X_37))]]) ).
cnf(refute_0_603,plain,
( converse(top) != top
| join(converse(top),X_37) != join(converse(top),X_37)
| join(converse(top),X_37) = join(top,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(top),X_37),join(converse(top),X_37)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_604,plain,
( converse(top) != top
| join(converse(top),X_37) = join(top,X_37) ),
inference(resolve,[$cnf( $equal(join(converse(top),X_37),join(converse(top),X_37)) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
join(converse(top),X_37) = join(top,X_37),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_601,refute_0_604]) ).
cnf(refute_0_606,plain,
( join(converse(top),X_37) != join(top,X_37)
| join(top,X_37) != top
| join(converse(top),X_37) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(converse(top),X_37))),bind(Y,$fot(join(top,X_37))),bind(Z,$fot(top))]]) ).
cnf(refute_0_607,plain,
( join(top,X_37) != top
| join(converse(top),X_37) = top ),
inference(resolve,[$cnf( $equal(join(converse(top),X_37),join(top,X_37)) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
join(converse(top),X_37) = top,
inference(resolve,[$cnf( $equal(join(top,X_37),top) )],[refute_0_535,refute_0_607]) ).
cnf(refute_0_609,plain,
( join(X_35,join(converse(complement(converse(X_35))),X_37)) != join(converse(top),X_37)
| join(converse(top),X_37) != top
| join(X_35,join(converse(complement(converse(X_35))),X_37)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_35,join(converse(complement(converse(X_35))),X_37)),top) ),[0],$fot(join(converse(top),X_37))]]) ).
cnf(refute_0_610,plain,
( join(X_35,join(converse(complement(converse(X_35))),X_37)) != join(converse(top),X_37)
| join(X_35,join(converse(complement(converse(X_35))),X_37)) = top ),
inference(resolve,[$cnf( $equal(join(converse(top),X_37),top) )],[refute_0_608,refute_0_609]) ).
cnf(refute_0_611,plain,
join(X_35,join(converse(complement(converse(X_35))),X_37)) = top,
inference(resolve,[$cnf( $equal(join(X_35,join(converse(complement(converse(X_35))),X_37)),join(converse(top),X_37)) )],[refute_0_433,refute_0_610]) ).
cnf(refute_0_612,plain,
join(X_35,join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35))))))))) = top,
inference(subst,[],[refute_0_611:[bind(X_37,$fot(complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35)))))))))]]) ).
cnf(refute_0_613,plain,
X_87 = join(meet(X_87,X_88),complement(join(complement(X_87),X_88))),
inference(subst,[],[refute_0_158:[bind(A,$fot(X_87)),bind(B,$fot(X_88))]]) ).
cnf(refute_0_614,plain,
join(complement(X_7),complement(X_6)) = join(complement(X_6),complement(X_7)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_7))),bind(B,$fot(complement(X_6)))]]) ).
cnf(refute_0_615,plain,
( join(complement(X_7),complement(X_6)) != join(complement(X_6),complement(X_7))
| join(complement(X_6),complement(X_7)) = join(complement(X_7),complement(X_6)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_7),complement(X_6)))),bind(Y,$fot(join(complement(X_6),complement(X_7))))]]) ).
cnf(refute_0_616,plain,
join(complement(X_6),complement(X_7)) = join(complement(X_7),complement(X_6)),
inference(resolve,[$cnf( $equal(join(complement(X_7),complement(X_6)),join(complement(X_6),complement(X_7))) )],[refute_0_614,refute_0_615]) ).
cnf(refute_0_617,plain,
( join(complement(X_6),complement(X_7)) != join(complement(X_7),complement(X_6))
| meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| meet(X_6,X_7) = complement(join(complement(X_7),complement(X_6))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) ),[1,0],$fot(join(complement(X_7),complement(X_6)))]]) ).
cnf(refute_0_618,plain,
( meet(X_6,X_7) != complement(join(complement(X_6),complement(X_7)))
| meet(X_6,X_7) = complement(join(complement(X_7),complement(X_6))) ),
inference(resolve,[$cnf( $equal(join(complement(X_6),complement(X_7)),join(complement(X_7),complement(X_6))) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
meet(X_6,X_7) = complement(join(complement(X_7),complement(X_6))),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_6),complement(X_7)))) )],[refute_0_258,refute_0_618]) ).
cnf(refute_0_620,plain,
complement(join(complement(X_7),complement(X_6))) = meet(X_7,X_6),
inference(subst,[],[refute_0_148:[bind(A,$fot(X_7)),bind(B,$fot(X_6))]]) ).
cnf(refute_0_621,plain,
( complement(join(complement(X_7),complement(X_6))) != meet(X_7,X_6)
| meet(X_6,X_7) != complement(join(complement(X_7),complement(X_6)))
| meet(X_6,X_7) = meet(X_7,X_6) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_7),complement(X_6)))) ),[1],$fot(meet(X_7,X_6))]]) ).
cnf(refute_0_622,plain,
( meet(X_6,X_7) != complement(join(complement(X_7),complement(X_6)))
| meet(X_6,X_7) = meet(X_7,X_6) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_7),complement(X_6))),meet(X_7,X_6)) )],[refute_0_620,refute_0_621]) ).
cnf(refute_0_623,plain,
meet(X_6,X_7) = meet(X_7,X_6),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),complement(join(complement(X_7),complement(X_6)))) )],[refute_0_619,refute_0_622]) ).
cnf(refute_0_624,plain,
meet(X_88,X_87) = meet(X_87,X_88),
inference(subst,[],[refute_0_623:[bind(X_6,$fot(X_88)),bind(X_7,$fot(X_87))]]) ).
cnf(refute_0_625,plain,
( meet(X_88,X_87) != meet(X_87,X_88)
| meet(X_87,X_88) = meet(X_88,X_87) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_88,X_87))),bind(Y,$fot(meet(X_87,X_88)))]]) ).
cnf(refute_0_626,plain,
meet(X_87,X_88) = meet(X_88,X_87),
inference(resolve,[$cnf( $equal(meet(X_88,X_87),meet(X_87,X_88)) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
( X_87 != join(meet(X_87,X_88),complement(join(complement(X_87),X_88)))
| meet(X_87,X_88) != meet(X_88,X_87)
| X_87 = join(meet(X_88,X_87),complement(join(complement(X_87),X_88))) ),
introduced(tautology,[equality,[$cnf( $equal(X_87,join(meet(X_87,X_88),complement(join(complement(X_87),X_88)))) ),[1,0],$fot(meet(X_88,X_87))]]) ).
cnf(refute_0_628,plain,
( X_87 != join(meet(X_87,X_88),complement(join(complement(X_87),X_88)))
| X_87 = join(meet(X_88,X_87),complement(join(complement(X_87),X_88))) ),
inference(resolve,[$cnf( $equal(meet(X_87,X_88),meet(X_88,X_87)) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
X_87 = join(meet(X_88,X_87),complement(join(complement(X_87),X_88))),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,X_88),complement(join(complement(X_87),X_88)))) )],[refute_0_613,refute_0_628]) ).
cnf(refute_0_630,plain,
composition(top,X_88) = join(meet(X_88,composition(top,X_88)),complement(join(complement(composition(top,X_88)),X_88))),
inference(subst,[],[refute_0_629:[bind(X_87,$fot(composition(top,X_88)))]]) ).
cnf(refute_0_631,plain,
X_87 = join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(join(complement(X_87),join(complement(complement(X_87)),X_37)))),
inference(subst,[],[refute_0_158:[bind(A,$fot(X_87)),bind(B,$fot(join(complement(complement(X_87)),X_37)))]]) ).
cnf(refute_0_632,plain,
( join(X_35,join(complement(X_35),X_37)) != join(top,X_37)
| join(top,X_37) != top
| join(X_35,join(complement(X_35),X_37)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_35,join(complement(X_35),X_37)),top) ),[0],$fot(join(top,X_37))]]) ).
cnf(refute_0_633,plain,
( join(X_35,join(complement(X_35),X_37)) != join(top,X_37)
| join(X_35,join(complement(X_35),X_37)) = top ),
inference(resolve,[$cnf( $equal(join(top,X_37),top) )],[refute_0_535,refute_0_632]) ).
cnf(refute_0_634,plain,
join(X_35,join(complement(X_35),X_37)) = top,
inference(resolve,[$cnf( $equal(join(X_35,join(complement(X_35),X_37)),join(top,X_37)) )],[refute_0_316,refute_0_633]) ).
cnf(refute_0_635,plain,
join(complement(X_87),join(complement(complement(X_87)),X_37)) = top,
inference(subst,[],[refute_0_634:[bind(X_35,$fot(complement(X_87)))]]) ).
cnf(refute_0_636,plain,
( X_87 != join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(join(complement(X_87),join(complement(complement(X_87)),X_37))))
| join(complement(X_87),join(complement(complement(X_87)),X_37)) != top
| X_87 = join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_87,join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(join(complement(X_87),join(complement(complement(X_87)),X_37))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_637,plain,
( X_87 != join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(join(complement(X_87),join(complement(complement(X_87)),X_37))))
| X_87 = join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_87),join(complement(complement(X_87)),X_37)),top) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
X_87 = join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(join(complement(X_87),join(complement(complement(X_87)),X_37))))) )],[refute_0_631,refute_0_637]) ).
cnf(refute_0_639,plain,
join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))) = join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))))]]) ).
cnf(refute_0_640,plain,
( complement(top) != zero
| join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))) != join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37)))
| join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))) = join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))),join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_641,plain,
( complement(top) != zero
| join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))) = join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))),join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37)))) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))) = join(zero,meet(X_87,join(complement(complement(X_87)),X_37))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_641]) ).
cnf(refute_0_643,plain,
join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)) = join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_87,join(complement(complement(X_87)),X_37))))]]) ).
cnf(refute_0_644,plain,
( join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))) != join(zero,meet(X_87,join(complement(complement(X_87)),X_37)))
| join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)) != join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37)))
| join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)) = join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))))),bind(Z,$fot(join(zero,meet(X_87,join(complement(complement(X_87)),X_37)))))]]) ).
cnf(refute_0_645,plain,
( join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))) != join(zero,meet(X_87,join(complement(complement(X_87)),X_37)))
| join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)) = join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) ),
inference(resolve,[$cnf( $equal(join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)),join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37)))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)) = join(zero,meet(X_87,join(complement(complement(X_87)),X_37))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_87,join(complement(complement(X_87)),X_37))),join(zero,meet(X_87,join(complement(complement(X_87)),X_37)))) )],[refute_0_642,refute_0_645]) ).
cnf(refute_0_647,plain,
( X_87 != join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top))
| join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)) != join(zero,meet(X_87,join(complement(complement(X_87)),X_37)))
| X_87 = join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_87,join(zero,meet(X_87,join(complement(complement(X_87)),X_37)))) ),[0],$fot(join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)))]]) ).
cnf(refute_0_648,plain,
( X_87 != join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top))
| X_87 = join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) ),
inference(resolve,[$cnf( $equal(join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top)),join(zero,meet(X_87,join(complement(complement(X_87)),X_37)))) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
X_87 = join(zero,meet(X_87,join(complement(complement(X_87)),X_37))),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,join(complement(complement(X_87)),X_37)),complement(top))) )],[refute_0_638,refute_0_648]) ).
cnf(refute_0_650,plain,
join(complement(complement(X_87)),X_37) = join(complement(complement(X_87)),X_37),
introduced(tautology,[refl,[$fot(join(complement(complement(X_87)),X_37))]]) ).
cnf(refute_0_651,plain,
( complement(complement(X_87)) != X_87
| join(complement(complement(X_87)),X_37) != join(complement(complement(X_87)),X_37)
| join(complement(complement(X_87)),X_37) = join(X_87,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_87)),X_37),join(complement(complement(X_87)),X_37)) ),[1,0],$fot(X_87)]]) ).
cnf(refute_0_652,plain,
( complement(complement(X_87)) != X_87
| join(complement(complement(X_87)),X_37) = join(X_87,X_37) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_87)),X_37),join(complement(complement(X_87)),X_37)) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
join(complement(complement(X_87)),X_37) = join(X_87,X_37),
inference(resolve,[$cnf( $equal(complement(complement(X_87)),X_87) )],[refute_0_383,refute_0_652]) ).
cnf(refute_0_654,plain,
meet(X_87,join(complement(complement(X_87)),X_37)) = meet(X_87,join(complement(complement(X_87)),X_37)),
introduced(tautology,[refl,[$fot(meet(X_87,join(complement(complement(X_87)),X_37)))]]) ).
cnf(refute_0_655,plain,
( join(complement(complement(X_87)),X_37) != join(X_87,X_37)
| meet(X_87,join(complement(complement(X_87)),X_37)) != meet(X_87,join(complement(complement(X_87)),X_37))
| meet(X_87,join(complement(complement(X_87)),X_37)) = meet(X_87,join(X_87,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_87,join(complement(complement(X_87)),X_37)),meet(X_87,join(complement(complement(X_87)),X_37))) ),[1,1],$fot(join(X_87,X_37))]]) ).
cnf(refute_0_656,plain,
( join(complement(complement(X_87)),X_37) != join(X_87,X_37)
| meet(X_87,join(complement(complement(X_87)),X_37)) = meet(X_87,join(X_87,X_37)) ),
inference(resolve,[$cnf( $equal(meet(X_87,join(complement(complement(X_87)),X_37)),meet(X_87,join(complement(complement(X_87)),X_37))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
meet(X_87,join(complement(complement(X_87)),X_37)) = meet(X_87,join(X_87,X_37)),
inference(resolve,[$cnf( $equal(join(complement(complement(X_87)),X_37),join(X_87,X_37)) )],[refute_0_653,refute_0_656]) ).
cnf(refute_0_658,plain,
X_87 = join(meet(X_87,complement(complement(X_87))),complement(join(complement(X_87),complement(complement(X_87))))),
inference(subst,[],[refute_0_158:[bind(A,$fot(X_87)),bind(B,$fot(complement(complement(X_87))))]]) ).
cnf(refute_0_659,plain,
top = join(complement(X_87),complement(complement(X_87))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_87)))]]) ).
cnf(refute_0_660,plain,
( top != join(complement(X_87),complement(complement(X_87)))
| join(complement(X_87),complement(complement(X_87))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_87),complement(complement(X_87)))))]]) ).
cnf(refute_0_661,plain,
join(complement(X_87),complement(complement(X_87))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_87),complement(complement(X_87)))) )],[refute_0_659,refute_0_660]) ).
cnf(refute_0_662,plain,
( X_87 != join(meet(X_87,complement(complement(X_87))),complement(join(complement(X_87),complement(complement(X_87)))))
| join(complement(X_87),complement(complement(X_87))) != top
| X_87 = join(meet(X_87,complement(complement(X_87))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_87,join(meet(X_87,complement(complement(X_87))),complement(join(complement(X_87),complement(complement(X_87)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_663,plain,
( X_87 != join(meet(X_87,complement(complement(X_87))),complement(join(complement(X_87),complement(complement(X_87)))))
| X_87 = join(meet(X_87,complement(complement(X_87))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_87),complement(complement(X_87))),top) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
X_87 = join(meet(X_87,complement(complement(X_87))),complement(top)),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,complement(complement(X_87))),complement(join(complement(X_87),complement(complement(X_87)))))) )],[refute_0_658,refute_0_663]) ).
cnf(refute_0_665,plain,
join(complement(top),meet(X_87,complement(complement(X_87)))) = join(complement(top),meet(X_87,complement(complement(X_87)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_87,complement(complement(X_87)))))]]) ).
cnf(refute_0_666,plain,
( complement(top) != zero
| join(complement(top),meet(X_87,complement(complement(X_87)))) != join(complement(top),meet(X_87,complement(complement(X_87))))
| join(complement(top),meet(X_87,complement(complement(X_87)))) = join(zero,meet(X_87,complement(complement(X_87)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_87,complement(complement(X_87)))),join(complement(top),meet(X_87,complement(complement(X_87))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_667,plain,
( complement(top) != zero
| join(complement(top),meet(X_87,complement(complement(X_87)))) = join(zero,meet(X_87,complement(complement(X_87)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_87,complement(complement(X_87)))),join(complement(top),meet(X_87,complement(complement(X_87))))) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
join(complement(top),meet(X_87,complement(complement(X_87)))) = join(zero,meet(X_87,complement(complement(X_87)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_667]) ).
cnf(refute_0_669,plain,
join(meet(X_87,complement(complement(X_87))),complement(top)) = join(complement(top),meet(X_87,complement(complement(X_87)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_87,complement(complement(X_87)))))]]) ).
cnf(refute_0_670,plain,
( join(complement(top),meet(X_87,complement(complement(X_87)))) != join(zero,meet(X_87,complement(complement(X_87))))
| join(meet(X_87,complement(complement(X_87))),complement(top)) != join(complement(top),meet(X_87,complement(complement(X_87))))
| join(meet(X_87,complement(complement(X_87))),complement(top)) = join(zero,meet(X_87,complement(complement(X_87)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(meet(X_87,complement(complement(X_87))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_87,complement(complement(X_87)))))),bind(Z,$fot(join(zero,meet(X_87,complement(complement(X_87))))))]]) ).
cnf(refute_0_671,plain,
( join(complement(top),meet(X_87,complement(complement(X_87)))) != join(zero,meet(X_87,complement(complement(X_87))))
| join(meet(X_87,complement(complement(X_87))),complement(top)) = join(zero,meet(X_87,complement(complement(X_87)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_87,complement(complement(X_87))),complement(top)),join(complement(top),meet(X_87,complement(complement(X_87))))) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
join(meet(X_87,complement(complement(X_87))),complement(top)) = join(zero,meet(X_87,complement(complement(X_87)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_87,complement(complement(X_87)))),join(zero,meet(X_87,complement(complement(X_87))))) )],[refute_0_668,refute_0_671]) ).
cnf(refute_0_673,plain,
( X_87 != join(meet(X_87,complement(complement(X_87))),complement(top))
| join(meet(X_87,complement(complement(X_87))),complement(top)) != join(zero,meet(X_87,complement(complement(X_87))))
| X_87 = join(zero,meet(X_87,complement(complement(X_87)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_87,join(zero,meet(X_87,complement(complement(X_87))))) ),[0],$fot(join(meet(X_87,complement(complement(X_87))),complement(top)))]]) ).
cnf(refute_0_674,plain,
( X_87 != join(meet(X_87,complement(complement(X_87))),complement(top))
| X_87 = join(zero,meet(X_87,complement(complement(X_87)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_87,complement(complement(X_87))),complement(top)),join(zero,meet(X_87,complement(complement(X_87))))) )],[refute_0_672,refute_0_673]) ).
cnf(refute_0_675,plain,
X_87 = join(zero,meet(X_87,complement(complement(X_87)))),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,complement(complement(X_87))),complement(top))) )],[refute_0_664,refute_0_674]) ).
cnf(refute_0_676,plain,
meet(X_87,X_87) = X_87,
inference(subst,[],[refute_0_387:[bind(B,$fot(X_87))]]) ).
cnf(refute_0_677,plain,
meet(X_87,complement(complement(X_87))) = meet(X_87,complement(complement(X_87))),
introduced(tautology,[refl,[$fot(meet(X_87,complement(complement(X_87))))]]) ).
cnf(refute_0_678,plain,
( complement(complement(X_87)) != X_87
| meet(X_87,complement(complement(X_87))) != meet(X_87,complement(complement(X_87)))
| meet(X_87,complement(complement(X_87))) = meet(X_87,X_87) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_87,complement(complement(X_87))),meet(X_87,complement(complement(X_87)))) ),[1,1],$fot(X_87)]]) ).
cnf(refute_0_679,plain,
( complement(complement(X_87)) != X_87
| meet(X_87,complement(complement(X_87))) = meet(X_87,X_87) ),
inference(resolve,[$cnf( $equal(meet(X_87,complement(complement(X_87))),meet(X_87,complement(complement(X_87)))) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
meet(X_87,complement(complement(X_87))) = meet(X_87,X_87),
inference(resolve,[$cnf( $equal(complement(complement(X_87)),X_87) )],[refute_0_383,refute_0_679]) ).
cnf(refute_0_681,plain,
( meet(X_87,X_87) != X_87
| meet(X_87,complement(complement(X_87))) != meet(X_87,X_87)
| meet(X_87,complement(complement(X_87))) = X_87 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(X_87,complement(complement(X_87))))),bind(Y,$fot(meet(X_87,X_87))),bind(Z,$fot(X_87))]]) ).
cnf(refute_0_682,plain,
( meet(X_87,X_87) != X_87
| meet(X_87,complement(complement(X_87))) = X_87 ),
inference(resolve,[$cnf( $equal(meet(X_87,complement(complement(X_87))),meet(X_87,X_87)) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
meet(X_87,complement(complement(X_87))) = X_87,
inference(resolve,[$cnf( $equal(meet(X_87,X_87),X_87) )],[refute_0_676,refute_0_682]) ).
cnf(refute_0_684,plain,
join(zero,meet(X_87,complement(complement(X_87)))) = join(zero,meet(X_87,complement(complement(X_87)))),
introduced(tautology,[refl,[$fot(join(zero,meet(X_87,complement(complement(X_87)))))]]) ).
cnf(refute_0_685,plain,
( join(zero,meet(X_87,complement(complement(X_87)))) != join(zero,meet(X_87,complement(complement(X_87))))
| meet(X_87,complement(complement(X_87))) != X_87
| join(zero,meet(X_87,complement(complement(X_87)))) = join(zero,X_87) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_87,complement(complement(X_87)))),join(zero,meet(X_87,complement(complement(X_87))))) ),[1,1],$fot(X_87)]]) ).
cnf(refute_0_686,plain,
( meet(X_87,complement(complement(X_87))) != X_87
| join(zero,meet(X_87,complement(complement(X_87)))) = join(zero,X_87) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_87,complement(complement(X_87)))),join(zero,meet(X_87,complement(complement(X_87))))) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
join(zero,meet(X_87,complement(complement(X_87)))) = join(zero,X_87),
inference(resolve,[$cnf( $equal(meet(X_87,complement(complement(X_87))),X_87) )],[refute_0_683,refute_0_686]) ).
cnf(refute_0_688,plain,
( X_87 != join(zero,meet(X_87,complement(complement(X_87))))
| join(zero,meet(X_87,complement(complement(X_87)))) != join(zero,X_87)
| X_87 = join(zero,X_87) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_87,join(zero,X_87)) ),[0],$fot(join(zero,meet(X_87,complement(complement(X_87)))))]]) ).
cnf(refute_0_689,plain,
( X_87 != join(zero,meet(X_87,complement(complement(X_87))))
| X_87 = join(zero,X_87) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_87,complement(complement(X_87)))),join(zero,X_87)) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
X_87 = join(zero,X_87),
inference(resolve,[$cnf( $equal(X_87,join(zero,meet(X_87,complement(complement(X_87))))) )],[refute_0_675,refute_0_689]) ).
cnf(refute_0_691,plain,
( X_87 != join(zero,X_87)
| join(zero,X_87) = X_87 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_87)),bind(Y,$fot(join(zero,X_87)))]]) ).
cnf(refute_0_692,plain,
join(zero,X_87) = X_87,
inference(resolve,[$cnf( $equal(X_87,join(zero,X_87)) )],[refute_0_690,refute_0_691]) ).
cnf(refute_0_693,plain,
join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) = meet(X_87,join(complement(complement(X_87)),X_37)),
inference(subst,[],[refute_0_692:[bind(X_87,$fot(meet(X_87,join(complement(complement(X_87)),X_37))))]]) ).
cnf(refute_0_694,plain,
( join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) != meet(X_87,join(complement(complement(X_87)),X_37))
| meet(X_87,join(complement(complement(X_87)),X_37)) != meet(X_87,join(X_87,X_37))
| join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) = meet(X_87,join(X_87,X_37)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(zero,meet(X_87,join(complement(complement(X_87)),X_37))))),bind(Y,$fot(meet(X_87,join(complement(complement(X_87)),X_37)))),bind(Z,$fot(meet(X_87,join(X_87,X_37))))]]) ).
cnf(refute_0_695,plain,
( meet(X_87,join(complement(complement(X_87)),X_37)) != meet(X_87,join(X_87,X_37))
| join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) = meet(X_87,join(X_87,X_37)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_87,join(complement(complement(X_87)),X_37))),meet(X_87,join(complement(complement(X_87)),X_37))) )],[refute_0_693,refute_0_694]) ).
cnf(refute_0_696,plain,
join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) = meet(X_87,join(X_87,X_37)),
inference(resolve,[$cnf( $equal(meet(X_87,join(complement(complement(X_87)),X_37)),meet(X_87,join(X_87,X_37))) )],[refute_0_657,refute_0_695]) ).
cnf(refute_0_697,plain,
( X_87 != join(zero,meet(X_87,join(complement(complement(X_87)),X_37)))
| join(zero,meet(X_87,join(complement(complement(X_87)),X_37))) != meet(X_87,join(X_87,X_37))
| X_87 = meet(X_87,join(X_87,X_37)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_87,meet(X_87,join(X_87,X_37))) ),[0],$fot(join(zero,meet(X_87,join(complement(complement(X_87)),X_37))))]]) ).
cnf(refute_0_698,plain,
( X_87 != join(zero,meet(X_87,join(complement(complement(X_87)),X_37)))
| X_87 = meet(X_87,join(X_87,X_37)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_87,join(complement(complement(X_87)),X_37))),meet(X_87,join(X_87,X_37))) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
X_87 = meet(X_87,join(X_87,X_37)),
inference(resolve,[$cnf( $equal(X_87,join(zero,meet(X_87,join(complement(complement(X_87)),X_37)))) )],[refute_0_649,refute_0_698]) ).
cnf(refute_0_700,plain,
X_109 = meet(X_109,join(X_109,composition(X_32,X_109))),
inference(subst,[],[refute_0_699:[bind(X_37,$fot(composition(X_32,X_109))),bind(X_87,$fot(X_109))]]) ).
cnf(refute_0_701,plain,
composition(join(X_32,one),X_109) = join(X_109,composition(X_32,X_109)),
inference(subst,[],[refute_0_61:[bind(X_34,$fot(X_109))]]) ).
cnf(refute_0_702,plain,
( composition(join(X_32,one),X_109) != join(X_109,composition(X_32,X_109))
| join(X_109,composition(X_32,X_109)) = composition(join(X_32,one),X_109) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_32,one),X_109))),bind(Y,$fot(join(X_109,composition(X_32,X_109))))]]) ).
cnf(refute_0_703,plain,
join(X_109,composition(X_32,X_109)) = composition(join(X_32,one),X_109),
inference(resolve,[$cnf( $equal(composition(join(X_32,one),X_109),join(X_109,composition(X_32,X_109))) )],[refute_0_701,refute_0_702]) ).
cnf(refute_0_704,plain,
( X_109 != meet(X_109,join(X_109,composition(X_32,X_109)))
| join(X_109,composition(X_32,X_109)) != composition(join(X_32,one),X_109)
| X_109 = meet(X_109,composition(join(X_32,one),X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(X_109,meet(X_109,join(X_109,composition(X_32,X_109)))) ),[1,1],$fot(composition(join(X_32,one),X_109))]]) ).
cnf(refute_0_705,plain,
( X_109 != meet(X_109,join(X_109,composition(X_32,X_109)))
| X_109 = meet(X_109,composition(join(X_32,one),X_109)) ),
inference(resolve,[$cnf( $equal(join(X_109,composition(X_32,X_109)),composition(join(X_32,one),X_109)) )],[refute_0_703,refute_0_704]) ).
cnf(refute_0_706,plain,
X_109 = meet(X_109,composition(join(X_32,one),X_109)),
inference(resolve,[$cnf( $equal(X_109,meet(X_109,join(X_109,composition(X_32,X_109)))) )],[refute_0_700,refute_0_705]) ).
cnf(refute_0_707,plain,
X_109 = meet(X_109,composition(join(top,one),X_109)),
inference(subst,[],[refute_0_706:[bind(X_32,$fot(top))]]) ).
cnf(refute_0_708,plain,
top = join(top,one),
inference(subst,[],[refute_0_532:[bind(X_35,$fot(one))]]) ).
cnf(refute_0_709,plain,
( top != join(top,one)
| join(top,one) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,one)))]]) ).
cnf(refute_0_710,plain,
join(top,one) = top,
inference(resolve,[$cnf( $equal(top,join(top,one)) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
( X_109 != meet(X_109,composition(join(top,one),X_109))
| join(top,one) != top
| X_109 = meet(X_109,composition(top,X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(X_109,meet(X_109,composition(join(top,one),X_109))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_712,plain,
( X_109 != meet(X_109,composition(join(top,one),X_109))
| X_109 = meet(X_109,composition(top,X_109)) ),
inference(resolve,[$cnf( $equal(join(top,one),top) )],[refute_0_710,refute_0_711]) ).
cnf(refute_0_713,plain,
X_109 = meet(X_109,composition(top,X_109)),
inference(resolve,[$cnf( $equal(X_109,meet(X_109,composition(join(top,one),X_109))) )],[refute_0_707,refute_0_712]) ).
cnf(refute_0_714,plain,
X_88 = meet(X_88,composition(top,X_88)),
inference(subst,[],[refute_0_713:[bind(X_109,$fot(X_88))]]) ).
cnf(refute_0_715,plain,
( X_88 != meet(X_88,composition(top,X_88))
| meet(X_88,composition(top,X_88)) = X_88 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_88)),bind(Y,$fot(meet(X_88,composition(top,X_88))))]]) ).
cnf(refute_0_716,plain,
meet(X_88,composition(top,X_88)) = X_88,
inference(resolve,[$cnf( $equal(X_88,meet(X_88,composition(top,X_88))) )],[refute_0_714,refute_0_715]) ).
cnf(refute_0_717,plain,
( composition(top,X_88) != join(meet(X_88,composition(top,X_88)),complement(join(complement(composition(top,X_88)),X_88)))
| meet(X_88,composition(top,X_88)) != X_88
| composition(top,X_88) = join(X_88,complement(join(complement(composition(top,X_88)),X_88))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,X_88),join(meet(X_88,composition(top,X_88)),complement(join(complement(composition(top,X_88)),X_88)))) ),[1,0],$fot(X_88)]]) ).
cnf(refute_0_718,plain,
( composition(top,X_88) != join(meet(X_88,composition(top,X_88)),complement(join(complement(composition(top,X_88)),X_88)))
| composition(top,X_88) = join(X_88,complement(join(complement(composition(top,X_88)),X_88))) ),
inference(resolve,[$cnf( $equal(meet(X_88,composition(top,X_88)),X_88) )],[refute_0_716,refute_0_717]) ).
cnf(refute_0_719,plain,
composition(top,X_88) = join(X_88,complement(join(complement(composition(top,X_88)),X_88))),
inference(resolve,[$cnf( $equal(composition(top,X_88),join(meet(X_88,composition(top,X_88)),complement(join(complement(composition(top,X_88)),X_88)))) )],[refute_0_630,refute_0_718]) ).
cnf(refute_0_720,plain,
join(complement(composition(top,X_88)),X_88) = join(X_88,complement(composition(top,X_88))),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_88)),bind(B,$fot(complement(composition(top,X_88))))]]) ).
cnf(refute_0_721,plain,
complement(join(complement(composition(top,X_88)),X_88)) = complement(join(complement(composition(top,X_88)),X_88)),
introduced(tautology,[refl,[$fot(complement(join(complement(composition(top,X_88)),X_88)))]]) ).
cnf(refute_0_722,plain,
( complement(join(complement(composition(top,X_88)),X_88)) != complement(join(complement(composition(top,X_88)),X_88))
| join(complement(composition(top,X_88)),X_88) != join(X_88,complement(composition(top,X_88)))
| complement(join(complement(composition(top,X_88)),X_88)) = complement(join(X_88,complement(composition(top,X_88)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(composition(top,X_88)),X_88)),complement(join(complement(composition(top,X_88)),X_88))) ),[1,0],$fot(join(X_88,complement(composition(top,X_88))))]]) ).
cnf(refute_0_723,plain,
( join(complement(composition(top,X_88)),X_88) != join(X_88,complement(composition(top,X_88)))
| complement(join(complement(composition(top,X_88)),X_88)) = complement(join(X_88,complement(composition(top,X_88)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(composition(top,X_88)),X_88)),complement(join(complement(composition(top,X_88)),X_88))) )],[refute_0_721,refute_0_722]) ).
cnf(refute_0_724,plain,
complement(join(complement(composition(top,X_88)),X_88)) = complement(join(X_88,complement(composition(top,X_88)))),
inference(resolve,[$cnf( $equal(join(complement(composition(top,X_88)),X_88),join(X_88,complement(composition(top,X_88)))) )],[refute_0_720,refute_0_723]) ).
cnf(refute_0_725,plain,
join(X_88,complement(join(complement(composition(top,X_88)),X_88))) = join(X_88,complement(join(complement(composition(top,X_88)),X_88))),
introduced(tautology,[refl,[$fot(join(X_88,complement(join(complement(composition(top,X_88)),X_88))))]]) ).
cnf(refute_0_726,plain,
( complement(join(complement(composition(top,X_88)),X_88)) != complement(join(X_88,complement(composition(top,X_88))))
| join(X_88,complement(join(complement(composition(top,X_88)),X_88))) != join(X_88,complement(join(complement(composition(top,X_88)),X_88)))
| join(X_88,complement(join(complement(composition(top,X_88)),X_88))) = join(X_88,complement(join(X_88,complement(composition(top,X_88))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_88,complement(join(complement(composition(top,X_88)),X_88))),join(X_88,complement(join(complement(composition(top,X_88)),X_88)))) ),[1,1],$fot(complement(join(X_88,complement(composition(top,X_88)))))]]) ).
cnf(refute_0_727,plain,
( complement(join(complement(composition(top,X_88)),X_88)) != complement(join(X_88,complement(composition(top,X_88))))
| join(X_88,complement(join(complement(composition(top,X_88)),X_88))) = join(X_88,complement(join(X_88,complement(composition(top,X_88))))) ),
inference(resolve,[$cnf( $equal(join(X_88,complement(join(complement(composition(top,X_88)),X_88))),join(X_88,complement(join(complement(composition(top,X_88)),X_88)))) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
join(X_88,complement(join(complement(composition(top,X_88)),X_88))) = join(X_88,complement(join(X_88,complement(composition(top,X_88))))),
inference(resolve,[$cnf( $equal(complement(join(complement(composition(top,X_88)),X_88)),complement(join(X_88,complement(composition(top,X_88))))) )],[refute_0_724,refute_0_727]) ).
cnf(refute_0_729,plain,
( composition(top,X_88) != join(X_88,complement(join(complement(composition(top,X_88)),X_88)))
| join(X_88,complement(join(complement(composition(top,X_88)),X_88))) != join(X_88,complement(join(X_88,complement(composition(top,X_88)))))
| composition(top,X_88) = join(X_88,complement(join(X_88,complement(composition(top,X_88))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(top,X_88),join(X_88,complement(join(X_88,complement(composition(top,X_88)))))) ),[0],$fot(join(X_88,complement(join(complement(composition(top,X_88)),X_88))))]]) ).
cnf(refute_0_730,plain,
( composition(top,X_88) != join(X_88,complement(join(complement(composition(top,X_88)),X_88)))
| composition(top,X_88) = join(X_88,complement(join(X_88,complement(composition(top,X_88))))) ),
inference(resolve,[$cnf( $equal(join(X_88,complement(join(complement(composition(top,X_88)),X_88))),join(X_88,complement(join(X_88,complement(composition(top,X_88)))))) )],[refute_0_728,refute_0_729]) ).
cnf(refute_0_731,plain,
composition(top,X_88) = join(X_88,complement(join(X_88,complement(composition(top,X_88))))),
inference(resolve,[$cnf( $equal(composition(top,X_88),join(X_88,complement(join(complement(composition(top,X_88)),X_88)))) )],[refute_0_719,refute_0_730]) ).
cnf(refute_0_732,plain,
composition(top,converse(complement(converse(X_35)))) = join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35)))))))),
inference(subst,[],[refute_0_731:[bind(X_88,$fot(converse(complement(converse(X_35)))))]]) ).
cnf(refute_0_733,plain,
( composition(top,converse(complement(converse(X_35)))) != join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35))))))))
| join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35)))))))) = composition(top,converse(complement(converse(X_35)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(top,converse(complement(converse(X_35)))))),bind(Y,$fot(join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35))))))))))]]) ).
cnf(refute_0_734,plain,
join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35)))))))) = composition(top,converse(complement(converse(X_35)))),
inference(resolve,[$cnf( $equal(composition(top,converse(complement(converse(X_35)))),join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35))))))))) )],[refute_0_732,refute_0_733]) ).
cnf(refute_0_735,plain,
( join(X_35,join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35))))))))) != top
| join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35)))))))) != composition(top,converse(complement(converse(X_35))))
| join(X_35,composition(top,converse(complement(converse(X_35))))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35))))))))),top) ),[0,1],$fot(composition(top,converse(complement(converse(X_35)))))]]) ).
cnf(refute_0_736,plain,
( join(X_35,join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35))))))))) != top
| join(X_35,composition(top,converse(complement(converse(X_35))))) = top ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35)))))))),composition(top,converse(complement(converse(X_35))))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
join(X_35,composition(top,converse(complement(converse(X_35))))) = top,
inference(resolve,[$cnf( $equal(join(X_35,join(converse(complement(converse(X_35))),complement(join(converse(complement(converse(X_35))),complement(composition(top,converse(complement(converse(X_35))))))))),top) )],[refute_0_612,refute_0_736]) ).
cnf(refute_0_738,plain,
converse(composition(X_22,converse(top))) = composition(top,converse(X_22)),
inference(subst,[],[refute_0_163:[bind(A,$fot(top))]]) ).
cnf(refute_0_739,plain,
( converse(composition(X_22,converse(top))) != composition(top,converse(X_22))
| converse(top) != top
| converse(composition(X_22,top)) = composition(top,converse(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_22,converse(top))),composition(top,converse(X_22))) ),[0,0,1],$fot(top)]]) ).
cnf(refute_0_740,plain,
( converse(composition(X_22,converse(top))) != composition(top,converse(X_22))
| converse(composition(X_22,top)) = composition(top,converse(X_22)) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_601,refute_0_739]) ).
cnf(refute_0_741,plain,
converse(composition(X_22,top)) = composition(top,converse(X_22)),
inference(resolve,[$cnf( $equal(converse(composition(X_22,converse(top))),composition(top,converse(X_22))) )],[refute_0_738,refute_0_740]) ).
cnf(refute_0_742,plain,
( converse(composition(X_22,top)) != composition(top,converse(X_22))
| composition(top,converse(X_22)) = converse(composition(X_22,top)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(X_22,top)))),bind(Y,$fot(composition(top,converse(X_22))))]]) ).
cnf(refute_0_743,plain,
composition(top,converse(X_22)) = converse(composition(X_22,top)),
inference(resolve,[$cnf( $equal(converse(composition(X_22,top)),composition(top,converse(X_22))) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
composition(top,converse(complement(converse(X_35)))) = converse(composition(complement(converse(X_35)),top)),
inference(subst,[],[refute_0_743:[bind(X_22,$fot(complement(converse(X_35))))]]) ).
cnf(refute_0_745,plain,
join(X_35,composition(top,converse(complement(converse(X_35))))) = join(X_35,composition(top,converse(complement(converse(X_35))))),
introduced(tautology,[refl,[$fot(join(X_35,composition(top,converse(complement(converse(X_35))))))]]) ).
cnf(refute_0_746,plain,
( composition(top,converse(complement(converse(X_35)))) != converse(composition(complement(converse(X_35)),top))
| join(X_35,composition(top,converse(complement(converse(X_35))))) != join(X_35,composition(top,converse(complement(converse(X_35)))))
| join(X_35,composition(top,converse(complement(converse(X_35))))) = join(X_35,converse(composition(complement(converse(X_35)),top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,composition(top,converse(complement(converse(X_35))))),join(X_35,composition(top,converse(complement(converse(X_35)))))) ),[1,1],$fot(converse(composition(complement(converse(X_35)),top)))]]) ).
cnf(refute_0_747,plain,
( composition(top,converse(complement(converse(X_35)))) != converse(composition(complement(converse(X_35)),top))
| join(X_35,composition(top,converse(complement(converse(X_35))))) = join(X_35,converse(composition(complement(converse(X_35)),top))) ),
inference(resolve,[$cnf( $equal(join(X_35,composition(top,converse(complement(converse(X_35))))),join(X_35,composition(top,converse(complement(converse(X_35)))))) )],[refute_0_745,refute_0_746]) ).
cnf(refute_0_748,plain,
join(X_35,composition(top,converse(complement(converse(X_35))))) = join(X_35,converse(composition(complement(converse(X_35)),top))),
inference(resolve,[$cnf( $equal(composition(top,converse(complement(converse(X_35)))),converse(composition(complement(converse(X_35)),top))) )],[refute_0_744,refute_0_747]) ).
cnf(refute_0_749,plain,
( join(X_35,composition(top,converse(complement(converse(X_35))))) != join(X_35,converse(composition(complement(converse(X_35)),top)))
| join(X_35,composition(top,converse(complement(converse(X_35))))) != top
| join(X_35,converse(composition(complement(converse(X_35)),top))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,composition(top,converse(complement(converse(X_35))))),top) ),[0],$fot(join(X_35,converse(composition(complement(converse(X_35)),top))))]]) ).
cnf(refute_0_750,plain,
( join(X_35,composition(top,converse(complement(converse(X_35))))) != top
| join(X_35,converse(composition(complement(converse(X_35)),top))) = top ),
inference(resolve,[$cnf( $equal(join(X_35,composition(top,converse(complement(converse(X_35))))),join(X_35,converse(composition(complement(converse(X_35)),top)))) )],[refute_0_748,refute_0_749]) ).
cnf(refute_0_751,plain,
join(X_35,converse(composition(complement(converse(X_35)),top))) = top,
inference(resolve,[$cnf( $equal(join(X_35,composition(top,converse(complement(converse(X_35))))),top) )],[refute_0_737,refute_0_750]) ).
cnf(refute_0_752,plain,
join(converse(A),converse(composition(complement(converse(converse(A))),top))) = top,
inference(subst,[],[refute_0_751:[bind(X_35,$fot(converse(A)))]]) ).
cnf(refute_0_753,plain,
( converse(join(converse(A),converse(composition(complement(converse(converse(A))),top)))) != join(A,converse(converse(composition(complement(converse(converse(A))),top))))
| join(converse(A),converse(composition(complement(converse(converse(A))),top))) != top
| converse(top) = join(A,converse(converse(composition(complement(converse(converse(A))),top)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),converse(composition(complement(converse(converse(A))),top)))),join(A,converse(converse(composition(complement(converse(converse(A))),top))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_754,plain,
( converse(join(converse(A),converse(composition(complement(converse(converse(A))),top)))) != join(A,converse(converse(composition(complement(converse(converse(A))),top))))
| converse(top) = join(A,converse(converse(composition(complement(converse(converse(A))),top)))) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(composition(complement(converse(converse(A))),top))),top) )],[refute_0_752,refute_0_753]) ).
cnf(refute_0_755,plain,
converse(top) = join(A,converse(converse(composition(complement(converse(converse(A))),top)))),
inference(resolve,[$cnf( $equal(converse(join(converse(A),converse(composition(complement(converse(converse(A))),top)))),join(A,converse(converse(composition(complement(converse(converse(A))),top))))) )],[refute_0_419,refute_0_754]) ).
cnf(refute_0_756,plain,
( converse(top) != join(A,converse(converse(composition(complement(converse(converse(A))),top))))
| converse(top) != top
| top = join(A,converse(converse(composition(complement(converse(converse(A))),top)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(A,converse(converse(composition(complement(converse(converse(A))),top))))) ),[0],$fot(top)]]) ).
cnf(refute_0_757,plain,
( converse(top) != join(A,converse(converse(composition(complement(converse(converse(A))),top))))
| top = join(A,converse(converse(composition(complement(converse(converse(A))),top)))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_601,refute_0_756]) ).
cnf(refute_0_758,plain,
complement(converse(converse(A))) = complement(converse(converse(A))),
introduced(tautology,[refl,[$fot(complement(converse(converse(A))))]]) ).
cnf(refute_0_759,plain,
( complement(converse(converse(A))) != complement(converse(converse(A)))
| converse(converse(A)) != A
| complement(converse(converse(A))) = complement(A) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(converse(A))),complement(converse(converse(A)))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_760,plain,
( converse(converse(A)) != A
| complement(converse(converse(A))) = complement(A) ),
inference(resolve,[$cnf( $equal(complement(converse(converse(A))),complement(converse(converse(A)))) )],[refute_0_758,refute_0_759]) ).
cnf(refute_0_761,plain,
complement(converse(converse(A))) = complement(A),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_760]) ).
cnf(refute_0_762,plain,
composition(complement(converse(converse(A))),top) = composition(complement(converse(converse(A))),top),
introduced(tautology,[refl,[$fot(composition(complement(converse(converse(A))),top))]]) ).
cnf(refute_0_763,plain,
( complement(converse(converse(A))) != complement(A)
| composition(complement(converse(converse(A))),top) != composition(complement(converse(converse(A))),top)
| composition(complement(converse(converse(A))),top) = composition(complement(A),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(converse(converse(A))),top),composition(complement(converse(converse(A))),top)) ),[1,0],$fot(complement(A))]]) ).
cnf(refute_0_764,plain,
( complement(converse(converse(A))) != complement(A)
| composition(complement(converse(converse(A))),top) = composition(complement(A),top) ),
inference(resolve,[$cnf( $equal(composition(complement(converse(converse(A))),top),composition(complement(converse(converse(A))),top)) )],[refute_0_762,refute_0_763]) ).
cnf(refute_0_765,plain,
composition(complement(converse(converse(A))),top) = composition(complement(A),top),
inference(resolve,[$cnf( $equal(complement(converse(converse(A))),complement(A)) )],[refute_0_761,refute_0_764]) ).
cnf(refute_0_766,plain,
converse(converse(composition(complement(converse(converse(A))),top))) = composition(complement(converse(converse(A))),top),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(complement(converse(converse(A))),top)))]]) ).
cnf(refute_0_767,plain,
( composition(complement(converse(converse(A))),top) != composition(complement(A),top)
| converse(converse(composition(complement(converse(converse(A))),top))) != composition(complement(converse(converse(A))),top)
| converse(converse(composition(complement(converse(converse(A))),top))) = composition(complement(A),top) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(converse(composition(complement(converse(converse(A))),top))))),bind(Y,$fot(composition(complement(converse(converse(A))),top))),bind(Z,$fot(composition(complement(A),top)))]]) ).
cnf(refute_0_768,plain,
( composition(complement(converse(converse(A))),top) != composition(complement(A),top)
| converse(converse(composition(complement(converse(converse(A))),top))) = composition(complement(A),top) ),
inference(resolve,[$cnf( $equal(converse(converse(composition(complement(converse(converse(A))),top))),composition(complement(converse(converse(A))),top)) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
converse(converse(composition(complement(converse(converse(A))),top))) = composition(complement(A),top),
inference(resolve,[$cnf( $equal(composition(complement(converse(converse(A))),top),composition(complement(A),top)) )],[refute_0_765,refute_0_768]) ).
cnf(refute_0_770,plain,
join(A,converse(converse(composition(complement(converse(converse(A))),top)))) = join(A,converse(converse(composition(complement(converse(converse(A))),top)))),
introduced(tautology,[refl,[$fot(join(A,converse(converse(composition(complement(converse(converse(A))),top)))))]]) ).
cnf(refute_0_771,plain,
( converse(converse(composition(complement(converse(converse(A))),top))) != composition(complement(A),top)
| join(A,converse(converse(composition(complement(converse(converse(A))),top)))) != join(A,converse(converse(composition(complement(converse(converse(A))),top))))
| join(A,converse(converse(composition(complement(converse(converse(A))),top)))) = join(A,composition(complement(A),top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,converse(converse(composition(complement(converse(converse(A))),top)))),join(A,converse(converse(composition(complement(converse(converse(A))),top))))) ),[1,1],$fot(composition(complement(A),top))]]) ).
cnf(refute_0_772,plain,
( converse(converse(composition(complement(converse(converse(A))),top))) != composition(complement(A),top)
| join(A,converse(converse(composition(complement(converse(converse(A))),top)))) = join(A,composition(complement(A),top)) ),
inference(resolve,[$cnf( $equal(join(A,converse(converse(composition(complement(converse(converse(A))),top)))),join(A,converse(converse(composition(complement(converse(converse(A))),top))))) )],[refute_0_770,refute_0_771]) ).
cnf(refute_0_773,plain,
join(A,converse(converse(composition(complement(converse(converse(A))),top)))) = join(A,composition(complement(A),top)),
inference(resolve,[$cnf( $equal(converse(converse(composition(complement(converse(converse(A))),top))),composition(complement(A),top)) )],[refute_0_769,refute_0_772]) ).
cnf(refute_0_774,plain,
( join(A,converse(converse(composition(complement(converse(converse(A))),top)))) != join(A,composition(complement(A),top))
| top != join(A,converse(converse(composition(complement(converse(converse(A))),top))))
| top = join(A,composition(complement(A),top)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(A,converse(converse(composition(complement(converse(converse(A))),top))))) ),[1],$fot(join(A,composition(complement(A),top)))]]) ).
cnf(refute_0_775,plain,
( top != join(A,converse(converse(composition(complement(converse(converse(A))),top))))
| top = join(A,composition(complement(A),top)) ),
inference(resolve,[$cnf( $equal(join(A,converse(converse(composition(complement(converse(converse(A))),top)))),join(A,composition(complement(A),top))) )],[refute_0_773,refute_0_774]) ).
cnf(refute_0_776,plain,
( converse(top) != join(A,converse(converse(composition(complement(converse(converse(A))),top))))
| top = join(A,composition(complement(A),top)) ),
inference(resolve,[$cnf( $equal(top,join(A,converse(converse(composition(complement(converse(converse(A))),top))))) )],[refute_0_757,refute_0_775]) ).
cnf(refute_0_777,plain,
top = join(A,composition(complement(A),top)),
inference(resolve,[$cnf( $equal(converse(top),join(A,converse(converse(composition(complement(converse(converse(A))),top))))) )],[refute_0_755,refute_0_776]) ).
cnf(refute_0_778,plain,
top = join(composition(A,top),composition(complement(composition(A,top)),top)),
inference(subst,[],[refute_0_777:[bind(A,$fot(composition(A,top)))]]) ).
cnf(refute_0_779,plain,
( top != join(composition(A,top),composition(complement(composition(A,top)),top))
| join(composition(A,top),composition(complement(composition(A,top)),top)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(composition(A,top),composition(complement(composition(A,top)),top))))]]) ).
cnf(refute_0_780,plain,
join(composition(A,top),composition(complement(composition(A,top)),top)) = top,
inference(resolve,[$cnf( $equal(top,join(composition(A,top),composition(complement(composition(A,top)),top))) )],[refute_0_778,refute_0_779]) ).
cnf(refute_0_781,plain,
( composition(join(A,complement(composition(A,top))),top) != join(composition(A,top),composition(complement(composition(A,top)),top))
| join(composition(A,top),composition(complement(composition(A,top)),top)) != top
| composition(join(A,complement(composition(A,top))),top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(A,complement(composition(A,top))),top),top) ),[0],$fot(join(composition(A,top),composition(complement(composition(A,top)),top)))]]) ).
cnf(refute_0_782,plain,
( composition(join(A,complement(composition(A,top))),top) != join(composition(A,top),composition(complement(composition(A,top)),top))
| composition(join(A,complement(composition(A,top))),top) = top ),
inference(resolve,[$cnf( $equal(join(composition(A,top),composition(complement(composition(A,top)),top)),top) )],[refute_0_780,refute_0_781]) ).
cnf(refute_0_783,plain,
composition(join(A,complement(composition(A,top))),top) = top,
inference(resolve,[$cnf( $equal(composition(join(A,complement(composition(A,top))),top),join(composition(A,top),composition(complement(composition(A,top)),top))) )],[refute_0_418,refute_0_782]) ).
cnf(refute_0_784,plain,
composition(join(converse(X_194),complement(composition(converse(X_194),top))),top) = top,
inference(subst,[],[refute_0_783:[bind(A,$fot(converse(X_194)))]]) ).
cnf(refute_0_785,plain,
( composition(join(converse(X_194),complement(composition(converse(X_194),top))),top) != top
| converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top)) != composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))
| converse(top) = composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top)),composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_786,plain,
( converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top)) != composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))
| converse(top) = composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top),top) )],[refute_0_784,refute_0_785]) ).
cnf(refute_0_787,plain,
converse(top) = composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))),
inference(resolve,[$cnf( $equal(converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top)),composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))) )],[refute_0_417,refute_0_786]) ).
cnf(refute_0_788,plain,
( converse(top) != composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))
| converse(top) != top
| top = composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))) ),[0],$fot(top)]]) ).
cnf(refute_0_789,plain,
( converse(top) != composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))
| top = composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_601,refute_0_788]) ).
cnf(refute_0_790,plain,
converse(composition(converse(top),X_23)) = composition(converse(X_23),top),
inference(subst,[],[refute_0_26:[bind(A,$fot(top))]]) ).
cnf(refute_0_791,plain,
( converse(composition(converse(top),X_23)) != composition(converse(X_23),top)
| converse(top) != top
| converse(composition(top,X_23)) = composition(converse(X_23),top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(top),X_23)),composition(converse(X_23),top)) ),[0,0,0],$fot(top)]]) ).
cnf(refute_0_792,plain,
( converse(composition(converse(top),X_23)) != composition(converse(X_23),top)
| converse(composition(top,X_23)) = composition(converse(X_23),top) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_601,refute_0_791]) ).
cnf(refute_0_793,plain,
converse(composition(top,X_23)) = composition(converse(X_23),top),
inference(resolve,[$cnf( $equal(converse(composition(converse(top),X_23)),composition(converse(X_23),top)) )],[refute_0_790,refute_0_792]) ).
cnf(refute_0_794,plain,
( converse(composition(top,X_23)) != composition(converse(X_23),top)
| composition(converse(X_23),top) = converse(composition(top,X_23)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(top,X_23)))),bind(Y,$fot(composition(converse(X_23),top)))]]) ).
cnf(refute_0_795,plain,
composition(converse(X_23),top) = converse(composition(top,X_23)),
inference(resolve,[$cnf( $equal(converse(composition(top,X_23)),composition(converse(X_23),top)) )],[refute_0_793,refute_0_794]) ).
cnf(refute_0_796,plain,
composition(converse(X_194),top) = converse(composition(top,X_194)),
inference(subst,[],[refute_0_795:[bind(X_23,$fot(X_194))]]) ).
cnf(refute_0_797,plain,
complement(composition(converse(X_194),top)) = complement(composition(converse(X_194),top)),
introduced(tautology,[refl,[$fot(complement(composition(converse(X_194),top)))]]) ).
cnf(refute_0_798,plain,
( complement(composition(converse(X_194),top)) != complement(composition(converse(X_194),top))
| composition(converse(X_194),top) != converse(composition(top,X_194))
| complement(composition(converse(X_194),top)) = complement(converse(composition(top,X_194))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(converse(X_194),top)),complement(composition(converse(X_194),top))) ),[1,0],$fot(converse(composition(top,X_194)))]]) ).
cnf(refute_0_799,plain,
( composition(converse(X_194),top) != converse(composition(top,X_194))
| complement(composition(converse(X_194),top)) = complement(converse(composition(top,X_194))) ),
inference(resolve,[$cnf( $equal(complement(composition(converse(X_194),top)),complement(composition(converse(X_194),top))) )],[refute_0_797,refute_0_798]) ).
cnf(refute_0_800,plain,
complement(composition(converse(X_194),top)) = complement(converse(composition(top,X_194))),
inference(resolve,[$cnf( $equal(composition(converse(X_194),top),converse(composition(top,X_194))) )],[refute_0_796,refute_0_799]) ).
cnf(refute_0_801,plain,
converse(complement(composition(converse(X_194),top))) = converse(complement(composition(converse(X_194),top))),
introduced(tautology,[refl,[$fot(converse(complement(composition(converse(X_194),top))))]]) ).
cnf(refute_0_802,plain,
( complement(composition(converse(X_194),top)) != complement(converse(composition(top,X_194)))
| converse(complement(composition(converse(X_194),top))) != converse(complement(composition(converse(X_194),top)))
| converse(complement(composition(converse(X_194),top))) = converse(complement(converse(composition(top,X_194)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(composition(converse(X_194),top))),converse(complement(composition(converse(X_194),top)))) ),[1,0],$fot(complement(converse(composition(top,X_194))))]]) ).
cnf(refute_0_803,plain,
( complement(composition(converse(X_194),top)) != complement(converse(composition(top,X_194)))
| converse(complement(composition(converse(X_194),top))) = converse(complement(converse(composition(top,X_194)))) ),
inference(resolve,[$cnf( $equal(converse(complement(composition(converse(X_194),top))),converse(complement(composition(converse(X_194),top)))) )],[refute_0_801,refute_0_802]) ).
cnf(refute_0_804,plain,
converse(complement(composition(converse(X_194),top))) = converse(complement(converse(composition(top,X_194)))),
inference(resolve,[$cnf( $equal(complement(composition(converse(X_194),top)),complement(converse(composition(top,X_194)))) )],[refute_0_800,refute_0_803]) ).
cnf(refute_0_805,plain,
join(X_194,converse(complement(composition(converse(X_194),top)))) = join(X_194,converse(complement(composition(converse(X_194),top)))),
introduced(tautology,[refl,[$fot(join(X_194,converse(complement(composition(converse(X_194),top)))))]]) ).
cnf(refute_0_806,plain,
( converse(complement(composition(converse(X_194),top))) != converse(complement(converse(composition(top,X_194))))
| join(X_194,converse(complement(composition(converse(X_194),top)))) != join(X_194,converse(complement(composition(converse(X_194),top))))
| join(X_194,converse(complement(composition(converse(X_194),top)))) = join(X_194,converse(complement(converse(composition(top,X_194))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_194,converse(complement(composition(converse(X_194),top)))),join(X_194,converse(complement(composition(converse(X_194),top))))) ),[1,1],$fot(converse(complement(converse(composition(top,X_194)))))]]) ).
cnf(refute_0_807,plain,
( converse(complement(composition(converse(X_194),top))) != converse(complement(converse(composition(top,X_194))))
| join(X_194,converse(complement(composition(converse(X_194),top)))) = join(X_194,converse(complement(converse(composition(top,X_194))))) ),
inference(resolve,[$cnf( $equal(join(X_194,converse(complement(composition(converse(X_194),top)))),join(X_194,converse(complement(composition(converse(X_194),top))))) )],[refute_0_805,refute_0_806]) ).
cnf(refute_0_808,plain,
join(X_194,converse(complement(composition(converse(X_194),top)))) = join(X_194,converse(complement(converse(composition(top,X_194))))),
inference(resolve,[$cnf( $equal(converse(complement(composition(converse(X_194),top))),converse(complement(converse(composition(top,X_194))))) )],[refute_0_804,refute_0_807]) ).
cnf(refute_0_809,plain,
composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))) = composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))),
introduced(tautology,[refl,[$fot(composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))))]]) ).
cnf(refute_0_810,plain,
( composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))) != composition(top,join(X_194,converse(complement(composition(converse(X_194),top)))))
| join(X_194,converse(complement(composition(converse(X_194),top)))) != join(X_194,converse(complement(converse(composition(top,X_194)))))
| composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))) = composition(top,join(X_194,converse(complement(converse(composition(top,X_194)))))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))),composition(top,join(X_194,converse(complement(composition(converse(X_194),top)))))) ),[1,1],$fot(join(X_194,converse(complement(converse(composition(top,X_194))))))]]) ).
cnf(refute_0_811,plain,
( join(X_194,converse(complement(composition(converse(X_194),top)))) != join(X_194,converse(complement(converse(composition(top,X_194)))))
| composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))) = composition(top,join(X_194,converse(complement(converse(composition(top,X_194)))))) ),
inference(resolve,[$cnf( $equal(composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))),composition(top,join(X_194,converse(complement(composition(converse(X_194),top)))))) )],[refute_0_809,refute_0_810]) ).
cnf(refute_0_812,plain,
composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))) = composition(top,join(X_194,converse(complement(converse(composition(top,X_194)))))),
inference(resolve,[$cnf( $equal(join(X_194,converse(complement(composition(converse(X_194),top)))),join(X_194,converse(complement(converse(composition(top,X_194)))))) )],[refute_0_808,refute_0_811]) ).
cnf(refute_0_813,plain,
converse(composition(join(converse(A),X_13),top)) = composition(top,converse(join(converse(A),X_13))),
inference(subst,[],[refute_0_741:[bind(X_22,$fot(join(converse(A),X_13)))]]) ).
cnf(refute_0_814,plain,
( converse(composition(join(converse(A),X_13),top)) != composition(top,converse(join(converse(A),X_13)))
| converse(join(converse(A),X_13)) != join(A,converse(X_13))
| converse(composition(join(converse(A),X_13),top)) = composition(top,join(A,converse(X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(converse(A),X_13),top)),composition(top,converse(join(converse(A),X_13)))) ),[1,1],$fot(join(A,converse(X_13)))]]) ).
cnf(refute_0_815,plain,
( converse(composition(join(converse(A),X_13),top)) != composition(top,converse(join(converse(A),X_13)))
| converse(composition(join(converse(A),X_13),top)) = composition(top,join(A,converse(X_13))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_13)),join(A,converse(X_13))) )],[refute_0_89,refute_0_814]) ).
cnf(refute_0_816,plain,
converse(composition(join(converse(A),X_13),top)) = composition(top,join(A,converse(X_13))),
inference(resolve,[$cnf( $equal(converse(composition(join(converse(A),X_13),top)),composition(top,converse(join(converse(A),X_13)))) )],[refute_0_813,refute_0_815]) ).
cnf(refute_0_817,plain,
converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top)) = composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))),
inference(subst,[],[refute_0_816:[bind(A,$fot(X_194)),bind(X_13,$fot(complement(composition(converse(X_194),top))))]]) ).
cnf(refute_0_818,plain,
( converse(composition(join(converse(A),X_13),X_23)) != composition(converse(X_23),join(A,converse(X_13)))
| composition(converse(X_23),join(A,converse(X_13))) = converse(composition(join(converse(A),X_13),X_23)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(join(converse(A),X_13),X_23)))),bind(Y,$fot(composition(converse(X_23),join(A,converse(X_13)))))]]) ).
cnf(refute_0_819,plain,
composition(converse(X_23),join(A,converse(X_13))) = converse(composition(join(converse(A),X_13),X_23)),
inference(resolve,[$cnf( $equal(converse(composition(join(converse(A),X_13),X_23)),composition(converse(X_23),join(A,converse(X_13)))) )],[refute_0_416,refute_0_818]) ).
cnf(refute_0_820,plain,
composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) = converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top)),
inference(subst,[],[refute_0_819:[bind(A,$fot(X_194)),bind(X_13,$fot(complement(composition(converse(X_194),top)))),bind(X_23,$fot(top))]]) ).
cnf(refute_0_821,plain,
( composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) != converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top))
| converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top)) != composition(top,join(X_194,converse(complement(composition(converse(X_194),top)))))
| composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) = composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))))),bind(Y,$fot(converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top)))),bind(Z,$fot(composition(top,join(X_194,converse(complement(composition(converse(X_194),top)))))))]]) ).
cnf(refute_0_822,plain,
( converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top)) != composition(top,join(X_194,converse(complement(composition(converse(X_194),top)))))
| composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) = composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))) ),
inference(resolve,[$cnf( $equal(composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))),converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top))) )],[refute_0_820,refute_0_821]) ).
cnf(refute_0_823,plain,
composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) = composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))),
inference(resolve,[$cnf( $equal(converse(composition(join(converse(X_194),complement(composition(converse(X_194),top))),top)),composition(top,join(X_194,converse(complement(composition(converse(X_194),top)))))) )],[refute_0_817,refute_0_822]) ).
cnf(refute_0_824,plain,
( composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) != composition(top,join(X_194,converse(complement(composition(converse(X_194),top)))))
| composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))) != composition(top,join(X_194,converse(complement(converse(composition(top,X_194))))))
| composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) = composition(top,join(X_194,converse(complement(converse(composition(top,X_194)))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))))),bind(Y,$fot(composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))))),bind(Z,$fot(composition(top,join(X_194,converse(complement(converse(composition(top,X_194))))))))]]) ).
cnf(refute_0_825,plain,
( composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))) != composition(top,join(X_194,converse(complement(converse(composition(top,X_194))))))
| composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) = composition(top,join(X_194,converse(complement(converse(composition(top,X_194)))))) ),
inference(resolve,[$cnf( $equal(composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))),composition(top,join(X_194,converse(complement(composition(converse(X_194),top)))))) )],[refute_0_823,refute_0_824]) ).
cnf(refute_0_826,plain,
composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) = composition(top,join(X_194,converse(complement(converse(composition(top,X_194)))))),
inference(resolve,[$cnf( $equal(composition(top,join(X_194,converse(complement(composition(converse(X_194),top))))),composition(top,join(X_194,converse(complement(converse(composition(top,X_194))))))) )],[refute_0_812,refute_0_825]) ).
cnf(refute_0_827,plain,
( composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))) != composition(top,join(X_194,converse(complement(converse(composition(top,X_194))))))
| top != composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))
| top = composition(top,join(X_194,converse(complement(converse(composition(top,X_194)))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))) ),[1],$fot(composition(top,join(X_194,converse(complement(converse(composition(top,X_194)))))))]]) ).
cnf(refute_0_828,plain,
( top != composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))
| top = composition(top,join(X_194,converse(complement(converse(composition(top,X_194)))))) ),
inference(resolve,[$cnf( $equal(composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top))))),composition(top,join(X_194,converse(complement(converse(composition(top,X_194))))))) )],[refute_0_826,refute_0_827]) ).
cnf(refute_0_829,plain,
( converse(top) != composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))
| top = composition(top,join(X_194,converse(complement(converse(composition(top,X_194)))))) ),
inference(resolve,[$cnf( $equal(top,composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))) )],[refute_0_789,refute_0_828]) ).
cnf(refute_0_830,plain,
top = composition(top,join(X_194,converse(complement(converse(composition(top,X_194)))))),
inference(resolve,[$cnf( $equal(converse(top),composition(converse(top),join(X_194,converse(complement(composition(converse(X_194),top)))))) )],[refute_0_787,refute_0_829]) ).
cnf(refute_0_831,plain,
top = composition(top,join(complement(one),converse(complement(converse(composition(top,complement(one))))))),
inference(subst,[],[refute_0_830:[bind(X_194,$fot(complement(one)))]]) ).
cnf(refute_0_832,plain,
converse(composition(top,complement(one))) = composition(converse(complement(one)),top),
inference(subst,[],[refute_0_793:[bind(X_23,$fot(complement(one)))]]) ).
cnf(refute_0_833,plain,
converse(join(converse(complement(one)),complement(one))) = converse(join(complement(one),converse(complement(one)))),
inference(subst,[],[refute_0_548:[bind(X_12,$fot(complement(one))),bind(X_13,$fot(converse(complement(one))))]]) ).
cnf(refute_0_834,plain,
join(complement(one),composition(converse(X_62),complement(composition(X_62,one)))) = complement(one),
inference(subst,[],[refute_0_78:[bind(A,$fot(X_62)),bind(B,$fot(one))]]) ).
cnf(refute_0_835,plain,
composition(X_62,one) = X_62,
inference(subst,[],[composition_identity_6:[bind(A,$fot(X_62))]]) ).
cnf(refute_0_836,plain,
( composition(X_62,one) != X_62
| join(complement(one),composition(converse(X_62),complement(composition(X_62,one)))) != complement(one)
| join(complement(one),composition(converse(X_62),complement(X_62))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(X_62),complement(composition(X_62,one)))),complement(one)) ),[0,1,1,0],$fot(X_62)]]) ).
cnf(refute_0_837,plain,
( join(complement(one),composition(converse(X_62),complement(composition(X_62,one)))) != complement(one)
| join(complement(one),composition(converse(X_62),complement(X_62))) = complement(one) ),
inference(resolve,[$cnf( $equal(composition(X_62,one),X_62) )],[refute_0_835,refute_0_836]) ).
cnf(refute_0_838,plain,
join(complement(one),composition(converse(X_62),complement(X_62))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(X_62),complement(composition(X_62,one)))),complement(one)) )],[refute_0_834,refute_0_837]) ).
cnf(refute_0_839,plain,
join(complement(one),composition(converse(composition(complement(one),join(one,complement(converse(complement(one)))))),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) = complement(one),
inference(subst,[],[refute_0_838:[bind(X_62,$fot(composition(complement(one),join(one,complement(converse(complement(one)))))))]]) ).
cnf(refute_0_840,plain,
composition(join(converse(B),one),converse(A)) = join(converse(A),composition(converse(B),converse(A))),
inference(subst,[],[refute_0_61:[bind(X_32,$fot(converse(B))),bind(X_34,$fot(converse(A)))]]) ).
cnf(refute_0_841,plain,
( converse(composition(A,B)) != composition(converse(B),converse(A))
| composition(converse(B),converse(A)) = converse(composition(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(A,B)))),bind(Y,$fot(composition(converse(B),converse(A))))]]) ).
cnf(refute_0_842,plain,
composition(converse(B),converse(A)) = converse(composition(A,B)),
inference(resolve,[$cnf( $equal(converse(composition(A,B)),composition(converse(B),converse(A))) )],[converse_multiplicativity_10,refute_0_841]) ).
cnf(refute_0_843,plain,
( composition(converse(B),converse(A)) != converse(composition(A,B))
| composition(join(converse(B),one),converse(A)) != join(converse(A),composition(converse(B),converse(A)))
| composition(join(converse(B),one),converse(A)) = join(converse(A),converse(composition(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(B),one),converse(A)),join(converse(A),composition(converse(B),converse(A)))) ),[1,1],$fot(converse(composition(A,B)))]]) ).
cnf(refute_0_844,plain,
( composition(join(converse(B),one),converse(A)) != join(converse(A),composition(converse(B),converse(A)))
| composition(join(converse(B),one),converse(A)) = join(converse(A),converse(composition(A,B))) ),
inference(resolve,[$cnf( $equal(composition(converse(B),converse(A)),converse(composition(A,B))) )],[refute_0_842,refute_0_843]) ).
cnf(refute_0_845,plain,
composition(join(converse(B),one),converse(A)) = join(converse(A),converse(composition(A,B))),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),join(converse(A),composition(converse(B),converse(A)))) )],[refute_0_840,refute_0_844]) ).
cnf(refute_0_846,plain,
join(converse(one),B) = join(converse(one),B),
introduced(tautology,[refl,[$fot(join(converse(one),B))]]) ).
cnf(refute_0_847,plain,
( converse(one) != one
| join(converse(one),B) != join(converse(one),B)
| join(converse(one),B) = join(one,B) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(one),B),join(converse(one),B)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_848,plain,
( converse(one) != one
| join(converse(one),B) = join(one,B) ),
inference(resolve,[$cnf( $equal(join(converse(one),B),join(converse(one),B)) )],[refute_0_846,refute_0_847]) ).
cnf(refute_0_849,plain,
join(converse(one),B) = join(one,B),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_44,refute_0_848]) ).
cnf(refute_0_850,plain,
composition(A,join(converse(one),B)) = composition(A,join(converse(one),B)),
introduced(tautology,[refl,[$fot(composition(A,join(converse(one),B)))]]) ).
cnf(refute_0_851,plain,
( composition(A,join(converse(one),B)) != composition(A,join(converse(one),B))
| join(converse(one),B) != join(one,B)
| composition(A,join(converse(one),B)) = composition(A,join(one,B)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(A,join(converse(one),B)),composition(A,join(converse(one),B))) ),[1,1],$fot(join(one,B))]]) ).
cnf(refute_0_852,plain,
( join(converse(one),B) != join(one,B)
| composition(A,join(converse(one),B)) = composition(A,join(one,B)) ),
inference(resolve,[$cnf( $equal(composition(A,join(converse(one),B)),composition(A,join(converse(one),B))) )],[refute_0_850,refute_0_851]) ).
cnf(refute_0_853,plain,
composition(A,join(converse(one),B)) = composition(A,join(one,B)),
inference(resolve,[$cnf( $equal(join(converse(one),B),join(one,B)) )],[refute_0_849,refute_0_852]) ).
cnf(refute_0_854,plain,
converse(composition(A,join(converse(one),B))) = converse(composition(A,join(converse(one),B))),
introduced(tautology,[refl,[$fot(converse(composition(A,join(converse(one),B))))]]) ).
cnf(refute_0_855,plain,
( composition(A,join(converse(one),B)) != composition(A,join(one,B))
| converse(composition(A,join(converse(one),B))) != converse(composition(A,join(converse(one),B)))
| converse(composition(A,join(converse(one),B))) = converse(composition(A,join(one,B))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(A,join(converse(one),B))),converse(composition(A,join(converse(one),B)))) ),[1,0],$fot(composition(A,join(one,B)))]]) ).
cnf(refute_0_856,plain,
( composition(A,join(converse(one),B)) != composition(A,join(one,B))
| converse(composition(A,join(converse(one),B))) = converse(composition(A,join(one,B))) ),
inference(resolve,[$cnf( $equal(converse(composition(A,join(converse(one),B))),converse(composition(A,join(converse(one),B)))) )],[refute_0_854,refute_0_855]) ).
cnf(refute_0_857,plain,
converse(composition(A,join(converse(one),B))) = converse(composition(A,join(one,B))),
inference(resolve,[$cnf( $equal(composition(A,join(converse(one),B)),composition(A,join(one,B))) )],[refute_0_853,refute_0_856]) ).
cnf(refute_0_858,plain,
converse(composition(X_22,join(converse(A),X_13))) = composition(converse(join(converse(A),X_13)),converse(X_22)),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(X_22)),bind(B,$fot(join(converse(A),X_13)))]]) ).
cnf(refute_0_859,plain,
( converse(composition(X_22,join(converse(A),X_13))) != composition(converse(join(converse(A),X_13)),converse(X_22))
| converse(join(converse(A),X_13)) != join(A,converse(X_13))
| converse(composition(X_22,join(converse(A),X_13))) = composition(join(A,converse(X_13)),converse(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_22,join(converse(A),X_13))),composition(converse(join(converse(A),X_13)),converse(X_22))) ),[1,0],$fot(join(A,converse(X_13)))]]) ).
cnf(refute_0_860,plain,
( converse(composition(X_22,join(converse(A),X_13))) != composition(converse(join(converse(A),X_13)),converse(X_22))
| converse(composition(X_22,join(converse(A),X_13))) = composition(join(A,converse(X_13)),converse(X_22)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_13)),join(A,converse(X_13))) )],[refute_0_89,refute_0_859]) ).
cnf(refute_0_861,plain,
converse(composition(X_22,join(converse(A),X_13))) = composition(join(A,converse(X_13)),converse(X_22)),
inference(resolve,[$cnf( $equal(converse(composition(X_22,join(converse(A),X_13))),composition(converse(join(converse(A),X_13)),converse(X_22))) )],[refute_0_858,refute_0_860]) ).
cnf(refute_0_862,plain,
( converse(composition(X_22,join(converse(A),X_13))) != composition(join(A,converse(X_13)),converse(X_22))
| composition(join(A,converse(X_13)),converse(X_22)) = converse(composition(X_22,join(converse(A),X_13))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(X_22,join(converse(A),X_13))))),bind(Y,$fot(composition(join(A,converse(X_13)),converse(X_22))))]]) ).
cnf(refute_0_863,plain,
composition(join(A,converse(X_13)),converse(X_22)) = converse(composition(X_22,join(converse(A),X_13))),
inference(resolve,[$cnf( $equal(converse(composition(X_22,join(converse(A),X_13))),composition(join(A,converse(X_13)),converse(X_22))) )],[refute_0_861,refute_0_862]) ).
cnf(refute_0_864,plain,
composition(join(one,converse(B)),converse(A)) = converse(composition(A,join(converse(one),B))),
inference(subst,[],[refute_0_863:[bind(A,$fot(one)),bind(X_13,$fot(B)),bind(X_22,$fot(A))]]) ).
cnf(refute_0_865,plain,
composition(join(converse(B),one),converse(A)) = composition(join(one,converse(B)),converse(A)),
inference(subst,[],[refute_0_122:[bind(X_46,$fot(converse(B))),bind(X_47,$fot(converse(A)))]]) ).
cnf(refute_0_866,plain,
( composition(join(converse(B),one),converse(A)) != composition(join(one,converse(B)),converse(A))
| composition(join(one,converse(B)),converse(A)) != converse(composition(A,join(converse(one),B)))
| composition(join(converse(B),one),converse(A)) = converse(composition(A,join(converse(one),B))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(converse(B),one),converse(A)))),bind(Y,$fot(composition(join(one,converse(B)),converse(A)))),bind(Z,$fot(converse(composition(A,join(converse(one),B)))))]]) ).
cnf(refute_0_867,plain,
( composition(join(one,converse(B)),converse(A)) != converse(composition(A,join(converse(one),B)))
| composition(join(converse(B),one),converse(A)) = converse(composition(A,join(converse(one),B))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),composition(join(one,converse(B)),converse(A))) )],[refute_0_865,refute_0_866]) ).
cnf(refute_0_868,plain,
composition(join(converse(B),one),converse(A)) = converse(composition(A,join(converse(one),B))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(B)),converse(A)),converse(composition(A,join(converse(one),B)))) )],[refute_0_864,refute_0_867]) ).
cnf(refute_0_869,plain,
( composition(join(converse(B),one),converse(A)) != converse(composition(A,join(converse(one),B)))
| converse(composition(A,join(converse(one),B))) != converse(composition(A,join(one,B)))
| composition(join(converse(B),one),converse(A)) = converse(composition(A,join(one,B))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(converse(B),one),converse(A)))),bind(Y,$fot(converse(composition(A,join(converse(one),B))))),bind(Z,$fot(converse(composition(A,join(one,B)))))]]) ).
cnf(refute_0_870,plain,
( converse(composition(A,join(converse(one),B))) != converse(composition(A,join(one,B)))
| composition(join(converse(B),one),converse(A)) = converse(composition(A,join(one,B))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),converse(composition(A,join(converse(one),B)))) )],[refute_0_868,refute_0_869]) ).
cnf(refute_0_871,plain,
composition(join(converse(B),one),converse(A)) = converse(composition(A,join(one,B))),
inference(resolve,[$cnf( $equal(converse(composition(A,join(converse(one),B))),converse(composition(A,join(one,B)))) )],[refute_0_857,refute_0_870]) ).
cnf(refute_0_872,plain,
( composition(join(converse(B),one),converse(A)) != converse(composition(A,join(one,B)))
| composition(join(converse(B),one),converse(A)) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(one,B))) = join(converse(A),converse(composition(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(B),one),converse(A)),join(converse(A),converse(composition(A,B)))) ),[0],$fot(converse(composition(A,join(one,B))))]]) ).
cnf(refute_0_873,plain,
( composition(join(converse(B),one),converse(A)) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(one,B))) = join(converse(A),converse(composition(A,B))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),converse(composition(A,join(one,B)))) )],[refute_0_871,refute_0_872]) ).
cnf(refute_0_874,plain,
join(converse(A),converse(composition(A,B))) = converse(join(A,composition(A,B))),
inference(subst,[],[refute_0_544:[bind(B,$fot(composition(A,B)))]]) ).
cnf(refute_0_875,plain,
( converse(composition(A,join(one,B))) != join(converse(A),converse(composition(A,B)))
| join(converse(A),converse(composition(A,B))) != converse(join(A,composition(A,B)))
| converse(composition(A,join(one,B))) = converse(join(A,composition(A,B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(composition(A,join(one,B))),converse(join(A,composition(A,B)))) ),[0],$fot(join(converse(A),converse(composition(A,B))))]]) ).
cnf(refute_0_876,plain,
( converse(composition(A,join(one,B))) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(one,B))) = converse(join(A,composition(A,B))) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(composition(A,B))),converse(join(A,composition(A,B)))) )],[refute_0_874,refute_0_875]) ).
cnf(refute_0_877,plain,
( composition(join(converse(B),one),converse(A)) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(one,B))) = converse(join(A,composition(A,B))) ),
inference(resolve,[$cnf( $equal(converse(composition(A,join(one,B))),join(converse(A),converse(composition(A,B)))) )],[refute_0_873,refute_0_876]) ).
cnf(refute_0_878,plain,
converse(composition(A,join(one,B))) = converse(join(A,composition(A,B))),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),join(converse(A),converse(composition(A,B)))) )],[refute_0_845,refute_0_877]) ).
cnf(refute_0_879,plain,
converse(composition(complement(one),join(one,complement(converse(complement(one)))))) = converse(join(complement(one),composition(complement(one),complement(converse(complement(one)))))),
inference(subst,[],[refute_0_878:[bind(A,$fot(complement(one))),bind(B,$fot(complement(converse(complement(one)))))]]) ).
cnf(refute_0_880,plain,
join(complement(one),composition(converse(converse(A)),complement(converse(A)))) = complement(one),
inference(subst,[],[refute_0_838:[bind(X_62,$fot(converse(A)))]]) ).
cnf(refute_0_881,plain,
( converse(converse(A)) != A
| join(complement(one),composition(converse(converse(A)),complement(converse(A)))) != complement(one)
| join(complement(one),composition(A,complement(converse(A)))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(converse(A)),complement(converse(A)))),complement(one)) ),[0,1,0],$fot(A)]]) ).
cnf(refute_0_882,plain,
( join(complement(one),composition(converse(converse(A)),complement(converse(A)))) != complement(one)
| join(complement(one),composition(A,complement(converse(A)))) = complement(one) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_881]) ).
cnf(refute_0_883,plain,
join(complement(one),composition(A,complement(converse(A)))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(converse(A)),complement(converse(A)))),complement(one)) )],[refute_0_880,refute_0_882]) ).
cnf(refute_0_884,plain,
join(complement(one),composition(complement(one),complement(converse(complement(one))))) = complement(one),
inference(subst,[],[refute_0_883:[bind(A,$fot(complement(one)))]]) ).
cnf(refute_0_885,plain,
( converse(composition(complement(one),join(one,complement(converse(complement(one)))))) != converse(join(complement(one),composition(complement(one),complement(converse(complement(one))))))
| join(complement(one),composition(complement(one),complement(converse(complement(one))))) != complement(one)
| converse(composition(complement(one),join(one,complement(converse(complement(one)))))) = converse(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(complement(one),join(one,complement(converse(complement(one)))))),converse(join(complement(one),composition(complement(one),complement(converse(complement(one))))))) ),[1,0],$fot(complement(one))]]) ).
cnf(refute_0_886,plain,
( converse(composition(complement(one),join(one,complement(converse(complement(one)))))) != converse(join(complement(one),composition(complement(one),complement(converse(complement(one))))))
| converse(composition(complement(one),join(one,complement(converse(complement(one)))))) = converse(complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(complement(one),complement(converse(complement(one))))),complement(one)) )],[refute_0_884,refute_0_885]) ).
cnf(refute_0_887,plain,
converse(composition(complement(one),join(one,complement(converse(complement(one)))))) = converse(complement(one)),
inference(resolve,[$cnf( $equal(converse(composition(complement(one),join(one,complement(converse(complement(one)))))),converse(join(complement(one),composition(complement(one),complement(converse(complement(one))))))) )],[refute_0_879,refute_0_886]) ).
cnf(refute_0_888,plain,
( converse(composition(complement(one),join(one,complement(converse(complement(one)))))) != converse(complement(one))
| join(complement(one),composition(converse(composition(complement(one),join(one,complement(converse(complement(one)))))),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) != complement(one)
| join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(composition(complement(one),join(one,complement(converse(complement(one)))))),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))),complement(one)) ),[0,1,0],$fot(converse(complement(one)))]]) ).
cnf(refute_0_889,plain,
( join(complement(one),composition(converse(composition(complement(one),join(one,complement(converse(complement(one)))))),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) != complement(one)
| join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) = complement(one) ),
inference(resolve,[$cnf( $equal(converse(composition(complement(one),join(one,complement(converse(complement(one)))))),converse(complement(one))) )],[refute_0_887,refute_0_888]) ).
cnf(refute_0_890,plain,
join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(composition(complement(one),join(one,complement(converse(complement(one)))))),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))),complement(one)) )],[refute_0_839,refute_0_889]) ).
cnf(refute_0_891,plain,
composition(converse(complement(one)),one) = converse(complement(one)),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(complement(one))))]]) ).
cnf(refute_0_892,plain,
complement(complement(one)) = one,
inference(subst,[],[refute_0_383:[bind(X_87,$fot(one))]]) ).
cnf(refute_0_893,plain,
converse(converse(composition(complement(one),join(one,complement(converse(complement(one))))))) = composition(complement(one),join(one,complement(converse(complement(one))))),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(complement(one),join(one,complement(converse(complement(one)))))))]]) ).
cnf(refute_0_894,plain,
( converse(composition(complement(one),join(one,complement(converse(complement(one)))))) != converse(complement(one))
| converse(converse(composition(complement(one),join(one,complement(converse(complement(one))))))) != composition(complement(one),join(one,complement(converse(complement(one)))))
| converse(converse(complement(one))) = composition(complement(one),join(one,complement(converse(complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(composition(complement(one),join(one,complement(converse(complement(one))))))),composition(complement(one),join(one,complement(converse(complement(one)))))) ),[0,0],$fot(converse(complement(one)))]]) ).
cnf(refute_0_895,plain,
( converse(converse(composition(complement(one),join(one,complement(converse(complement(one))))))) != composition(complement(one),join(one,complement(converse(complement(one)))))
| converse(converse(complement(one))) = composition(complement(one),join(one,complement(converse(complement(one))))) ),
inference(resolve,[$cnf( $equal(converse(composition(complement(one),join(one,complement(converse(complement(one)))))),converse(complement(one))) )],[refute_0_887,refute_0_894]) ).
cnf(refute_0_896,plain,
converse(converse(complement(one))) = composition(complement(one),join(one,complement(converse(complement(one))))),
inference(resolve,[$cnf( $equal(converse(converse(composition(complement(one),join(one,complement(converse(complement(one))))))),composition(complement(one),join(one,complement(converse(complement(one)))))) )],[refute_0_893,refute_0_895]) ).
cnf(refute_0_897,plain,
converse(converse(complement(one))) = complement(one),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(one)))]]) ).
cnf(refute_0_898,plain,
( converse(converse(complement(one))) != complement(one)
| converse(converse(complement(one))) != composition(complement(one),join(one,complement(converse(complement(one)))))
| complement(one) = composition(complement(one),join(one,complement(converse(complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(complement(one))),composition(complement(one),join(one,complement(converse(complement(one)))))) ),[0],$fot(complement(one))]]) ).
cnf(refute_0_899,plain,
( converse(converse(complement(one))) != composition(complement(one),join(one,complement(converse(complement(one)))))
| complement(one) = composition(complement(one),join(one,complement(converse(complement(one))))) ),
inference(resolve,[$cnf( $equal(converse(converse(complement(one))),complement(one)) )],[refute_0_897,refute_0_898]) ).
cnf(refute_0_900,plain,
complement(one) = composition(complement(one),join(one,complement(converse(complement(one))))),
inference(resolve,[$cnf( $equal(converse(converse(complement(one))),composition(complement(one),join(one,complement(converse(complement(one)))))) )],[refute_0_896,refute_0_899]) ).
cnf(refute_0_901,plain,
( complement(one) != composition(complement(one),join(one,complement(converse(complement(one)))))
| composition(complement(one),join(one,complement(converse(complement(one))))) = complement(one) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(one))),bind(Y,$fot(composition(complement(one),join(one,complement(converse(complement(one)))))))]]) ).
cnf(refute_0_902,plain,
composition(complement(one),join(one,complement(converse(complement(one))))) = complement(one),
inference(resolve,[$cnf( $equal(complement(one),composition(complement(one),join(one,complement(converse(complement(one)))))) )],[refute_0_900,refute_0_901]) ).
cnf(refute_0_903,plain,
complement(composition(complement(one),join(one,complement(converse(complement(one)))))) = complement(composition(complement(one),join(one,complement(converse(complement(one)))))),
introduced(tautology,[refl,[$fot(complement(composition(complement(one),join(one,complement(converse(complement(one)))))))]]) ).
cnf(refute_0_904,plain,
( complement(composition(complement(one),join(one,complement(converse(complement(one)))))) != complement(composition(complement(one),join(one,complement(converse(complement(one))))))
| composition(complement(one),join(one,complement(converse(complement(one))))) != complement(one)
| complement(composition(complement(one),join(one,complement(converse(complement(one)))))) = complement(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(complement(one),join(one,complement(converse(complement(one)))))),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) ),[1,0],$fot(complement(one))]]) ).
cnf(refute_0_905,plain,
( composition(complement(one),join(one,complement(converse(complement(one))))) != complement(one)
| complement(composition(complement(one),join(one,complement(converse(complement(one)))))) = complement(complement(one)) ),
inference(resolve,[$cnf( $equal(complement(composition(complement(one),join(one,complement(converse(complement(one)))))),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) )],[refute_0_903,refute_0_904]) ).
cnf(refute_0_906,plain,
complement(composition(complement(one),join(one,complement(converse(complement(one)))))) = complement(complement(one)),
inference(resolve,[$cnf( $equal(composition(complement(one),join(one,complement(converse(complement(one))))),complement(one)) )],[refute_0_902,refute_0_905]) ).
cnf(refute_0_907,plain,
( complement(complement(one)) != one
| complement(composition(complement(one),join(one,complement(converse(complement(one)))))) != complement(complement(one))
| complement(composition(complement(one),join(one,complement(converse(complement(one)))))) = one ),
inference(subst,[],[refute_0_7:[bind(X,$fot(complement(composition(complement(one),join(one,complement(converse(complement(one)))))))),bind(Y,$fot(complement(complement(one)))),bind(Z,$fot(one))]]) ).
cnf(refute_0_908,plain,
( complement(complement(one)) != one
| complement(composition(complement(one),join(one,complement(converse(complement(one)))))) = one ),
inference(resolve,[$cnf( $equal(complement(composition(complement(one),join(one,complement(converse(complement(one)))))),complement(complement(one))) )],[refute_0_906,refute_0_907]) ).
cnf(refute_0_909,plain,
complement(composition(complement(one),join(one,complement(converse(complement(one)))))) = one,
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_892,refute_0_908]) ).
cnf(refute_0_910,plain,
composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) = composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))),
introduced(tautology,[refl,[$fot(composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))))]]) ).
cnf(refute_0_911,plain,
( complement(composition(complement(one),join(one,complement(converse(complement(one)))))) != one
| composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) != composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))
| composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) = composition(converse(complement(one)),one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_912,plain,
( complement(composition(complement(one),join(one,complement(converse(complement(one)))))) != one
| composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) = composition(converse(complement(one)),one) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) )],[refute_0_910,refute_0_911]) ).
cnf(refute_0_913,plain,
composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) = composition(converse(complement(one)),one),
inference(resolve,[$cnf( $equal(complement(composition(complement(one),join(one,complement(converse(complement(one)))))),one) )],[refute_0_909,refute_0_912]) ).
cnf(refute_0_914,plain,
( composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) != composition(converse(complement(one)),one)
| composition(converse(complement(one)),one) != converse(complement(one))
| composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) = converse(complement(one)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))))),bind(Y,$fot(composition(converse(complement(one)),one))),bind(Z,$fot(converse(complement(one))))]]) ).
cnf(refute_0_915,plain,
( composition(converse(complement(one)),one) != converse(complement(one))
| composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) = converse(complement(one)) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))),composition(converse(complement(one)),one)) )],[refute_0_913,refute_0_914]) ).
cnf(refute_0_916,plain,
composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) = converse(complement(one)),
inference(resolve,[$cnf( $equal(composition(converse(complement(one)),one),converse(complement(one))) )],[refute_0_891,refute_0_915]) ).
cnf(refute_0_917,plain,
join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) = join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))),
introduced(tautology,[refl,[$fot(join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))))]]) ).
cnf(refute_0_918,plain,
( composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) != converse(complement(one))
| join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) != join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))))
| join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) = join(complement(one),converse(complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))),join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))))) ),[1,1],$fot(converse(complement(one)))]]) ).
cnf(refute_0_919,plain,
( composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))) != converse(complement(one))
| join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) = join(complement(one),converse(complement(one))) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))),join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))))) )],[refute_0_917,refute_0_918]) ).
cnf(refute_0_920,plain,
join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) = join(complement(one),converse(complement(one))),
inference(resolve,[$cnf( $equal(composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one))))))),converse(complement(one))) )],[refute_0_916,refute_0_919]) ).
cnf(refute_0_921,plain,
( join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) != complement(one)
| join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) != join(complement(one),converse(complement(one)))
| join(complement(one),converse(complement(one))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))),complement(one)) ),[0],$fot(join(complement(one),converse(complement(one))))]]) ).
cnf(refute_0_922,plain,
( join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))) != complement(one)
| join(complement(one),converse(complement(one))) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))),join(complement(one),converse(complement(one)))) )],[refute_0_920,refute_0_921]) ).
cnf(refute_0_923,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(complement(one)),complement(composition(complement(one),join(one,complement(converse(complement(one)))))))),complement(one)) )],[refute_0_890,refute_0_922]) ).
cnf(refute_0_924,plain,
( converse(join(converse(complement(one)),complement(one))) != converse(join(complement(one),converse(complement(one))))
| join(complement(one),converse(complement(one))) != complement(one)
| converse(join(converse(complement(one)),complement(one))) = converse(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(one)),complement(one))),converse(join(complement(one),converse(complement(one))))) ),[1,0],$fot(complement(one))]]) ).
cnf(refute_0_925,plain,
( converse(join(converse(complement(one)),complement(one))) != converse(join(complement(one),converse(complement(one))))
| converse(join(converse(complement(one)),complement(one))) = converse(complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(one),converse(complement(one))),complement(one)) )],[refute_0_923,refute_0_924]) ).
cnf(refute_0_926,plain,
converse(join(converse(complement(one)),complement(one))) = converse(complement(one)),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(one)),complement(one))),converse(join(complement(one),converse(complement(one))))) )],[refute_0_833,refute_0_925]) ).
cnf(refute_0_927,plain,
join(converse(complement(one)),complement(one)) = join(complement(one),converse(complement(one))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(one))),bind(B,$fot(converse(complement(one))))]]) ).
cnf(refute_0_928,plain,
( join(complement(one),converse(complement(one))) != complement(one)
| join(converse(complement(one)),complement(one)) != join(complement(one),converse(complement(one)))
| join(converse(complement(one)),complement(one)) = complement(one) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(converse(complement(one)),complement(one)))),bind(Y,$fot(join(complement(one),converse(complement(one))))),bind(Z,$fot(complement(one)))]]) ).
cnf(refute_0_929,plain,
( join(complement(one),converse(complement(one))) != complement(one)
| join(converse(complement(one)),complement(one)) = complement(one) ),
inference(resolve,[$cnf( $equal(join(converse(complement(one)),complement(one)),join(complement(one),converse(complement(one)))) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
join(converse(complement(one)),complement(one)) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),converse(complement(one))),complement(one)) )],[refute_0_923,refute_0_929]) ).
cnf(refute_0_931,plain,
converse(join(complement(one),converse(complement(one)))) = join(converse(complement(one)),complement(one)),
inference(subst,[],[refute_0_567:[bind(A,$fot(complement(one))),bind(X_12,$fot(complement(one)))]]) ).
cnf(refute_0_932,plain,
( converse(join(complement(one),converse(complement(one)))) != join(converse(complement(one)),complement(one))
| join(converse(complement(one)),complement(one)) != complement(one)
| converse(join(complement(one),converse(complement(one)))) = complement(one) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(complement(one),converse(complement(one)))))),bind(Y,$fot(join(converse(complement(one)),complement(one)))),bind(Z,$fot(complement(one)))]]) ).
cnf(refute_0_933,plain,
( join(converse(complement(one)),complement(one)) != complement(one)
| converse(join(complement(one),converse(complement(one)))) = complement(one) ),
inference(resolve,[$cnf( $equal(converse(join(complement(one),converse(complement(one)))),join(converse(complement(one)),complement(one))) )],[refute_0_931,refute_0_932]) ).
cnf(refute_0_934,plain,
converse(join(complement(one),converse(complement(one)))) = complement(one),
inference(resolve,[$cnf( $equal(join(converse(complement(one)),complement(one)),complement(one)) )],[refute_0_930,refute_0_933]) ).
cnf(refute_0_935,plain,
( converse(join(complement(one),converse(complement(one)))) != complement(one)
| converse(join(converse(complement(one)),complement(one))) != converse(join(complement(one),converse(complement(one))))
| converse(join(converse(complement(one)),complement(one))) = complement(one) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(converse(complement(one)),complement(one))))),bind(Y,$fot(converse(join(complement(one),converse(complement(one)))))),bind(Z,$fot(complement(one)))]]) ).
cnf(refute_0_936,plain,
( converse(join(complement(one),converse(complement(one)))) != complement(one)
| converse(join(converse(complement(one)),complement(one))) = complement(one) ),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(one)),complement(one))),converse(join(complement(one),converse(complement(one))))) )],[refute_0_833,refute_0_935]) ).
cnf(refute_0_937,plain,
converse(join(converse(complement(one)),complement(one))) = complement(one),
inference(resolve,[$cnf( $equal(converse(join(complement(one),converse(complement(one)))),complement(one)) )],[refute_0_934,refute_0_936]) ).
cnf(refute_0_938,plain,
( converse(join(converse(complement(one)),complement(one))) != complement(one)
| converse(join(converse(complement(one)),complement(one))) != converse(complement(one))
| complement(one) = converse(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(one)),complement(one))),converse(complement(one))) ),[0],$fot(complement(one))]]) ).
cnf(refute_0_939,plain,
( converse(join(converse(complement(one)),complement(one))) != converse(complement(one))
| complement(one) = converse(complement(one)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(one)),complement(one))),complement(one)) )],[refute_0_937,refute_0_938]) ).
cnf(refute_0_940,plain,
complement(one) = converse(complement(one)),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(one)),complement(one))),converse(complement(one))) )],[refute_0_926,refute_0_939]) ).
cnf(refute_0_941,plain,
( complement(one) != converse(complement(one))
| converse(complement(one)) = complement(one) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(one))),bind(Y,$fot(converse(complement(one))))]]) ).
cnf(refute_0_942,plain,
converse(complement(one)) = complement(one),
inference(resolve,[$cnf( $equal(complement(one),converse(complement(one))) )],[refute_0_940,refute_0_941]) ).
cnf(refute_0_943,plain,
( converse(complement(one)) != complement(one)
| converse(composition(top,complement(one))) != composition(converse(complement(one)),top)
| converse(composition(top,complement(one))) = composition(complement(one),top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(top,complement(one))),composition(converse(complement(one)),top)) ),[1,0],$fot(complement(one))]]) ).
cnf(refute_0_944,plain,
( converse(composition(top,complement(one))) != composition(converse(complement(one)),top)
| converse(composition(top,complement(one))) = composition(complement(one),top) ),
inference(resolve,[$cnf( $equal(converse(complement(one)),complement(one)) )],[refute_0_942,refute_0_943]) ).
cnf(refute_0_945,plain,
converse(composition(top,complement(one))) = composition(complement(one),top),
inference(resolve,[$cnf( $equal(converse(composition(top,complement(one))),composition(converse(complement(one)),top)) )],[refute_0_832,refute_0_944]) ).
cnf(refute_0_946,plain,
( converse(composition(top,complement(one))) != composition(complement(one),top)
| top != composition(top,join(complement(one),converse(complement(converse(composition(top,complement(one)))))))
| top = composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,composition(top,join(complement(one),converse(complement(converse(composition(top,complement(one)))))))) ),[1,1,1,0,0],$fot(composition(complement(one),top))]]) ).
cnf(refute_0_947,plain,
( top != composition(top,join(complement(one),converse(complement(converse(composition(top,complement(one)))))))
| top = composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) ),
inference(resolve,[$cnf( $equal(converse(composition(top,complement(one))),composition(complement(one),top)) )],[refute_0_945,refute_0_946]) ).
cnf(refute_0_948,plain,
top = composition(top,join(complement(one),converse(complement(composition(complement(one),top))))),
inference(resolve,[$cnf( $equal(top,composition(top,join(complement(one),converse(complement(converse(composition(top,complement(one)))))))) )],[refute_0_831,refute_0_947]) ).
cnf(refute_0_949,plain,
composition(top,converse(complement(meet(one,composition(complement(one),top))))) = converse(composition(complement(meet(one,composition(complement(one),top))),top)),
inference(subst,[],[refute_0_743:[bind(X_22,$fot(complement(meet(one,composition(complement(one),top)))))]]) ).
cnf(refute_0_950,plain,
join(complement(one),complement(composition(complement(one),top))) = complement(meet(one,composition(complement(one),top))),
inference(subst,[],[refute_0_400:[bind(A,$fot(one)),bind(B,$fot(composition(complement(one),top)))]]) ).
cnf(refute_0_951,plain,
converse(join(complement(one),complement(composition(complement(one),top)))) = converse(join(complement(one),complement(composition(complement(one),top)))),
introduced(tautology,[refl,[$fot(converse(join(complement(one),complement(composition(complement(one),top)))))]]) ).
cnf(refute_0_952,plain,
( converse(join(complement(one),complement(composition(complement(one),top)))) != converse(join(complement(one),complement(composition(complement(one),top))))
| join(complement(one),complement(composition(complement(one),top))) != complement(meet(one,composition(complement(one),top)))
| converse(join(complement(one),complement(composition(complement(one),top)))) = converse(complement(meet(one,composition(complement(one),top)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(one),complement(composition(complement(one),top)))),converse(join(complement(one),complement(composition(complement(one),top))))) ),[1,0],$fot(complement(meet(one,composition(complement(one),top))))]]) ).
cnf(refute_0_953,plain,
( join(complement(one),complement(composition(complement(one),top))) != complement(meet(one,composition(complement(one),top)))
| converse(join(complement(one),complement(composition(complement(one),top)))) = converse(complement(meet(one,composition(complement(one),top)))) ),
inference(resolve,[$cnf( $equal(converse(join(complement(one),complement(composition(complement(one),top)))),converse(join(complement(one),complement(composition(complement(one),top))))) )],[refute_0_951,refute_0_952]) ).
cnf(refute_0_954,plain,
converse(join(complement(one),complement(composition(complement(one),top)))) = converse(complement(meet(one,composition(complement(one),top)))),
inference(resolve,[$cnf( $equal(join(complement(one),complement(composition(complement(one),top))),complement(meet(one,composition(complement(one),top)))) )],[refute_0_950,refute_0_953]) ).
cnf(refute_0_955,plain,
converse(join(converse(complement(one)),X_13)) = join(complement(one),converse(X_13)),
inference(subst,[],[refute_0_89:[bind(A,$fot(complement(one)))]]) ).
cnf(refute_0_956,plain,
( converse(complement(one)) != complement(one)
| converse(join(converse(complement(one)),X_13)) != join(complement(one),converse(X_13))
| converse(join(complement(one),X_13)) = join(complement(one),converse(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(one)),X_13)),join(complement(one),converse(X_13))) ),[0,0,0],$fot(complement(one))]]) ).
cnf(refute_0_957,plain,
( converse(join(converse(complement(one)),X_13)) != join(complement(one),converse(X_13))
| converse(join(complement(one),X_13)) = join(complement(one),converse(X_13)) ),
inference(resolve,[$cnf( $equal(converse(complement(one)),complement(one)) )],[refute_0_942,refute_0_956]) ).
cnf(refute_0_958,plain,
converse(join(complement(one),X_13)) = join(complement(one),converse(X_13)),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(one)),X_13)),join(complement(one),converse(X_13))) )],[refute_0_955,refute_0_957]) ).
cnf(refute_0_959,plain,
( converse(join(complement(one),X_13)) != join(complement(one),converse(X_13))
| join(complement(one),converse(X_13)) = converse(join(complement(one),X_13)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(complement(one),X_13)))),bind(Y,$fot(join(complement(one),converse(X_13))))]]) ).
cnf(refute_0_960,plain,
join(complement(one),converse(X_13)) = converse(join(complement(one),X_13)),
inference(resolve,[$cnf( $equal(converse(join(complement(one),X_13)),join(complement(one),converse(X_13))) )],[refute_0_958,refute_0_959]) ).
cnf(refute_0_961,plain,
join(complement(one),converse(complement(composition(complement(one),top)))) = converse(join(complement(one),complement(composition(complement(one),top)))),
inference(subst,[],[refute_0_960:[bind(X_13,$fot(complement(composition(complement(one),top))))]]) ).
cnf(refute_0_962,plain,
( converse(join(complement(one),complement(composition(complement(one),top)))) != converse(complement(meet(one,composition(complement(one),top))))
| join(complement(one),converse(complement(composition(complement(one),top)))) != converse(join(complement(one),complement(composition(complement(one),top))))
| join(complement(one),converse(complement(composition(complement(one),top)))) = converse(complement(meet(one,composition(complement(one),top)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(one),converse(complement(composition(complement(one),top)))))),bind(Y,$fot(converse(join(complement(one),complement(composition(complement(one),top)))))),bind(Z,$fot(converse(complement(meet(one,composition(complement(one),top))))))]]) ).
cnf(refute_0_963,plain,
( converse(join(complement(one),complement(composition(complement(one),top)))) != converse(complement(meet(one,composition(complement(one),top))))
| join(complement(one),converse(complement(composition(complement(one),top)))) = converse(complement(meet(one,composition(complement(one),top)))) ),
inference(resolve,[$cnf( $equal(join(complement(one),converse(complement(composition(complement(one),top)))),converse(join(complement(one),complement(composition(complement(one),top))))) )],[refute_0_961,refute_0_962]) ).
cnf(refute_0_964,plain,
join(complement(one),converse(complement(composition(complement(one),top)))) = converse(complement(meet(one,composition(complement(one),top)))),
inference(resolve,[$cnf( $equal(converse(join(complement(one),complement(composition(complement(one),top)))),converse(complement(meet(one,composition(complement(one),top))))) )],[refute_0_954,refute_0_963]) ).
cnf(refute_0_965,plain,
composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) = composition(top,join(complement(one),converse(complement(composition(complement(one),top))))),
introduced(tautology,[refl,[$fot(composition(top,join(complement(one),converse(complement(composition(complement(one),top))))))]]) ).
cnf(refute_0_966,plain,
( composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) != composition(top,join(complement(one),converse(complement(composition(complement(one),top)))))
| join(complement(one),converse(complement(composition(complement(one),top)))) != converse(complement(meet(one,composition(complement(one),top))))
| composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) = composition(top,converse(complement(meet(one,composition(complement(one),top))))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,join(complement(one),converse(complement(composition(complement(one),top))))),composition(top,join(complement(one),converse(complement(composition(complement(one),top)))))) ),[1,1],$fot(converse(complement(meet(one,composition(complement(one),top)))))]]) ).
cnf(refute_0_967,plain,
( join(complement(one),converse(complement(composition(complement(one),top)))) != converse(complement(meet(one,composition(complement(one),top))))
| composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) = composition(top,converse(complement(meet(one,composition(complement(one),top))))) ),
inference(resolve,[$cnf( $equal(composition(top,join(complement(one),converse(complement(composition(complement(one),top))))),composition(top,join(complement(one),converse(complement(composition(complement(one),top)))))) )],[refute_0_965,refute_0_966]) ).
cnf(refute_0_968,plain,
composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) = composition(top,converse(complement(meet(one,composition(complement(one),top))))),
inference(resolve,[$cnf( $equal(join(complement(one),converse(complement(composition(complement(one),top)))),converse(complement(meet(one,composition(complement(one),top))))) )],[refute_0_964,refute_0_967]) ).
cnf(refute_0_969,plain,
( composition(top,converse(complement(meet(one,composition(complement(one),top))))) != converse(composition(complement(meet(one,composition(complement(one),top))),top))
| composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) != composition(top,converse(complement(meet(one,composition(complement(one),top)))))
| composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) = converse(composition(complement(meet(one,composition(complement(one),top))),top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(top,join(complement(one),converse(complement(composition(complement(one),top))))))),bind(Y,$fot(composition(top,converse(complement(meet(one,composition(complement(one),top))))))),bind(Z,$fot(converse(composition(complement(meet(one,composition(complement(one),top))),top))))]]) ).
cnf(refute_0_970,plain,
( composition(top,converse(complement(meet(one,composition(complement(one),top))))) != converse(composition(complement(meet(one,composition(complement(one),top))),top))
| composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) = converse(composition(complement(meet(one,composition(complement(one),top))),top)) ),
inference(resolve,[$cnf( $equal(composition(top,join(complement(one),converse(complement(composition(complement(one),top))))),composition(top,converse(complement(meet(one,composition(complement(one),top)))))) )],[refute_0_968,refute_0_969]) ).
cnf(refute_0_971,plain,
composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) = converse(composition(complement(meet(one,composition(complement(one),top))),top)),
inference(resolve,[$cnf( $equal(composition(top,converse(complement(meet(one,composition(complement(one),top))))),converse(composition(complement(meet(one,composition(complement(one),top))),top))) )],[refute_0_949,refute_0_970]) ).
cnf(refute_0_972,plain,
( composition(top,join(complement(one),converse(complement(composition(complement(one),top))))) != converse(composition(complement(meet(one,composition(complement(one),top))),top))
| top != composition(top,join(complement(one),converse(complement(composition(complement(one),top)))))
| top = converse(composition(complement(meet(one,composition(complement(one),top))),top)) ),
introduced(tautology,[equality,[$cnf( $equal(top,composition(top,join(complement(one),converse(complement(composition(complement(one),top)))))) ),[1],$fot(converse(composition(complement(meet(one,composition(complement(one),top))),top)))]]) ).
cnf(refute_0_973,plain,
( top != composition(top,join(complement(one),converse(complement(composition(complement(one),top)))))
| top = converse(composition(complement(meet(one,composition(complement(one),top))),top)) ),
inference(resolve,[$cnf( $equal(composition(top,join(complement(one),converse(complement(composition(complement(one),top))))),converse(composition(complement(meet(one,composition(complement(one),top))),top))) )],[refute_0_971,refute_0_972]) ).
cnf(refute_0_974,plain,
top = converse(composition(complement(meet(one,composition(complement(one),top))),top)),
inference(resolve,[$cnf( $equal(top,composition(top,join(complement(one),converse(complement(composition(complement(one),top)))))) )],[refute_0_948,refute_0_973]) ).
cnf(refute_0_975,plain,
( top != converse(composition(complement(meet(one,composition(complement(one),top))),top))
| converse(composition(complement(meet(one,composition(complement(one),top))),top)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(converse(composition(complement(meet(one,composition(complement(one),top))),top))))]]) ).
cnf(refute_0_976,plain,
converse(composition(complement(meet(one,composition(complement(one),top))),top)) = top,
inference(resolve,[$cnf( $equal(top,converse(composition(complement(meet(one,composition(complement(one),top))),top))) )],[refute_0_974,refute_0_975]) ).
cnf(refute_0_977,plain,
( converse(composition(X_22,converse(composition(complement(meet(one,composition(complement(one),top))),top)))) != composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22))
| converse(composition(complement(meet(one,composition(complement(one),top))),top)) != top
| converse(composition(X_22,top)) = composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_22,converse(composition(complement(meet(one,composition(complement(one),top))),top)))),composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22))) ),[0,0,1],$fot(top)]]) ).
cnf(refute_0_978,plain,
( converse(composition(X_22,converse(composition(complement(meet(one,composition(complement(one),top))),top)))) != composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22))
| converse(composition(X_22,top)) = composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)) ),
inference(resolve,[$cnf( $equal(converse(composition(complement(meet(one,composition(complement(one),top))),top)),top) )],[refute_0_976,refute_0_977]) ).
cnf(refute_0_979,plain,
converse(composition(X_22,top)) = composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)),
inference(resolve,[$cnf( $equal(converse(composition(X_22,converse(composition(complement(meet(one,composition(complement(one),top))),top)))),composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22))) )],[refute_0_412,refute_0_978]) ).
cnf(refute_0_980,plain,
composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))) = composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))),
introduced(tautology,[refl,[$fot(composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))))]]) ).
cnf(refute_0_981,plain,
( composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))) != composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22)))
| composition(top,converse(X_22)) != converse(composition(X_22,top))
| composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))) = composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))),composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22)))) ),[1,1],$fot(converse(composition(X_22,top)))]]) ).
cnf(refute_0_982,plain,
( composition(top,converse(X_22)) != converse(composition(X_22,top))
| composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))) = composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) ),
inference(resolve,[$cnf( $equal(composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))),composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22)))) )],[refute_0_980,refute_0_981]) ).
cnf(refute_0_983,plain,
composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))) = composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))),
inference(resolve,[$cnf( $equal(composition(top,converse(X_22)),converse(composition(X_22,top))) )],[refute_0_743,refute_0_982]) ).
cnf(refute_0_984,plain,
composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)) = composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))),
inference(subst,[],[refute_0_209:[bind(A,$fot(complement(meet(one,composition(complement(one),top))))),bind(B,$fot(top)),bind(C,$fot(converse(X_22)))]]) ).
cnf(refute_0_985,plain,
( composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))) != composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))
| composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)) != composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22)))
| composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)) = composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)))),bind(Y,$fot(composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))))),bind(Z,$fot(composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))))]]) ).
cnf(refute_0_986,plain,
( composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))) != composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))
| composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)) = composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) ),
inference(resolve,[$cnf( $equal(composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)),composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22)))) )],[refute_0_984,refute_0_985]) ).
cnf(refute_0_987,plain,
composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)) = composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))),
inference(resolve,[$cnf( $equal(composition(complement(meet(one,composition(complement(one),top))),composition(top,converse(X_22))),composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))) )],[refute_0_983,refute_0_986]) ).
cnf(refute_0_988,plain,
( composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)) != composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))
| converse(composition(X_22,top)) != composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22))
| converse(composition(X_22,top)) = composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_22,top)),composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22))) ),[1],$fot(composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))))]]) ).
cnf(refute_0_989,plain,
( converse(composition(X_22,top)) != composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22))
| converse(composition(X_22,top)) = composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) ),
inference(resolve,[$cnf( $equal(composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22)),composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))) )],[refute_0_987,refute_0_988]) ).
cnf(refute_0_990,plain,
converse(composition(X_22,top)) = composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))),
inference(resolve,[$cnf( $equal(converse(composition(X_22,top)),composition(composition(complement(meet(one,composition(complement(one),top))),top),converse(X_22))) )],[refute_0_979,refute_0_989]) ).
cnf(refute_0_991,plain,
converse(composition(composition(top,complement(one)),top)) = composition(top,converse(composition(top,complement(one)))),
inference(subst,[],[refute_0_741:[bind(X_22,$fot(composition(top,complement(one))))]]) ).
cnf(refute_0_992,plain,
( converse(composition(composition(top,complement(one)),top)) != composition(top,converse(composition(top,complement(one))))
| converse(composition(top,complement(one))) != composition(complement(one),top)
| converse(composition(composition(top,complement(one)),top)) = composition(top,composition(complement(one),top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(composition(top,complement(one)),top)),composition(top,converse(composition(top,complement(one))))) ),[1,1],$fot(composition(complement(one),top))]]) ).
cnf(refute_0_993,plain,
( converse(composition(composition(top,complement(one)),top)) != composition(top,converse(composition(top,complement(one))))
| converse(composition(composition(top,complement(one)),top)) = composition(top,composition(complement(one),top)) ),
inference(resolve,[$cnf( $equal(converse(composition(top,complement(one))),composition(complement(one),top)) )],[refute_0_945,refute_0_992]) ).
cnf(refute_0_994,plain,
converse(composition(composition(top,complement(one)),top)) = composition(top,composition(complement(one),top)),
inference(resolve,[$cnf( $equal(converse(composition(composition(top,complement(one)),top)),composition(top,converse(composition(top,complement(one))))) )],[refute_0_991,refute_0_993]) ).
cnf(refute_0_995,plain,
composition(composition(top,complement(one)),top) = composition(top,composition(complement(one),top)),
inference(subst,[],[refute_0_209:[bind(A,$fot(top)),bind(B,$fot(complement(one))),bind(C,$fot(top))]]) ).
cnf(refute_0_996,plain,
converse(composition(composition(top,complement(one)),top)) = converse(composition(composition(top,complement(one)),top)),
introduced(tautology,[refl,[$fot(converse(composition(composition(top,complement(one)),top)))]]) ).
cnf(refute_0_997,plain,
( composition(composition(top,complement(one)),top) != composition(top,composition(complement(one),top))
| converse(composition(composition(top,complement(one)),top)) != converse(composition(composition(top,complement(one)),top))
| converse(composition(composition(top,complement(one)),top)) = converse(composition(top,composition(complement(one),top))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(composition(top,complement(one)),top)),converse(composition(composition(top,complement(one)),top))) ),[1,0],$fot(composition(top,composition(complement(one),top)))]]) ).
cnf(refute_0_998,plain,
( composition(composition(top,complement(one)),top) != composition(top,composition(complement(one),top))
| converse(composition(composition(top,complement(one)),top)) = converse(composition(top,composition(complement(one),top))) ),
inference(resolve,[$cnf( $equal(converse(composition(composition(top,complement(one)),top)),converse(composition(composition(top,complement(one)),top))) )],[refute_0_996,refute_0_997]) ).
cnf(refute_0_999,plain,
converse(composition(composition(top,complement(one)),top)) = converse(composition(top,composition(complement(one),top))),
inference(resolve,[$cnf( $equal(composition(composition(top,complement(one)),top),composition(top,composition(complement(one),top))) )],[refute_0_995,refute_0_998]) ).
cnf(refute_0_1000,plain,
( converse(composition(composition(top,complement(one)),top)) != composition(top,composition(complement(one),top))
| converse(composition(composition(top,complement(one)),top)) != converse(composition(top,composition(complement(one),top)))
| converse(composition(top,composition(complement(one),top))) = composition(top,composition(complement(one),top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(composition(top,complement(one)),top)),composition(top,composition(complement(one),top))) ),[0],$fot(converse(composition(top,composition(complement(one),top))))]]) ).
cnf(refute_0_1001,plain,
( converse(composition(composition(top,complement(one)),top)) != composition(top,composition(complement(one),top))
| converse(composition(top,composition(complement(one),top))) = composition(top,composition(complement(one),top)) ),
inference(resolve,[$cnf( $equal(converse(composition(composition(top,complement(one)),top)),converse(composition(top,composition(complement(one),top)))) )],[refute_0_999,refute_0_1000]) ).
cnf(refute_0_1002,plain,
converse(composition(top,composition(complement(one),top))) = composition(top,composition(complement(one),top)),
inference(resolve,[$cnf( $equal(converse(composition(composition(top,complement(one)),top)),composition(top,composition(complement(one),top))) )],[refute_0_994,refute_0_1001]) ).
cnf(refute_0_1003,plain,
converse(composition(complement(one),top)) = composition(top,converse(complement(one))),
inference(subst,[],[refute_0_741:[bind(X_22,$fot(complement(one)))]]) ).
cnf(refute_0_1004,plain,
( converse(complement(one)) != complement(one)
| converse(composition(complement(one),top)) != composition(top,converse(complement(one)))
| converse(composition(complement(one),top)) = composition(top,complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(complement(one),top)),composition(top,converse(complement(one)))) ),[1,1],$fot(complement(one))]]) ).
cnf(refute_0_1005,plain,
( converse(composition(complement(one),top)) != composition(top,converse(complement(one)))
| converse(composition(complement(one),top)) = composition(top,complement(one)) ),
inference(resolve,[$cnf( $equal(converse(complement(one)),complement(one)) )],[refute_0_942,refute_0_1004]) ).
cnf(refute_0_1006,plain,
converse(composition(complement(one),top)) = composition(top,complement(one)),
inference(resolve,[$cnf( $equal(converse(composition(complement(one),top)),composition(top,converse(complement(one)))) )],[refute_0_1003,refute_0_1005]) ).
cnf(refute_0_1007,plain,
join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(composition(top,complement(composition(complement(one),top)))))) = complement(complement(composition(complement(one),top))),
inference(subst,[],[refute_0_78:[bind(A,$fot(top)),bind(B,$fot(complement(composition(complement(one),top))))]]) ).
cnf(refute_0_1008,plain,
composition(join(complement(one),one),complement(composition(complement(one),top))) = join(complement(composition(complement(one),top)),composition(complement(one),complement(composition(complement(one),top)))),
inference(subst,[],[refute_0_61:[bind(X_32,$fot(complement(one))),bind(X_34,$fot(complement(composition(complement(one),top))))]]) ).
cnf(refute_0_1009,plain,
join(complement(top),composition(converse(X_62),complement(composition(X_62,top)))) = complement(top),
inference(subst,[],[refute_0_78:[bind(A,$fot(X_62)),bind(B,$fot(top))]]) ).
cnf(refute_0_1010,plain,
( complement(top) != zero
| join(complement(top),composition(converse(X_62),complement(composition(X_62,top)))) != complement(top)
| join(zero,composition(converse(X_62),complement(composition(X_62,top)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(X_62),complement(composition(X_62,top)))),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_1011,plain,
( join(complement(top),composition(converse(X_62),complement(composition(X_62,top)))) != complement(top)
| join(zero,composition(converse(X_62),complement(composition(X_62,top)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_1010]) ).
cnf(refute_0_1012,plain,
join(zero,composition(converse(X_62),complement(composition(X_62,top)))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(X_62),complement(composition(X_62,top)))),complement(top)) )],[refute_0_1009,refute_0_1011]) ).
cnf(refute_0_1013,plain,
( complement(top) != zero
| join(zero,composition(converse(X_62),complement(composition(X_62,top)))) != complement(top)
| join(zero,composition(converse(X_62),complement(composition(X_62,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(X_62),complement(composition(X_62,top)))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_1014,plain,
( join(zero,composition(converse(X_62),complement(composition(X_62,top)))) != complement(top)
| join(zero,composition(converse(X_62),complement(composition(X_62,top)))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_1013]) ).
cnf(refute_0_1015,plain,
join(zero,composition(converse(X_62),complement(composition(X_62,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_62),complement(composition(X_62,top)))),complement(top)) )],[refute_0_1012,refute_0_1014]) ).
cnf(refute_0_1016,plain,
join(zero,composition(converse(X_62),complement(composition(X_62,top)))) = composition(converse(X_62),complement(composition(X_62,top))),
inference(subst,[],[refute_0_692:[bind(X_87,$fot(composition(converse(X_62),complement(composition(X_62,top)))))]]) ).
cnf(refute_0_1017,plain,
( join(zero,composition(converse(X_62),complement(composition(X_62,top)))) != composition(converse(X_62),complement(composition(X_62,top)))
| join(zero,composition(converse(X_62),complement(composition(X_62,top)))) != zero
| composition(converse(X_62),complement(composition(X_62,top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(X_62),complement(composition(X_62,top)))),zero) ),[0],$fot(composition(converse(X_62),complement(composition(X_62,top))))]]) ).
cnf(refute_0_1018,plain,
( join(zero,composition(converse(X_62),complement(composition(X_62,top)))) != zero
| composition(converse(X_62),complement(composition(X_62,top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_62),complement(composition(X_62,top)))),composition(converse(X_62),complement(composition(X_62,top)))) )],[refute_0_1016,refute_0_1017]) ).
cnf(refute_0_1019,plain,
composition(converse(X_62),complement(composition(X_62,top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_62),complement(composition(X_62,top)))),zero) )],[refute_0_1015,refute_0_1018]) ).
cnf(refute_0_1020,plain,
composition(converse(complement(one)),complement(composition(complement(one),top))) = zero,
inference(subst,[],[refute_0_1019:[bind(X_62,$fot(complement(one)))]]) ).
cnf(refute_0_1021,plain,
( composition(converse(complement(one)),complement(composition(complement(one),top))) != zero
| converse(complement(one)) != complement(one)
| composition(complement(one),complement(composition(complement(one),top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(one)),complement(composition(complement(one),top))),zero) ),[0,0],$fot(complement(one))]]) ).
cnf(refute_0_1022,plain,
( composition(converse(complement(one)),complement(composition(complement(one),top))) != zero
| composition(complement(one),complement(composition(complement(one),top))) = zero ),
inference(resolve,[$cnf( $equal(converse(complement(one)),complement(one)) )],[refute_0_942,refute_0_1021]) ).
cnf(refute_0_1023,plain,
composition(complement(one),complement(composition(complement(one),top))) = zero,
inference(resolve,[$cnf( $equal(composition(converse(complement(one)),complement(composition(complement(one),top))),zero) )],[refute_0_1020,refute_0_1022]) ).
cnf(refute_0_1024,plain,
( composition(complement(one),complement(composition(complement(one),top))) != zero
| composition(join(complement(one),one),complement(composition(complement(one),top))) != join(complement(composition(complement(one),top)),composition(complement(one),complement(composition(complement(one),top))))
| composition(join(complement(one),one),complement(composition(complement(one),top))) = join(complement(composition(complement(one),top)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(complement(one),one),complement(composition(complement(one),top))),join(complement(composition(complement(one),top)),composition(complement(one),complement(composition(complement(one),top))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_1025,plain,
( composition(join(complement(one),one),complement(composition(complement(one),top))) != join(complement(composition(complement(one),top)),composition(complement(one),complement(composition(complement(one),top))))
| composition(join(complement(one),one),complement(composition(complement(one),top))) = join(complement(composition(complement(one),top)),zero) ),
inference(resolve,[$cnf( $equal(composition(complement(one),complement(composition(complement(one),top))),zero) )],[refute_0_1023,refute_0_1024]) ).
cnf(refute_0_1026,plain,
composition(join(complement(one),one),complement(composition(complement(one),top))) = join(complement(composition(complement(one),top)),zero),
inference(resolve,[$cnf( $equal(composition(join(complement(one),one),complement(composition(complement(one),top))),join(complement(composition(complement(one),top)),composition(complement(one),complement(composition(complement(one),top))))) )],[refute_0_1008,refute_0_1025]) ).
cnf(refute_0_1027,plain,
join(one,complement(one)) = top,
inference(subst,[],[refute_0_265:[bind(A,$fot(one))]]) ).
cnf(refute_0_1028,plain,
composition(join(one,complement(one)),complement(composition(complement(one),top))) = composition(join(one,complement(one)),complement(composition(complement(one),top))),
introduced(tautology,[refl,[$fot(composition(join(one,complement(one)),complement(composition(complement(one),top))))]]) ).
cnf(refute_0_1029,plain,
( composition(join(one,complement(one)),complement(composition(complement(one),top))) != composition(join(one,complement(one)),complement(composition(complement(one),top)))
| join(one,complement(one)) != top
| composition(join(one,complement(one)),complement(composition(complement(one),top))) = composition(top,complement(composition(complement(one),top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,complement(one)),complement(composition(complement(one),top))),composition(join(one,complement(one)),complement(composition(complement(one),top)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1030,plain,
( join(one,complement(one)) != top
| composition(join(one,complement(one)),complement(composition(complement(one),top))) = composition(top,complement(composition(complement(one),top))) ),
inference(resolve,[$cnf( $equal(composition(join(one,complement(one)),complement(composition(complement(one),top))),composition(join(one,complement(one)),complement(composition(complement(one),top)))) )],[refute_0_1028,refute_0_1029]) ).
cnf(refute_0_1031,plain,
composition(join(one,complement(one)),complement(composition(complement(one),top))) = composition(top,complement(composition(complement(one),top))),
inference(resolve,[$cnf( $equal(join(one,complement(one)),top) )],[refute_0_1027,refute_0_1030]) ).
cnf(refute_0_1032,plain,
join(composition(X_33,X_34),composition(X_32,X_34)) = join(composition(X_32,X_34),composition(X_33,X_34)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(composition(X_33,X_34))),bind(B,$fot(composition(X_32,X_34)))]]) ).
cnf(refute_0_1033,plain,
composition(join(X_32,X_33),X_34) = join(composition(X_32,X_34),composition(X_33,X_34)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_32)),bind(B,$fot(X_33)),bind(C,$fot(X_34))]]) ).
cnf(refute_0_1034,plain,
( composition(join(X_32,X_33),X_34) != join(composition(X_32,X_34),composition(X_33,X_34))
| join(composition(X_32,X_34),composition(X_33,X_34)) = composition(join(X_32,X_33),X_34) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_32,X_33),X_34))),bind(Y,$fot(join(composition(X_32,X_34),composition(X_33,X_34))))]]) ).
cnf(refute_0_1035,plain,
join(composition(X_32,X_34),composition(X_33,X_34)) = composition(join(X_32,X_33),X_34),
inference(resolve,[$cnf( $equal(composition(join(X_32,X_33),X_34),join(composition(X_32,X_34),composition(X_33,X_34))) )],[refute_0_1033,refute_0_1034]) ).
cnf(refute_0_1036,plain,
( join(composition(X_32,X_34),composition(X_33,X_34)) != composition(join(X_32,X_33),X_34)
| join(composition(X_33,X_34),composition(X_32,X_34)) != join(composition(X_32,X_34),composition(X_33,X_34))
| join(composition(X_33,X_34),composition(X_32,X_34)) = composition(join(X_32,X_33),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_33,X_34),composition(X_32,X_34)),join(composition(X_32,X_34),composition(X_33,X_34))) ),[1],$fot(composition(join(X_32,X_33),X_34))]]) ).
cnf(refute_0_1037,plain,
( join(composition(X_33,X_34),composition(X_32,X_34)) != join(composition(X_32,X_34),composition(X_33,X_34))
| join(composition(X_33,X_34),composition(X_32,X_34)) = composition(join(X_32,X_33),X_34) ),
inference(resolve,[$cnf( $equal(join(composition(X_32,X_34),composition(X_33,X_34)),composition(join(X_32,X_33),X_34)) )],[refute_0_1035,refute_0_1036]) ).
cnf(refute_0_1038,plain,
join(composition(X_33,X_34),composition(X_32,X_34)) = composition(join(X_32,X_33),X_34),
inference(resolve,[$cnf( $equal(join(composition(X_33,X_34),composition(X_32,X_34)),join(composition(X_32,X_34),composition(X_33,X_34))) )],[refute_0_1032,refute_0_1037]) ).
cnf(refute_0_1039,plain,
( composition(join(A,B),C) != join(composition(A,C),composition(B,C))
| join(composition(A,C),composition(B,C)) = composition(join(A,B),C) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(A,B),C))),bind(Y,$fot(join(composition(A,C),composition(B,C))))]]) ).
cnf(refute_0_1040,plain,
join(composition(A,C),composition(B,C)) = composition(join(A,B),C),
inference(resolve,[$cnf( $equal(composition(join(A,B),C),join(composition(A,C),composition(B,C))) )],[composition_distributivity_7,refute_0_1039]) ).
cnf(refute_0_1041,plain,
join(composition(X_33,X_34),composition(X_32,X_34)) = composition(join(X_33,X_32),X_34),
inference(subst,[],[refute_0_1040:[bind(A,$fot(X_33)),bind(B,$fot(X_32)),bind(C,$fot(X_34))]]) ).
cnf(refute_0_1042,plain,
( join(composition(X_33,X_34),composition(X_32,X_34)) != composition(join(X_32,X_33),X_34)
| join(composition(X_33,X_34),composition(X_32,X_34)) != composition(join(X_33,X_32),X_34)
| composition(join(X_33,X_32),X_34) = composition(join(X_32,X_33),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_33,X_34),composition(X_32,X_34)),composition(join(X_32,X_33),X_34)) ),[0],$fot(composition(join(X_33,X_32),X_34))]]) ).
cnf(refute_0_1043,plain,
( join(composition(X_33,X_34),composition(X_32,X_34)) != composition(join(X_32,X_33),X_34)
| composition(join(X_33,X_32),X_34) = composition(join(X_32,X_33),X_34) ),
inference(resolve,[$cnf( $equal(join(composition(X_33,X_34),composition(X_32,X_34)),composition(join(X_33,X_32),X_34)) )],[refute_0_1041,refute_0_1042]) ).
cnf(refute_0_1044,plain,
composition(join(X_33,X_32),X_34) = composition(join(X_32,X_33),X_34),
inference(resolve,[$cnf( $equal(join(composition(X_33,X_34),composition(X_32,X_34)),composition(join(X_32,X_33),X_34)) )],[refute_0_1038,refute_0_1043]) ).
cnf(refute_0_1045,plain,
composition(join(X_85,X_84),X_56) = composition(join(X_84,X_85),X_56),
inference(subst,[],[refute_0_1044:[bind(X_32,$fot(X_84)),bind(X_33,$fot(X_85)),bind(X_34,$fot(X_56))]]) ).
cnf(refute_0_1046,plain,
composition(join(complement(one),one),complement(composition(complement(one),top))) = composition(join(one,complement(one)),complement(composition(complement(one),top))),
inference(subst,[],[refute_0_1045:[bind(X_56,$fot(complement(composition(complement(one),top)))),bind(X_84,$fot(one)),bind(X_85,$fot(complement(one)))]]) ).
cnf(refute_0_1047,plain,
( composition(join(complement(one),one),complement(composition(complement(one),top))) != composition(join(one,complement(one)),complement(composition(complement(one),top)))
| composition(join(one,complement(one)),complement(composition(complement(one),top))) != composition(top,complement(composition(complement(one),top)))
| composition(join(complement(one),one),complement(composition(complement(one),top))) = composition(top,complement(composition(complement(one),top))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(complement(one),one),complement(composition(complement(one),top))))),bind(Y,$fot(composition(join(one,complement(one)),complement(composition(complement(one),top))))),bind(Z,$fot(composition(top,complement(composition(complement(one),top)))))]]) ).
cnf(refute_0_1048,plain,
( composition(join(one,complement(one)),complement(composition(complement(one),top))) != composition(top,complement(composition(complement(one),top)))
| composition(join(complement(one),one),complement(composition(complement(one),top))) = composition(top,complement(composition(complement(one),top))) ),
inference(resolve,[$cnf( $equal(composition(join(complement(one),one),complement(composition(complement(one),top))),composition(join(one,complement(one)),complement(composition(complement(one),top)))) )],[refute_0_1046,refute_0_1047]) ).
cnf(refute_0_1049,plain,
composition(join(complement(one),one),complement(composition(complement(one),top))) = composition(top,complement(composition(complement(one),top))),
inference(resolve,[$cnf( $equal(composition(join(one,complement(one)),complement(composition(complement(one),top))),composition(top,complement(composition(complement(one),top)))) )],[refute_0_1031,refute_0_1048]) ).
cnf(refute_0_1050,plain,
( composition(join(complement(one),one),complement(composition(complement(one),top))) != composition(top,complement(composition(complement(one),top)))
| composition(join(complement(one),one),complement(composition(complement(one),top))) != join(complement(composition(complement(one),top)),zero)
| composition(top,complement(composition(complement(one),top))) = join(complement(composition(complement(one),top)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(complement(one),one),complement(composition(complement(one),top))),join(complement(composition(complement(one),top)),zero)) ),[0],$fot(composition(top,complement(composition(complement(one),top))))]]) ).
cnf(refute_0_1051,plain,
( composition(join(complement(one),one),complement(composition(complement(one),top))) != join(complement(composition(complement(one),top)),zero)
| composition(top,complement(composition(complement(one),top))) = join(complement(composition(complement(one),top)),zero) ),
inference(resolve,[$cnf( $equal(composition(join(complement(one),one),complement(composition(complement(one),top))),composition(top,complement(composition(complement(one),top)))) )],[refute_0_1049,refute_0_1050]) ).
cnf(refute_0_1052,plain,
A = join(meet(A,top),complement(join(complement(A),top))),
inference(subst,[],[refute_0_158:[bind(B,$fot(top))]]) ).
cnf(refute_0_1053,plain,
X_89 = join(zero,meet(top,X_89)),
inference(subst,[],[refute_0_363:[bind(X_87,$fot(X_89))]]) ).
cnf(refute_0_1054,plain,
meet(X_89,top) = meet(top,X_89),
inference(subst,[],[refute_0_623:[bind(X_6,$fot(X_89)),bind(X_7,$fot(top))]]) ).
cnf(refute_0_1055,plain,
( meet(X_89,top) != meet(top,X_89)
| meet(top,X_89) = meet(X_89,top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_89,top))),bind(Y,$fot(meet(top,X_89)))]]) ).
cnf(refute_0_1056,plain,
meet(top,X_89) = meet(X_89,top),
inference(resolve,[$cnf( $equal(meet(X_89,top),meet(top,X_89)) )],[refute_0_1054,refute_0_1055]) ).
cnf(refute_0_1057,plain,
( X_89 != join(zero,meet(top,X_89))
| meet(top,X_89) != meet(X_89,top)
| X_89 = join(zero,meet(X_89,top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_89,join(zero,meet(top,X_89))) ),[1,1],$fot(meet(X_89,top))]]) ).
cnf(refute_0_1058,plain,
( X_89 != join(zero,meet(top,X_89))
| X_89 = join(zero,meet(X_89,top)) ),
inference(resolve,[$cnf( $equal(meet(top,X_89),meet(X_89,top)) )],[refute_0_1056,refute_0_1057]) ).
cnf(refute_0_1059,plain,
X_89 = join(zero,meet(X_89,top)),
inference(resolve,[$cnf( $equal(X_89,join(zero,meet(top,X_89))) )],[refute_0_1053,refute_0_1058]) ).
cnf(refute_0_1060,plain,
join(zero,meet(X_89,top)) = meet(X_89,top),
inference(subst,[],[refute_0_692:[bind(X_87,$fot(meet(X_89,top)))]]) ).
cnf(refute_0_1061,plain,
( X_89 != join(zero,meet(X_89,top))
| join(zero,meet(X_89,top)) != meet(X_89,top)
| X_89 = meet(X_89,top) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_89,meet(X_89,top)) ),[0],$fot(join(zero,meet(X_89,top)))]]) ).
cnf(refute_0_1062,plain,
( X_89 != join(zero,meet(X_89,top))
| X_89 = meet(X_89,top) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_89,top)),meet(X_89,top)) )],[refute_0_1060,refute_0_1061]) ).
cnf(refute_0_1063,plain,
X_89 = meet(X_89,top),
inference(resolve,[$cnf( $equal(X_89,join(zero,meet(X_89,top))) )],[refute_0_1059,refute_0_1062]) ).
cnf(refute_0_1064,plain,
A = meet(A,top),
inference(subst,[],[refute_0_1063:[bind(X_89,$fot(A))]]) ).
cnf(refute_0_1065,plain,
( A != meet(A,top)
| meet(A,top) = A ),
inference(subst,[],[refute_0_2:[bind(X,$fot(A)),bind(Y,$fot(meet(A,top)))]]) ).
cnf(refute_0_1066,plain,
meet(A,top) = A,
inference(resolve,[$cnf( $equal(A,meet(A,top)) )],[refute_0_1064,refute_0_1065]) ).
cnf(refute_0_1067,plain,
( A != join(meet(A,top),complement(join(complement(A),top)))
| meet(A,top) != A
| A = join(A,complement(join(complement(A),top))) ),
introduced(tautology,[equality,[$cnf( $equal(A,join(meet(A,top),complement(join(complement(A),top)))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_1068,plain,
( A != join(meet(A,top),complement(join(complement(A),top)))
| A = join(A,complement(join(complement(A),top))) ),
inference(resolve,[$cnf( $equal(meet(A,top),A) )],[refute_0_1066,refute_0_1067]) ).
cnf(refute_0_1069,plain,
A = join(A,complement(join(complement(A),top))),
inference(resolve,[$cnf( $equal(A,join(meet(A,top),complement(join(complement(A),top)))) )],[refute_0_1052,refute_0_1068]) ).
cnf(refute_0_1070,plain,
join(complement(A),top) = top,
inference(subst,[],[refute_0_345:[bind(X_41,$fot(complement(A)))]]) ).
cnf(refute_0_1071,plain,
complement(join(complement(A),top)) = complement(join(complement(A),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),top)))]]) ).
cnf(refute_0_1072,plain,
( complement(join(complement(A),top)) != complement(join(complement(A),top))
| join(complement(A),top) != top
| complement(join(complement(A),top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),top)),complement(join(complement(A),top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1073,plain,
( join(complement(A),top) != top
| complement(join(complement(A),top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),top)),complement(join(complement(A),top))) )],[refute_0_1071,refute_0_1072]) ).
cnf(refute_0_1074,plain,
complement(join(complement(A),top)) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(A),top),top) )],[refute_0_1070,refute_0_1073]) ).
cnf(refute_0_1075,plain,
( complement(join(complement(A),top)) != complement(top)
| complement(top) != zero
| complement(join(complement(A),top)) = zero ),
inference(subst,[],[refute_0_7:[bind(X,$fot(complement(join(complement(A),top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1076,plain,
( complement(top) != zero
| complement(join(complement(A),top)) = zero ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),top)),complement(top)) )],[refute_0_1074,refute_0_1075]) ).
cnf(refute_0_1077,plain,
complement(join(complement(A),top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_1076]) ).
cnf(refute_0_1078,plain,
join(A,complement(join(complement(A),top))) = join(A,complement(join(complement(A),top))),
introduced(tautology,[refl,[$fot(join(A,complement(join(complement(A),top))))]]) ).
cnf(refute_0_1079,plain,
( complement(join(complement(A),top)) != zero
| join(A,complement(join(complement(A),top))) != join(A,complement(join(complement(A),top)))
| join(A,complement(join(complement(A),top))) = join(A,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,complement(join(complement(A),top))),join(A,complement(join(complement(A),top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_1080,plain,
( complement(join(complement(A),top)) != zero
| join(A,complement(join(complement(A),top))) = join(A,zero) ),
inference(resolve,[$cnf( $equal(join(A,complement(join(complement(A),top))),join(A,complement(join(complement(A),top)))) )],[refute_0_1078,refute_0_1079]) ).
cnf(refute_0_1081,plain,
join(A,complement(join(complement(A),top))) = join(A,zero),
inference(resolve,[$cnf( $equal(complement(join(complement(A),top)),zero) )],[refute_0_1077,refute_0_1080]) ).
cnf(refute_0_1082,plain,
( A != join(A,complement(join(complement(A),top)))
| join(A,complement(join(complement(A),top))) != join(A,zero)
| A = join(A,zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,join(A,zero)) ),[0],$fot(join(A,complement(join(complement(A),top))))]]) ).
cnf(refute_0_1083,plain,
( A != join(A,complement(join(complement(A),top)))
| A = join(A,zero) ),
inference(resolve,[$cnf( $equal(join(A,complement(join(complement(A),top))),join(A,zero)) )],[refute_0_1081,refute_0_1082]) ).
cnf(refute_0_1084,plain,
A = join(A,zero),
inference(resolve,[$cnf( $equal(A,join(A,complement(join(complement(A),top)))) )],[refute_0_1069,refute_0_1083]) ).
cnf(refute_0_1085,plain,
complement(composition(complement(one),top)) = join(complement(composition(complement(one),top)),zero),
inference(subst,[],[refute_0_1084:[bind(A,$fot(complement(composition(complement(one),top))))]]) ).
cnf(refute_0_1086,plain,
( complement(composition(complement(one),top)) != join(complement(composition(complement(one),top)),zero)
| join(complement(composition(complement(one),top)),zero) = complement(composition(complement(one),top)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(composition(complement(one),top)))),bind(Y,$fot(join(complement(composition(complement(one),top)),zero)))]]) ).
cnf(refute_0_1087,plain,
join(complement(composition(complement(one),top)),zero) = complement(composition(complement(one),top)),
inference(resolve,[$cnf( $equal(complement(composition(complement(one),top)),join(complement(composition(complement(one),top)),zero)) )],[refute_0_1085,refute_0_1086]) ).
cnf(refute_0_1088,plain,
( composition(top,complement(composition(complement(one),top))) != join(complement(composition(complement(one),top)),zero)
| join(complement(composition(complement(one),top)),zero) != complement(composition(complement(one),top))
| composition(top,complement(composition(complement(one),top))) = complement(composition(complement(one),top)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(top,complement(composition(complement(one),top))),complement(composition(complement(one),top))) ),[0],$fot(join(complement(composition(complement(one),top)),zero))]]) ).
cnf(refute_0_1089,plain,
( composition(top,complement(composition(complement(one),top))) != join(complement(composition(complement(one),top)),zero)
| composition(top,complement(composition(complement(one),top))) = complement(composition(complement(one),top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(complement(one),top)),zero),complement(composition(complement(one),top))) )],[refute_0_1087,refute_0_1088]) ).
cnf(refute_0_1090,plain,
( composition(join(complement(one),one),complement(composition(complement(one),top))) != join(complement(composition(complement(one),top)),zero)
| composition(top,complement(composition(complement(one),top))) = complement(composition(complement(one),top)) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(complement(one),top))),join(complement(composition(complement(one),top)),zero)) )],[refute_0_1051,refute_0_1089]) ).
cnf(refute_0_1091,plain,
composition(top,complement(composition(complement(one),top))) = complement(composition(complement(one),top)),
inference(resolve,[$cnf( $equal(composition(join(complement(one),one),complement(composition(complement(one),top))),join(complement(composition(complement(one),top)),zero)) )],[refute_0_1026,refute_0_1090]) ).
cnf(refute_0_1092,plain,
( composition(top,complement(composition(complement(one),top))) != complement(composition(complement(one),top))
| join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(composition(top,complement(composition(complement(one),top)))))) != complement(complement(composition(complement(one),top)))
| join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) = complement(complement(composition(complement(one),top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(composition(top,complement(composition(complement(one),top)))))),complement(complement(composition(complement(one),top)))) ),[0,1,1,0],$fot(complement(composition(complement(one),top)))]]) ).
cnf(refute_0_1093,plain,
( join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(composition(top,complement(composition(complement(one),top)))))) != complement(complement(composition(complement(one),top)))
| join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) = complement(complement(composition(complement(one),top))) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(complement(one),top))),complement(composition(complement(one),top))) )],[refute_0_1091,refute_0_1092]) ).
cnf(refute_0_1094,plain,
join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) = complement(complement(composition(complement(one),top))),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(composition(top,complement(composition(complement(one),top)))))),complement(complement(composition(complement(one),top)))) )],[refute_0_1007,refute_0_1093]) ).
cnf(refute_0_1095,plain,
complement(complement(composition(complement(one),top))) = composition(complement(one),top),
inference(subst,[],[refute_0_383:[bind(X_87,$fot(composition(complement(one),top)))]]) ).
cnf(refute_0_1096,plain,
composition(top,complement(complement(composition(complement(one),top)))) = composition(top,complement(complement(composition(complement(one),top)))),
introduced(tautology,[refl,[$fot(composition(top,complement(complement(composition(complement(one),top)))))]]) ).
cnf(refute_0_1097,plain,
( complement(complement(composition(complement(one),top))) != composition(complement(one),top)
| composition(top,complement(complement(composition(complement(one),top)))) != composition(top,complement(complement(composition(complement(one),top))))
| composition(top,complement(complement(composition(complement(one),top)))) = composition(top,composition(complement(one),top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(complement(composition(complement(one),top)))),composition(top,complement(complement(composition(complement(one),top))))) ),[1,1],$fot(composition(complement(one),top))]]) ).
cnf(refute_0_1098,plain,
( complement(complement(composition(complement(one),top))) != composition(complement(one),top)
| composition(top,complement(complement(composition(complement(one),top)))) = composition(top,composition(complement(one),top)) ),
inference(resolve,[$cnf( $equal(composition(top,complement(complement(composition(complement(one),top)))),composition(top,complement(complement(composition(complement(one),top))))) )],[refute_0_1096,refute_0_1097]) ).
cnf(refute_0_1099,plain,
composition(top,complement(complement(composition(complement(one),top)))) = composition(top,composition(complement(one),top)),
inference(resolve,[$cnf( $equal(complement(complement(composition(complement(one),top))),composition(complement(one),top)) )],[refute_0_1095,refute_0_1098]) ).
cnf(refute_0_1100,plain,
join(one,top) = top,
inference(subst,[],[refute_0_345:[bind(X_41,$fot(one))]]) ).
cnf(refute_0_1101,plain,
converse(join(one,top)) = converse(join(one,top)),
introduced(tautology,[refl,[$fot(converse(join(one,top)))]]) ).
cnf(refute_0_1102,plain,
( converse(join(one,top)) != converse(join(one,top))
| join(one,top) != top
| converse(join(one,top)) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,top)),converse(join(one,top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1103,plain,
( join(one,top) != top
| converse(join(one,top)) = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(one,top)),converse(join(one,top))) )],[refute_0_1101,refute_0_1102]) ).
cnf(refute_0_1104,plain,
converse(join(one,top)) = converse(top),
inference(resolve,[$cnf( $equal(join(one,top),top) )],[refute_0_1100,refute_0_1103]) ).
cnf(refute_0_1105,plain,
( converse(join(one,top)) != converse(top)
| converse(top) != top
| converse(join(one,top)) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(one,top)))),bind(Y,$fot(converse(top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1106,plain,
( converse(top) != top
| converse(join(one,top)) = top ),
inference(resolve,[$cnf( $equal(converse(join(one,top)),converse(top)) )],[refute_0_1104,refute_0_1105]) ).
cnf(refute_0_1107,plain,
converse(join(one,top)) = top,
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_601,refute_0_1106]) ).
cnf(refute_0_1108,plain,
join(one,converse(top)) = converse(join(one,top)),
inference(subst,[],[refute_0_99:[bind(X_13,$fot(top))]]) ).
cnf(refute_0_1109,plain,
( converse(join(one,top)) != top
| join(one,converse(top)) != converse(join(one,top))
| join(one,converse(top)) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,converse(top)))),bind(Y,$fot(converse(join(one,top)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1110,plain,
( converse(join(one,top)) != top
| join(one,converse(top)) = top ),
inference(resolve,[$cnf( $equal(join(one,converse(top)),converse(join(one,top))) )],[refute_0_1108,refute_0_1109]) ).
cnf(refute_0_1111,plain,
join(one,converse(top)) = top,
inference(resolve,[$cnf( $equal(converse(join(one,top)),top) )],[refute_0_1107,refute_0_1110]) ).
cnf(refute_0_1112,plain,
composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) = composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))),
introduced(tautology,[refl,[$fot(composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))))]]) ).
cnf(refute_0_1113,plain,
( composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) != composition(join(one,converse(top)),complement(complement(composition(complement(one),top))))
| join(one,converse(top)) != top
| composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) = composition(top,complement(complement(composition(complement(one),top)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))),composition(join(one,converse(top)),complement(complement(composition(complement(one),top))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1114,plain,
( join(one,converse(top)) != top
| composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) = composition(top,complement(complement(composition(complement(one),top)))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))),composition(join(one,converse(top)),complement(complement(composition(complement(one),top))))) )],[refute_0_1112,refute_0_1113]) ).
cnf(refute_0_1115,plain,
composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) = composition(top,complement(complement(composition(complement(one),top)))),
inference(resolve,[$cnf( $equal(join(one,converse(top)),top) )],[refute_0_1111,refute_0_1114]) ).
cnf(refute_0_1116,plain,
( composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) != composition(top,complement(complement(composition(complement(one),top))))
| composition(top,complement(complement(composition(complement(one),top)))) != composition(top,composition(complement(one),top))
| composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) = composition(top,composition(complement(one),top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))))),bind(Y,$fot(composition(top,complement(complement(composition(complement(one),top)))))),bind(Z,$fot(composition(top,composition(complement(one),top))))]]) ).
cnf(refute_0_1117,plain,
( composition(top,complement(complement(composition(complement(one),top)))) != composition(top,composition(complement(one),top))
| composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) = composition(top,composition(complement(one),top)) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))),composition(top,complement(complement(composition(complement(one),top))))) )],[refute_0_1115,refute_0_1116]) ).
cnf(refute_0_1118,plain,
composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) = composition(top,composition(complement(one),top)),
inference(resolve,[$cnf( $equal(composition(top,complement(complement(composition(complement(one),top)))),composition(top,composition(complement(one),top))) )],[refute_0_1099,refute_0_1117]) ).
cnf(refute_0_1119,plain,
composition(join(converse(top),one),complement(complement(composition(complement(one),top)))) = composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))),
inference(subst,[],[refute_0_1045:[bind(X_56,$fot(complement(complement(composition(complement(one),top))))),bind(X_84,$fot(one)),bind(X_85,$fot(converse(top)))]]) ).
cnf(refute_0_1120,plain,
join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) = composition(join(converse(top),one),complement(complement(composition(complement(one),top)))),
inference(subst,[],[refute_0_116:[bind(X_32,$fot(converse(top))),bind(X_34,$fot(complement(complement(composition(complement(one),top)))))]]) ).
cnf(refute_0_1121,plain,
( composition(join(converse(top),one),complement(complement(composition(complement(one),top)))) != composition(join(one,converse(top)),complement(complement(composition(complement(one),top))))
| join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) != composition(join(converse(top),one),complement(complement(composition(complement(one),top))))
| join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) = composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))))),bind(Y,$fot(composition(join(converse(top),one),complement(complement(composition(complement(one),top)))))),bind(Z,$fot(composition(join(one,converse(top)),complement(complement(composition(complement(one),top))))))]]) ).
cnf(refute_0_1122,plain,
( composition(join(converse(top),one),complement(complement(composition(complement(one),top)))) != composition(join(one,converse(top)),complement(complement(composition(complement(one),top))))
| join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) = composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))),composition(join(converse(top),one),complement(complement(composition(complement(one),top))))) )],[refute_0_1120,refute_0_1121]) ).
cnf(refute_0_1123,plain,
join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) = composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))),
inference(resolve,[$cnf( $equal(composition(join(converse(top),one),complement(complement(composition(complement(one),top)))),composition(join(one,converse(top)),complement(complement(composition(complement(one),top))))) )],[refute_0_1119,refute_0_1122]) ).
cnf(refute_0_1124,plain,
( composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) != composition(top,composition(complement(one),top))
| join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) != composition(join(one,converse(top)),complement(complement(composition(complement(one),top))))
| join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) = composition(top,composition(complement(one),top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))))),bind(Y,$fot(composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))))),bind(Z,$fot(composition(top,composition(complement(one),top))))]]) ).
cnf(refute_0_1125,plain,
( composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))) != composition(top,composition(complement(one),top))
| join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) = composition(top,composition(complement(one),top)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))),composition(join(one,converse(top)),complement(complement(composition(complement(one),top))))) )],[refute_0_1123,refute_0_1124]) ).
cnf(refute_0_1126,plain,
join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) = composition(top,composition(complement(one),top)),
inference(resolve,[$cnf( $equal(composition(join(one,converse(top)),complement(complement(composition(complement(one),top)))),composition(top,composition(complement(one),top))) )],[refute_0_1118,refute_0_1125]) ).
cnf(refute_0_1127,plain,
( join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) != complement(complement(composition(complement(one),top)))
| join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) != composition(top,composition(complement(one),top))
| composition(top,composition(complement(one),top)) = complement(complement(composition(complement(one),top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))),complement(complement(composition(complement(one),top)))) ),[0],$fot(composition(top,composition(complement(one),top)))]]) ).
cnf(refute_0_1128,plain,
( join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) != complement(complement(composition(complement(one),top)))
| composition(top,composition(complement(one),top)) = complement(complement(composition(complement(one),top))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))),composition(top,composition(complement(one),top))) )],[refute_0_1126,refute_0_1127]) ).
cnf(refute_0_1129,plain,
( complement(complement(composition(complement(one),top))) != composition(complement(one),top)
| composition(top,composition(complement(one),top)) != complement(complement(composition(complement(one),top)))
| composition(top,composition(complement(one),top)) = composition(complement(one),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(complement(one),top)),complement(complement(composition(complement(one),top)))) ),[1],$fot(composition(complement(one),top))]]) ).
cnf(refute_0_1130,plain,
( composition(top,composition(complement(one),top)) != complement(complement(composition(complement(one),top)))
| composition(top,composition(complement(one),top)) = composition(complement(one),top) ),
inference(resolve,[$cnf( $equal(complement(complement(composition(complement(one),top))),composition(complement(one),top)) )],[refute_0_1095,refute_0_1129]) ).
cnf(refute_0_1131,plain,
( join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))) != complement(complement(composition(complement(one),top)))
| composition(top,composition(complement(one),top)) = composition(complement(one),top) ),
inference(resolve,[$cnf( $equal(composition(top,composition(complement(one),top)),complement(complement(composition(complement(one),top)))) )],[refute_0_1128,refute_0_1130]) ).
cnf(refute_0_1132,plain,
composition(top,composition(complement(one),top)) = composition(complement(one),top),
inference(resolve,[$cnf( $equal(join(complement(complement(composition(complement(one),top))),composition(converse(top),complement(complement(composition(complement(one),top))))),complement(complement(composition(complement(one),top)))) )],[refute_0_1094,refute_0_1131]) ).
cnf(refute_0_1133,plain,
converse(composition(top,composition(complement(one),top))) = converse(composition(top,composition(complement(one),top))),
introduced(tautology,[refl,[$fot(converse(composition(top,composition(complement(one),top))))]]) ).
cnf(refute_0_1134,plain,
( composition(top,composition(complement(one),top)) != composition(complement(one),top)
| converse(composition(top,composition(complement(one),top))) != converse(composition(top,composition(complement(one),top)))
| converse(composition(top,composition(complement(one),top))) = converse(composition(complement(one),top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(top,composition(complement(one),top))),converse(composition(top,composition(complement(one),top)))) ),[1,0],$fot(composition(complement(one),top))]]) ).
cnf(refute_0_1135,plain,
( composition(top,composition(complement(one),top)) != composition(complement(one),top)
| converse(composition(top,composition(complement(one),top))) = converse(composition(complement(one),top)) ),
inference(resolve,[$cnf( $equal(converse(composition(top,composition(complement(one),top))),converse(composition(top,composition(complement(one),top)))) )],[refute_0_1133,refute_0_1134]) ).
cnf(refute_0_1136,plain,
converse(composition(top,composition(complement(one),top))) = converse(composition(complement(one),top)),
inference(resolve,[$cnf( $equal(composition(top,composition(complement(one),top)),composition(complement(one),top)) )],[refute_0_1132,refute_0_1135]) ).
cnf(refute_0_1137,plain,
( converse(composition(complement(one),top)) != composition(top,complement(one))
| converse(composition(top,composition(complement(one),top))) != converse(composition(complement(one),top))
| converse(composition(top,composition(complement(one),top))) = composition(top,complement(one)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(composition(top,composition(complement(one),top))))),bind(Y,$fot(converse(composition(complement(one),top)))),bind(Z,$fot(composition(top,complement(one))))]]) ).
cnf(refute_0_1138,plain,
( converse(composition(complement(one),top)) != composition(top,complement(one))
| converse(composition(top,composition(complement(one),top))) = composition(top,complement(one)) ),
inference(resolve,[$cnf( $equal(converse(composition(top,composition(complement(one),top))),converse(composition(complement(one),top))) )],[refute_0_1136,refute_0_1137]) ).
cnf(refute_0_1139,plain,
converse(composition(top,composition(complement(one),top))) = composition(top,complement(one)),
inference(resolve,[$cnf( $equal(converse(composition(complement(one),top)),composition(top,complement(one))) )],[refute_0_1006,refute_0_1138]) ).
cnf(refute_0_1140,plain,
( converse(composition(top,composition(complement(one),top))) != composition(top,complement(one))
| converse(composition(top,composition(complement(one),top))) != composition(top,composition(complement(one),top))
| composition(top,complement(one)) = composition(top,composition(complement(one),top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(top,composition(complement(one),top))),composition(top,composition(complement(one),top))) ),[0],$fot(composition(top,complement(one)))]]) ).
cnf(refute_0_1141,plain,
( converse(composition(top,composition(complement(one),top))) != composition(top,composition(complement(one),top))
| composition(top,complement(one)) = composition(top,composition(complement(one),top)) ),
inference(resolve,[$cnf( $equal(converse(composition(top,composition(complement(one),top))),composition(top,complement(one))) )],[refute_0_1139,refute_0_1140]) ).
cnf(refute_0_1142,plain,
( composition(top,complement(one)) != composition(top,composition(complement(one),top))
| composition(top,composition(complement(one),top)) != composition(complement(one),top)
| composition(top,complement(one)) = composition(complement(one),top) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(top,complement(one)),composition(complement(one),top)) ),[0],$fot(composition(top,composition(complement(one),top)))]]) ).
cnf(refute_0_1143,plain,
( composition(top,complement(one)) != composition(top,composition(complement(one),top))
| composition(top,complement(one)) = composition(complement(one),top) ),
inference(resolve,[$cnf( $equal(composition(top,composition(complement(one),top)),composition(complement(one),top)) )],[refute_0_1132,refute_0_1142]) ).
cnf(refute_0_1144,plain,
( converse(composition(top,composition(complement(one),top))) != composition(top,composition(complement(one),top))
| composition(top,complement(one)) = composition(complement(one),top) ),
inference(resolve,[$cnf( $equal(composition(top,complement(one)),composition(top,composition(complement(one),top))) )],[refute_0_1141,refute_0_1143]) ).
cnf(refute_0_1145,plain,
composition(top,complement(one)) = composition(complement(one),top),
inference(resolve,[$cnf( $equal(converse(composition(top,composition(complement(one),top))),composition(top,composition(complement(one),top))) )],[refute_0_1002,refute_0_1144]) ).
cnf(refute_0_1146,plain,
( composition(top,complement(one)) != composition(complement(one),top)
| composition(complement(one),top) = composition(top,complement(one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(top,complement(one)))),bind(Y,$fot(composition(complement(one),top)))]]) ).
cnf(refute_0_1147,plain,
composition(complement(one),top) = composition(top,complement(one)),
inference(resolve,[$cnf( $equal(composition(top,complement(one)),composition(complement(one),top)) )],[refute_0_1145,refute_0_1146]) ).
cnf(refute_0_1148,plain,
meet(one,composition(complement(one),top)) = meet(one,composition(complement(one),top)),
introduced(tautology,[refl,[$fot(meet(one,composition(complement(one),top)))]]) ).
cnf(refute_0_1149,plain,
( composition(complement(one),top) != composition(top,complement(one))
| meet(one,composition(complement(one),top)) != meet(one,composition(complement(one),top))
| meet(one,composition(complement(one),top)) = meet(one,composition(top,complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,composition(complement(one),top)),meet(one,composition(complement(one),top))) ),[1,1],$fot(composition(top,complement(one)))]]) ).
cnf(refute_0_1150,plain,
( composition(complement(one),top) != composition(top,complement(one))
| meet(one,composition(complement(one),top)) = meet(one,composition(top,complement(one))) ),
inference(resolve,[$cnf( $equal(meet(one,composition(complement(one),top)),meet(one,composition(complement(one),top))) )],[refute_0_1148,refute_0_1149]) ).
cnf(refute_0_1151,plain,
meet(one,composition(complement(one),top)) = meet(one,composition(top,complement(one))),
inference(resolve,[$cnf( $equal(composition(complement(one),top),composition(top,complement(one))) )],[refute_0_1147,refute_0_1150]) ).
cnf(refute_0_1152,plain,
complement(meet(one,composition(complement(one),top))) = complement(meet(one,composition(complement(one),top))),
introduced(tautology,[refl,[$fot(complement(meet(one,composition(complement(one),top))))]]) ).
cnf(refute_0_1153,plain,
( complement(meet(one,composition(complement(one),top))) != complement(meet(one,composition(complement(one),top)))
| meet(one,composition(complement(one),top)) != meet(one,composition(top,complement(one)))
| complement(meet(one,composition(complement(one),top))) = complement(meet(one,composition(top,complement(one)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(one,composition(complement(one),top))),complement(meet(one,composition(complement(one),top)))) ),[1,0],$fot(meet(one,composition(top,complement(one))))]]) ).
cnf(refute_0_1154,plain,
( meet(one,composition(complement(one),top)) != meet(one,composition(top,complement(one)))
| complement(meet(one,composition(complement(one),top))) = complement(meet(one,composition(top,complement(one)))) ),
inference(resolve,[$cnf( $equal(complement(meet(one,composition(complement(one),top))),complement(meet(one,composition(complement(one),top)))) )],[refute_0_1152,refute_0_1153]) ).
cnf(refute_0_1155,plain,
complement(meet(one,composition(complement(one),top))) = complement(meet(one,composition(top,complement(one)))),
inference(resolve,[$cnf( $equal(meet(one,composition(complement(one),top)),meet(one,composition(top,complement(one)))) )],[refute_0_1151,refute_0_1154]) ).
cnf(refute_0_1156,plain,
composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) = composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))),
introduced(tautology,[refl,[$fot(composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))))]]) ).
cnf(refute_0_1157,plain,
( complement(meet(one,composition(complement(one),top))) != complement(meet(one,composition(top,complement(one))))
| composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) != composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))
| composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) = composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_22,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))),composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))) ),[1,0],$fot(complement(meet(one,composition(top,complement(one)))))]]) ).
cnf(refute_0_1158,plain,
( complement(meet(one,composition(complement(one),top))) != complement(meet(one,composition(top,complement(one))))
| composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) = composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_22,top))) ),
inference(resolve,[$cnf( $equal(composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))),composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))) )],[refute_0_1156,refute_0_1157]) ).
cnf(refute_0_1159,plain,
composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) = composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_22,top))),
inference(resolve,[$cnf( $equal(complement(meet(one,composition(complement(one),top))),complement(meet(one,composition(top,complement(one))))) )],[refute_0_1155,refute_0_1158]) ).
cnf(refute_0_1160,plain,
( composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))) != composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_22,top)))
| converse(composition(X_22,top)) != composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))
| converse(composition(X_22,top)) = composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_22,top))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_22,top)),composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))) ),[1],$fot(composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_22,top))))]]) ).
cnf(refute_0_1161,plain,
( converse(composition(X_22,top)) != composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))
| converse(composition(X_22,top)) = composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_22,top))) ),
inference(resolve,[$cnf( $equal(composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top))),composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_22,top)))) )],[refute_0_1159,refute_0_1160]) ).
cnf(refute_0_1162,plain,
converse(composition(X_22,top)) = composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_22,top))),
inference(resolve,[$cnf( $equal(converse(composition(X_22,top)),composition(complement(meet(one,composition(complement(one),top))),converse(composition(X_22,top)))) )],[refute_0_990,refute_0_1161]) ).
cnf(refute_0_1163,plain,
converse(composition(X_475,top)) = composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top))),
inference(subst,[],[refute_0_1162:[bind(X_22,$fot(X_475))]]) ).
cnf(refute_0_1164,plain,
( converse(composition(X_475,top)) != composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top)))
| composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top))) = converse(composition(X_475,top)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(X_475,top)))),bind(Y,$fot(composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top)))))]]) ).
cnf(refute_0_1165,plain,
composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top))) = converse(composition(X_475,top)),
inference(resolve,[$cnf( $equal(converse(composition(X_475,top)),composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top)))) )],[refute_0_1163,refute_0_1164]) ).
cnf(refute_0_1166,plain,
( composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top))) != converse(composition(X_475,top))
| join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top)))))) != complement(converse(composition(X_475,top)))
| join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) = complement(converse(composition(X_475,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top)))))),complement(converse(composition(X_475,top)))) ),[0,1,1,0],$fot(converse(composition(X_475,top)))]]) ).
cnf(refute_0_1167,plain,
( join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top)))))) != complement(converse(composition(X_475,top)))
| join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) = complement(converse(composition(X_475,top))) ),
inference(resolve,[$cnf( $equal(composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top))),converse(composition(X_475,top))) )],[refute_0_1165,refute_0_1166]) ).
cnf(refute_0_1168,plain,
join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) = complement(converse(composition(X_475,top))),
inference(resolve,[$cnf( $equal(join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(composition(complement(meet(one,composition(top,complement(one)))),converse(composition(X_475,top)))))),complement(converse(composition(X_475,top)))) )],[refute_0_411,refute_0_1167]) ).
cnf(refute_0_1169,plain,
join(X_35,join(complement(X_35),complement(X_325))) = top,
inference(subst,[],[refute_0_634:[bind(X_37,$fot(complement(X_325)))]]) ).
cnf(refute_0_1170,plain,
join(complement(X_35),complement(X_325)) = complement(meet(X_35,X_325)),
inference(subst,[],[refute_0_400:[bind(A,$fot(X_35)),bind(B,$fot(X_325))]]) ).
cnf(refute_0_1171,plain,
( join(X_35,join(complement(X_35),complement(X_325))) != top
| join(complement(X_35),complement(X_325)) != complement(meet(X_35,X_325))
| join(X_35,complement(meet(X_35,X_325))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,join(complement(X_35),complement(X_325))),top) ),[0,1],$fot(complement(meet(X_35,X_325)))]]) ).
cnf(refute_0_1172,plain,
( join(X_35,join(complement(X_35),complement(X_325))) != top
| join(X_35,complement(meet(X_35,X_325))) = top ),
inference(resolve,[$cnf( $equal(join(complement(X_35),complement(X_325)),complement(meet(X_35,X_325))) )],[refute_0_1170,refute_0_1171]) ).
cnf(refute_0_1173,plain,
join(X_35,complement(meet(X_35,X_325))) = top,
inference(resolve,[$cnf( $equal(join(X_35,join(complement(X_35),complement(X_325))),top) )],[refute_0_1169,refute_0_1172]) ).
cnf(refute_0_1174,plain,
join(one,complement(meet(one,composition(top,complement(one))))) = top,
inference(subst,[],[refute_0_1173:[bind(X_325,$fot(composition(top,complement(one)))),bind(X_35,$fot(one))]]) ).
cnf(refute_0_1175,plain,
join(converse(one),complement(meet(one,composition(top,complement(one))))) = join(converse(one),complement(meet(one,composition(top,complement(one))))),
introduced(tautology,[refl,[$fot(join(converse(one),complement(meet(one,composition(top,complement(one))))))]]) ).
cnf(refute_0_1176,plain,
( converse(one) != one
| join(converse(one),complement(meet(one,composition(top,complement(one))))) != join(converse(one),complement(meet(one,composition(top,complement(one)))))
| join(converse(one),complement(meet(one,composition(top,complement(one))))) = join(one,complement(meet(one,composition(top,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(one),complement(meet(one,composition(top,complement(one))))),join(converse(one),complement(meet(one,composition(top,complement(one)))))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1177,plain,
( converse(one) != one
| join(converse(one),complement(meet(one,composition(top,complement(one))))) = join(one,complement(meet(one,composition(top,complement(one))))) ),
inference(resolve,[$cnf( $equal(join(converse(one),complement(meet(one,composition(top,complement(one))))),join(converse(one),complement(meet(one,composition(top,complement(one)))))) )],[refute_0_1175,refute_0_1176]) ).
cnf(refute_0_1178,plain,
join(converse(one),complement(meet(one,composition(top,complement(one))))) = join(one,complement(meet(one,composition(top,complement(one))))),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_44,refute_0_1177]) ).
cnf(refute_0_1179,plain,
( join(converse(one),complement(meet(one,composition(top,complement(one))))) != join(one,complement(meet(one,composition(top,complement(one)))))
| join(one,complement(meet(one,composition(top,complement(one))))) != top
| join(converse(one),complement(meet(one,composition(top,complement(one))))) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(converse(one),complement(meet(one,composition(top,complement(one))))))),bind(Y,$fot(join(one,complement(meet(one,composition(top,complement(one))))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1180,plain,
( join(one,complement(meet(one,composition(top,complement(one))))) != top
| join(converse(one),complement(meet(one,composition(top,complement(one))))) = top ),
inference(resolve,[$cnf( $equal(join(converse(one),complement(meet(one,composition(top,complement(one))))),join(one,complement(meet(one,composition(top,complement(one)))))) )],[refute_0_1178,refute_0_1179]) ).
cnf(refute_0_1181,plain,
join(converse(one),complement(meet(one,composition(top,complement(one))))) = top,
inference(resolve,[$cnf( $equal(join(one,complement(meet(one,composition(top,complement(one))))),top) )],[refute_0_1174,refute_0_1180]) ).
cnf(refute_0_1182,plain,
composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))) = composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))),
introduced(tautology,[refl,[$fot(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))]]) ).
cnf(refute_0_1183,plain,
( composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))) != composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))
| join(converse(one),complement(meet(one,composition(top,complement(one))))) != top
| composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))) = composition(complement(composition(X_475,top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))),composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1184,plain,
( join(converse(one),complement(meet(one,composition(top,complement(one))))) != top
| composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))) = composition(complement(composition(X_475,top)),top) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))),composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) )],[refute_0_1182,refute_0_1183]) ).
cnf(refute_0_1185,plain,
composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))) = composition(complement(composition(X_475,top)),top),
inference(resolve,[$cnf( $equal(join(converse(one),complement(meet(one,composition(top,complement(one))))),top) )],[refute_0_1181,refute_0_1184]) ).
cnf(refute_0_1186,plain,
converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) = converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))),
introduced(tautology,[refl,[$fot(converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))))]]) ).
cnf(refute_0_1187,plain,
( composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))) != composition(complement(composition(X_475,top)),top)
| converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) != converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))
| converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) = converse(composition(complement(composition(X_475,top)),top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))),converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))) ),[1,0],$fot(composition(complement(composition(X_475,top)),top))]]) ).
cnf(refute_0_1188,plain,
( composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))) != composition(complement(composition(X_475,top)),top)
| converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) = converse(composition(complement(composition(X_475,top)),top)) ),
inference(resolve,[$cnf( $equal(converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))),converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))) )],[refute_0_1186,refute_0_1187]) ).
cnf(refute_0_1189,plain,
converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) = converse(composition(complement(composition(X_475,top)),top)),
inference(resolve,[$cnf( $equal(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))),composition(complement(composition(X_475,top)),top)) )],[refute_0_1185,refute_0_1188]) ).
cnf(refute_0_1190,plain,
converse(composition(complement(X_208),join(converse(X_319),X_320))) = composition(join(X_319,converse(X_320)),converse(complement(X_208))),
inference(subst,[],[refute_0_861:[bind(A,$fot(X_319)),bind(X_13,$fot(X_320)),bind(X_22,$fot(complement(X_208)))]]) ).
cnf(refute_0_1191,plain,
join(X_88,complement(X_87)) = join(complement(X_87),X_88),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_88)),bind(B,$fot(complement(X_87)))]]) ).
cnf(refute_0_1192,plain,
( join(X_88,complement(X_87)) != join(complement(X_87),X_88)
| join(complement(X_87),X_88) = join(X_88,complement(X_87)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_88,complement(X_87)))),bind(Y,$fot(join(complement(X_87),X_88)))]]) ).
cnf(refute_0_1193,plain,
join(complement(X_87),X_88) = join(X_88,complement(X_87)),
inference(resolve,[$cnf( $equal(join(X_88,complement(X_87)),join(complement(X_87),X_88)) )],[refute_0_1191,refute_0_1192]) ).
cnf(refute_0_1194,plain,
( X_87 != join(meet(X_87,X_88),complement(join(complement(X_87),X_88)))
| join(complement(X_87),X_88) != join(X_88,complement(X_87))
| X_87 = join(meet(X_87,X_88),complement(join(X_88,complement(X_87)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_87,join(meet(X_87,X_88),complement(join(complement(X_87),X_88)))) ),[1,1,0],$fot(join(X_88,complement(X_87)))]]) ).
cnf(refute_0_1195,plain,
( X_87 != join(meet(X_87,X_88),complement(join(complement(X_87),X_88)))
| X_87 = join(meet(X_87,X_88),complement(join(X_88,complement(X_87)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_87),X_88),join(X_88,complement(X_87))) )],[refute_0_1193,refute_0_1194]) ).
cnf(refute_0_1196,plain,
X_87 = join(meet(X_87,X_88),complement(join(X_88,complement(X_87)))),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,X_88),complement(join(complement(X_87),X_88)))) )],[refute_0_613,refute_0_1195]) ).
cnf(refute_0_1197,plain,
complement(converse(X_208)) = join(meet(complement(converse(X_208)),converse(complement(X_208))),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))),
inference(subst,[],[refute_0_1196:[bind(X_87,$fot(complement(converse(X_208)))),bind(X_88,$fot(converse(complement(X_208))))]]) ).
cnf(refute_0_1198,plain,
converse(A) = meet(converse(A),join(converse(A),converse(B))),
inference(subst,[],[refute_0_699:[bind(X_37,$fot(converse(B))),bind(X_87,$fot(converse(A)))]]) ).
cnf(refute_0_1199,plain,
( converse(A) != meet(converse(A),join(converse(A),converse(B)))
| join(converse(A),converse(B)) != converse(join(A,B))
| converse(A) = meet(converse(A),converse(join(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(A),meet(converse(A),join(converse(A),converse(B)))) ),[1,1],$fot(converse(join(A,B)))]]) ).
cnf(refute_0_1200,plain,
( converse(A) != meet(converse(A),join(converse(A),converse(B)))
| converse(A) = meet(converse(A),converse(join(A,B))) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(B)),converse(join(A,B))) )],[refute_0_544,refute_0_1199]) ).
cnf(refute_0_1201,plain,
converse(A) = meet(converse(A),converse(join(A,B))),
inference(resolve,[$cnf( $equal(converse(A),meet(converse(A),join(converse(A),converse(B)))) )],[refute_0_1198,refute_0_1200]) ).
cnf(refute_0_1202,plain,
converse(complement(X_207)) = meet(converse(complement(X_207)),converse(join(complement(X_207),meet(X_207,converse(complement(converse(X_207))))))),
inference(subst,[],[refute_0_1201:[bind(A,$fot(complement(X_207))),bind(B,$fot(meet(X_207,converse(complement(converse(X_207))))))]]) ).
cnf(refute_0_1203,plain,
X_87 = join(meet(X_87,complement(B)),complement(join(complement(X_87),complement(B)))),
inference(subst,[],[refute_0_158:[bind(A,$fot(X_87)),bind(B,$fot(complement(B)))]]) ).
cnf(refute_0_1204,plain,
meet(X_87,B) = complement(join(complement(X_87),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_87))]]) ).
cnf(refute_0_1205,plain,
( meet(X_87,B) != complement(join(complement(X_87),complement(B)))
| complement(join(complement(X_87),complement(B))) = meet(X_87,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_87,B))),bind(Y,$fot(complement(join(complement(X_87),complement(B)))))]]) ).
cnf(refute_0_1206,plain,
complement(join(complement(X_87),complement(B))) = meet(X_87,B),
inference(resolve,[$cnf( $equal(meet(X_87,B),complement(join(complement(X_87),complement(B)))) )],[refute_0_1204,refute_0_1205]) ).
cnf(refute_0_1207,plain,
( X_87 != join(meet(X_87,complement(B)),complement(join(complement(X_87),complement(B))))
| complement(join(complement(X_87),complement(B))) != meet(X_87,B)
| X_87 = join(meet(X_87,complement(B)),meet(X_87,B)) ),
introduced(tautology,[equality,[$cnf( $equal(X_87,join(meet(X_87,complement(B)),complement(join(complement(X_87),complement(B))))) ),[1,1],$fot(meet(X_87,B))]]) ).
cnf(refute_0_1208,plain,
( X_87 != join(meet(X_87,complement(B)),complement(join(complement(X_87),complement(B))))
| X_87 = join(meet(X_87,complement(B)),meet(X_87,B)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_87),complement(B))),meet(X_87,B)) )],[refute_0_1206,refute_0_1207]) ).
cnf(refute_0_1209,plain,
X_87 = join(meet(X_87,complement(B)),meet(X_87,B)),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,complement(B)),complement(join(complement(X_87),complement(B))))) )],[refute_0_1203,refute_0_1208]) ).
cnf(refute_0_1210,plain,
join(meet(X_87,complement(B)),meet(X_87,B)) = join(meet(X_87,B),meet(X_87,complement(B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(X_87,B))),bind(B,$fot(meet(X_87,complement(B))))]]) ).
cnf(refute_0_1211,plain,
( X_87 != join(meet(X_87,complement(B)),meet(X_87,B))
| join(meet(X_87,complement(B)),meet(X_87,B)) != join(meet(X_87,B),meet(X_87,complement(B)))
| X_87 = join(meet(X_87,B),meet(X_87,complement(B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_87,join(meet(X_87,B),meet(X_87,complement(B)))) ),[0],$fot(join(meet(X_87,complement(B)),meet(X_87,B)))]]) ).
cnf(refute_0_1212,plain,
( X_87 != join(meet(X_87,complement(B)),meet(X_87,B))
| X_87 = join(meet(X_87,B),meet(X_87,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_87,complement(B)),meet(X_87,B)),join(meet(X_87,B),meet(X_87,complement(B)))) )],[refute_0_1210,refute_0_1211]) ).
cnf(refute_0_1213,plain,
X_87 = join(meet(X_87,B),meet(X_87,complement(B))),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,complement(B)),meet(X_87,B))) )],[refute_0_1209,refute_0_1212]) ).
cnf(refute_0_1214,plain,
X_104 = join(meet(X_104,X_103),meet(X_104,complement(X_103))),
inference(subst,[],[refute_0_1213:[bind(B,$fot(X_103)),bind(X_87,$fot(X_104))]]) ).
cnf(refute_0_1215,plain,
meet(complement(X_103),X_104) = meet(X_104,complement(X_103)),
inference(subst,[],[refute_0_623:[bind(X_6,$fot(complement(X_103))),bind(X_7,$fot(X_104))]]) ).
cnf(refute_0_1216,plain,
( meet(complement(X_103),X_104) != meet(X_104,complement(X_103))
| meet(X_104,complement(X_103)) = meet(complement(X_103),X_104) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_103),X_104))),bind(Y,$fot(meet(X_104,complement(X_103))))]]) ).
cnf(refute_0_1217,plain,
meet(X_104,complement(X_103)) = meet(complement(X_103),X_104),
inference(resolve,[$cnf( $equal(meet(complement(X_103),X_104),meet(X_104,complement(X_103))) )],[refute_0_1215,refute_0_1216]) ).
cnf(refute_0_1218,plain,
( X_104 != join(meet(X_104,X_103),meet(X_104,complement(X_103)))
| meet(X_104,complement(X_103)) != meet(complement(X_103),X_104)
| X_104 = join(meet(X_104,X_103),meet(complement(X_103),X_104)) ),
introduced(tautology,[equality,[$cnf( $equal(X_104,join(meet(X_104,X_103),meet(X_104,complement(X_103)))) ),[1,1],$fot(meet(complement(X_103),X_104))]]) ).
cnf(refute_0_1219,plain,
( X_104 != join(meet(X_104,X_103),meet(X_104,complement(X_103)))
| X_104 = join(meet(X_104,X_103),meet(complement(X_103),X_104)) ),
inference(resolve,[$cnf( $equal(meet(X_104,complement(X_103)),meet(complement(X_103),X_104)) )],[refute_0_1217,refute_0_1218]) ).
cnf(refute_0_1220,plain,
X_104 = join(meet(X_104,X_103),meet(complement(X_103),X_104)),
inference(resolve,[$cnf( $equal(X_104,join(meet(X_104,X_103),meet(X_104,complement(X_103)))) )],[refute_0_1214,refute_0_1219]) ).
cnf(refute_0_1221,plain,
converse(complement(converse(complement(complement(X_140))))) = join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),meet(complement(X_140),converse(complement(converse(complement(complement(X_140))))))),
inference(subst,[],[refute_0_1220:[bind(X_103,$fot(X_140)),bind(X_104,$fot(converse(complement(converse(complement(complement(X_140)))))))]]) ).
cnf(refute_0_1222,plain,
X_87 = join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(join(complement(X_87),converse(complement(converse(complement(X_87))))))),
inference(subst,[],[refute_0_158:[bind(A,$fot(X_87)),bind(B,$fot(converse(complement(converse(complement(X_87))))))]]) ).
cnf(refute_0_1223,plain,
( converse(top) != join(X_16,converse(complement(converse(X_16))))
| converse(top) != top
| top = join(X_16,converse(complement(converse(X_16)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_16,converse(complement(converse(X_16))))) ),[0],$fot(top)]]) ).
cnf(refute_0_1224,plain,
( converse(top) != join(X_16,converse(complement(converse(X_16))))
| top = join(X_16,converse(complement(converse(X_16)))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_601,refute_0_1223]) ).
cnf(refute_0_1225,plain,
top = join(X_16,converse(complement(converse(X_16)))),
inference(resolve,[$cnf( $equal(converse(top),join(X_16,converse(complement(converse(X_16))))) )],[refute_0_427,refute_0_1224]) ).
cnf(refute_0_1226,plain,
top = join(complement(X_87),converse(complement(converse(complement(X_87))))),
inference(subst,[],[refute_0_1225:[bind(X_16,$fot(complement(X_87)))]]) ).
cnf(refute_0_1227,plain,
( top != join(complement(X_87),converse(complement(converse(complement(X_87)))))
| join(complement(X_87),converse(complement(converse(complement(X_87))))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_87),converse(complement(converse(complement(X_87)))))))]]) ).
cnf(refute_0_1228,plain,
join(complement(X_87),converse(complement(converse(complement(X_87))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_87),converse(complement(converse(complement(X_87)))))) )],[refute_0_1226,refute_0_1227]) ).
cnf(refute_0_1229,plain,
( X_87 != join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(join(complement(X_87),converse(complement(converse(complement(X_87)))))))
| join(complement(X_87),converse(complement(converse(complement(X_87))))) != top
| X_87 = join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_87,join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(join(complement(X_87),converse(complement(converse(complement(X_87)))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_1230,plain,
( X_87 != join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(join(complement(X_87),converse(complement(converse(complement(X_87)))))))
| X_87 = join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_87),converse(complement(converse(complement(X_87))))),top) )],[refute_0_1228,refute_0_1229]) ).
cnf(refute_0_1231,plain,
X_87 = join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(join(complement(X_87),converse(complement(converse(complement(X_87)))))))) )],[refute_0_1222,refute_0_1230]) ).
cnf(refute_0_1232,plain,
join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))) = join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))))]]) ).
cnf(refute_0_1233,plain,
( complement(top) != zero
| join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))) != join(complement(top),meet(X_87,converse(complement(converse(complement(X_87))))))
| join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))) = join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))),join(complement(top),meet(X_87,converse(complement(converse(complement(X_87))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1234,plain,
( complement(top) != zero
| join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))) = join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))),join(complement(top),meet(X_87,converse(complement(converse(complement(X_87))))))) )],[refute_0_1232,refute_0_1233]) ).
cnf(refute_0_1235,plain,
join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))) = join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_1234]) ).
cnf(refute_0_1236,plain,
join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)) = join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_87,converse(complement(converse(complement(X_87)))))))]]) ).
cnf(refute_0_1237,plain,
( join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))) != join(zero,meet(X_87,converse(complement(converse(complement(X_87))))))
| join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)) != join(complement(top),meet(X_87,converse(complement(converse(complement(X_87))))))
| join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)) = join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))))),bind(Z,$fot(join(zero,meet(X_87,converse(complement(converse(complement(X_87))))))))]]) ).
cnf(refute_0_1238,plain,
( join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))) != join(zero,meet(X_87,converse(complement(converse(complement(X_87))))))
| join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)) = join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)),join(complement(top),meet(X_87,converse(complement(converse(complement(X_87))))))) )],[refute_0_1236,refute_0_1237]) ).
cnf(refute_0_1239,plain,
join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)) = join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_87,converse(complement(converse(complement(X_87)))))),join(zero,meet(X_87,converse(complement(converse(complement(X_87))))))) )],[refute_0_1235,refute_0_1238]) ).
cnf(refute_0_1240,plain,
( X_87 != join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top))
| join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)) != join(zero,meet(X_87,converse(complement(converse(complement(X_87))))))
| X_87 = join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_87,join(zero,meet(X_87,converse(complement(converse(complement(X_87))))))) ),[0],$fot(join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)))]]) ).
cnf(refute_0_1241,plain,
( X_87 != join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top))
| X_87 = join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top)),join(zero,meet(X_87,converse(complement(converse(complement(X_87))))))) )],[refute_0_1239,refute_0_1240]) ).
cnf(refute_0_1242,plain,
X_87 = join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))),
inference(resolve,[$cnf( $equal(X_87,join(meet(X_87,converse(complement(converse(complement(X_87))))),complement(top))) )],[refute_0_1231,refute_0_1241]) ).
cnf(refute_0_1243,plain,
join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))) = meet(X_87,converse(complement(converse(complement(X_87))))),
inference(subst,[],[refute_0_692:[bind(X_87,$fot(meet(X_87,converse(complement(converse(complement(X_87)))))))]]) ).
cnf(refute_0_1244,plain,
( X_87 != join(zero,meet(X_87,converse(complement(converse(complement(X_87))))))
| join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))) != meet(X_87,converse(complement(converse(complement(X_87)))))
| X_87 = meet(X_87,converse(complement(converse(complement(X_87))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_87,meet(X_87,converse(complement(converse(complement(X_87)))))) ),[0],$fot(join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))))]]) ).
cnf(refute_0_1245,plain,
( X_87 != join(zero,meet(X_87,converse(complement(converse(complement(X_87))))))
| X_87 = meet(X_87,converse(complement(converse(complement(X_87))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_87,converse(complement(converse(complement(X_87)))))),meet(X_87,converse(complement(converse(complement(X_87)))))) )],[refute_0_1243,refute_0_1244]) ).
cnf(refute_0_1246,plain,
X_87 = meet(X_87,converse(complement(converse(complement(X_87))))),
inference(resolve,[$cnf( $equal(X_87,join(zero,meet(X_87,converse(complement(converse(complement(X_87))))))) )],[refute_0_1242,refute_0_1245]) ).
cnf(refute_0_1247,plain,
complement(X_140) = meet(complement(X_140),converse(complement(converse(complement(complement(X_140)))))),
inference(subst,[],[refute_0_1246:[bind(X_87,$fot(complement(X_140)))]]) ).
cnf(refute_0_1248,plain,
( complement(X_140) != meet(complement(X_140),converse(complement(converse(complement(complement(X_140))))))
| meet(complement(X_140),converse(complement(converse(complement(complement(X_140)))))) = complement(X_140) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_140))),bind(Y,$fot(meet(complement(X_140),converse(complement(converse(complement(complement(X_140))))))))]]) ).
cnf(refute_0_1249,plain,
meet(complement(X_140),converse(complement(converse(complement(complement(X_140)))))) = complement(X_140),
inference(resolve,[$cnf( $equal(complement(X_140),meet(complement(X_140),converse(complement(converse(complement(complement(X_140))))))) )],[refute_0_1247,refute_0_1248]) ).
cnf(refute_0_1250,plain,
( converse(complement(converse(complement(complement(X_140))))) != join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),meet(complement(X_140),converse(complement(converse(complement(complement(X_140)))))))
| meet(complement(X_140),converse(complement(converse(complement(complement(X_140)))))) != complement(X_140)
| converse(complement(converse(complement(complement(X_140))))) = join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_140))))),join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),meet(complement(X_140),converse(complement(converse(complement(complement(X_140)))))))) ),[1,1],$fot(complement(X_140))]]) ).
cnf(refute_0_1251,plain,
( converse(complement(converse(complement(complement(X_140))))) != join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),meet(complement(X_140),converse(complement(converse(complement(complement(X_140)))))))
| converse(complement(converse(complement(complement(X_140))))) = join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)) ),
inference(resolve,[$cnf( $equal(meet(complement(X_140),converse(complement(converse(complement(complement(X_140)))))),complement(X_140)) )],[refute_0_1249,refute_0_1250]) ).
cnf(refute_0_1252,plain,
converse(complement(converse(complement(complement(X_140))))) = join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_140))))),join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),meet(complement(X_140),converse(complement(converse(complement(complement(X_140)))))))) )],[refute_0_1221,refute_0_1251]) ).
cnf(refute_0_1253,plain,
complement(complement(X_140)) = X_140,
inference(subst,[],[refute_0_383:[bind(X_87,$fot(X_140))]]) ).
cnf(refute_0_1254,plain,
converse(complement(complement(X_140))) = converse(complement(complement(X_140))),
introduced(tautology,[refl,[$fot(converse(complement(complement(X_140))))]]) ).
cnf(refute_0_1255,plain,
( complement(complement(X_140)) != X_140
| converse(complement(complement(X_140))) != converse(complement(complement(X_140)))
| converse(complement(complement(X_140))) = converse(X_140) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(complement(X_140))),converse(complement(complement(X_140)))) ),[1,0],$fot(X_140)]]) ).
cnf(refute_0_1256,plain,
( complement(complement(X_140)) != X_140
| converse(complement(complement(X_140))) = converse(X_140) ),
inference(resolve,[$cnf( $equal(converse(complement(complement(X_140))),converse(complement(complement(X_140)))) )],[refute_0_1254,refute_0_1255]) ).
cnf(refute_0_1257,plain,
converse(complement(complement(X_140))) = converse(X_140),
inference(resolve,[$cnf( $equal(complement(complement(X_140)),X_140) )],[refute_0_1253,refute_0_1256]) ).
cnf(refute_0_1258,plain,
complement(converse(complement(complement(X_140)))) = complement(converse(complement(complement(X_140)))),
introduced(tautology,[refl,[$fot(complement(converse(complement(complement(X_140)))))]]) ).
cnf(refute_0_1259,plain,
( complement(converse(complement(complement(X_140)))) != complement(converse(complement(complement(X_140))))
| converse(complement(complement(X_140))) != converse(X_140)
| complement(converse(complement(complement(X_140)))) = complement(converse(X_140)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(complement(complement(X_140)))),complement(converse(complement(complement(X_140))))) ),[1,0],$fot(converse(X_140))]]) ).
cnf(refute_0_1260,plain,
( converse(complement(complement(X_140))) != converse(X_140)
| complement(converse(complement(complement(X_140)))) = complement(converse(X_140)) ),
inference(resolve,[$cnf( $equal(complement(converse(complement(complement(X_140)))),complement(converse(complement(complement(X_140))))) )],[refute_0_1258,refute_0_1259]) ).
cnf(refute_0_1261,plain,
complement(converse(complement(complement(X_140)))) = complement(converse(X_140)),
inference(resolve,[$cnf( $equal(converse(complement(complement(X_140))),converse(X_140)) )],[refute_0_1257,refute_0_1260]) ).
cnf(refute_0_1262,plain,
converse(complement(converse(complement(complement(X_140))))) = converse(complement(converse(complement(complement(X_140))))),
introduced(tautology,[refl,[$fot(converse(complement(converse(complement(complement(X_140))))))]]) ).
cnf(refute_0_1263,plain,
( complement(converse(complement(complement(X_140)))) != complement(converse(X_140))
| converse(complement(converse(complement(complement(X_140))))) != converse(complement(converse(complement(complement(X_140)))))
| converse(complement(converse(complement(complement(X_140))))) = converse(complement(converse(X_140))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_140))))),converse(complement(converse(complement(complement(X_140)))))) ),[1,0],$fot(complement(converse(X_140)))]]) ).
cnf(refute_0_1264,plain,
( complement(converse(complement(complement(X_140)))) != complement(converse(X_140))
| converse(complement(converse(complement(complement(X_140))))) = converse(complement(converse(X_140))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_140))))),converse(complement(converse(complement(complement(X_140)))))) )],[refute_0_1262,refute_0_1263]) ).
cnf(refute_0_1265,plain,
converse(complement(converse(complement(complement(X_140))))) = converse(complement(converse(X_140))),
inference(resolve,[$cnf( $equal(complement(converse(complement(complement(X_140)))),complement(converse(X_140))) )],[refute_0_1261,refute_0_1264]) ).
cnf(refute_0_1266,plain,
( converse(complement(converse(complement(complement(X_140))))) != converse(complement(converse(X_140)))
| converse(complement(converse(complement(complement(X_140))))) != join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140))
| converse(complement(converse(X_140))) = join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_140))))),join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140))) ),[0],$fot(converse(complement(converse(X_140))))]]) ).
cnf(refute_0_1267,plain,
( converse(complement(converse(complement(complement(X_140))))) != join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140))
| converse(complement(converse(X_140))) = join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_140))))),converse(complement(converse(X_140)))) )],[refute_0_1265,refute_0_1266]) ).
cnf(refute_0_1268,plain,
meet(X_140,converse(complement(converse(complement(complement(X_140)))))) = meet(X_140,converse(complement(converse(complement(complement(X_140)))))),
introduced(tautology,[refl,[$fot(meet(X_140,converse(complement(converse(complement(complement(X_140)))))))]]) ).
cnf(refute_0_1269,plain,
( converse(complement(converse(complement(complement(X_140))))) != converse(complement(converse(X_140)))
| meet(X_140,converse(complement(converse(complement(complement(X_140)))))) != meet(X_140,converse(complement(converse(complement(complement(X_140))))))
| meet(X_140,converse(complement(converse(complement(complement(X_140)))))) = meet(X_140,converse(complement(converse(X_140)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_140,converse(complement(converse(complement(complement(X_140)))))),meet(X_140,converse(complement(converse(complement(complement(X_140))))))) ),[1,1],$fot(converse(complement(converse(X_140))))]]) ).
cnf(refute_0_1270,plain,
( converse(complement(converse(complement(complement(X_140))))) != converse(complement(converse(X_140)))
| meet(X_140,converse(complement(converse(complement(complement(X_140)))))) = meet(X_140,converse(complement(converse(X_140)))) ),
inference(resolve,[$cnf( $equal(meet(X_140,converse(complement(converse(complement(complement(X_140)))))),meet(X_140,converse(complement(converse(complement(complement(X_140))))))) )],[refute_0_1268,refute_0_1269]) ).
cnf(refute_0_1271,plain,
meet(X_140,converse(complement(converse(complement(complement(X_140)))))) = meet(X_140,converse(complement(converse(X_140)))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_140))))),converse(complement(converse(X_140)))) )],[refute_0_1265,refute_0_1270]) ).
cnf(refute_0_1272,plain,
( meet(X_6,X_7) != meet(X_7,X_6)
| meet(X_7,X_6) = meet(X_6,X_7) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_6,X_7))),bind(Y,$fot(meet(X_7,X_6)))]]) ).
cnf(refute_0_1273,plain,
meet(X_7,X_6) = meet(X_6,X_7),
inference(resolve,[$cnf( $equal(meet(X_6,X_7),meet(X_7,X_6)) )],[refute_0_623,refute_0_1272]) ).
cnf(refute_0_1274,plain,
meet(converse(complement(converse(complement(complement(X_140))))),X_140) = meet(X_140,converse(complement(converse(complement(complement(X_140)))))),
inference(subst,[],[refute_0_1273:[bind(X_6,$fot(X_140)),bind(X_7,$fot(converse(complement(converse(complement(complement(X_140)))))))]]) ).
cnf(refute_0_1275,plain,
( meet(X_140,converse(complement(converse(complement(complement(X_140)))))) != meet(X_140,converse(complement(converse(X_140))))
| meet(converse(complement(converse(complement(complement(X_140))))),X_140) != meet(X_140,converse(complement(converse(complement(complement(X_140))))))
| meet(converse(complement(converse(complement(complement(X_140))))),X_140) = meet(X_140,converse(complement(converse(X_140)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(converse(complement(converse(complement(complement(X_140))))),X_140))),bind(Y,$fot(meet(X_140,converse(complement(converse(complement(complement(X_140)))))))),bind(Z,$fot(meet(X_140,converse(complement(converse(X_140))))))]]) ).
cnf(refute_0_1276,plain,
( meet(X_140,converse(complement(converse(complement(complement(X_140)))))) != meet(X_140,converse(complement(converse(X_140))))
| meet(converse(complement(converse(complement(complement(X_140))))),X_140) = meet(X_140,converse(complement(converse(X_140)))) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(complement(complement(X_140))))),X_140),meet(X_140,converse(complement(converse(complement(complement(X_140))))))) )],[refute_0_1274,refute_0_1275]) ).
cnf(refute_0_1277,plain,
meet(converse(complement(converse(complement(complement(X_140))))),X_140) = meet(X_140,converse(complement(converse(X_140)))),
inference(resolve,[$cnf( $equal(meet(X_140,converse(complement(converse(complement(complement(X_140)))))),meet(X_140,converse(complement(converse(X_140))))) )],[refute_0_1271,refute_0_1276]) ).
cnf(refute_0_1278,plain,
join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)) = join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)),
introduced(tautology,[refl,[$fot(join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)))]]) ).
cnf(refute_0_1279,plain,
( join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)) != join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140))
| meet(converse(complement(converse(complement(complement(X_140))))),X_140) != meet(X_140,converse(complement(converse(X_140))))
| join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)) = join(complement(X_140),meet(X_140,converse(complement(converse(X_140))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)),join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140))) ),[1,1],$fot(meet(X_140,converse(complement(converse(X_140)))))]]) ).
cnf(refute_0_1280,plain,
( meet(converse(complement(converse(complement(complement(X_140))))),X_140) != meet(X_140,converse(complement(converse(X_140))))
| join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)) = join(complement(X_140),meet(X_140,converse(complement(converse(X_140))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)),join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140))) )],[refute_0_1278,refute_0_1279]) ).
cnf(refute_0_1281,plain,
join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)) = join(complement(X_140),meet(X_140,converse(complement(converse(X_140))))),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(complement(complement(X_140))))),X_140),meet(X_140,converse(complement(converse(X_140))))) )],[refute_0_1277,refute_0_1280]) ).
cnf(refute_0_1282,plain,
join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)) = join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_140))),bind(B,$fot(meet(converse(complement(converse(complement(complement(X_140))))),X_140)))]]) ).
cnf(refute_0_1283,plain,
( join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)) != join(complement(X_140),meet(X_140,converse(complement(converse(X_140)))))
| join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)) != join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140))
| join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)) = join(complement(X_140),meet(X_140,converse(complement(converse(X_140))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)))),bind(Y,$fot(join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)))),bind(Z,$fot(join(complement(X_140),meet(X_140,converse(complement(converse(X_140)))))))]]) ).
cnf(refute_0_1284,plain,
( join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)) != join(complement(X_140),meet(X_140,converse(complement(converse(X_140)))))
| join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)) = join(complement(X_140),meet(X_140,converse(complement(converse(X_140))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)),join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140))) )],[refute_0_1282,refute_0_1283]) ).
cnf(refute_0_1285,plain,
join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)) = join(complement(X_140),meet(X_140,converse(complement(converse(X_140))))),
inference(resolve,[$cnf( $equal(join(complement(X_140),meet(converse(complement(converse(complement(complement(X_140))))),X_140)),join(complement(X_140),meet(X_140,converse(complement(converse(X_140)))))) )],[refute_0_1281,refute_0_1284]) ).
cnf(refute_0_1286,plain,
( converse(complement(converse(X_140))) != join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140))
| join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)) != join(complement(X_140),meet(X_140,converse(complement(converse(X_140)))))
| converse(complement(converse(X_140))) = join(complement(X_140),meet(X_140,converse(complement(converse(X_140))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(converse(X_140))),join(complement(X_140),meet(X_140,converse(complement(converse(X_140)))))) ),[0],$fot(join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)))]]) ).
cnf(refute_0_1287,plain,
( converse(complement(converse(X_140))) != join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140))
| converse(complement(converse(X_140))) = join(complement(X_140),meet(X_140,converse(complement(converse(X_140))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140)),join(complement(X_140),meet(X_140,converse(complement(converse(X_140)))))) )],[refute_0_1285,refute_0_1286]) ).
cnf(refute_0_1288,plain,
( converse(complement(converse(complement(complement(X_140))))) != join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140))
| converse(complement(converse(X_140))) = join(complement(X_140),meet(X_140,converse(complement(converse(X_140))))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_140))),join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140))) )],[refute_0_1267,refute_0_1287]) ).
cnf(refute_0_1289,plain,
converse(complement(converse(X_140))) = join(complement(X_140),meet(X_140,converse(complement(converse(X_140))))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_140))))),join(meet(converse(complement(converse(complement(complement(X_140))))),X_140),complement(X_140))) )],[refute_0_1252,refute_0_1288]) ).
cnf(refute_0_1290,plain,
converse(complement(converse(X_207))) = join(complement(X_207),meet(X_207,converse(complement(converse(X_207))))),
inference(subst,[],[refute_0_1289:[bind(X_140,$fot(X_207))]]) ).
cnf(refute_0_1291,plain,
( converse(complement(converse(X_207))) != join(complement(X_207),meet(X_207,converse(complement(converse(X_207)))))
| join(complement(X_207),meet(X_207,converse(complement(converse(X_207))))) = converse(complement(converse(X_207))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(complement(converse(X_207))))),bind(Y,$fot(join(complement(X_207),meet(X_207,converse(complement(converse(X_207)))))))]]) ).
cnf(refute_0_1292,plain,
join(complement(X_207),meet(X_207,converse(complement(converse(X_207))))) = converse(complement(converse(X_207))),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_207))),join(complement(X_207),meet(X_207,converse(complement(converse(X_207)))))) )],[refute_0_1290,refute_0_1291]) ).
cnf(refute_0_1293,plain,
( converse(complement(X_207)) != meet(converse(complement(X_207)),converse(join(complement(X_207),meet(X_207,converse(complement(converse(X_207)))))))
| join(complement(X_207),meet(X_207,converse(complement(converse(X_207))))) != converse(complement(converse(X_207)))
| converse(complement(X_207)) = meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(X_207)),meet(converse(complement(X_207)),converse(join(complement(X_207),meet(X_207,converse(complement(converse(X_207)))))))) ),[1,1,0],$fot(converse(complement(converse(X_207))))]]) ).
cnf(refute_0_1294,plain,
( converse(complement(X_207)) != meet(converse(complement(X_207)),converse(join(complement(X_207),meet(X_207,converse(complement(converse(X_207)))))))
| converse(complement(X_207)) = meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_207),meet(X_207,converse(complement(converse(X_207))))),converse(complement(converse(X_207)))) )],[refute_0_1292,refute_0_1293]) ).
cnf(refute_0_1295,plain,
converse(complement(X_207)) = meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))),
inference(resolve,[$cnf( $equal(converse(complement(X_207)),meet(converse(complement(X_207)),converse(join(complement(X_207),meet(X_207,converse(complement(converse(X_207)))))))) )],[refute_0_1202,refute_0_1294]) ).
cnf(refute_0_1296,plain,
meet(converse(complement(X_207)),complement(converse(X_207))) = meet(complement(converse(X_207)),converse(complement(X_207))),
inference(subst,[],[refute_0_1273:[bind(X_6,$fot(complement(converse(X_207)))),bind(X_7,$fot(converse(complement(X_207))))]]) ).
cnf(refute_0_1297,plain,
converse(converse(complement(converse(X_207)))) = complement(converse(X_207)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(converse(X_207))))]]) ).
cnf(refute_0_1298,plain,
meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) = meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))),
introduced(tautology,[refl,[$fot(meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))))]]) ).
cnf(refute_0_1299,plain,
( converse(converse(complement(converse(X_207)))) != complement(converse(X_207))
| meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) != meet(converse(complement(X_207)),converse(converse(complement(converse(X_207)))))
| meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) = meet(converse(complement(X_207)),complement(converse(X_207))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))),meet(converse(complement(X_207)),converse(converse(complement(converse(X_207)))))) ),[1,1],$fot(complement(converse(X_207)))]]) ).
cnf(refute_0_1300,plain,
( converse(converse(complement(converse(X_207)))) != complement(converse(X_207))
| meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) = meet(converse(complement(X_207)),complement(converse(X_207))) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))),meet(converse(complement(X_207)),converse(converse(complement(converse(X_207)))))) )],[refute_0_1298,refute_0_1299]) ).
cnf(refute_0_1301,plain,
meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) = meet(converse(complement(X_207)),complement(converse(X_207))),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(X_207)))),complement(converse(X_207))) )],[refute_0_1297,refute_0_1300]) ).
cnf(refute_0_1302,plain,
( meet(converse(complement(X_207)),complement(converse(X_207))) != meet(complement(converse(X_207)),converse(complement(X_207)))
| meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) != meet(converse(complement(X_207)),complement(converse(X_207)))
| meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) = meet(complement(converse(X_207)),converse(complement(X_207))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))))),bind(Y,$fot(meet(converse(complement(X_207)),complement(converse(X_207))))),bind(Z,$fot(meet(complement(converse(X_207)),converse(complement(X_207)))))]]) ).
cnf(refute_0_1303,plain,
( meet(converse(complement(X_207)),complement(converse(X_207))) != meet(complement(converse(X_207)),converse(complement(X_207)))
| meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) = meet(complement(converse(X_207)),converse(complement(X_207))) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))),meet(converse(complement(X_207)),complement(converse(X_207)))) )],[refute_0_1301,refute_0_1302]) ).
cnf(refute_0_1304,plain,
meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) = meet(complement(converse(X_207)),converse(complement(X_207))),
inference(resolve,[$cnf( $equal(meet(converse(complement(X_207)),complement(converse(X_207))),meet(complement(converse(X_207)),converse(complement(X_207)))) )],[refute_0_1296,refute_0_1303]) ).
cnf(refute_0_1305,plain,
( converse(complement(X_207)) != meet(converse(complement(X_207)),converse(converse(complement(converse(X_207)))))
| meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))) != meet(complement(converse(X_207)),converse(complement(X_207)))
| converse(complement(X_207)) = meet(complement(converse(X_207)),converse(complement(X_207))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(X_207)),meet(complement(converse(X_207)),converse(complement(X_207)))) ),[0],$fot(meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))))]]) ).
cnf(refute_0_1306,plain,
( converse(complement(X_207)) != meet(converse(complement(X_207)),converse(converse(complement(converse(X_207)))))
| converse(complement(X_207)) = meet(complement(converse(X_207)),converse(complement(X_207))) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(X_207)),converse(converse(complement(converse(X_207))))),meet(complement(converse(X_207)),converse(complement(X_207)))) )],[refute_0_1304,refute_0_1305]) ).
cnf(refute_0_1307,plain,
converse(complement(X_207)) = meet(complement(converse(X_207)),converse(complement(X_207))),
inference(resolve,[$cnf( $equal(converse(complement(X_207)),meet(converse(complement(X_207)),converse(converse(complement(converse(X_207)))))) )],[refute_0_1295,refute_0_1306]) ).
cnf(refute_0_1308,plain,
converse(complement(X_208)) = meet(complement(converse(X_208)),converse(complement(X_208))),
inference(subst,[],[refute_0_1307:[bind(X_207,$fot(X_208))]]) ).
cnf(refute_0_1309,plain,
( converse(complement(X_208)) != meet(complement(converse(X_208)),converse(complement(X_208)))
| meet(complement(converse(X_208)),converse(complement(X_208))) = converse(complement(X_208)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(complement(X_208)))),bind(Y,$fot(meet(complement(converse(X_208)),converse(complement(X_208)))))]]) ).
cnf(refute_0_1310,plain,
meet(complement(converse(X_208)),converse(complement(X_208))) = converse(complement(X_208)),
inference(resolve,[$cnf( $equal(converse(complement(X_208)),meet(complement(converse(X_208)),converse(complement(X_208)))) )],[refute_0_1308,refute_0_1309]) ).
cnf(refute_0_1311,plain,
( complement(converse(X_208)) != join(meet(complement(converse(X_208)),converse(complement(X_208))),complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))
| meet(complement(converse(X_208)),converse(complement(X_208))) != converse(complement(X_208))
| complement(converse(X_208)) = join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(X_208)),join(meet(complement(converse(X_208)),converse(complement(X_208))),complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))) ),[1,0],$fot(converse(complement(X_208)))]]) ).
cnf(refute_0_1312,plain,
( complement(converse(X_208)) != join(meet(complement(converse(X_208)),converse(complement(X_208))),complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))
| complement(converse(X_208)) = join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) ),
inference(resolve,[$cnf( $equal(meet(complement(converse(X_208)),converse(complement(X_208))),converse(complement(X_208))) )],[refute_0_1310,refute_0_1311]) ).
cnf(refute_0_1313,plain,
complement(converse(X_208)) = join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))),
inference(resolve,[$cnf( $equal(complement(converse(X_208)),join(meet(complement(converse(X_208)),converse(complement(X_208))),complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))) )],[refute_0_1197,refute_0_1312]) ).
cnf(refute_0_1314,plain,
( A != join(A,zero)
| join(A,zero) = A ),
inference(subst,[],[refute_0_2:[bind(X,$fot(A)),bind(Y,$fot(join(A,zero)))]]) ).
cnf(refute_0_1315,plain,
join(A,zero) = A,
inference(resolve,[$cnf( $equal(A,join(A,zero)) )],[refute_0_1084,refute_0_1314]) ).
cnf(refute_0_1316,plain,
join(converse(complement(X_208)),zero) = converse(complement(X_208)),
inference(subst,[],[refute_0_1315:[bind(A,$fot(converse(complement(X_208))))]]) ).
cnf(refute_0_1317,plain,
join(X_208,complement(X_208)) = top,
inference(subst,[],[refute_0_265:[bind(A,$fot(X_208))]]) ).
cnf(refute_0_1318,plain,
converse(join(X_208,complement(X_208))) = converse(join(X_208,complement(X_208))),
introduced(tautology,[refl,[$fot(converse(join(X_208,complement(X_208))))]]) ).
cnf(refute_0_1319,plain,
( converse(join(X_208,complement(X_208))) != converse(join(X_208,complement(X_208)))
| join(X_208,complement(X_208)) != top
| converse(join(X_208,complement(X_208))) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_208,complement(X_208))),converse(join(X_208,complement(X_208)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1320,plain,
( join(X_208,complement(X_208)) != top
| converse(join(X_208,complement(X_208))) = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(X_208,complement(X_208))),converse(join(X_208,complement(X_208)))) )],[refute_0_1318,refute_0_1319]) ).
cnf(refute_0_1321,plain,
converse(join(X_208,complement(X_208))) = converse(top),
inference(resolve,[$cnf( $equal(join(X_208,complement(X_208)),top) )],[refute_0_1317,refute_0_1320]) ).
cnf(refute_0_1322,plain,
( converse(join(X_208,complement(X_208))) != converse(top)
| converse(top) != top
| converse(join(X_208,complement(X_208))) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(X_208,complement(X_208))))),bind(Y,$fot(converse(top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1323,plain,
( converse(top) != top
| converse(join(X_208,complement(X_208))) = top ),
inference(resolve,[$cnf( $equal(converse(join(X_208,complement(X_208))),converse(top)) )],[refute_0_1321,refute_0_1322]) ).
cnf(refute_0_1324,plain,
converse(join(X_208,complement(X_208))) = top,
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_601,refute_0_1323]) ).
cnf(refute_0_1325,plain,
converse(join(X_51,X_51)) = converse(join(X_51,X_51)),
inference(subst,[],[refute_0_548:[bind(X_12,$fot(X_51)),bind(X_13,$fot(X_51))]]) ).
cnf(refute_0_1326,plain,
join(X_51,X_51) = composition(X_51,join(one,one)),
inference(subst,[],[refute_0_186:[bind(A,$fot(X_51))]]) ).
cnf(refute_0_1327,plain,
( converse(join(X_51,X_51)) != converse(join(X_51,X_51))
| join(X_51,X_51) != composition(X_51,join(one,one))
| converse(composition(X_51,join(one,one))) = converse(join(X_51,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_51,X_51)),converse(join(X_51,X_51))) ),[0,0],$fot(composition(X_51,join(one,one)))]]) ).
cnf(refute_0_1328,plain,
( converse(join(X_51,X_51)) != converse(join(X_51,X_51))
| converse(composition(X_51,join(one,one))) = converse(join(X_51,X_51)) ),
inference(resolve,[$cnf( $equal(join(X_51,X_51),composition(X_51,join(one,one))) )],[refute_0_1326,refute_0_1327]) ).
cnf(refute_0_1329,plain,
converse(composition(X_51,join(one,one))) = converse(join(X_51,X_51)),
inference(resolve,[$cnf( $equal(converse(join(X_51,X_51)),converse(join(X_51,X_51))) )],[refute_0_1325,refute_0_1328]) ).
cnf(refute_0_1330,plain,
converse(composition(join(X_85,X_84),join(one,one))) = converse(join(join(X_85,X_84),join(X_85,X_84))),
inference(subst,[],[refute_0_1329:[bind(X_51,$fot(join(X_85,X_84)))]]) ).
cnf(refute_0_1331,plain,
composition(join(X_85,X_84),join(one,one)) = composition(join(X_84,X_85),join(one,one)),
inference(subst,[],[refute_0_1044:[bind(X_32,$fot(X_84)),bind(X_33,$fot(X_85)),bind(X_34,$fot(join(one,one)))]]) ).
cnf(refute_0_1332,plain,
( composition(join(X_85,X_84),join(one,one)) != composition(join(X_84,X_85),join(one,one))
| converse(composition(join(X_85,X_84),join(one,one))) != converse(join(join(X_85,X_84),join(X_85,X_84)))
| converse(composition(join(X_84,X_85),join(one,one))) = converse(join(join(X_85,X_84),join(X_85,X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(X_85,X_84),join(one,one))),converse(join(join(X_85,X_84),join(X_85,X_84)))) ),[0,0],$fot(composition(join(X_84,X_85),join(one,one)))]]) ).
cnf(refute_0_1333,plain,
( converse(composition(join(X_85,X_84),join(one,one))) != converse(join(join(X_85,X_84),join(X_85,X_84)))
| converse(composition(join(X_84,X_85),join(one,one))) = converse(join(join(X_85,X_84),join(X_85,X_84))) ),
inference(resolve,[$cnf( $equal(composition(join(X_85,X_84),join(one,one)),composition(join(X_84,X_85),join(one,one))) )],[refute_0_1331,refute_0_1332]) ).
cnf(refute_0_1334,plain,
converse(composition(join(X_84,X_85),join(one,one))) = converse(join(join(X_85,X_84),join(X_85,X_84))),
inference(resolve,[$cnf( $equal(converse(composition(join(X_85,X_84),join(one,one))),converse(join(join(X_85,X_84),join(X_85,X_84)))) )],[refute_0_1330,refute_0_1333]) ).
cnf(refute_0_1335,plain,
composition(join(one,one),X_51) = join(X_51,X_51),
inference(subst,[],[refute_0_68:[bind(X_47,$fot(X_51))]]) ).
cnf(refute_0_1336,plain,
( composition(join(one,one),X_51) != join(X_51,X_51)
| join(X_51,X_51) = composition(join(one,one),X_51) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),X_51))),bind(Y,$fot(join(X_51,X_51)))]]) ).
cnf(refute_0_1337,plain,
join(X_51,X_51) = composition(join(one,one),X_51),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_51),join(X_51,X_51)) )],[refute_0_1335,refute_0_1336]) ).
cnf(refute_0_1338,plain,
( converse(join(X_51,X_51)) != converse(join(X_51,X_51))
| join(X_51,X_51) != composition(join(one,one),X_51)
| converse(composition(join(one,one),X_51)) = converse(join(X_51,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_51,X_51)),converse(join(X_51,X_51))) ),[0,0],$fot(composition(join(one,one),X_51))]]) ).
cnf(refute_0_1339,plain,
( converse(join(X_51,X_51)) != converse(join(X_51,X_51))
| converse(composition(join(one,one),X_51)) = converse(join(X_51,X_51)) ),
inference(resolve,[$cnf( $equal(join(X_51,X_51),composition(join(one,one),X_51)) )],[refute_0_1337,refute_0_1338]) ).
cnf(refute_0_1340,plain,
converse(composition(join(one,one),X_51)) = converse(join(X_51,X_51)),
inference(resolve,[$cnf( $equal(converse(join(X_51,X_51)),converse(join(X_51,X_51))) )],[refute_0_1325,refute_0_1339]) ).
cnf(refute_0_1341,plain,
( converse(composition(join(one,one),X_51)) != converse(join(X_51,X_51))
| converse(join(X_51,X_51)) = converse(composition(join(one,one),X_51)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(join(one,one),X_51)))),bind(Y,$fot(converse(join(X_51,X_51))))]]) ).
cnf(refute_0_1342,plain,
converse(join(X_51,X_51)) = converse(composition(join(one,one),X_51)),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),X_51)),converse(join(X_51,X_51))) )],[refute_0_1340,refute_0_1341]) ).
cnf(refute_0_1343,plain,
converse(join(join(X_85,X_84),join(X_85,X_84))) = converse(composition(join(one,one),join(X_85,X_84))),
inference(subst,[],[refute_0_1342:[bind(X_51,$fot(join(X_85,X_84)))]]) ).
cnf(refute_0_1344,plain,
( converse(composition(join(X_84,X_85),join(one,one))) != converse(join(join(X_85,X_84),join(X_85,X_84)))
| converse(join(join(X_85,X_84),join(X_85,X_84))) != converse(composition(join(one,one),join(X_85,X_84)))
| converse(composition(join(X_84,X_85),join(one,one))) = converse(composition(join(one,one),join(X_85,X_84))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(composition(join(X_84,X_85),join(one,one))),converse(composition(join(one,one),join(X_85,X_84)))) ),[0],$fot(converse(join(join(X_85,X_84),join(X_85,X_84))))]]) ).
cnf(refute_0_1345,plain,
( converse(composition(join(X_84,X_85),join(one,one))) != converse(join(join(X_85,X_84),join(X_85,X_84)))
| converse(composition(join(X_84,X_85),join(one,one))) = converse(composition(join(one,one),join(X_85,X_84))) ),
inference(resolve,[$cnf( $equal(converse(join(join(X_85,X_84),join(X_85,X_84))),converse(composition(join(one,one),join(X_85,X_84)))) )],[refute_0_1343,refute_0_1344]) ).
cnf(refute_0_1346,plain,
converse(composition(join(X_84,X_85),join(one,one))) = converse(composition(join(one,one),join(X_85,X_84))),
inference(resolve,[$cnf( $equal(converse(composition(join(X_84,X_85),join(one,one))),converse(join(join(X_85,X_84),join(X_85,X_84)))) )],[refute_0_1334,refute_0_1345]) ).
cnf(refute_0_1347,plain,
composition(join(X_84,X_85),one) = join(X_84,X_85),
inference(subst,[],[composition_identity_6:[bind(A,$fot(join(X_84,X_85)))]]) ).
cnf(refute_0_1348,plain,
meet(A,composition(join(one,one),A)) = complement(join(complement(A),complement(composition(join(one,one),A)))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(composition(join(one,one),A)))]]) ).
cnf(refute_0_1349,plain,
join(complement(X_63),composition(converse(join(one,one)),complement(composition(join(one,one),X_63)))) = complement(X_63),
inference(subst,[],[refute_0_78:[bind(A,$fot(join(one,one))),bind(B,$fot(X_63))]]) ).
cnf(refute_0_1350,plain,
( converse(join(one,one)) != join(one,one)
| join(complement(X_63),composition(converse(join(one,one)),complement(composition(join(one,one),X_63)))) != complement(X_63)
| join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))) = complement(X_63) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_63),composition(converse(join(one,one)),complement(composition(join(one,one),X_63)))),complement(X_63)) ),[0,1,0],$fot(join(one,one))]]) ).
cnf(refute_0_1351,plain,
( join(complement(X_63),composition(converse(join(one,one)),complement(composition(join(one,one),X_63)))) != complement(X_63)
| join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))) = complement(X_63) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_97,refute_0_1350]) ).
cnf(refute_0_1352,plain,
join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))) = complement(X_63),
inference(resolve,[$cnf( $equal(join(complement(X_63),composition(converse(join(one,one)),complement(composition(join(one,one),X_63)))),complement(X_63)) )],[refute_0_1349,refute_0_1351]) ).
cnf(refute_0_1353,plain,
composition(join(one,one),complement(composition(join(one,one),X_63))) = complement(composition(join(one,one),X_63)),
inference(subst,[],[refute_0_133:[bind(X_63,$fot(composition(join(one,one),X_63)))]]) ).
cnf(refute_0_1354,plain,
join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))) = join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))),
introduced(tautology,[refl,[$fot(join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))))]]) ).
cnf(refute_0_1355,plain,
( composition(join(one,one),complement(composition(join(one,one),X_63))) != complement(composition(join(one,one),X_63))
| join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))) != join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63))))
| join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))) = join(complement(X_63),complement(composition(join(one,one),X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))),join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63))))) ),[1,1],$fot(complement(composition(join(one,one),X_63)))]]) ).
cnf(refute_0_1356,plain,
( composition(join(one,one),complement(composition(join(one,one),X_63))) != complement(composition(join(one,one),X_63))
| join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))) = join(complement(X_63),complement(composition(join(one,one),X_63))) ),
inference(resolve,[$cnf( $equal(join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))),join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63))))) )],[refute_0_1354,refute_0_1355]) ).
cnf(refute_0_1357,plain,
join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))) = join(complement(X_63),complement(composition(join(one,one),X_63))),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),X_63))),complement(composition(join(one,one),X_63))) )],[refute_0_1353,refute_0_1356]) ).
cnf(refute_0_1358,plain,
( join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))) != complement(X_63)
| join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))) != join(complement(X_63),complement(composition(join(one,one),X_63)))
| join(complement(X_63),complement(composition(join(one,one),X_63))) = complement(X_63) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))),complement(X_63)) ),[0],$fot(join(complement(X_63),complement(composition(join(one,one),X_63))))]]) ).
cnf(refute_0_1359,plain,
( join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))) != complement(X_63)
| join(complement(X_63),complement(composition(join(one,one),X_63))) = complement(X_63) ),
inference(resolve,[$cnf( $equal(join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))),join(complement(X_63),complement(composition(join(one,one),X_63)))) )],[refute_0_1357,refute_0_1358]) ).
cnf(refute_0_1360,plain,
join(complement(X_63),complement(composition(join(one,one),X_63))) = complement(X_63),
inference(resolve,[$cnf( $equal(join(complement(X_63),composition(join(one,one),complement(composition(join(one,one),X_63)))),complement(X_63)) )],[refute_0_1352,refute_0_1359]) ).
cnf(refute_0_1361,plain,
join(complement(A),complement(composition(join(one,one),A))) = complement(A),
inference(subst,[],[refute_0_1360:[bind(X_63,$fot(A))]]) ).
cnf(refute_0_1362,plain,
( join(complement(A),complement(composition(join(one,one),A))) != complement(A)
| meet(A,composition(join(one,one),A)) != complement(join(complement(A),complement(composition(join(one,one),A))))
| meet(A,composition(join(one,one),A)) = complement(complement(A)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,composition(join(one,one),A)),complement(join(complement(A),complement(composition(join(one,one),A))))) ),[1,0],$fot(complement(A))]]) ).
cnf(refute_0_1363,plain,
( meet(A,composition(join(one,one),A)) != complement(join(complement(A),complement(composition(join(one,one),A))))
| meet(A,composition(join(one,one),A)) = complement(complement(A)) ),
inference(resolve,[$cnf( $equal(join(complement(A),complement(composition(join(one,one),A))),complement(A)) )],[refute_0_1361,refute_0_1362]) ).
cnf(refute_0_1364,plain,
meet(A,composition(join(one,one),A)) = complement(complement(A)),
inference(resolve,[$cnf( $equal(meet(A,composition(join(one,one),A)),complement(join(complement(A),complement(composition(join(one,one),A))))) )],[refute_0_1348,refute_0_1363]) ).
cnf(refute_0_1365,plain,
meet(join(X_56,X_56),composition(join(one,one),join(X_56,X_56))) = complement(complement(join(X_56,X_56))),
inference(subst,[],[refute_0_1364:[bind(A,$fot(join(X_56,X_56)))]]) ).
cnf(refute_0_1366,plain,
composition(X_54,composition(join(one,one),X_56)) = composition(composition(X_54,join(one,one)),X_56),
inference(subst,[],[composition_associativity_5:[bind(A,$fot(X_54)),bind(B,$fot(join(one,one))),bind(C,$fot(X_56))]]) ).
cnf(refute_0_1367,plain,
composition(join(one,one),X_56) = join(X_56,X_56),
inference(subst,[],[refute_0_68:[bind(X_47,$fot(X_56))]]) ).
cnf(refute_0_1368,plain,
( composition(X_54,composition(join(one,one),X_56)) != composition(composition(X_54,join(one,one)),X_56)
| composition(join(one,one),X_56) != join(X_56,X_56)
| composition(X_54,join(X_56,X_56)) = composition(composition(X_54,join(one,one)),X_56) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_54,composition(join(one,one),X_56)),composition(composition(X_54,join(one,one)),X_56)) ),[0,1],$fot(join(X_56,X_56))]]) ).
cnf(refute_0_1369,plain,
( composition(X_54,composition(join(one,one),X_56)) != composition(composition(X_54,join(one,one)),X_56)
| composition(X_54,join(X_56,X_56)) = composition(composition(X_54,join(one,one)),X_56) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_56),join(X_56,X_56)) )],[refute_0_1367,refute_0_1368]) ).
cnf(refute_0_1370,plain,
composition(X_54,join(X_56,X_56)) = composition(composition(X_54,join(one,one)),X_56),
inference(resolve,[$cnf( $equal(composition(X_54,composition(join(one,one),X_56)),composition(composition(X_54,join(one,one)),X_56)) )],[refute_0_1366,refute_0_1369]) ).
cnf(refute_0_1371,plain,
composition(composition(X_54,join(one,one)),X_56) = composition(X_54,composition(join(one,one),X_56)),
inference(subst,[],[refute_0_209:[bind(A,$fot(X_54)),bind(B,$fot(join(one,one))),bind(C,$fot(X_56))]]) ).
cnf(refute_0_1372,plain,
( composition(X_54,join(X_56,X_56)) != composition(composition(X_54,join(one,one)),X_56)
| composition(composition(X_54,join(one,one)),X_56) != composition(X_54,composition(join(one,one),X_56))
| composition(X_54,join(X_56,X_56)) = composition(X_54,composition(join(one,one),X_56)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(X_54,join(X_56,X_56)),composition(X_54,composition(join(one,one),X_56))) ),[0],$fot(composition(composition(X_54,join(one,one)),X_56))]]) ).
cnf(refute_0_1373,plain,
( composition(X_54,join(X_56,X_56)) != composition(composition(X_54,join(one,one)),X_56)
| composition(X_54,join(X_56,X_56)) = composition(X_54,composition(join(one,one),X_56)) ),
inference(resolve,[$cnf( $equal(composition(composition(X_54,join(one,one)),X_56),composition(X_54,composition(join(one,one),X_56))) )],[refute_0_1371,refute_0_1372]) ).
cnf(refute_0_1374,plain,
composition(X_54,join(X_56,X_56)) = composition(X_54,composition(join(one,one),X_56)),
inference(resolve,[$cnf( $equal(composition(X_54,join(X_56,X_56)),composition(composition(X_54,join(one,one)),X_56)) )],[refute_0_1370,refute_0_1373]) ).
cnf(refute_0_1375,plain,
composition(join(one,one),join(X_56,X_56)) = composition(join(one,one),composition(join(one,one),X_56)),
inference(subst,[],[refute_0_1374:[bind(X_54,$fot(join(one,one)))]]) ).
cnf(refute_0_1376,plain,
( composition(join(one,one),join(X_56,X_56)) != composition(join(one,one),composition(join(one,one),X_56))
| meet(join(X_56,X_56),composition(join(one,one),join(X_56,X_56))) != complement(complement(join(X_56,X_56)))
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = complement(complement(join(X_56,X_56))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_56,X_56),composition(join(one,one),join(X_56,X_56))),complement(complement(join(X_56,X_56)))) ),[0,1],$fot(composition(join(one,one),composition(join(one,one),X_56)))]]) ).
cnf(refute_0_1377,plain,
( meet(join(X_56,X_56),composition(join(one,one),join(X_56,X_56))) != complement(complement(join(X_56,X_56)))
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = complement(complement(join(X_56,X_56))) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(X_56,X_56)),composition(join(one,one),composition(join(one,one),X_56))) )],[refute_0_1375,refute_0_1376]) ).
cnf(refute_0_1378,plain,
meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = complement(complement(join(X_56,X_56))),
inference(resolve,[$cnf( $equal(meet(join(X_56,X_56),composition(join(one,one),join(X_56,X_56))),complement(complement(join(X_56,X_56)))) )],[refute_0_1365,refute_0_1377]) ).
cnf(refute_0_1379,plain,
complement(complement(join(X_56,X_56))) = join(X_56,X_56),
inference(subst,[],[refute_0_383:[bind(X_87,$fot(join(X_56,X_56)))]]) ).
cnf(refute_0_1380,plain,
( complement(complement(join(X_56,X_56))) != join(X_56,X_56)
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) != complement(complement(join(X_56,X_56)))
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = join(X_56,X_56) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))),complement(complement(join(X_56,X_56)))) ),[1],$fot(join(X_56,X_56))]]) ).
cnf(refute_0_1381,plain,
( meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) != complement(complement(join(X_56,X_56)))
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = join(X_56,X_56) ),
inference(resolve,[$cnf( $equal(complement(complement(join(X_56,X_56))),join(X_56,X_56)) )],[refute_0_1379,refute_0_1380]) ).
cnf(refute_0_1382,plain,
meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = join(X_56,X_56),
inference(resolve,[$cnf( $equal(meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))),complement(complement(join(X_56,X_56)))) )],[refute_0_1378,refute_0_1381]) ).
cnf(refute_0_1383,plain,
X_109 = meet(X_109,join(X_109,X_108)),
inference(subst,[],[refute_0_699:[bind(X_37,$fot(X_108)),bind(X_87,$fot(X_109))]]) ).
cnf(refute_0_1384,plain,
join(X_108,X_109) = join(X_109,X_108),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_108)),bind(B,$fot(X_109))]]) ).
cnf(refute_0_1385,plain,
( join(X_108,X_109) != join(X_109,X_108)
| join(X_109,X_108) = join(X_108,X_109) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_108,X_109))),bind(Y,$fot(join(X_109,X_108)))]]) ).
cnf(refute_0_1386,plain,
join(X_109,X_108) = join(X_108,X_109),
inference(resolve,[$cnf( $equal(join(X_108,X_109),join(X_109,X_108)) )],[refute_0_1384,refute_0_1385]) ).
cnf(refute_0_1387,plain,
( X_109 != meet(X_109,join(X_109,X_108))
| join(X_109,X_108) != join(X_108,X_109)
| X_109 = meet(X_109,join(X_108,X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(X_109,meet(X_109,join(X_109,X_108))) ),[1,1],$fot(join(X_108,X_109))]]) ).
cnf(refute_0_1388,plain,
( X_109 != meet(X_109,join(X_109,X_108))
| X_109 = meet(X_109,join(X_108,X_109)) ),
inference(resolve,[$cnf( $equal(join(X_109,X_108),join(X_108,X_109)) )],[refute_0_1386,refute_0_1387]) ).
cnf(refute_0_1389,plain,
X_109 = meet(X_109,join(X_108,X_109)),
inference(resolve,[$cnf( $equal(X_109,meet(X_109,join(X_109,X_108))) )],[refute_0_1383,refute_0_1388]) ).
cnf(refute_0_1390,plain,
( X_109 != meet(X_109,join(X_108,X_109))
| meet(X_109,join(X_108,X_109)) = X_109 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_109)),bind(Y,$fot(meet(X_109,join(X_108,X_109))))]]) ).
cnf(refute_0_1391,plain,
meet(X_109,join(X_108,X_109)) = X_109,
inference(resolve,[$cnf( $equal(X_109,meet(X_109,join(X_108,X_109))) )],[refute_0_1389,refute_0_1390]) ).
cnf(refute_0_1392,plain,
meet(X_56,join(X_56,X_56)) = X_56,
inference(subst,[],[refute_0_1391:[bind(X_108,$fot(X_56)),bind(X_109,$fot(X_56))]]) ).
cnf(refute_0_1393,plain,
meet(join(X_56,X_56),X_56) = meet(X_56,join(X_56,X_56)),
inference(subst,[],[refute_0_1273:[bind(X_6,$fot(X_56)),bind(X_7,$fot(join(X_56,X_56)))]]) ).
cnf(refute_0_1394,plain,
( meet(X_56,join(X_56,X_56)) != X_56
| meet(join(X_56,X_56),X_56) != meet(X_56,join(X_56,X_56))
| meet(join(X_56,X_56),X_56) = X_56 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(join(X_56,X_56),X_56))),bind(Y,$fot(meet(X_56,join(X_56,X_56)))),bind(Z,$fot(X_56))]]) ).
cnf(refute_0_1395,plain,
( meet(X_56,join(X_56,X_56)) != X_56
| meet(join(X_56,X_56),X_56) = X_56 ),
inference(resolve,[$cnf( $equal(meet(join(X_56,X_56),X_56),meet(X_56,join(X_56,X_56))) )],[refute_0_1393,refute_0_1394]) ).
cnf(refute_0_1396,plain,
meet(join(X_56,X_56),X_56) = X_56,
inference(resolve,[$cnf( $equal(meet(X_56,join(X_56,X_56)),X_56) )],[refute_0_1392,refute_0_1395]) ).
cnf(refute_0_1397,plain,
composition(join(one,one),composition(join(one,one),C)) = composition(composition(join(one,one),join(one,one)),C),
inference(subst,[],[composition_associativity_5:[bind(A,$fot(join(one,one))),bind(B,$fot(join(one,one)))]]) ).
cnf(refute_0_1398,plain,
composition(join(one,one),join(one,one)) = join(meet(one,composition(join(one,one),join(one,one))),complement(join(complement(composition(join(one,one),join(one,one))),one))),
inference(subst,[],[refute_0_629:[bind(X_87,$fot(composition(join(one,one),join(one,one)))),bind(X_88,$fot(one))]]) ).
cnf(refute_0_1399,plain,
meet(one,composition(join(one,one),join(one,one))) = complement(join(complement(one),complement(composition(join(one,one),join(one,one))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(one)),bind(B,$fot(composition(join(one,one),join(one,one))))]]) ).
cnf(refute_0_1400,plain,
join(complement(one),composition(converse(composition(join(one,one),join(one,one))),complement(composition(join(one,one),join(one,one))))) = complement(one),
inference(subst,[],[refute_0_838:[bind(X_62,$fot(composition(join(one,one),join(one,one))))]]) ).
cnf(refute_0_1401,plain,
converse(join(one,join(one,join(one,one)))) = join(one,converse(join(one,join(one,one)))),
inference(subst,[],[refute_0_93:[bind(X_13,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_1402,plain,
converse(join(one,join(one,one))) = join(one,converse(join(one,one))),
inference(subst,[],[refute_0_93:[bind(X_13,$fot(join(one,one)))]]) ).
cnf(refute_0_1403,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_1404,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( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_97,refute_0_1403]) ).
cnf(refute_0_1405,plain,
converse(join(one,join(one,one))) = join(one,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,one))),join(one,converse(join(one,one)))) )],[refute_0_1402,refute_0_1404]) ).
cnf(refute_0_1406,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,converse(join(one,join(one,one))))
| converse(join(one,join(one,one))) != join(one,join(one,one))
| converse(join(one,join(one,join(one,one)))) = join(one,join(one,join(one,one))) ),
introduced(tautology,[equality,[$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_1407,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( $equal(converse(join(one,join(one,one))),join(one,join(one,one))) )],[refute_0_1405,refute_0_1406]) ).
cnf(refute_0_1408,plain,
converse(join(one,join(one,join(one,one)))) = join(one,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),join(one,converse(join(one,join(one,one))))) )],[refute_0_1401,refute_0_1407]) ).
cnf(refute_0_1409,plain,
join(A,join(B,join(A,B))) = join(join(A,B),join(A,B)),
inference(subst,[],[maddux2_join_associativity_2:[bind(C,$fot(join(A,B)))]]) ).
cnf(refute_0_1410,plain,
composition(join(one,one),join(A,B)) = join(join(A,B),join(A,B)),
inference(subst,[],[refute_0_68:[bind(X_47,$fot(join(A,B)))]]) ).
cnf(refute_0_1411,plain,
( composition(join(one,one),join(A,B)) != join(join(A,B),join(A,B))
| join(join(A,B),join(A,B)) = composition(join(one,one),join(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),join(A,B)))),bind(Y,$fot(join(join(A,B),join(A,B))))]]) ).
cnf(refute_0_1412,plain,
join(join(A,B),join(A,B)) = composition(join(one,one),join(A,B)),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(A,B)),join(join(A,B),join(A,B))) )],[refute_0_1410,refute_0_1411]) ).
cnf(refute_0_1413,plain,
( join(A,join(B,join(A,B))) != join(join(A,B),join(A,B))
| join(join(A,B),join(A,B)) != composition(join(one,one),join(A,B))
| join(A,join(B,join(A,B))) = composition(join(one,one),join(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(B,join(A,B))),composition(join(one,one),join(A,B))) ),[0],$fot(join(join(A,B),join(A,B)))]]) ).
cnf(refute_0_1414,plain,
( join(A,join(B,join(A,B))) != join(join(A,B),join(A,B))
| join(A,join(B,join(A,B))) = composition(join(one,one),join(A,B)) ),
inference(resolve,[$cnf( $equal(join(join(A,B),join(A,B)),composition(join(one,one),join(A,B))) )],[refute_0_1412,refute_0_1413]) ).
cnf(refute_0_1415,plain,
join(A,join(B,join(A,B))) = composition(join(one,one),join(A,B)),
inference(resolve,[$cnf( $equal(join(A,join(B,join(A,B))),join(join(A,B),join(A,B))) )],[refute_0_1409,refute_0_1414]) ).
cnf(refute_0_1416,plain,
join(one,join(one,join(one,one))) = composition(join(one,one),join(one,one)),
inference(subst,[],[refute_0_1415:[bind(A,$fot(one)),bind(B,$fot(one))]]) ).
cnf(refute_0_1417,plain,
converse(join(one,join(one,join(one,one)))) = converse(join(one,join(one,join(one,one)))),
introduced(tautology,[refl,[$fot(converse(join(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_1418,plain,
( converse(join(one,join(one,join(one,one)))) != converse(join(one,join(one,join(one,one))))
| join(one,join(one,join(one,one))) != composition(join(one,one),join(one,one))
| converse(join(one,join(one,join(one,one)))) = converse(composition(join(one,one),join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),converse(join(one,join(one,join(one,one))))) ),[1,0],$fot(composition(join(one,one),join(one,one)))]]) ).
cnf(refute_0_1419,plain,
( join(one,join(one,join(one,one))) != composition(join(one,one),join(one,one))
| converse(join(one,join(one,join(one,one)))) = converse(composition(join(one,one),join(one,one))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),converse(join(one,join(one,join(one,one))))) )],[refute_0_1417,refute_0_1418]) ).
cnf(refute_0_1420,plain,
converse(join(one,join(one,join(one,one)))) = converse(composition(join(one,one),join(one,one))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,one))),composition(join(one,one),join(one,one))) )],[refute_0_1416,refute_0_1419]) ).
cnf(refute_0_1421,plain,
( converse(join(one,join(one,join(one,one)))) != converse(composition(join(one,one),join(one,one)))
| converse(join(one,join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| converse(composition(join(one,one),join(one,one))) = join(one,join(one,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),join(one,join(one,join(one,one)))) ),[0],$fot(converse(composition(join(one,one),join(one,one))))]]) ).
cnf(refute_0_1422,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| converse(composition(join(one,one),join(one,one))) = join(one,join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),converse(composition(join(one,one),join(one,one)))) )],[refute_0_1420,refute_0_1421]) ).
cnf(refute_0_1423,plain,
( converse(composition(join(one,one),join(one,one))) != join(one,join(one,join(one,one)))
| join(one,join(one,join(one,one))) != composition(join(one,one),join(one,one))
| converse(composition(join(one,one),join(one,one))) = composition(join(one,one),join(one,one)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(composition(join(one,one),join(one,one))),composition(join(one,one),join(one,one))) ),[0],$fot(join(one,join(one,join(one,one))))]]) ).
cnf(refute_0_1424,plain,
( converse(composition(join(one,one),join(one,one))) != join(one,join(one,join(one,one)))
| converse(composition(join(one,one),join(one,one))) = composition(join(one,one),join(one,one)) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,one))),composition(join(one,one),join(one,one))) )],[refute_0_1416,refute_0_1423]) ).
cnf(refute_0_1425,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| converse(composition(join(one,one),join(one,one))) = composition(join(one,one),join(one,one)) ),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),join(one,one))),join(one,join(one,join(one,one)))) )],[refute_0_1422,refute_0_1424]) ).
cnf(refute_0_1426,plain,
converse(composition(join(one,one),join(one,one))) = composition(join(one,one),join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),join(one,join(one,join(one,one)))) )],[refute_0_1408,refute_0_1425]) ).
cnf(refute_0_1427,plain,
( converse(composition(join(one,one),join(one,one))) != composition(join(one,one),join(one,one))
| join(complement(one),composition(converse(composition(join(one,one),join(one,one))),complement(composition(join(one,one),join(one,one))))) != complement(one)
| join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(composition(join(one,one),join(one,one))),complement(composition(join(one,one),join(one,one))))),complement(one)) ),[0,1,0],$fot(composition(join(one,one),join(one,one)))]]) ).
cnf(refute_0_1428,plain,
( join(complement(one),composition(converse(composition(join(one,one),join(one,one))),complement(composition(join(one,one),join(one,one))))) != complement(one)
| join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))) = complement(one) ),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),join(one,one))),composition(join(one,one),join(one,one))) )],[refute_0_1426,refute_0_1427]) ).
cnf(refute_0_1429,plain,
join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(composition(join(one,one),join(one,one))),complement(composition(join(one,one),join(one,one))))),complement(one)) )],[refute_0_1400,refute_0_1428]) ).
cnf(refute_0_1430,plain,
composition(join(one,one),complement(composition(join(one,one),join(one,one)))) = complement(composition(join(one,one),join(one,one))),
inference(subst,[],[refute_0_133:[bind(X_63,$fot(composition(join(one,one),join(one,one))))]]) ).
cnf(refute_0_1431,plain,
composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) = composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))),
introduced(tautology,[refl,[$fot(composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))))]]) ).
cnf(refute_0_1432,plain,
( composition(join(one,one),complement(composition(join(one,one),join(one,one)))) != complement(composition(join(one,one),join(one,one)))
| composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) != composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one)))))
| composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) = composition(join(one,one),complement(composition(join(one,one),join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))),composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one)))))) ),[1,1],$fot(complement(composition(join(one,one),join(one,one))))]]) ).
cnf(refute_0_1433,plain,
( composition(join(one,one),complement(composition(join(one,one),join(one,one)))) != complement(composition(join(one,one),join(one,one)))
| composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) = composition(join(one,one),complement(composition(join(one,one),join(one,one)))) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))),composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one)))))) )],[refute_0_1431,refute_0_1432]) ).
cnf(refute_0_1434,plain,
composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) = composition(join(one,one),complement(composition(join(one,one),join(one,one)))),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),join(one,one)))),complement(composition(join(one,one),join(one,one)))) )],[refute_0_1430,refute_0_1433]) ).
cnf(refute_0_1435,plain,
( composition(join(one,one),complement(composition(join(one,one),join(one,one)))) != complement(composition(join(one,one),join(one,one)))
| composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) != composition(join(one,one),complement(composition(join(one,one),join(one,one))))
| composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) = complement(composition(join(one,one),join(one,one))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))))),bind(Y,$fot(composition(join(one,one),complement(composition(join(one,one),join(one,one)))))),bind(Z,$fot(complement(composition(join(one,one),join(one,one)))))]]) ).
cnf(refute_0_1436,plain,
( composition(join(one,one),complement(composition(join(one,one),join(one,one)))) != complement(composition(join(one,one),join(one,one)))
| composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) = complement(composition(join(one,one),join(one,one))) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) )],[refute_0_1434,refute_0_1435]) ).
cnf(refute_0_1437,plain,
composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) = complement(composition(join(one,one),join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),join(one,one)))),complement(composition(join(one,one),join(one,one)))) )],[refute_0_1430,refute_0_1436]) ).
cnf(refute_0_1438,plain,
composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))) = composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))),
inference(subst,[],[refute_0_209:[bind(A,$fot(join(one,one))),bind(B,$fot(join(one,one))),bind(C,$fot(complement(composition(join(one,one),join(one,one)))))]]) ).
cnf(refute_0_1439,plain,
( composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))) != composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one)))))
| composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) != complement(composition(join(one,one),join(one,one)))
| composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))) = complement(composition(join(one,one),join(one,one))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))))),bind(Y,$fot(composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))))),bind(Z,$fot(complement(composition(join(one,one),join(one,one)))))]]) ).
cnf(refute_0_1440,plain,
( composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))) != complement(composition(join(one,one),join(one,one)))
| composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))) = complement(composition(join(one,one),join(one,one))) ),
inference(resolve,[$cnf( $equal(composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))),composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one)))))) )],[refute_0_1438,refute_0_1439]) ).
cnf(refute_0_1441,plain,
composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))) = complement(composition(join(one,one),join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(join(one,one),complement(composition(join(one,one),join(one,one))))),complement(composition(join(one,one),join(one,one)))) )],[refute_0_1437,refute_0_1440]) ).
cnf(refute_0_1442,plain,
join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))) = join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))),
introduced(tautology,[refl,[$fot(join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))))]]) ).
cnf(refute_0_1443,plain,
( composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))) != complement(composition(join(one,one),join(one,one)))
| join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))) != join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))))
| join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))) = join(complement(one),complement(composition(join(one,one),join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))),join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))))) ),[1,1],$fot(complement(composition(join(one,one),join(one,one))))]]) ).
cnf(refute_0_1444,plain,
( composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))) != complement(composition(join(one,one),join(one,one)))
| join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))) = join(complement(one),complement(composition(join(one,one),join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))),join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))))) )],[refute_0_1442,refute_0_1443]) ).
cnf(refute_0_1445,plain,
join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))) = join(complement(one),complement(composition(join(one,one),join(one,one)))),
inference(resolve,[$cnf( $equal(composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one)))),complement(composition(join(one,one),join(one,one)))) )],[refute_0_1441,refute_0_1444]) ).
cnf(refute_0_1446,plain,
( join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))) != complement(one)
| join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))) != join(complement(one),complement(composition(join(one,one),join(one,one))))
| join(complement(one),complement(composition(join(one,one),join(one,one)))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))),complement(one)) ),[0],$fot(join(complement(one),complement(composition(join(one,one),join(one,one)))))]]) ).
cnf(refute_0_1447,plain,
( join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))) != complement(one)
| join(complement(one),complement(composition(join(one,one),join(one,one)))) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))),join(complement(one),complement(composition(join(one,one),join(one,one))))) )],[refute_0_1445,refute_0_1446]) ).
cnf(refute_0_1448,plain,
join(complement(one),complement(composition(join(one,one),join(one,one)))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(composition(join(one,one),join(one,one)),complement(composition(join(one,one),join(one,one))))),complement(one)) )],[refute_0_1429,refute_0_1447]) ).
cnf(refute_0_1449,plain,
( join(complement(one),complement(composition(join(one,one),join(one,one)))) != complement(one)
| meet(one,composition(join(one,one),join(one,one))) != complement(join(complement(one),complement(composition(join(one,one),join(one,one)))))
| meet(one,composition(join(one,one),join(one,one))) = complement(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,composition(join(one,one),join(one,one))),complement(join(complement(one),complement(composition(join(one,one),join(one,one)))))) ),[1,0],$fot(complement(one))]]) ).
cnf(refute_0_1450,plain,
( meet(one,composition(join(one,one),join(one,one))) != complement(join(complement(one),complement(composition(join(one,one),join(one,one)))))
| meet(one,composition(join(one,one),join(one,one))) = complement(complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(one),complement(composition(join(one,one),join(one,one)))),complement(one)) )],[refute_0_1448,refute_0_1449]) ).
cnf(refute_0_1451,plain,
meet(one,composition(join(one,one),join(one,one))) = complement(complement(one)),
inference(resolve,[$cnf( $equal(meet(one,composition(join(one,one),join(one,one))),complement(join(complement(one),complement(composition(join(one,one),join(one,one)))))) )],[refute_0_1399,refute_0_1450]) ).
cnf(refute_0_1452,plain,
( complement(complement(one)) != one
| meet(one,composition(join(one,one),join(one,one))) != complement(complement(one))
| meet(one,composition(join(one,one),join(one,one))) = one ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,composition(join(one,one),join(one,one))),complement(complement(one))) ),[1],$fot(one)]]) ).
cnf(refute_0_1453,plain,
( meet(one,composition(join(one,one),join(one,one))) != complement(complement(one))
| meet(one,composition(join(one,one),join(one,one))) = one ),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_892,refute_0_1452]) ).
cnf(refute_0_1454,plain,
meet(one,composition(join(one,one),join(one,one))) = one,
inference(resolve,[$cnf( $equal(meet(one,composition(join(one,one),join(one,one))),complement(complement(one))) )],[refute_0_1451,refute_0_1453]) ).
cnf(refute_0_1455,plain,
( composition(join(one,one),join(one,one)) != join(meet(one,composition(join(one,one),join(one,one))),complement(join(complement(composition(join(one,one),join(one,one))),one)))
| meet(one,composition(join(one,one),join(one,one))) != one
| composition(join(one,one),join(one,one)) = join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),join(one,one)),join(meet(one,composition(join(one,one),join(one,one))),complement(join(complement(composition(join(one,one),join(one,one))),one)))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1456,plain,
( composition(join(one,one),join(one,one)) != join(meet(one,composition(join(one,one),join(one,one))),complement(join(complement(composition(join(one,one),join(one,one))),one)))
| composition(join(one,one),join(one,one)) = join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))) ),
inference(resolve,[$cnf( $equal(meet(one,composition(join(one,one),join(one,one))),one) )],[refute_0_1454,refute_0_1455]) ).
cnf(refute_0_1457,plain,
composition(join(one,one),join(one,one)) = join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(one,one)),join(meet(one,composition(join(one,one),join(one,one))),complement(join(complement(composition(join(one,one),join(one,one))),one)))) )],[refute_0_1398,refute_0_1456]) ).
cnf(refute_0_1458,plain,
join(complement(composition(join(one,one),join(one,one))),one) = join(one,complement(composition(join(one,one),join(one,one)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(one)),bind(B,$fot(complement(composition(join(one,one),join(one,one)))))]]) ).
cnf(refute_0_1459,plain,
complement(join(complement(composition(join(one,one),join(one,one))),one)) = complement(join(complement(composition(join(one,one),join(one,one))),one)),
introduced(tautology,[refl,[$fot(complement(join(complement(composition(join(one,one),join(one,one))),one)))]]) ).
cnf(refute_0_1460,plain,
( complement(join(complement(composition(join(one,one),join(one,one))),one)) != complement(join(complement(composition(join(one,one),join(one,one))),one))
| join(complement(composition(join(one,one),join(one,one))),one) != join(one,complement(composition(join(one,one),join(one,one))))
| complement(join(complement(composition(join(one,one),join(one,one))),one)) = complement(join(one,complement(composition(join(one,one),join(one,one))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(composition(join(one,one),join(one,one))),one)),complement(join(complement(composition(join(one,one),join(one,one))),one))) ),[1,0],$fot(join(one,complement(composition(join(one,one),join(one,one)))))]]) ).
cnf(refute_0_1461,plain,
( join(complement(composition(join(one,one),join(one,one))),one) != join(one,complement(composition(join(one,one),join(one,one))))
| complement(join(complement(composition(join(one,one),join(one,one))),one)) = complement(join(one,complement(composition(join(one,one),join(one,one))))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(composition(join(one,one),join(one,one))),one)),complement(join(complement(composition(join(one,one),join(one,one))),one))) )],[refute_0_1459,refute_0_1460]) ).
cnf(refute_0_1462,plain,
complement(join(complement(composition(join(one,one),join(one,one))),one)) = complement(join(one,complement(composition(join(one,one),join(one,one))))),
inference(resolve,[$cnf( $equal(join(complement(composition(join(one,one),join(one,one))),one),join(one,complement(composition(join(one,one),join(one,one))))) )],[refute_0_1458,refute_0_1461]) ).
cnf(refute_0_1463,plain,
join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))) = join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))),
introduced(tautology,[refl,[$fot(join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))))]]) ).
cnf(refute_0_1464,plain,
( complement(join(complement(composition(join(one,one),join(one,one))),one)) != complement(join(one,complement(composition(join(one,one),join(one,one)))))
| join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))) != join(one,complement(join(complement(composition(join(one,one),join(one,one))),one)))
| join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))) = join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))),join(one,complement(join(complement(composition(join(one,one),join(one,one))),one)))) ),[1,1],$fot(complement(join(one,complement(composition(join(one,one),join(one,one))))))]]) ).
cnf(refute_0_1465,plain,
( complement(join(complement(composition(join(one,one),join(one,one))),one)) != complement(join(one,complement(composition(join(one,one),join(one,one)))))
| join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))) = join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))),join(one,complement(join(complement(composition(join(one,one),join(one,one))),one)))) )],[refute_0_1463,refute_0_1464]) ).
cnf(refute_0_1466,plain,
join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))) = join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))),
inference(resolve,[$cnf( $equal(complement(join(complement(composition(join(one,one),join(one,one))),one)),complement(join(one,complement(composition(join(one,one),join(one,one)))))) )],[refute_0_1462,refute_0_1465]) ).
cnf(refute_0_1467,plain,
( composition(join(one,one),join(one,one)) != join(one,complement(join(complement(composition(join(one,one),join(one,one))),one)))
| join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))) != join(one,complement(join(one,complement(composition(join(one,one),join(one,one))))))
| composition(join(one,one),join(one,one)) = join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,one),join(one,one)),join(one,complement(join(one,complement(composition(join(one,one),join(one,one))))))) ),[0],$fot(join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))))]]) ).
cnf(refute_0_1468,plain,
( composition(join(one,one),join(one,one)) != join(one,complement(join(complement(composition(join(one,one),join(one,one))),one)))
| composition(join(one,one),join(one,one)) = join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(complement(composition(join(one,one),join(one,one))),one))),join(one,complement(join(one,complement(composition(join(one,one),join(one,one))))))) )],[refute_0_1466,refute_0_1467]) ).
cnf(refute_0_1469,plain,
composition(join(one,one),join(one,one)) = join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(one,one)),join(one,complement(join(complement(composition(join(one,one),join(one,one))),one)))) )],[refute_0_1457,refute_0_1468]) ).
cnf(refute_0_1470,plain,
join(one,zero) = one,
inference(subst,[],[refute_0_1315:[bind(A,$fot(one))]]) ).
cnf(refute_0_1471,plain,
complement(X_117) = join(meet(X_117,complement(X_117)),complement(join(complement(complement(X_117)),X_117))),
inference(subst,[],[refute_0_629:[bind(X_87,$fot(complement(X_117))),bind(X_88,$fot(X_117))]]) ).
cnf(refute_0_1472,plain,
zero = meet(X_117,complement(X_117)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_117))]]) ).
cnf(refute_0_1473,plain,
( zero != meet(X_117,complement(X_117))
| meet(X_117,complement(X_117)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_117,complement(X_117))))]]) ).
cnf(refute_0_1474,plain,
meet(X_117,complement(X_117)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_117,complement(X_117))) )],[refute_0_1472,refute_0_1473]) ).
cnf(refute_0_1475,plain,
( complement(X_117) != join(meet(X_117,complement(X_117)),complement(join(complement(complement(X_117)),X_117)))
| meet(X_117,complement(X_117)) != zero
| complement(X_117) = join(zero,complement(join(complement(complement(X_117)),X_117))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_117),join(meet(X_117,complement(X_117)),complement(join(complement(complement(X_117)),X_117)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1476,plain,
( complement(X_117) != join(meet(X_117,complement(X_117)),complement(join(complement(complement(X_117)),X_117)))
| complement(X_117) = join(zero,complement(join(complement(complement(X_117)),X_117))) ),
inference(resolve,[$cnf( $equal(meet(X_117,complement(X_117)),zero) )],[refute_0_1474,refute_0_1475]) ).
cnf(refute_0_1477,plain,
complement(X_117) = join(zero,complement(join(complement(complement(X_117)),X_117))),
inference(resolve,[$cnf( $equal(complement(X_117),join(meet(X_117,complement(X_117)),complement(join(complement(complement(X_117)),X_117)))) )],[refute_0_1471,refute_0_1476]) ).
cnf(refute_0_1478,plain,
complement(complement(X_117)) = X_117,
inference(subst,[],[refute_0_383:[bind(X_87,$fot(X_117))]]) ).
cnf(refute_0_1479,plain,
join(X_117,complement(complement(X_117))) = join(X_117,complement(complement(X_117))),
introduced(tautology,[refl,[$fot(join(X_117,complement(complement(X_117))))]]) ).
cnf(refute_0_1480,plain,
( complement(complement(X_117)) != X_117
| join(X_117,complement(complement(X_117))) != join(X_117,complement(complement(X_117)))
| join(X_117,complement(complement(X_117))) = join(X_117,X_117) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_117,complement(complement(X_117))),join(X_117,complement(complement(X_117)))) ),[1,1],$fot(X_117)]]) ).
cnf(refute_0_1481,plain,
( complement(complement(X_117)) != X_117
| join(X_117,complement(complement(X_117))) = join(X_117,X_117) ),
inference(resolve,[$cnf( $equal(join(X_117,complement(complement(X_117))),join(X_117,complement(complement(X_117)))) )],[refute_0_1479,refute_0_1480]) ).
cnf(refute_0_1482,plain,
join(X_117,complement(complement(X_117))) = join(X_117,X_117),
inference(resolve,[$cnf( $equal(complement(complement(X_117)),X_117) )],[refute_0_1478,refute_0_1481]) ).
cnf(refute_0_1483,plain,
join(complement(complement(X_117)),X_117) = join(X_117,complement(complement(X_117))),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_117)),bind(B,$fot(complement(complement(X_117))))]]) ).
cnf(refute_0_1484,plain,
( join(X_117,complement(complement(X_117))) != join(X_117,X_117)
| join(complement(complement(X_117)),X_117) != join(X_117,complement(complement(X_117)))
| join(complement(complement(X_117)),X_117) = join(X_117,X_117) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(complement(X_117)),X_117))),bind(Y,$fot(join(X_117,complement(complement(X_117))))),bind(Z,$fot(join(X_117,X_117)))]]) ).
cnf(refute_0_1485,plain,
( join(X_117,complement(complement(X_117))) != join(X_117,X_117)
| join(complement(complement(X_117)),X_117) = join(X_117,X_117) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_117)),X_117),join(X_117,complement(complement(X_117)))) )],[refute_0_1483,refute_0_1484]) ).
cnf(refute_0_1486,plain,
join(complement(complement(X_117)),X_117) = join(X_117,X_117),
inference(resolve,[$cnf( $equal(join(X_117,complement(complement(X_117))),join(X_117,X_117)) )],[refute_0_1482,refute_0_1485]) ).
cnf(refute_0_1487,plain,
complement(join(complement(complement(X_117)),X_117)) = complement(join(complement(complement(X_117)),X_117)),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(X_117)),X_117)))]]) ).
cnf(refute_0_1488,plain,
( complement(join(complement(complement(X_117)),X_117)) != complement(join(complement(complement(X_117)),X_117))
| join(complement(complement(X_117)),X_117) != join(X_117,X_117)
| complement(join(complement(complement(X_117)),X_117)) = complement(join(X_117,X_117)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(X_117)),X_117)),complement(join(complement(complement(X_117)),X_117))) ),[1,0],$fot(join(X_117,X_117))]]) ).
cnf(refute_0_1489,plain,
( join(complement(complement(X_117)),X_117) != join(X_117,X_117)
| complement(join(complement(complement(X_117)),X_117)) = complement(join(X_117,X_117)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_117)),X_117)),complement(join(complement(complement(X_117)),X_117))) )],[refute_0_1487,refute_0_1488]) ).
cnf(refute_0_1490,plain,
complement(join(complement(complement(X_117)),X_117)) = complement(join(X_117,X_117)),
inference(resolve,[$cnf( $equal(join(complement(complement(X_117)),X_117),join(X_117,X_117)) )],[refute_0_1486,refute_0_1489]) ).
cnf(refute_0_1491,plain,
join(zero,complement(join(complement(complement(X_117)),X_117))) = complement(join(complement(complement(X_117)),X_117)),
inference(subst,[],[refute_0_692:[bind(X_87,$fot(complement(join(complement(complement(X_117)),X_117))))]]) ).
cnf(refute_0_1492,plain,
( complement(join(complement(complement(X_117)),X_117)) != complement(join(X_117,X_117))
| join(zero,complement(join(complement(complement(X_117)),X_117))) != complement(join(complement(complement(X_117)),X_117))
| join(zero,complement(join(complement(complement(X_117)),X_117))) = complement(join(X_117,X_117)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(zero,complement(join(complement(complement(X_117)),X_117))))),bind(Y,$fot(complement(join(complement(complement(X_117)),X_117)))),bind(Z,$fot(complement(join(X_117,X_117))))]]) ).
cnf(refute_0_1493,plain,
( complement(join(complement(complement(X_117)),X_117)) != complement(join(X_117,X_117))
| join(zero,complement(join(complement(complement(X_117)),X_117))) = complement(join(X_117,X_117)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(complement(X_117)),X_117))),complement(join(complement(complement(X_117)),X_117))) )],[refute_0_1491,refute_0_1492]) ).
cnf(refute_0_1494,plain,
join(zero,complement(join(complement(complement(X_117)),X_117))) = complement(join(X_117,X_117)),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_117)),X_117)),complement(join(X_117,X_117))) )],[refute_0_1490,refute_0_1493]) ).
cnf(refute_0_1495,plain,
( complement(X_117) != join(zero,complement(join(complement(complement(X_117)),X_117)))
| join(zero,complement(join(complement(complement(X_117)),X_117))) != complement(join(X_117,X_117))
| complement(X_117) = complement(join(X_117,X_117)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_117),complement(join(X_117,X_117))) ),[0],$fot(join(zero,complement(join(complement(complement(X_117)),X_117))))]]) ).
cnf(refute_0_1496,plain,
( complement(X_117) != join(zero,complement(join(complement(complement(X_117)),X_117)))
| complement(X_117) = complement(join(X_117,X_117)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(complement(X_117)),X_117))),complement(join(X_117,X_117))) )],[refute_0_1494,refute_0_1495]) ).
cnf(refute_0_1497,plain,
complement(X_117) = complement(join(X_117,X_117)),
inference(resolve,[$cnf( $equal(complement(X_117),join(zero,complement(join(complement(complement(X_117)),X_117)))) )],[refute_0_1477,refute_0_1496]) ).
cnf(refute_0_1498,plain,
( complement(X_117) != complement(join(X_117,X_117))
| complement(join(X_117,X_117)) = complement(X_117) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_117))),bind(Y,$fot(complement(join(X_117,X_117))))]]) ).
cnf(refute_0_1499,plain,
complement(join(X_117,X_117)) = complement(X_117),
inference(resolve,[$cnf( $equal(complement(X_117),complement(join(X_117,X_117))) )],[refute_0_1497,refute_0_1498]) ).
cnf(refute_0_1500,plain,
complement(join(one,one)) = complement(one),
inference(subst,[],[refute_0_1499:[bind(X_117,$fot(one))]]) ).
cnf(refute_0_1501,plain,
complement(X_118) = complement(join(X_118,X_118)),
inference(subst,[],[refute_0_1497:[bind(X_117,$fot(X_118))]]) ).
cnf(refute_0_1502,plain,
join(X_118,X_118) = composition(X_118,join(one,one)),
inference(subst,[],[refute_0_186:[bind(A,$fot(X_118))]]) ).
cnf(refute_0_1503,plain,
( complement(X_118) != complement(join(X_118,X_118))
| join(X_118,X_118) != composition(X_118,join(one,one))
| complement(X_118) = complement(composition(X_118,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_118),complement(join(X_118,X_118))) ),[1,0],$fot(composition(X_118,join(one,one)))]]) ).
cnf(refute_0_1504,plain,
( complement(X_118) != complement(join(X_118,X_118))
| complement(X_118) = complement(composition(X_118,join(one,one))) ),
inference(resolve,[$cnf( $equal(join(X_118,X_118),composition(X_118,join(one,one))) )],[refute_0_1502,refute_0_1503]) ).
cnf(refute_0_1505,plain,
complement(X_118) = complement(composition(X_118,join(one,one))),
inference(resolve,[$cnf( $equal(complement(X_118),complement(join(X_118,X_118))) )],[refute_0_1501,refute_0_1504]) ).
cnf(refute_0_1506,plain,
( complement(X_118) != complement(composition(X_118,join(one,one)))
| complement(composition(X_118,join(one,one))) = complement(X_118) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_118))),bind(Y,$fot(complement(composition(X_118,join(one,one)))))]]) ).
cnf(refute_0_1507,plain,
complement(composition(X_118,join(one,one))) = complement(X_118),
inference(resolve,[$cnf( $equal(complement(X_118),complement(composition(X_118,join(one,one)))) )],[refute_0_1505,refute_0_1506]) ).
cnf(refute_0_1508,plain,
complement(composition(join(one,one),join(one,one))) = complement(join(one,one)),
inference(subst,[],[refute_0_1507:[bind(X_118,$fot(join(one,one)))]]) ).
cnf(refute_0_1509,plain,
( complement(composition(join(one,one),join(one,one))) != complement(join(one,one))
| complement(join(one,one)) != complement(one)
| complement(composition(join(one,one),join(one,one))) = complement(one) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(complement(composition(join(one,one),join(one,one))))),bind(Y,$fot(complement(join(one,one)))),bind(Z,$fot(complement(one)))]]) ).
cnf(refute_0_1510,plain,
( complement(join(one,one)) != complement(one)
| complement(composition(join(one,one),join(one,one))) = complement(one) ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),join(one,one))),complement(join(one,one))) )],[refute_0_1508,refute_0_1509]) ).
cnf(refute_0_1511,plain,
complement(composition(join(one,one),join(one,one))) = complement(one),
inference(resolve,[$cnf( $equal(complement(join(one,one)),complement(one)) )],[refute_0_1500,refute_0_1510]) ).
cnf(refute_0_1512,plain,
join(one,complement(composition(join(one,one),join(one,one)))) = join(one,complement(composition(join(one,one),join(one,one)))),
introduced(tautology,[refl,[$fot(join(one,complement(composition(join(one,one),join(one,one)))))]]) ).
cnf(refute_0_1513,plain,
( complement(composition(join(one,one),join(one,one))) != complement(one)
| join(one,complement(composition(join(one,one),join(one,one)))) != join(one,complement(composition(join(one,one),join(one,one))))
| join(one,complement(composition(join(one,one),join(one,one)))) = join(one,complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(composition(join(one,one),join(one,one)))),join(one,complement(composition(join(one,one),join(one,one))))) ),[1,1],$fot(complement(one))]]) ).
cnf(refute_0_1514,plain,
( complement(composition(join(one,one),join(one,one))) != complement(one)
| join(one,complement(composition(join(one,one),join(one,one)))) = join(one,complement(one)) ),
inference(resolve,[$cnf( $equal(join(one,complement(composition(join(one,one),join(one,one)))),join(one,complement(composition(join(one,one),join(one,one))))) )],[refute_0_1512,refute_0_1513]) ).
cnf(refute_0_1515,plain,
join(one,complement(composition(join(one,one),join(one,one)))) = join(one,complement(one)),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),join(one,one))),complement(one)) )],[refute_0_1511,refute_0_1514]) ).
cnf(refute_0_1516,plain,
( join(one,complement(composition(join(one,one),join(one,one)))) != join(one,complement(one))
| join(one,complement(one)) != top
| join(one,complement(composition(join(one,one),join(one,one)))) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,complement(composition(join(one,one),join(one,one)))))),bind(Y,$fot(join(one,complement(one)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1517,plain,
( join(one,complement(one)) != top
| join(one,complement(composition(join(one,one),join(one,one)))) = top ),
inference(resolve,[$cnf( $equal(join(one,complement(composition(join(one,one),join(one,one)))),join(one,complement(one))) )],[refute_0_1515,refute_0_1516]) ).
cnf(refute_0_1518,plain,
join(one,complement(composition(join(one,one),join(one,one)))) = top,
inference(resolve,[$cnf( $equal(join(one,complement(one)),top) )],[refute_0_1027,refute_0_1517]) ).
cnf(refute_0_1519,plain,
complement(join(one,complement(composition(join(one,one),join(one,one))))) = complement(join(one,complement(composition(join(one,one),join(one,one))))),
introduced(tautology,[refl,[$fot(complement(join(one,complement(composition(join(one,one),join(one,one))))))]]) ).
cnf(refute_0_1520,plain,
( complement(join(one,complement(composition(join(one,one),join(one,one))))) != complement(join(one,complement(composition(join(one,one),join(one,one)))))
| join(one,complement(composition(join(one,one),join(one,one)))) != top
| complement(join(one,complement(composition(join(one,one),join(one,one))))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(one,complement(composition(join(one,one),join(one,one))))),complement(join(one,complement(composition(join(one,one),join(one,one)))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1521,plain,
( join(one,complement(composition(join(one,one),join(one,one)))) != top
| complement(join(one,complement(composition(join(one,one),join(one,one))))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(one,complement(composition(join(one,one),join(one,one))))),complement(join(one,complement(composition(join(one,one),join(one,one)))))) )],[refute_0_1519,refute_0_1520]) ).
cnf(refute_0_1522,plain,
complement(join(one,complement(composition(join(one,one),join(one,one))))) = complement(top),
inference(resolve,[$cnf( $equal(join(one,complement(composition(join(one,one),join(one,one)))),top) )],[refute_0_1518,refute_0_1521]) ).
cnf(refute_0_1523,plain,
( complement(join(one,complement(composition(join(one,one),join(one,one))))) != complement(top)
| complement(top) != zero
| complement(join(one,complement(composition(join(one,one),join(one,one))))) = zero ),
inference(subst,[],[refute_0_7:[bind(X,$fot(complement(join(one,complement(composition(join(one,one),join(one,one))))))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1524,plain,
( complement(top) != zero
| complement(join(one,complement(composition(join(one,one),join(one,one))))) = zero ),
inference(resolve,[$cnf( $equal(complement(join(one,complement(composition(join(one,one),join(one,one))))),complement(top)) )],[refute_0_1522,refute_0_1523]) ).
cnf(refute_0_1525,plain,
complement(join(one,complement(composition(join(one,one),join(one,one))))) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_1524]) ).
cnf(refute_0_1526,plain,
join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) = join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))),
introduced(tautology,[refl,[$fot(join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))))]]) ).
cnf(refute_0_1527,plain,
( complement(join(one,complement(composition(join(one,one),join(one,one))))) != zero
| join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) != join(one,complement(join(one,complement(composition(join(one,one),join(one,one))))))
| join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) = join(one,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))),join(one,complement(join(one,complement(composition(join(one,one),join(one,one))))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_1528,plain,
( complement(join(one,complement(composition(join(one,one),join(one,one))))) != zero
| join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) = join(one,zero) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))),join(one,complement(join(one,complement(composition(join(one,one),join(one,one))))))) )],[refute_0_1526,refute_0_1527]) ).
cnf(refute_0_1529,plain,
join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) = join(one,zero),
inference(resolve,[$cnf( $equal(complement(join(one,complement(composition(join(one,one),join(one,one))))),zero) )],[refute_0_1525,refute_0_1528]) ).
cnf(refute_0_1530,plain,
( join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) != join(one,zero)
| join(one,zero) != one
| join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) = one ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))))),bind(Y,$fot(join(one,zero))),bind(Z,$fot(one))]]) ).
cnf(refute_0_1531,plain,
( join(one,zero) != one
| join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) = one ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))),join(one,zero)) )],[refute_0_1529,refute_0_1530]) ).
cnf(refute_0_1532,plain,
join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) = one,
inference(resolve,[$cnf( $equal(join(one,zero),one) )],[refute_0_1470,refute_0_1531]) ).
cnf(refute_0_1533,plain,
( composition(join(one,one),join(one,one)) != join(one,complement(join(one,complement(composition(join(one,one),join(one,one))))))
| join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))) != one
| composition(join(one,one),join(one,one)) = one ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,one),join(one,one)),one) ),[0],$fot(join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))))]]) ).
cnf(refute_0_1534,plain,
( composition(join(one,one),join(one,one)) != join(one,complement(join(one,complement(composition(join(one,one),join(one,one))))))
| composition(join(one,one),join(one,one)) = one ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,complement(composition(join(one,one),join(one,one)))))),one) )],[refute_0_1532,refute_0_1533]) ).
cnf(refute_0_1535,plain,
composition(join(one,one),join(one,one)) = one,
inference(resolve,[$cnf( $equal(composition(join(one,one),join(one,one)),join(one,complement(join(one,complement(composition(join(one,one),join(one,one))))))) )],[refute_0_1469,refute_0_1534]) ).
cnf(refute_0_1536,plain,
( composition(join(one,one),composition(join(one,one),C)) != composition(composition(join(one,one),join(one,one)),C)
| composition(join(one,one),join(one,one)) != one
| composition(join(one,one),composition(join(one,one),C)) = composition(one,C) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),composition(join(one,one),C)),composition(composition(join(one,one),join(one,one)),C)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1537,plain,
( composition(join(one,one),composition(join(one,one),C)) != composition(composition(join(one,one),join(one,one)),C)
| composition(join(one,one),composition(join(one,one),C)) = composition(one,C) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(one,one)),one) )],[refute_0_1535,refute_0_1536]) ).
cnf(refute_0_1538,plain,
composition(join(one,one),composition(join(one,one),C)) = composition(one,C),
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(join(one,one),C)),composition(composition(join(one,one),join(one,one)),C)) )],[refute_0_1397,refute_0_1537]) ).
cnf(refute_0_1539,plain,
( X_24 != composition(one,X_24)
| composition(one,X_24) = X_24 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_24)),bind(Y,$fot(composition(one,X_24)))]]) ).
cnf(refute_0_1540,plain,
composition(one,X_24) = X_24,
inference(resolve,[$cnf( $equal(X_24,composition(one,X_24)) )],[refute_0_51,refute_0_1539]) ).
cnf(refute_0_1541,plain,
composition(one,C) = C,
inference(subst,[],[refute_0_1540:[bind(X_24,$fot(C))]]) ).
cnf(refute_0_1542,plain,
( composition(join(one,one),composition(join(one,one),C)) != composition(one,C)
| composition(one,C) != C
| composition(join(one,one),composition(join(one,one),C)) = C ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,one),composition(join(one,one),C)),C) ),[0],$fot(composition(one,C))]]) ).
cnf(refute_0_1543,plain,
( composition(join(one,one),composition(join(one,one),C)) != composition(one,C)
| composition(join(one,one),composition(join(one,one),C)) = C ),
inference(resolve,[$cnf( $equal(composition(one,C),C) )],[refute_0_1541,refute_0_1542]) ).
cnf(refute_0_1544,plain,
composition(join(one,one),composition(join(one,one),C)) = C,
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(join(one,one),C)),composition(one,C)) )],[refute_0_1538,refute_0_1543]) ).
cnf(refute_0_1545,plain,
composition(join(one,one),composition(join(one,one),X_56)) = X_56,
inference(subst,[],[refute_0_1544:[bind(C,$fot(X_56))]]) ).
cnf(refute_0_1546,plain,
meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))),
introduced(tautology,[refl,[$fot(meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))))]]) ).
cnf(refute_0_1547,plain,
( composition(join(one,one),composition(join(one,one),X_56)) != X_56
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) != meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56)))
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = meet(join(X_56,X_56),X_56) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))),meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56)))) ),[1,1],$fot(X_56)]]) ).
cnf(refute_0_1548,plain,
( composition(join(one,one),composition(join(one,one),X_56)) != X_56
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = meet(join(X_56,X_56),X_56) ),
inference(resolve,[$cnf( $equal(meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))),meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56)))) )],[refute_0_1546,refute_0_1547]) ).
cnf(refute_0_1549,plain,
meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = meet(join(X_56,X_56),X_56),
inference(resolve,[$cnf( $equal(composition(join(one,one),composition(join(one,one),X_56)),X_56) )],[refute_0_1545,refute_0_1548]) ).
cnf(refute_0_1550,plain,
( meet(join(X_56,X_56),X_56) != X_56
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) != meet(join(X_56,X_56),X_56)
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = X_56 ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))))),bind(Y,$fot(meet(join(X_56,X_56),X_56))),bind(Z,$fot(X_56))]]) ).
cnf(refute_0_1551,plain,
( meet(join(X_56,X_56),X_56) != X_56
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = X_56 ),
inference(resolve,[$cnf( $equal(meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))),meet(join(X_56,X_56),X_56)) )],[refute_0_1549,refute_0_1550]) ).
cnf(refute_0_1552,plain,
meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) = X_56,
inference(resolve,[$cnf( $equal(meet(join(X_56,X_56),X_56),X_56) )],[refute_0_1396,refute_0_1551]) ).
cnf(refute_0_1553,plain,
( meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) != X_56
| meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) != join(X_56,X_56)
| X_56 = join(X_56,X_56) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))),join(X_56,X_56)) ),[0],$fot(X_56)]]) ).
cnf(refute_0_1554,plain,
( meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))) != join(X_56,X_56)
| X_56 = join(X_56,X_56) ),
inference(resolve,[$cnf( $equal(meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))),X_56) )],[refute_0_1552,refute_0_1553]) ).
cnf(refute_0_1555,plain,
X_56 = join(X_56,X_56),
inference(resolve,[$cnf( $equal(meet(join(X_56,X_56),composition(join(one,one),composition(join(one,one),X_56))),join(X_56,X_56)) )],[refute_0_1382,refute_0_1554]) ).
cnf(refute_0_1556,plain,
( X_56 != join(X_56,X_56)
| join(X_56,X_56) = X_56 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_56)),bind(Y,$fot(join(X_56,X_56)))]]) ).
cnf(refute_0_1557,plain,
join(X_56,X_56) = X_56,
inference(resolve,[$cnf( $equal(X_56,join(X_56,X_56)) )],[refute_0_1555,refute_0_1556]) ).
cnf(refute_0_1558,plain,
join(one,one) = one,
inference(subst,[],[refute_0_1557:[bind(X_56,$fot(one))]]) ).
cnf(refute_0_1559,plain,
composition(join(X_84,X_85),join(one,one)) = composition(join(X_84,X_85),join(one,one)),
introduced(tautology,[refl,[$fot(composition(join(X_84,X_85),join(one,one)))]]) ).
cnf(refute_0_1560,plain,
( composition(join(X_84,X_85),join(one,one)) != composition(join(X_84,X_85),join(one,one))
| join(one,one) != one
| composition(join(X_84,X_85),join(one,one)) = composition(join(X_84,X_85),one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_84,X_85),join(one,one)),composition(join(X_84,X_85),join(one,one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1561,plain,
( join(one,one) != one
| composition(join(X_84,X_85),join(one,one)) = composition(join(X_84,X_85),one) ),
inference(resolve,[$cnf( $equal(composition(join(X_84,X_85),join(one,one)),composition(join(X_84,X_85),join(one,one))) )],[refute_0_1559,refute_0_1560]) ).
cnf(refute_0_1562,plain,
composition(join(X_84,X_85),join(one,one)) = composition(join(X_84,X_85),one),
inference(resolve,[$cnf( $equal(join(one,one),one) )],[refute_0_1558,refute_0_1561]) ).
cnf(refute_0_1563,plain,
( composition(join(X_84,X_85),join(one,one)) != composition(join(X_84,X_85),one)
| composition(join(X_84,X_85),one) != join(X_84,X_85)
| composition(join(X_84,X_85),join(one,one)) = join(X_84,X_85) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(X_84,X_85),join(one,one)))),bind(Y,$fot(composition(join(X_84,X_85),one))),bind(Z,$fot(join(X_84,X_85)))]]) ).
cnf(refute_0_1564,plain,
( composition(join(X_84,X_85),one) != join(X_84,X_85)
| composition(join(X_84,X_85),join(one,one)) = join(X_84,X_85) ),
inference(resolve,[$cnf( $equal(composition(join(X_84,X_85),join(one,one)),composition(join(X_84,X_85),one)) )],[refute_0_1562,refute_0_1563]) ).
cnf(refute_0_1565,plain,
composition(join(X_84,X_85),join(one,one)) = join(X_84,X_85),
inference(resolve,[$cnf( $equal(composition(join(X_84,X_85),one),join(X_84,X_85)) )],[refute_0_1347,refute_0_1564]) ).
cnf(refute_0_1566,plain,
converse(composition(join(X_84,X_85),join(one,one))) = converse(composition(join(X_84,X_85),join(one,one))),
introduced(tautology,[refl,[$fot(converse(composition(join(X_84,X_85),join(one,one))))]]) ).
cnf(refute_0_1567,plain,
( composition(join(X_84,X_85),join(one,one)) != join(X_84,X_85)
| converse(composition(join(X_84,X_85),join(one,one))) != converse(composition(join(X_84,X_85),join(one,one)))
| converse(composition(join(X_84,X_85),join(one,one))) = converse(join(X_84,X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(X_84,X_85),join(one,one))),converse(composition(join(X_84,X_85),join(one,one)))) ),[1,0],$fot(join(X_84,X_85))]]) ).
cnf(refute_0_1568,plain,
( composition(join(X_84,X_85),join(one,one)) != join(X_84,X_85)
| converse(composition(join(X_84,X_85),join(one,one))) = converse(join(X_84,X_85)) ),
inference(resolve,[$cnf( $equal(converse(composition(join(X_84,X_85),join(one,one))),converse(composition(join(X_84,X_85),join(one,one)))) )],[refute_0_1566,refute_0_1567]) ).
cnf(refute_0_1569,plain,
converse(composition(join(X_84,X_85),join(one,one))) = converse(join(X_84,X_85)),
inference(resolve,[$cnf( $equal(composition(join(X_84,X_85),join(one,one)),join(X_84,X_85)) )],[refute_0_1565,refute_0_1568]) ).
cnf(refute_0_1570,plain,
( converse(composition(join(X_84,X_85),join(one,one))) != converse(composition(join(one,one),join(X_85,X_84)))
| converse(composition(join(X_84,X_85),join(one,one))) != converse(join(X_84,X_85))
| converse(join(X_84,X_85)) = converse(composition(join(one,one),join(X_85,X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(X_84,X_85),join(one,one))),converse(composition(join(one,one),join(X_85,X_84)))) ),[0],$fot(converse(join(X_84,X_85)))]]) ).
cnf(refute_0_1571,plain,
( converse(composition(join(X_84,X_85),join(one,one))) != converse(composition(join(one,one),join(X_85,X_84)))
| converse(join(X_84,X_85)) = converse(composition(join(one,one),join(X_85,X_84))) ),
inference(resolve,[$cnf( $equal(converse(composition(join(X_84,X_85),join(one,one))),converse(join(X_84,X_85))) )],[refute_0_1569,refute_0_1570]) ).
cnf(refute_0_1572,plain,
composition(one,join(X_85,X_84)) = join(X_85,X_84),
inference(subst,[],[refute_0_1540:[bind(X_24,$fot(join(X_85,X_84)))]]) ).
cnf(refute_0_1573,plain,
composition(join(one,one),join(X_85,X_84)) = composition(join(one,one),join(X_85,X_84)),
introduced(tautology,[refl,[$fot(composition(join(one,one),join(X_85,X_84)))]]) ).
cnf(refute_0_1574,plain,
( composition(join(one,one),join(X_85,X_84)) != composition(join(one,one),join(X_85,X_84))
| join(one,one) != one
| composition(join(one,one),join(X_85,X_84)) = composition(one,join(X_85,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),join(X_85,X_84)),composition(join(one,one),join(X_85,X_84))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1575,plain,
( join(one,one) != one
| composition(join(one,one),join(X_85,X_84)) = composition(one,join(X_85,X_84)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(X_85,X_84)),composition(join(one,one),join(X_85,X_84))) )],[refute_0_1573,refute_0_1574]) ).
cnf(refute_0_1576,plain,
composition(join(one,one),join(X_85,X_84)) = composition(one,join(X_85,X_84)),
inference(resolve,[$cnf( $equal(join(one,one),one) )],[refute_0_1558,refute_0_1575]) ).
cnf(refute_0_1577,plain,
( composition(join(one,one),join(X_85,X_84)) != composition(one,join(X_85,X_84))
| composition(one,join(X_85,X_84)) != join(X_85,X_84)
| composition(join(one,one),join(X_85,X_84)) = join(X_85,X_84) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(one,one),join(X_85,X_84)))),bind(Y,$fot(composition(one,join(X_85,X_84)))),bind(Z,$fot(join(X_85,X_84)))]]) ).
cnf(refute_0_1578,plain,
( composition(one,join(X_85,X_84)) != join(X_85,X_84)
| composition(join(one,one),join(X_85,X_84)) = join(X_85,X_84) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(X_85,X_84)),composition(one,join(X_85,X_84))) )],[refute_0_1576,refute_0_1577]) ).
cnf(refute_0_1579,plain,
composition(join(one,one),join(X_85,X_84)) = join(X_85,X_84),
inference(resolve,[$cnf( $equal(composition(one,join(X_85,X_84)),join(X_85,X_84)) )],[refute_0_1572,refute_0_1578]) ).
cnf(refute_0_1580,plain,
converse(composition(join(one,one),join(X_85,X_84))) = converse(composition(join(one,one),join(X_85,X_84))),
introduced(tautology,[refl,[$fot(converse(composition(join(one,one),join(X_85,X_84))))]]) ).
cnf(refute_0_1581,plain,
( composition(join(one,one),join(X_85,X_84)) != join(X_85,X_84)
| converse(composition(join(one,one),join(X_85,X_84))) != converse(composition(join(one,one),join(X_85,X_84)))
| converse(composition(join(one,one),join(X_85,X_84))) = converse(join(X_85,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(one,one),join(X_85,X_84))),converse(composition(join(one,one),join(X_85,X_84)))) ),[1,0],$fot(join(X_85,X_84))]]) ).
cnf(refute_0_1582,plain,
( composition(join(one,one),join(X_85,X_84)) != join(X_85,X_84)
| converse(composition(join(one,one),join(X_85,X_84))) = converse(join(X_85,X_84)) ),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),join(X_85,X_84))),converse(composition(join(one,one),join(X_85,X_84)))) )],[refute_0_1580,refute_0_1581]) ).
cnf(refute_0_1583,plain,
converse(composition(join(one,one),join(X_85,X_84))) = converse(join(X_85,X_84)),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(X_85,X_84)),join(X_85,X_84)) )],[refute_0_1579,refute_0_1582]) ).
cnf(refute_0_1584,plain,
( converse(composition(join(one,one),join(X_85,X_84))) != converse(join(X_85,X_84))
| converse(join(X_84,X_85)) != converse(composition(join(one,one),join(X_85,X_84)))
| converse(join(X_84,X_85)) = converse(join(X_85,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_84,X_85)),converse(composition(join(one,one),join(X_85,X_84)))) ),[1],$fot(converse(join(X_85,X_84)))]]) ).
cnf(refute_0_1585,plain,
( converse(join(X_84,X_85)) != converse(composition(join(one,one),join(X_85,X_84)))
| converse(join(X_84,X_85)) = converse(join(X_85,X_84)) ),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),join(X_85,X_84))),converse(join(X_85,X_84))) )],[refute_0_1583,refute_0_1584]) ).
cnf(refute_0_1586,plain,
( converse(composition(join(X_84,X_85),join(one,one))) != converse(composition(join(one,one),join(X_85,X_84)))
| converse(join(X_84,X_85)) = converse(join(X_85,X_84)) ),
inference(resolve,[$cnf( $equal(converse(join(X_84,X_85)),converse(composition(join(one,one),join(X_85,X_84)))) )],[refute_0_1571,refute_0_1585]) ).
cnf(refute_0_1587,plain,
converse(join(X_84,X_85)) = converse(join(X_85,X_84)),
inference(resolve,[$cnf( $equal(converse(composition(join(X_84,X_85),join(one,one))),converse(composition(join(one,one),join(X_85,X_84)))) )],[refute_0_1346,refute_0_1586]) ).
cnf(refute_0_1588,plain,
( converse(join(X_84,X_85)) != converse(join(X_85,X_84))
| converse(join(X_85,X_84)) = converse(join(X_84,X_85)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_84,X_85)))),bind(Y,$fot(converse(join(X_85,X_84))))]]) ).
cnf(refute_0_1589,plain,
converse(join(X_85,X_84)) = converse(join(X_84,X_85)),
inference(resolve,[$cnf( $equal(converse(join(X_84,X_85)),converse(join(X_85,X_84))) )],[refute_0_1587,refute_0_1588]) ).
cnf(refute_0_1590,plain,
converse(join(complement(X_208),X_208)) = converse(join(X_208,complement(X_208))),
inference(subst,[],[refute_0_1589:[bind(X_84,$fot(X_208)),bind(X_85,$fot(complement(X_208)))]]) ).
cnf(refute_0_1591,plain,
( converse(join(X_208,complement(X_208))) != top
| converse(join(complement(X_208),X_208)) != converse(join(X_208,complement(X_208)))
| converse(join(complement(X_208),X_208)) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(complement(X_208),X_208)))),bind(Y,$fot(converse(join(X_208,complement(X_208))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1592,plain,
( converse(join(X_208,complement(X_208))) != top
| converse(join(complement(X_208),X_208)) = top ),
inference(resolve,[$cnf( $equal(converse(join(complement(X_208),X_208)),converse(join(X_208,complement(X_208)))) )],[refute_0_1590,refute_0_1591]) ).
cnf(refute_0_1593,plain,
converse(join(complement(X_208),X_208)) = top,
inference(resolve,[$cnf( $equal(converse(join(X_208,complement(X_208))),top) )],[refute_0_1324,refute_0_1592]) ).
cnf(refute_0_1594,plain,
join(converse(complement(X_208)),converse(X_208)) = converse(join(complement(X_208),X_208)),
inference(subst,[],[refute_0_544:[bind(A,$fot(complement(X_208))),bind(B,$fot(X_208))]]) ).
cnf(refute_0_1595,plain,
( converse(join(complement(X_208),X_208)) != top
| join(converse(complement(X_208)),converse(X_208)) != converse(join(complement(X_208),X_208))
| join(converse(complement(X_208)),converse(X_208)) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(converse(complement(X_208)),converse(X_208)))),bind(Y,$fot(converse(join(complement(X_208),X_208)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1596,plain,
( converse(join(complement(X_208),X_208)) != top
| join(converse(complement(X_208)),converse(X_208)) = top ),
inference(resolve,[$cnf( $equal(join(converse(complement(X_208)),converse(X_208)),converse(join(complement(X_208),X_208))) )],[refute_0_1594,refute_0_1595]) ).
cnf(refute_0_1597,plain,
join(converse(complement(X_208)),converse(X_208)) = top,
inference(resolve,[$cnf( $equal(converse(join(complement(X_208),X_208)),top) )],[refute_0_1593,refute_0_1596]) ).
cnf(refute_0_1598,plain,
complement(complement(converse(X_208))) = converse(X_208),
inference(subst,[],[refute_0_383:[bind(X_87,$fot(converse(X_208)))]]) ).
cnf(refute_0_1599,plain,
join(converse(complement(X_208)),complement(complement(converse(X_208)))) = join(converse(complement(X_208)),complement(complement(converse(X_208)))),
introduced(tautology,[refl,[$fot(join(converse(complement(X_208)),complement(complement(converse(X_208)))))]]) ).
cnf(refute_0_1600,plain,
( complement(complement(converse(X_208))) != converse(X_208)
| join(converse(complement(X_208)),complement(complement(converse(X_208)))) != join(converse(complement(X_208)),complement(complement(converse(X_208))))
| join(converse(complement(X_208)),complement(complement(converse(X_208)))) = join(converse(complement(X_208)),converse(X_208)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(complement(X_208)),complement(complement(converse(X_208)))),join(converse(complement(X_208)),complement(complement(converse(X_208))))) ),[1,1],$fot(converse(X_208))]]) ).
cnf(refute_0_1601,plain,
( complement(complement(converse(X_208))) != converse(X_208)
| join(converse(complement(X_208)),complement(complement(converse(X_208)))) = join(converse(complement(X_208)),converse(X_208)) ),
inference(resolve,[$cnf( $equal(join(converse(complement(X_208)),complement(complement(converse(X_208)))),join(converse(complement(X_208)),complement(complement(converse(X_208))))) )],[refute_0_1599,refute_0_1600]) ).
cnf(refute_0_1602,plain,
join(converse(complement(X_208)),complement(complement(converse(X_208)))) = join(converse(complement(X_208)),converse(X_208)),
inference(resolve,[$cnf( $equal(complement(complement(converse(X_208))),converse(X_208)) )],[refute_0_1598,refute_0_1601]) ).
cnf(refute_0_1603,plain,
( join(converse(complement(X_208)),complement(complement(converse(X_208)))) != join(converse(complement(X_208)),converse(X_208))
| join(converse(complement(X_208)),converse(X_208)) != top
| join(converse(complement(X_208)),complement(complement(converse(X_208)))) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(converse(complement(X_208)),complement(complement(converse(X_208)))))),bind(Y,$fot(join(converse(complement(X_208)),converse(X_208)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1604,plain,
( join(converse(complement(X_208)),converse(X_208)) != top
| join(converse(complement(X_208)),complement(complement(converse(X_208)))) = top ),
inference(resolve,[$cnf( $equal(join(converse(complement(X_208)),complement(complement(converse(X_208)))),join(converse(complement(X_208)),converse(X_208))) )],[refute_0_1602,refute_0_1603]) ).
cnf(refute_0_1605,plain,
join(converse(complement(X_208)),complement(complement(converse(X_208)))) = top,
inference(resolve,[$cnf( $equal(join(converse(complement(X_208)),converse(X_208)),top) )],[refute_0_1597,refute_0_1604]) ).
cnf(refute_0_1606,plain,
complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))) = complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))),
introduced(tautology,[refl,[$fot(complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))]]) ).
cnf(refute_0_1607,plain,
( complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))) != complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))
| join(converse(complement(X_208)),complement(complement(converse(X_208)))) != top
| complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1608,plain,
( join(converse(complement(X_208)),complement(complement(converse(X_208)))) != top
| complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) )],[refute_0_1606,refute_0_1607]) ).
cnf(refute_0_1609,plain,
complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))) = complement(top),
inference(resolve,[$cnf( $equal(join(converse(complement(X_208)),complement(complement(converse(X_208)))),top) )],[refute_0_1605,refute_0_1608]) ).
cnf(refute_0_1610,plain,
( complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))) != complement(top)
| complement(top) != zero
| complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))) = zero ),
inference(subst,[],[refute_0_7:[bind(X,$fot(complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1611,plain,
( complement(top) != zero
| complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))) = zero ),
inference(resolve,[$cnf( $equal(complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))),complement(top)) )],[refute_0_1609,refute_0_1610]) ).
cnf(refute_0_1612,plain,
complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_283,refute_0_1611]) ).
cnf(refute_0_1613,plain,
join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) = join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))),
introduced(tautology,[refl,[$fot(join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))))]]) ).
cnf(refute_0_1614,plain,
( complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))) != zero
| join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) != join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))
| join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) = join(converse(complement(X_208)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))),join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_1615,plain,
( complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))) != zero
| join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) = join(converse(complement(X_208)),zero) ),
inference(resolve,[$cnf( $equal(join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))),join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))) )],[refute_0_1613,refute_0_1614]) ).
cnf(refute_0_1616,plain,
join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) = join(converse(complement(X_208)),zero),
inference(resolve,[$cnf( $equal(complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))),zero) )],[refute_0_1612,refute_0_1615]) ).
cnf(refute_0_1617,plain,
( join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) != join(converse(complement(X_208)),zero)
| join(converse(complement(X_208)),zero) != converse(complement(X_208))
| join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) = converse(complement(X_208)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))))),bind(Y,$fot(join(converse(complement(X_208)),zero))),bind(Z,$fot(converse(complement(X_208))))]]) ).
cnf(refute_0_1618,plain,
( join(converse(complement(X_208)),zero) != converse(complement(X_208))
| join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) = converse(complement(X_208)) ),
inference(resolve,[$cnf( $equal(join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))),join(converse(complement(X_208)),zero)) )],[refute_0_1616,refute_0_1617]) ).
cnf(refute_0_1619,plain,
join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) = converse(complement(X_208)),
inference(resolve,[$cnf( $equal(join(converse(complement(X_208)),zero),converse(complement(X_208))) )],[refute_0_1316,refute_0_1618]) ).
cnf(refute_0_1620,plain,
( complement(converse(X_208)) != join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))
| join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))) != converse(complement(X_208))
| complement(converse(X_208)) = converse(complement(X_208)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(converse(X_208)),converse(complement(X_208))) ),[0],$fot(join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))))]]) ).
cnf(refute_0_1621,plain,
( complement(converse(X_208)) != join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))
| complement(converse(X_208)) = converse(complement(X_208)) ),
inference(resolve,[$cnf( $equal(join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208)))))),converse(complement(X_208))) )],[refute_0_1619,refute_0_1620]) ).
cnf(refute_0_1622,plain,
complement(converse(X_208)) = converse(complement(X_208)),
inference(resolve,[$cnf( $equal(complement(converse(X_208)),join(converse(complement(X_208)),complement(join(converse(complement(X_208)),complement(complement(converse(X_208))))))) )],[refute_0_1313,refute_0_1621]) ).
cnf(refute_0_1623,plain,
( complement(converse(X_208)) != converse(complement(X_208))
| converse(complement(X_208)) = complement(converse(X_208)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(converse(X_208)))),bind(Y,$fot(converse(complement(X_208))))]]) ).
cnf(refute_0_1624,plain,
converse(complement(X_208)) = complement(converse(X_208)),
inference(resolve,[$cnf( $equal(complement(converse(X_208)),converse(complement(X_208))) )],[refute_0_1622,refute_0_1623]) ).
cnf(refute_0_1625,plain,
( converse(complement(X_208)) != complement(converse(X_208))
| converse(composition(complement(X_208),join(converse(X_319),X_320))) != composition(join(X_319,converse(X_320)),converse(complement(X_208)))
| converse(composition(complement(X_208),join(converse(X_319),X_320))) = composition(join(X_319,converse(X_320)),complement(converse(X_208))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(complement(X_208),join(converse(X_319),X_320))),composition(join(X_319,converse(X_320)),converse(complement(X_208)))) ),[1,1],$fot(complement(converse(X_208)))]]) ).
cnf(refute_0_1626,plain,
( converse(composition(complement(X_208),join(converse(X_319),X_320))) != composition(join(X_319,converse(X_320)),converse(complement(X_208)))
| converse(composition(complement(X_208),join(converse(X_319),X_320))) = composition(join(X_319,converse(X_320)),complement(converse(X_208))) ),
inference(resolve,[$cnf( $equal(converse(complement(X_208)),complement(converse(X_208))) )],[refute_0_1624,refute_0_1625]) ).
cnf(refute_0_1627,plain,
converse(composition(complement(X_208),join(converse(X_319),X_320))) = composition(join(X_319,converse(X_320)),complement(converse(X_208))),
inference(resolve,[$cnf( $equal(converse(composition(complement(X_208),join(converse(X_319),X_320))),composition(join(X_319,converse(X_320)),converse(complement(X_208)))) )],[refute_0_1190,refute_0_1626]) ).
cnf(refute_0_1628,plain,
( converse(composition(complement(X_208),join(converse(X_319),X_320))) != composition(join(X_319,converse(X_320)),complement(converse(X_208)))
| composition(join(X_319,converse(X_320)),complement(converse(X_208))) = converse(composition(complement(X_208),join(converse(X_319),X_320))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(complement(X_208),join(converse(X_319),X_320))))),bind(Y,$fot(composition(join(X_319,converse(X_320)),complement(converse(X_208)))))]]) ).
cnf(refute_0_1629,plain,
composition(join(X_319,converse(X_320)),complement(converse(X_208))) = converse(composition(complement(X_208),join(converse(X_319),X_320))),
inference(resolve,[$cnf( $equal(converse(composition(complement(X_208),join(converse(X_319),X_320))),composition(join(X_319,converse(X_320)),complement(converse(X_208)))) )],[refute_0_1627,refute_0_1628]) ).
cnf(refute_0_1630,plain,
composition(join(one,converse(complement(meet(one,composition(top,complement(one)))))),complement(converse(composition(X_475,top)))) = converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))),
inference(subst,[],[refute_0_1629:[bind(X_208,$fot(composition(X_475,top))),bind(X_319,$fot(one)),bind(X_320,$fot(complement(meet(one,composition(top,complement(one))))))]]) ).
cnf(refute_0_1631,plain,
X_141 = join(meet(X_141,X_140),meet(complement(X_140),X_141)),
inference(subst,[],[refute_0_1220:[bind(X_103,$fot(X_140)),bind(X_104,$fot(X_141))]]) ).
cnf(refute_0_1632,plain,
meet(X_140,X_141) = meet(X_141,X_140),
inference(subst,[],[refute_0_623:[bind(X_6,$fot(X_140)),bind(X_7,$fot(X_141))]]) ).
cnf(refute_0_1633,plain,
( meet(X_140,X_141) != meet(X_141,X_140)
| meet(X_141,X_140) = meet(X_140,X_141) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_140,X_141))),bind(Y,$fot(meet(X_141,X_140)))]]) ).
cnf(refute_0_1634,plain,
meet(X_141,X_140) = meet(X_140,X_141),
inference(resolve,[$cnf( $equal(meet(X_140,X_141),meet(X_141,X_140)) )],[refute_0_1632,refute_0_1633]) ).
cnf(refute_0_1635,plain,
( X_141 != join(meet(X_141,X_140),meet(complement(X_140),X_141))
| meet(X_141,X_140) != meet(X_140,X_141)
| X_141 = join(meet(X_140,X_141),meet(complement(X_140),X_141)) ),
introduced(tautology,[equality,[$cnf( $equal(X_141,join(meet(X_141,X_140),meet(complement(X_140),X_141))) ),[1,0],$fot(meet(X_140,X_141))]]) ).
cnf(refute_0_1636,plain,
( X_141 != join(meet(X_141,X_140),meet(complement(X_140),X_141))
| X_141 = join(meet(X_140,X_141),meet(complement(X_140),X_141)) ),
inference(resolve,[$cnf( $equal(meet(X_141,X_140),meet(X_140,X_141)) )],[refute_0_1634,refute_0_1635]) ).
cnf(refute_0_1637,plain,
X_141 = join(meet(X_140,X_141),meet(complement(X_140),X_141)),
inference(resolve,[$cnf( $equal(X_141,join(meet(X_141,X_140),meet(complement(X_140),X_141))) )],[refute_0_1631,refute_0_1636]) ).
cnf(refute_0_1638,plain,
composition(join(X_32,one),X_233) = join(meet(X_233,composition(join(X_32,one),X_233)),meet(complement(X_233),composition(join(X_32,one),X_233))),
inference(subst,[],[refute_0_1637:[bind(X_140,$fot(X_233)),bind(X_141,$fot(composition(join(X_32,one),X_233)))]]) ).
cnf(refute_0_1639,plain,
X_233 = meet(X_233,composition(join(X_32,one),X_233)),
inference(subst,[],[refute_0_706:[bind(X_109,$fot(X_233))]]) ).
cnf(refute_0_1640,plain,
( X_233 != meet(X_233,composition(join(X_32,one),X_233))
| meet(X_233,composition(join(X_32,one),X_233)) = X_233 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_233)),bind(Y,$fot(meet(X_233,composition(join(X_32,one),X_233))))]]) ).
cnf(refute_0_1641,plain,
meet(X_233,composition(join(X_32,one),X_233)) = X_233,
inference(resolve,[$cnf( $equal(X_233,meet(X_233,composition(join(X_32,one),X_233))) )],[refute_0_1639,refute_0_1640]) ).
cnf(refute_0_1642,plain,
( composition(join(X_32,one),X_233) != join(meet(X_233,composition(join(X_32,one),X_233)),meet(complement(X_233),composition(join(X_32,one),X_233)))
| meet(X_233,composition(join(X_32,one),X_233)) != X_233
| composition(join(X_32,one),X_233) = join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_32,one),X_233),join(meet(X_233,composition(join(X_32,one),X_233)),meet(complement(X_233),composition(join(X_32,one),X_233)))) ),[1,0],$fot(X_233)]]) ).
cnf(refute_0_1643,plain,
( composition(join(X_32,one),X_233) != join(meet(X_233,composition(join(X_32,one),X_233)),meet(complement(X_233),composition(join(X_32,one),X_233)))
| composition(join(X_32,one),X_233) = join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) ),
inference(resolve,[$cnf( $equal(meet(X_233,composition(join(X_32,one),X_233)),X_233) )],[refute_0_1641,refute_0_1642]) ).
cnf(refute_0_1644,plain,
composition(join(X_32,one),X_233) = join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))),
inference(resolve,[$cnf( $equal(composition(join(X_32,one),X_233),join(meet(X_233,composition(join(X_32,one),X_233)),meet(complement(X_233),composition(join(X_32,one),X_233)))) )],[refute_0_1638,refute_0_1643]) ).
cnf(refute_0_1645,plain,
join(one,join(converse(X_13),X_37)) = join(join(one,converse(X_13)),X_37),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(one)),bind(B,$fot(converse(X_13))),bind(C,$fot(X_37))]]) ).
cnf(refute_0_1646,plain,
( join(one,converse(X_13)) != converse(join(one,X_13))
| join(one,join(converse(X_13),X_37)) != join(join(one,converse(X_13)),X_37)
| join(one,join(converse(X_13),X_37)) = join(converse(join(one,X_13)),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(converse(X_13),X_37)),join(join(one,converse(X_13)),X_37)) ),[1,0],$fot(converse(join(one,X_13)))]]) ).
cnf(refute_0_1647,plain,
( join(one,join(converse(X_13),X_37)) != join(join(one,converse(X_13)),X_37)
| join(one,join(converse(X_13),X_37)) = join(converse(join(one,X_13)),X_37) ),
inference(resolve,[$cnf( $equal(join(one,converse(X_13)),converse(join(one,X_13))) )],[refute_0_99,refute_0_1646]) ).
cnf(refute_0_1648,plain,
join(one,join(converse(X_13),X_37)) = join(converse(join(one,X_13)),X_37),
inference(resolve,[$cnf( $equal(join(one,join(converse(X_13),X_37)),join(join(one,converse(X_13)),X_37)) )],[refute_0_1645,refute_0_1647]) ).
cnf(refute_0_1649,plain,
join(one,join(converse(one),X_284)) = join(converse(join(one,one)),X_284),
inference(subst,[],[refute_0_1648:[bind(X_13,$fot(one)),bind(X_37,$fot(X_284))]]) ).
cnf(refute_0_1650,plain,
( converse(one) != one
| join(one,join(converse(one),X_284)) != join(converse(join(one,one)),X_284)
| join(one,join(one,X_284)) = join(converse(join(one,one)),X_284) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(converse(one),X_284)),join(converse(join(one,one)),X_284)) ),[0,1,0],$fot(one)]]) ).
cnf(refute_0_1651,plain,
( join(one,join(converse(one),X_284)) != join(converse(join(one,one)),X_284)
| join(one,join(one,X_284)) = join(converse(join(one,one)),X_284) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_44,refute_0_1650]) ).
cnf(refute_0_1652,plain,
join(one,join(one,X_284)) = join(converse(join(one,one)),X_284),
inference(resolve,[$cnf( $equal(join(one,join(converse(one),X_284)),join(converse(join(one,one)),X_284)) )],[refute_0_1649,refute_0_1651]) ).
cnf(refute_0_1653,plain,
composition(join(A,B),join(one,one)) = join(composition(A,join(one,one)),composition(B,join(one,one))),
inference(subst,[],[composition_distributivity_7:[bind(C,$fot(join(one,one)))]]) ).
cnf(refute_0_1654,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_1655,plain,
composition(A,join(one,one)) = join(A,A),
inference(resolve,[$cnf( $equal(join(A,A),composition(A,join(one,one))) )],[refute_0_186,refute_0_1654]) ).
cnf(refute_0_1656,plain,
( composition(A,join(one,one)) != join(A,A)
| composition(join(A,B),join(one,one)) != join(composition(A,join(one,one)),composition(B,join(one,one)))
| composition(join(A,B),join(one,one)) = join(join(A,A),composition(B,join(one,one))) ),
introduced(tautology,[equality,[$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_1657,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( $equal(composition(A,join(one,one)),join(A,A)) )],[refute_0_1655,refute_0_1656]) ).
cnf(refute_0_1658,plain,
composition(join(A,B),join(one,one)) = join(join(A,A),composition(B,join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),join(composition(A,join(one,one)),composition(B,join(one,one)))) )],[refute_0_1653,refute_0_1657]) ).
cnf(refute_0_1659,plain,
join(join(A,A),composition(B,join(one,one))) = join(A,join(A,composition(B,join(one,one)))),
inference(subst,[],[refute_0_440:[bind(B,$fot(A)),bind(C,$fot(composition(B,join(one,one))))]]) ).
cnf(refute_0_1660,plain,
( composition(join(A,B),join(one,one)) != join(join(A,A),composition(B,join(one,one)))
| join(join(A,A),composition(B,join(one,one))) != join(A,join(A,composition(B,join(one,one))))
| composition(join(A,B),join(one,one)) = join(A,join(A,composition(B,join(one,one)))) ),
introduced(tautology,[equality,[$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_1661,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( $equal(join(join(A,A),composition(B,join(one,one))),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_1659,refute_0_1660]) ).
cnf(refute_0_1662,plain,
composition(join(A,B),join(one,one)) = join(A,join(A,composition(B,join(one,one)))),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),join(join(A,A),composition(B,join(one,one)))) )],[refute_0_1658,refute_0_1661]) ).
cnf(refute_0_1663,plain,
composition(join(A,B),one) = join(A,B),
inference(subst,[],[composition_identity_6:[bind(A,$fot(join(A,B)))]]) ).
cnf(refute_0_1664,plain,
composition(join(A,B),join(one,one)) = composition(join(A,B),join(one,one)),
introduced(tautology,[refl,[$fot(composition(join(A,B),join(one,one)))]]) ).
cnf(refute_0_1665,plain,
( composition(join(A,B),join(one,one)) != composition(join(A,B),join(one,one))
| join(one,one) != one
| composition(join(A,B),join(one,one)) = composition(join(A,B),one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(A,B),join(one,one)),composition(join(A,B),join(one,one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1666,plain,
( join(one,one) != one
| composition(join(A,B),join(one,one)) = composition(join(A,B),one) ),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),composition(join(A,B),join(one,one))) )],[refute_0_1664,refute_0_1665]) ).
cnf(refute_0_1667,plain,
composition(join(A,B),join(one,one)) = composition(join(A,B),one),
inference(resolve,[$cnf( $equal(join(one,one),one) )],[refute_0_1558,refute_0_1666]) ).
cnf(refute_0_1668,plain,
( composition(join(A,B),join(one,one)) != composition(join(A,B),one)
| composition(join(A,B),one) != join(A,B)
| composition(join(A,B),join(one,one)) = join(A,B) ),
inference(subst,[],[refute_0_7:[bind(X,$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_1669,plain,
( composition(join(A,B),one) != join(A,B)
| composition(join(A,B),join(one,one)) = join(A,B) ),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),composition(join(A,B),one)) )],[refute_0_1667,refute_0_1668]) ).
cnf(refute_0_1670,plain,
composition(join(A,B),join(one,one)) = join(A,B),
inference(resolve,[$cnf( $equal(composition(join(A,B),one),join(A,B)) )],[refute_0_1663,refute_0_1669]) ).
cnf(refute_0_1671,plain,
( composition(join(A,B),join(one,one)) != join(A,B)
| composition(join(A,B),join(one,one)) != join(A,join(A,composition(B,join(one,one))))
| join(A,B) = join(A,join(A,composition(B,join(one,one)))) ),
introduced(tautology,[equality,[$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_1672,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( $equal(composition(join(A,B),join(one,one)),join(A,B)) )],[refute_0_1670,refute_0_1671]) ).
cnf(refute_0_1673,plain,
composition(B,one) = B,
inference(subst,[],[composition_identity_6:[bind(A,$fot(B))]]) ).
cnf(refute_0_1674,plain,
composition(B,join(one,one)) = composition(B,join(one,one)),
introduced(tautology,[refl,[$fot(composition(B,join(one,one)))]]) ).
cnf(refute_0_1675,plain,
( composition(B,join(one,one)) != composition(B,join(one,one))
| join(one,one) != one
| composition(B,join(one,one)) = composition(B,one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(B,join(one,one)),composition(B,join(one,one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1676,plain,
( join(one,one) != one
| composition(B,join(one,one)) = composition(B,one) ),
inference(resolve,[$cnf( $equal(composition(B,join(one,one)),composition(B,join(one,one))) )],[refute_0_1674,refute_0_1675]) ).
cnf(refute_0_1677,plain,
composition(B,join(one,one)) = composition(B,one),
inference(resolve,[$cnf( $equal(join(one,one),one) )],[refute_0_1558,refute_0_1676]) ).
cnf(refute_0_1678,plain,
( composition(B,join(one,one)) != composition(B,one)
| composition(B,one) != B
| composition(B,join(one,one)) = B ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(B,join(one,one)))),bind(Y,$fot(composition(B,one))),bind(Z,$fot(B))]]) ).
cnf(refute_0_1679,plain,
( composition(B,one) != B
| composition(B,join(one,one)) = B ),
inference(resolve,[$cnf( $equal(composition(B,join(one,one)),composition(B,one)) )],[refute_0_1677,refute_0_1678]) ).
cnf(refute_0_1680,plain,
composition(B,join(one,one)) = B,
inference(resolve,[$cnf( $equal(composition(B,one),B) )],[refute_0_1673,refute_0_1679]) ).
cnf(refute_0_1681,plain,
join(A,composition(B,join(one,one))) = join(A,composition(B,join(one,one))),
introduced(tautology,[refl,[$fot(join(A,composition(B,join(one,one))))]]) ).
cnf(refute_0_1682,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_1683,plain,
( composition(B,join(one,one)) != B
| join(A,composition(B,join(one,one))) = join(A,B) ),
inference(resolve,[$cnf( $equal(join(A,composition(B,join(one,one))),join(A,composition(B,join(one,one)))) )],[refute_0_1681,refute_0_1682]) ).
cnf(refute_0_1684,plain,
join(A,composition(B,join(one,one))) = join(A,B),
inference(resolve,[$cnf( $equal(composition(B,join(one,one)),B) )],[refute_0_1680,refute_0_1683]) ).
cnf(refute_0_1685,plain,
join(A,join(A,composition(B,join(one,one)))) = join(A,join(A,composition(B,join(one,one)))),
introduced(tautology,[refl,[$fot(join(A,join(A,composition(B,join(one,one)))))]]) ).
cnf(refute_0_1686,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_1687,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( $equal(join(A,join(A,composition(B,join(one,one)))),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_1685,refute_0_1686]) ).
cnf(refute_0_1688,plain,
join(A,join(A,composition(B,join(one,one)))) = join(A,join(A,B)),
inference(resolve,[$cnf( $equal(join(A,composition(B,join(one,one))),join(A,B)) )],[refute_0_1684,refute_0_1687]) ).
cnf(refute_0_1689,plain,
( join(A,B) != join(A,join(A,composition(B,join(one,one))))
| join(A,join(A,composition(B,join(one,one)))) != join(A,join(A,B))
| join(A,B) = join(A,join(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,B),join(A,join(A,B))) ),[0],$fot(join(A,join(A,composition(B,join(one,one)))))]]) ).
cnf(refute_0_1690,plain,
( join(A,B) != join(A,join(A,composition(B,join(one,one))))
| join(A,B) = join(A,join(A,B)) ),
inference(resolve,[$cnf( $equal(join(A,join(A,composition(B,join(one,one)))),join(A,join(A,B))) )],[refute_0_1688,refute_0_1689]) ).
cnf(refute_0_1691,plain,
( composition(join(A,B),join(one,one)) != join(A,join(A,composition(B,join(one,one))))
| join(A,B) = join(A,join(A,B)) ),
inference(resolve,[$cnf( $equal(join(A,B),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_1672,refute_0_1690]) ).
cnf(refute_0_1692,plain,
join(A,B) = join(A,join(A,B)),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_1662,refute_0_1691]) ).
cnf(refute_0_1693,plain,
( join(A,B) != join(A,join(A,B))
| join(A,join(A,B)) = join(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(A,join(A,B))))]]) ).
cnf(refute_0_1694,plain,
join(A,join(A,B)) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(A,join(A,B))) )],[refute_0_1692,refute_0_1693]) ).
cnf(refute_0_1695,plain,
join(one,join(one,X_284)) = join(one,X_284),
inference(subst,[],[refute_0_1694:[bind(A,$fot(one)),bind(B,$fot(X_284))]]) ).
cnf(refute_0_1696,plain,
( join(one,join(one,X_284)) != join(converse(join(one,one)),X_284)
| join(one,join(one,X_284)) != join(one,X_284)
| join(one,X_284) = join(converse(join(one,one)),X_284) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,X_284)),join(converse(join(one,one)),X_284)) ),[0],$fot(join(one,X_284))]]) ).
cnf(refute_0_1697,plain,
( join(one,join(one,X_284)) != join(converse(join(one,one)),X_284)
| join(one,X_284) = join(converse(join(one,one)),X_284) ),
inference(resolve,[$cnf( $equal(join(one,join(one,X_284)),join(one,X_284)) )],[refute_0_1695,refute_0_1696]) ).
cnf(refute_0_1698,plain,
join(X_284,converse(one)) = join(X_284,converse(one)),
introduced(tautology,[refl,[$fot(join(X_284,converse(one)))]]) ).
cnf(refute_0_1699,plain,
( converse(one) != one
| join(X_284,converse(one)) != join(X_284,converse(one))
| join(X_284,converse(one)) = join(X_284,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_284,converse(one)),join(X_284,converse(one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1700,plain,
( converse(one) != one
| join(X_284,converse(one)) = join(X_284,one) ),
inference(resolve,[$cnf( $equal(join(X_284,converse(one)),join(X_284,converse(one))) )],[refute_0_1698,refute_0_1699]) ).
cnf(refute_0_1701,plain,
join(X_284,converse(one)) = join(X_284,one),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_44,refute_0_1700]) ).
cnf(refute_0_1702,plain,
join(one,join(X_284,converse(one))) = join(one,join(X_284,converse(one))),
introduced(tautology,[refl,[$fot(join(one,join(X_284,converse(one))))]]) ).
cnf(refute_0_1703,plain,
( join(X_284,converse(one)) != join(X_284,one)
| join(one,join(X_284,converse(one))) != join(one,join(X_284,converse(one)))
| join(one,join(X_284,converse(one))) = join(one,join(X_284,one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(X_284,converse(one))),join(one,join(X_284,converse(one)))) ),[1,1],$fot(join(X_284,one))]]) ).
cnf(refute_0_1704,plain,
( join(X_284,converse(one)) != join(X_284,one)
| join(one,join(X_284,converse(one))) = join(one,join(X_284,one)) ),
inference(resolve,[$cnf( $equal(join(one,join(X_284,converse(one))),join(one,join(X_284,converse(one)))) )],[refute_0_1702,refute_0_1703]) ).
cnf(refute_0_1705,plain,
join(one,join(X_284,converse(one))) = join(one,join(X_284,one)),
inference(resolve,[$cnf( $equal(join(X_284,converse(one)),join(X_284,one)) )],[refute_0_1701,refute_0_1704]) ).
cnf(refute_0_1706,plain,
converse(join(join(X_35,X_36),converse(A))) = join(converse(join(X_35,X_36)),A),
inference(subst,[],[refute_0_567:[bind(X_12,$fot(join(X_35,X_36)))]]) ).
cnf(refute_0_1707,plain,
join(X_35,join(X_36,converse(A))) = join(join(X_35,X_36),converse(A)),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_35)),bind(B,$fot(X_36)),bind(C,$fot(converse(A)))]]) ).
cnf(refute_0_1708,plain,
( join(X_35,join(X_36,converse(A))) != join(join(X_35,X_36),converse(A))
| join(join(X_35,X_36),converse(A)) = join(X_35,join(X_36,converse(A))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_35,join(X_36,converse(A))))),bind(Y,$fot(join(join(X_35,X_36),converse(A))))]]) ).
cnf(refute_0_1709,plain,
join(join(X_35,X_36),converse(A)) = join(X_35,join(X_36,converse(A))),
inference(resolve,[$cnf( $equal(join(X_35,join(X_36,converse(A))),join(join(X_35,X_36),converse(A))) )],[refute_0_1707,refute_0_1708]) ).
cnf(refute_0_1710,plain,
( converse(join(join(X_35,X_36),converse(A))) != join(converse(join(X_35,X_36)),A)
| join(join(X_35,X_36),converse(A)) != join(X_35,join(X_36,converse(A)))
| converse(join(X_35,join(X_36,converse(A)))) = join(converse(join(X_35,X_36)),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(X_35,X_36),converse(A))),join(converse(join(X_35,X_36)),A)) ),[0,0],$fot(join(X_35,join(X_36,converse(A))))]]) ).
cnf(refute_0_1711,plain,
( converse(join(join(X_35,X_36),converse(A))) != join(converse(join(X_35,X_36)),A)
| converse(join(X_35,join(X_36,converse(A)))) = join(converse(join(X_35,X_36)),A) ),
inference(resolve,[$cnf( $equal(join(join(X_35,X_36),converse(A)),join(X_35,join(X_36,converse(A)))) )],[refute_0_1709,refute_0_1710]) ).
cnf(refute_0_1712,plain,
converse(join(X_35,join(X_36,converse(A)))) = join(converse(join(X_35,X_36)),A),
inference(resolve,[$cnf( $equal(converse(join(join(X_35,X_36),converse(A))),join(converse(join(X_35,X_36)),A)) )],[refute_0_1706,refute_0_1711]) ).
cnf(refute_0_1713,plain,
converse(join(X_253,join(one,converse(X_252)))) = join(converse(join(X_253,one)),X_252),
inference(subst,[],[refute_0_1712:[bind(A,$fot(X_252)),bind(X_35,$fot(X_253)),bind(X_36,$fot(one))]]) ).
cnf(refute_0_1714,plain,
converse(join(one,X_252)) = join(one,converse(X_252)),
inference(subst,[],[refute_0_93:[bind(X_13,$fot(X_252))]]) ).
cnf(refute_0_1715,plain,
( converse(join(one,X_252)) != join(one,converse(X_252))
| join(one,converse(X_252)) = converse(join(one,X_252)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(one,X_252)))),bind(Y,$fot(join(one,converse(X_252))))]]) ).
cnf(refute_0_1716,plain,
join(one,converse(X_252)) = converse(join(one,X_252)),
inference(resolve,[$cnf( $equal(converse(join(one,X_252)),join(one,converse(X_252))) )],[refute_0_1714,refute_0_1715]) ).
cnf(refute_0_1717,plain,
( converse(join(X_253,join(one,converse(X_252)))) != join(converse(join(X_253,one)),X_252)
| join(one,converse(X_252)) != converse(join(one,X_252))
| converse(join(X_253,converse(join(one,X_252)))) = join(converse(join(X_253,one)),X_252) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_253,join(one,converse(X_252)))),join(converse(join(X_253,one)),X_252)) ),[0,0,1],$fot(converse(join(one,X_252)))]]) ).
cnf(refute_0_1718,plain,
( converse(join(X_253,join(one,converse(X_252)))) != join(converse(join(X_253,one)),X_252)
| converse(join(X_253,converse(join(one,X_252)))) = join(converse(join(X_253,one)),X_252) ),
inference(resolve,[$cnf( $equal(join(one,converse(X_252)),converse(join(one,X_252))) )],[refute_0_1716,refute_0_1717]) ).
cnf(refute_0_1719,plain,
converse(join(X_253,converse(join(one,X_252)))) = join(converse(join(X_253,one)),X_252),
inference(resolve,[$cnf( $equal(converse(join(X_253,join(one,converse(X_252)))),join(converse(join(X_253,one)),X_252)) )],[refute_0_1713,refute_0_1718]) ).
cnf(refute_0_1720,plain,
join(X_241,join(X_242,X_243)) = join(X_242,join(X_241,X_243)),
inference(subst,[],[refute_0_511:[bind(X_35,$fot(X_241)),bind(X_36,$fot(X_242)),bind(X_37,$fot(X_243))]]) ).
cnf(refute_0_1721,plain,
join(X_243,X_242) = join(X_242,X_243),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_243)),bind(B,$fot(X_242))]]) ).
cnf(refute_0_1722,plain,
( join(X_243,X_242) != join(X_242,X_243)
| join(X_242,X_243) = join(X_243,X_242) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_243,X_242))),bind(Y,$fot(join(X_242,X_243)))]]) ).
cnf(refute_0_1723,plain,
join(X_242,X_243) = join(X_243,X_242),
inference(resolve,[$cnf( $equal(join(X_243,X_242),join(X_242,X_243)) )],[refute_0_1721,refute_0_1722]) ).
cnf(refute_0_1724,plain,
( join(X_241,join(X_242,X_243)) != join(X_242,join(X_241,X_243))
| join(X_242,X_243) != join(X_243,X_242)
| join(X_241,join(X_243,X_242)) = join(X_242,join(X_241,X_243)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_241,join(X_242,X_243)),join(X_242,join(X_241,X_243))) ),[0,1],$fot(join(X_243,X_242))]]) ).
cnf(refute_0_1725,plain,
( join(X_241,join(X_242,X_243)) != join(X_242,join(X_241,X_243))
| join(X_241,join(X_243,X_242)) = join(X_242,join(X_241,X_243)) ),
inference(resolve,[$cnf( $equal(join(X_242,X_243),join(X_243,X_242)) )],[refute_0_1723,refute_0_1724]) ).
cnf(refute_0_1726,plain,
join(X_241,join(X_243,X_242)) = join(X_242,join(X_241,X_243)),
inference(resolve,[$cnf( $equal(join(X_241,join(X_242,X_243)),join(X_242,join(X_241,X_243))) )],[refute_0_1720,refute_0_1725]) ).
cnf(refute_0_1727,plain,
( join(X_241,join(X_243,X_242)) != join(X_242,join(X_241,X_243))
| join(X_242,join(X_241,X_243)) = join(X_241,join(X_243,X_242)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_241,join(X_243,X_242)))),bind(Y,$fot(join(X_242,join(X_241,X_243))))]]) ).
cnf(refute_0_1728,plain,
join(X_242,join(X_241,X_243)) = join(X_241,join(X_243,X_242)),
inference(resolve,[$cnf( $equal(join(X_241,join(X_243,X_242)),join(X_242,join(X_241,X_243))) )],[refute_0_1726,refute_0_1727]) ).
cnf(refute_0_1729,plain,
join(converse(X_253),join(one,X_252)) = join(one,join(X_252,converse(X_253))),
inference(subst,[],[refute_0_1728:[bind(X_241,$fot(one)),bind(X_242,$fot(converse(X_253))),bind(X_243,$fot(X_252))]]) ).
cnf(refute_0_1730,plain,
converse(join(X_253,converse(join(one,X_252)))) = join(converse(X_253),join(one,X_252)),
inference(subst,[],[refute_0_567:[bind(A,$fot(join(one,X_252))),bind(X_12,$fot(X_253))]]) ).
cnf(refute_0_1731,plain,
( converse(join(X_253,converse(join(one,X_252)))) != join(converse(X_253),join(one,X_252))
| join(converse(X_253),join(one,X_252)) != join(one,join(X_252,converse(X_253)))
| converse(join(X_253,converse(join(one,X_252)))) = join(one,join(X_252,converse(X_253))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(X_253,converse(join(one,X_252)))))),bind(Y,$fot(join(converse(X_253),join(one,X_252)))),bind(Z,$fot(join(one,join(X_252,converse(X_253)))))]]) ).
cnf(refute_0_1732,plain,
( join(converse(X_253),join(one,X_252)) != join(one,join(X_252,converse(X_253)))
| converse(join(X_253,converse(join(one,X_252)))) = join(one,join(X_252,converse(X_253))) ),
inference(resolve,[$cnf( $equal(converse(join(X_253,converse(join(one,X_252)))),join(converse(X_253),join(one,X_252))) )],[refute_0_1730,refute_0_1731]) ).
cnf(refute_0_1733,plain,
converse(join(X_253,converse(join(one,X_252)))) = join(one,join(X_252,converse(X_253))),
inference(resolve,[$cnf( $equal(join(converse(X_253),join(one,X_252)),join(one,join(X_252,converse(X_253)))) )],[refute_0_1729,refute_0_1732]) ).
cnf(refute_0_1734,plain,
( converse(join(X_253,converse(join(one,X_252)))) != join(converse(join(X_253,one)),X_252)
| converse(join(X_253,converse(join(one,X_252)))) != join(one,join(X_252,converse(X_253)))
| join(one,join(X_252,converse(X_253))) = join(converse(join(X_253,one)),X_252) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_253,converse(join(one,X_252)))),join(converse(join(X_253,one)),X_252)) ),[0],$fot(join(one,join(X_252,converse(X_253))))]]) ).
cnf(refute_0_1735,plain,
( converse(join(X_253,converse(join(one,X_252)))) != join(converse(join(X_253,one)),X_252)
| join(one,join(X_252,converse(X_253))) = join(converse(join(X_253,one)),X_252) ),
inference(resolve,[$cnf( $equal(converse(join(X_253,converse(join(one,X_252)))),join(one,join(X_252,converse(X_253)))) )],[refute_0_1733,refute_0_1734]) ).
cnf(refute_0_1736,plain,
join(one,join(X_252,converse(X_253))) = join(converse(join(X_253,one)),X_252),
inference(resolve,[$cnf( $equal(converse(join(X_253,converse(join(one,X_252)))),join(converse(join(X_253,one)),X_252)) )],[refute_0_1719,refute_0_1735]) ).
cnf(refute_0_1737,plain,
( join(one,join(X_252,converse(X_253))) != join(converse(join(X_253,one)),X_252)
| join(converse(join(X_253,one)),X_252) = join(one,join(X_252,converse(X_253))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,join(X_252,converse(X_253))))),bind(Y,$fot(join(converse(join(X_253,one)),X_252)))]]) ).
cnf(refute_0_1738,plain,
join(converse(join(X_253,one)),X_252) = join(one,join(X_252,converse(X_253))),
inference(resolve,[$cnf( $equal(join(one,join(X_252,converse(X_253))),join(converse(join(X_253,one)),X_252)) )],[refute_0_1736,refute_0_1737]) ).
cnf(refute_0_1739,plain,
join(converse(join(one,one)),X_284) = join(one,join(X_284,converse(one))),
inference(subst,[],[refute_0_1738:[bind(X_252,$fot(X_284)),bind(X_253,$fot(one))]]) ).
cnf(refute_0_1740,plain,
( join(converse(join(one,one)),X_284) != join(one,join(X_284,converse(one)))
| join(one,join(X_284,converse(one))) != join(one,join(X_284,one))
| join(converse(join(one,one)),X_284) = join(one,join(X_284,one)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(converse(join(one,one)),X_284))),bind(Y,$fot(join(one,join(X_284,converse(one))))),bind(Z,$fot(join(one,join(X_284,one))))]]) ).
cnf(refute_0_1741,plain,
( join(one,join(X_284,converse(one))) != join(one,join(X_284,one))
| join(converse(join(one,one)),X_284) = join(one,join(X_284,one)) ),
inference(resolve,[$cnf( $equal(join(converse(join(one,one)),X_284),join(one,join(X_284,converse(one)))) )],[refute_0_1739,refute_0_1740]) ).
cnf(refute_0_1742,plain,
join(converse(join(one,one)),X_284) = join(one,join(X_284,one)),
inference(resolve,[$cnf( $equal(join(one,join(X_284,converse(one))),join(one,join(X_284,one))) )],[refute_0_1705,refute_0_1741]) ).
cnf(refute_0_1743,plain,
( join(converse(join(one,one)),X_284) != join(one,join(X_284,one))
| join(one,X_284) != join(converse(join(one,one)),X_284)
| join(one,X_284) = join(one,join(X_284,one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,X_284),join(converse(join(one,one)),X_284)) ),[1],$fot(join(one,join(X_284,one)))]]) ).
cnf(refute_0_1744,plain,
( join(one,X_284) != join(converse(join(one,one)),X_284)
| join(one,X_284) = join(one,join(X_284,one)) ),
inference(resolve,[$cnf( $equal(join(converse(join(one,one)),X_284),join(one,join(X_284,one))) )],[refute_0_1742,refute_0_1743]) ).
cnf(refute_0_1745,plain,
( join(one,join(one,X_284)) != join(converse(join(one,one)),X_284)
| join(one,X_284) = join(one,join(X_284,one)) ),
inference(resolve,[$cnf( $equal(join(one,X_284),join(converse(join(one,one)),X_284)) )],[refute_0_1697,refute_0_1744]) ).
cnf(refute_0_1746,plain,
join(one,X_284) = join(one,join(X_284,one)),
inference(resolve,[$cnf( $equal(join(one,join(one,X_284)),join(converse(join(one,one)),X_284)) )],[refute_0_1652,refute_0_1745]) ).
cnf(refute_0_1747,plain,
( join(one,X_284) != join(one,join(X_284,one))
| join(one,join(X_284,one)) = join(one,X_284) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,X_284))),bind(Y,$fot(join(one,join(X_284,one))))]]) ).
cnf(refute_0_1748,plain,
join(one,join(X_284,one)) = join(one,X_284),
inference(resolve,[$cnf( $equal(join(one,X_284),join(one,join(X_284,one))) )],[refute_0_1746,refute_0_1747]) ).
cnf(refute_0_1749,plain,
join(one,join(X_32,one)) = join(one,X_32),
inference(subst,[],[refute_0_1748:[bind(X_284,$fot(X_32))]]) ).
cnf(refute_0_1750,plain,
composition(join(one,join(X_32,one)),X_233) = composition(join(one,join(X_32,one)),X_233),
introduced(tautology,[refl,[$fot(composition(join(one,join(X_32,one)),X_233))]]) ).
cnf(refute_0_1751,plain,
( composition(join(one,join(X_32,one)),X_233) != composition(join(one,join(X_32,one)),X_233)
| join(one,join(X_32,one)) != join(one,X_32)
| composition(join(one,join(X_32,one)),X_233) = composition(join(one,X_32),X_233) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(X_32,one)),X_233),composition(join(one,join(X_32,one)),X_233)) ),[1,0],$fot(join(one,X_32))]]) ).
cnf(refute_0_1752,plain,
( join(one,join(X_32,one)) != join(one,X_32)
| composition(join(one,join(X_32,one)),X_233) = composition(join(one,X_32),X_233) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(X_32,one)),X_233),composition(join(one,join(X_32,one)),X_233)) )],[refute_0_1750,refute_0_1751]) ).
cnf(refute_0_1753,plain,
composition(join(one,join(X_32,one)),X_233) = composition(join(one,X_32),X_233),
inference(resolve,[$cnf( $equal(join(one,join(X_32,one)),join(one,X_32)) )],[refute_0_1749,refute_0_1752]) ).
cnf(refute_0_1754,plain,
composition(join(join(X_32,one),one),X_233) = composition(join(one,join(X_32,one)),X_233),
inference(subst,[],[refute_0_1045:[bind(X_56,$fot(X_233)),bind(X_84,$fot(one)),bind(X_85,$fot(join(X_32,one)))]]) ).
cnf(refute_0_1755,plain,
join(X_233,composition(join(X_32,one),X_233)) = composition(join(join(X_32,one),one),X_233),
inference(subst,[],[refute_0_116:[bind(X_32,$fot(join(X_32,one))),bind(X_34,$fot(X_233))]]) ).
cnf(refute_0_1756,plain,
( composition(join(join(X_32,one),one),X_233) != composition(join(one,join(X_32,one)),X_233)
| join(X_233,composition(join(X_32,one),X_233)) != composition(join(join(X_32,one),one),X_233)
| join(X_233,composition(join(X_32,one),X_233)) = composition(join(one,join(X_32,one)),X_233) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X_233,composition(join(X_32,one),X_233)))),bind(Y,$fot(composition(join(join(X_32,one),one),X_233))),bind(Z,$fot(composition(join(one,join(X_32,one)),X_233)))]]) ).
cnf(refute_0_1757,plain,
( composition(join(join(X_32,one),one),X_233) != composition(join(one,join(X_32,one)),X_233)
| join(X_233,composition(join(X_32,one),X_233)) = composition(join(one,join(X_32,one)),X_233) ),
inference(resolve,[$cnf( $equal(join(X_233,composition(join(X_32,one),X_233)),composition(join(join(X_32,one),one),X_233)) )],[refute_0_1755,refute_0_1756]) ).
cnf(refute_0_1758,plain,
join(X_233,composition(join(X_32,one),X_233)) = composition(join(one,join(X_32,one)),X_233),
inference(resolve,[$cnf( $equal(composition(join(join(X_32,one),one),X_233),composition(join(one,join(X_32,one)),X_233)) )],[refute_0_1754,refute_0_1757]) ).
cnf(refute_0_1759,plain,
join(X_233,X_37) = join(meet(X_233,join(X_233,X_37)),meet(complement(X_233),join(X_233,X_37))),
inference(subst,[],[refute_0_1637:[bind(X_140,$fot(X_233)),bind(X_141,$fot(join(X_233,X_37)))]]) ).
cnf(refute_0_1760,plain,
X_233 = meet(X_233,join(X_233,X_37)),
inference(subst,[],[refute_0_699:[bind(X_87,$fot(X_233))]]) ).
cnf(refute_0_1761,plain,
( X_233 != meet(X_233,join(X_233,X_37))
| meet(X_233,join(X_233,X_37)) = X_233 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_233)),bind(Y,$fot(meet(X_233,join(X_233,X_37))))]]) ).
cnf(refute_0_1762,plain,
meet(X_233,join(X_233,X_37)) = X_233,
inference(resolve,[$cnf( $equal(X_233,meet(X_233,join(X_233,X_37))) )],[refute_0_1760,refute_0_1761]) ).
cnf(refute_0_1763,plain,
( join(X_233,X_37) != join(meet(X_233,join(X_233,X_37)),meet(complement(X_233),join(X_233,X_37)))
| meet(X_233,join(X_233,X_37)) != X_233
| join(X_233,X_37) = join(X_233,meet(complement(X_233),join(X_233,X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_233,X_37),join(meet(X_233,join(X_233,X_37)),meet(complement(X_233),join(X_233,X_37)))) ),[1,0],$fot(X_233)]]) ).
cnf(refute_0_1764,plain,
( join(X_233,X_37) != join(meet(X_233,join(X_233,X_37)),meet(complement(X_233),join(X_233,X_37)))
| join(X_233,X_37) = join(X_233,meet(complement(X_233),join(X_233,X_37))) ),
inference(resolve,[$cnf( $equal(meet(X_233,join(X_233,X_37)),X_233) )],[refute_0_1762,refute_0_1763]) ).
cnf(refute_0_1765,plain,
join(X_233,X_37) = join(X_233,meet(complement(X_233),join(X_233,X_37))),
inference(resolve,[$cnf( $equal(join(X_233,X_37),join(meet(X_233,join(X_233,X_37)),meet(complement(X_233),join(X_233,X_37)))) )],[refute_0_1759,refute_0_1764]) ).
cnf(refute_0_1766,plain,
join(complement(X_6),complement(X_7)) = complement(meet(X_6,X_7)),
inference(subst,[],[refute_0_400:[bind(A,$fot(X_6)),bind(B,$fot(X_7))]]) ).
cnf(refute_0_1767,plain,
meet(join(complement(X_6),complement(X_7)),B) = meet(join(complement(X_6),complement(X_7)),B),
introduced(tautology,[refl,[$fot(meet(join(complement(X_6),complement(X_7)),B))]]) ).
cnf(refute_0_1768,plain,
( join(complement(X_6),complement(X_7)) != complement(meet(X_6,X_7))
| meet(join(complement(X_6),complement(X_7)),B) != meet(join(complement(X_6),complement(X_7)),B)
| meet(join(complement(X_6),complement(X_7)),B) = meet(complement(meet(X_6,X_7)),B) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),B),meet(join(complement(X_6),complement(X_7)),B)) ),[1,0],$fot(complement(meet(X_6,X_7)))]]) ).
cnf(refute_0_1769,plain,
( join(complement(X_6),complement(X_7)) != complement(meet(X_6,X_7))
| meet(join(complement(X_6),complement(X_7)),B) = meet(complement(meet(X_6,X_7)),B) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),B),meet(join(complement(X_6),complement(X_7)),B)) )],[refute_0_1767,refute_0_1768]) ).
cnf(refute_0_1770,plain,
meet(join(complement(X_6),complement(X_7)),B) = meet(complement(meet(X_6,X_7)),B),
inference(resolve,[$cnf( $equal(join(complement(X_6),complement(X_7)),complement(meet(X_6,X_7))) )],[refute_0_1766,refute_0_1769]) ).
cnf(refute_0_1771,plain,
( meet(join(complement(X_6),complement(X_7)),B) != complement(join(meet(X_6,X_7),complement(B)))
| meet(join(complement(X_6),complement(X_7)),B) != meet(complement(meet(X_6,X_7)),B)
| meet(complement(meet(X_6,X_7)),B) = complement(join(meet(X_6,X_7),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),B),complement(join(meet(X_6,X_7),complement(B)))) ),[0],$fot(meet(complement(meet(X_6,X_7)),B))]]) ).
cnf(refute_0_1772,plain,
( meet(join(complement(X_6),complement(X_7)),B) != complement(join(meet(X_6,X_7),complement(B)))
| meet(complement(meet(X_6,X_7)),B) = complement(join(meet(X_6,X_7),complement(B))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),B),meet(complement(meet(X_6,X_7)),B)) )],[refute_0_1770,refute_0_1771]) ).
cnf(refute_0_1773,plain,
meet(complement(meet(X_6,X_7)),B) = complement(join(meet(X_6,X_7),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_6),complement(X_7)),B),complement(join(meet(X_6,X_7),complement(B)))) )],[refute_0_274,refute_0_1772]) ).
cnf(refute_0_1774,plain,
meet(complement(meet(X_260,X_261)),join(complement(X_261),X_260)) = complement(join(meet(X_260,X_261),complement(join(complement(X_261),X_260)))),
inference(subst,[],[refute_0_1773:[bind(B,$fot(join(complement(X_261),X_260))),bind(X_6,$fot(X_260)),bind(X_7,$fot(X_261))]]) ).
cnf(refute_0_1775,plain,
X_261 = join(meet(X_260,X_261),complement(join(complement(X_261),X_260))),
inference(subst,[],[refute_0_629:[bind(X_87,$fot(X_261)),bind(X_88,$fot(X_260))]]) ).
cnf(refute_0_1776,plain,
( X_261 != join(meet(X_260,X_261),complement(join(complement(X_261),X_260)))
| join(meet(X_260,X_261),complement(join(complement(X_261),X_260))) = X_261 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_261)),bind(Y,$fot(join(meet(X_260,X_261),complement(join(complement(X_261),X_260)))))]]) ).
cnf(refute_0_1777,plain,
join(meet(X_260,X_261),complement(join(complement(X_261),X_260))) = X_261,
inference(resolve,[$cnf( $equal(X_261,join(meet(X_260,X_261),complement(join(complement(X_261),X_260)))) )],[refute_0_1775,refute_0_1776]) ).
cnf(refute_0_1778,plain,
( join(meet(X_260,X_261),complement(join(complement(X_261),X_260))) != X_261
| meet(complement(meet(X_260,X_261)),join(complement(X_261),X_260)) != complement(join(meet(X_260,X_261),complement(join(complement(X_261),X_260))))
| meet(complement(meet(X_260,X_261)),join(complement(X_261),X_260)) = complement(X_261) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(X_260,X_261)),join(complement(X_261),X_260)),complement(join(meet(X_260,X_261),complement(join(complement(X_261),X_260))))) ),[1,0],$fot(X_261)]]) ).
cnf(refute_0_1779,plain,
( meet(complement(meet(X_260,X_261)),join(complement(X_261),X_260)) != complement(join(meet(X_260,X_261),complement(join(complement(X_261),X_260))))
| meet(complement(meet(X_260,X_261)),join(complement(X_261),X_260)) = complement(X_261) ),
inference(resolve,[$cnf( $equal(join(meet(X_260,X_261),complement(join(complement(X_261),X_260))),X_261) )],[refute_0_1777,refute_0_1778]) ).
cnf(refute_0_1780,plain,
meet(complement(meet(X_260,X_261)),join(complement(X_261),X_260)) = complement(X_261),
inference(resolve,[$cnf( $equal(meet(complement(meet(X_260,X_261)),join(complement(X_261),X_260)),complement(join(meet(X_260,X_261),complement(join(complement(X_261),X_260))))) )],[refute_0_1774,refute_0_1779]) ).
cnf(refute_0_1781,plain,
meet(complement(meet(join(X_357,X_356),join(X_357,complement(X_356)))),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) = complement(join(X_357,complement(X_356))),
inference(subst,[],[refute_0_1780:[bind(X_260,$fot(join(X_357,X_356))),bind(X_261,$fot(join(X_357,complement(X_356))))]]) ).
cnf(refute_0_1782,plain,
meet(complement(meet(X_260,X_261)),join(complement(X_260),X_261)) = complement(join(meet(X_260,X_261),complement(join(complement(X_260),X_261)))),
inference(subst,[],[refute_0_1773:[bind(B,$fot(join(complement(X_260),X_261))),bind(X_6,$fot(X_260)),bind(X_7,$fot(X_261))]]) ).
cnf(refute_0_1783,plain,
X_260 = join(meet(X_260,X_261),complement(join(complement(X_260),X_261))),
inference(subst,[],[refute_0_158:[bind(A,$fot(X_260)),bind(B,$fot(X_261))]]) ).
cnf(refute_0_1784,plain,
( X_260 != join(meet(X_260,X_261),complement(join(complement(X_260),X_261)))
| join(meet(X_260,X_261),complement(join(complement(X_260),X_261))) = X_260 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_260)),bind(Y,$fot(join(meet(X_260,X_261),complement(join(complement(X_260),X_261)))))]]) ).
cnf(refute_0_1785,plain,
join(meet(X_260,X_261),complement(join(complement(X_260),X_261))) = X_260,
inference(resolve,[$cnf( $equal(X_260,join(meet(X_260,X_261),complement(join(complement(X_260),X_261)))) )],[refute_0_1783,refute_0_1784]) ).
cnf(refute_0_1786,plain,
( join(meet(X_260,X_261),complement(join(complement(X_260),X_261))) != X_260
| meet(complement(meet(X_260,X_261)),join(complement(X_260),X_261)) != complement(join(meet(X_260,X_261),complement(join(complement(X_260),X_261))))
| meet(complement(meet(X_260,X_261)),join(complement(X_260),X_261)) = complement(X_260) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(X_260,X_261)),join(complement(X_260),X_261)),complement(join(meet(X_260,X_261),complement(join(complement(X_260),X_261))))) ),[1,0],$fot(X_260)]]) ).
cnf(refute_0_1787,plain,
( meet(complement(meet(X_260,X_261)),join(complement(X_260),X_261)) != complement(join(meet(X_260,X_261),complement(join(complement(X_260),X_261))))
| meet(complement(meet(X_260,X_261)),join(complement(X_260),X_261)) = complement(X_260) ),
inference(resolve,[$cnf( $equal(join(meet(X_260,X_261),complement(join(complement(X_260),X_261))),X_260) )],[refute_0_1785,refute_0_1786]) ).
cnf(refute_0_1788,plain,
meet(complement(meet(X_260,X_261)),join(complement(X_260),X_261)) = complement(X_260),
inference(resolve,[$cnf( $equal(meet(complement(meet(X_260,X_261)),join(complement(X_260),X_261)),complement(join(meet(X_260,X_261),complement(join(complement(X_260),X_261))))) )],[refute_0_1782,refute_0_1787]) ).
cnf(refute_0_1789,plain,
meet(complement(meet(complement(X_87),X_267)),join(complement(complement(X_87)),X_267)) = complement(complement(X_87)),
inference(subst,[],[refute_0_1788:[bind(X_260,$fot(complement(X_87))),bind(X_261,$fot(X_267))]]) ).
cnf(refute_0_1790,plain,
( complement(complement(X_87)) != X_87
| meet(complement(meet(complement(X_87),X_267)),join(complement(complement(X_87)),X_267)) != complement(complement(X_87))
| meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) = complement(complement(X_87)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(complement(X_87),X_267)),join(complement(complement(X_87)),X_267)),complement(complement(X_87))) ),[0,1,0],$fot(X_87)]]) ).
cnf(refute_0_1791,plain,
( meet(complement(meet(complement(X_87),X_267)),join(complement(complement(X_87)),X_267)) != complement(complement(X_87))
| meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) = complement(complement(X_87)) ),
inference(resolve,[$cnf( $equal(complement(complement(X_87)),X_87) )],[refute_0_383,refute_0_1790]) ).
cnf(refute_0_1792,plain,
meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) = complement(complement(X_87)),
inference(resolve,[$cnf( $equal(meet(complement(meet(complement(X_87),X_267)),join(complement(complement(X_87)),X_267)),complement(complement(X_87))) )],[refute_0_1789,refute_0_1791]) ).
cnf(refute_0_1793,plain,
join(X_263,complement(X_262)) = complement(complement(join(X_263,complement(X_262)))),
inference(subst,[],[refute_0_381:[bind(X_87,$fot(join(X_263,complement(X_262))))]]) ).
cnf(refute_0_1794,plain,
meet(complement(meet(top,X_261)),X_259) = complement(join(meet(top,X_261),complement(X_259))),
inference(subst,[],[refute_0_1773:[bind(B,$fot(X_259)),bind(X_6,$fot(top)),bind(X_7,$fot(X_261))]]) ).
cnf(refute_0_1795,plain,
join(zero,complement(B)) = complement(B),
inference(subst,[],[refute_0_377:[bind(X_92,$fot(B))]]) ).
cnf(refute_0_1796,plain,
complement(join(zero,complement(B))) = complement(join(zero,complement(B))),
introduced(tautology,[refl,[$fot(complement(join(zero,complement(B))))]]) ).
cnf(refute_0_1797,plain,
( complement(join(zero,complement(B))) != complement(join(zero,complement(B)))
| join(zero,complement(B)) != complement(B)
| complement(join(zero,complement(B))) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,complement(B))),complement(join(zero,complement(B)))) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_1798,plain,
( join(zero,complement(B)) != complement(B)
| complement(join(zero,complement(B))) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),complement(join(zero,complement(B)))) )],[refute_0_1796,refute_0_1797]) ).
cnf(refute_0_1799,plain,
complement(join(zero,complement(B))) = complement(complement(B)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(B)) )],[refute_0_1795,refute_0_1798]) ).
cnf(refute_0_1800,plain,
( complement(join(zero,complement(B))) != complement(complement(B))
| meet(top,B) != complement(join(zero,complement(B)))
| meet(top,B) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) ),[1],$fot(complement(complement(B)))]]) ).
cnf(refute_0_1801,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| meet(top,B) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),complement(complement(B))) )],[refute_0_1799,refute_0_1800]) ).
cnf(refute_0_1802,plain,
meet(top,B) = complement(complement(B)),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_290,refute_0_1801]) ).
cnf(refute_0_1803,plain,
( complement(complement(B)) != B
| meet(top,B) != complement(complement(B))
| meet(top,B) = B ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(complement(B))) ),[1],$fot(B)]]) ).
cnf(refute_0_1804,plain,
( meet(top,B) != complement(complement(B))
| meet(top,B) = B ),
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_384,refute_0_1803]) ).
cnf(refute_0_1805,plain,
meet(top,B) = B,
inference(resolve,[$cnf( $equal(meet(top,B),complement(complement(B))) )],[refute_0_1802,refute_0_1804]) ).
cnf(refute_0_1806,plain,
meet(top,X_261) = X_261,
inference(subst,[],[refute_0_1805:[bind(B,$fot(X_261))]]) ).
cnf(refute_0_1807,plain,
( meet(complement(meet(top,X_261)),X_259) != complement(join(meet(top,X_261),complement(X_259)))
| meet(top,X_261) != X_261
| meet(complement(meet(top,X_261)),X_259) = complement(join(X_261,complement(X_259))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(top,X_261)),X_259),complement(join(meet(top,X_261),complement(X_259)))) ),[1,0,0],$fot(X_261)]]) ).
cnf(refute_0_1808,plain,
( meet(complement(meet(top,X_261)),X_259) != complement(join(meet(top,X_261),complement(X_259)))
| meet(complement(meet(top,X_261)),X_259) = complement(join(X_261,complement(X_259))) ),
inference(resolve,[$cnf( $equal(meet(top,X_261),X_261) )],[refute_0_1806,refute_0_1807]) ).
cnf(refute_0_1809,plain,
meet(complement(meet(top,X_261)),X_259) = complement(join(X_261,complement(X_259))),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_261)),X_259),complement(join(meet(top,X_261),complement(X_259)))) )],[refute_0_1794,refute_0_1808]) ).
cnf(refute_0_1810,plain,
complement(meet(top,X_261)) = complement(meet(top,X_261)),
introduced(tautology,[refl,[$fot(complement(meet(top,X_261)))]]) ).
cnf(refute_0_1811,plain,
( complement(meet(top,X_261)) != complement(meet(top,X_261))
| meet(top,X_261) != X_261
| complement(meet(top,X_261)) = complement(X_261) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,X_261)),complement(meet(top,X_261))) ),[1,0],$fot(X_261)]]) ).
cnf(refute_0_1812,plain,
( meet(top,X_261) != X_261
| complement(meet(top,X_261)) = complement(X_261) ),
inference(resolve,[$cnf( $equal(complement(meet(top,X_261)),complement(meet(top,X_261))) )],[refute_0_1810,refute_0_1811]) ).
cnf(refute_0_1813,plain,
complement(meet(top,X_261)) = complement(X_261),
inference(resolve,[$cnf( $equal(meet(top,X_261),X_261) )],[refute_0_1806,refute_0_1812]) ).
cnf(refute_0_1814,plain,
meet(complement(meet(top,X_261)),X_259) = meet(complement(meet(top,X_261)),X_259),
introduced(tautology,[refl,[$fot(meet(complement(meet(top,X_261)),X_259))]]) ).
cnf(refute_0_1815,plain,
( complement(meet(top,X_261)) != complement(X_261)
| meet(complement(meet(top,X_261)),X_259) != meet(complement(meet(top,X_261)),X_259)
| meet(complement(meet(top,X_261)),X_259) = meet(complement(X_261),X_259) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(top,X_261)),X_259),meet(complement(meet(top,X_261)),X_259)) ),[1,0],$fot(complement(X_261))]]) ).
cnf(refute_0_1816,plain,
( complement(meet(top,X_261)) != complement(X_261)
| meet(complement(meet(top,X_261)),X_259) = meet(complement(X_261),X_259) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_261)),X_259),meet(complement(meet(top,X_261)),X_259)) )],[refute_0_1814,refute_0_1815]) ).
cnf(refute_0_1817,plain,
meet(complement(meet(top,X_261)),X_259) = meet(complement(X_261),X_259),
inference(resolve,[$cnf( $equal(complement(meet(top,X_261)),complement(X_261)) )],[refute_0_1813,refute_0_1816]) ).
cnf(refute_0_1818,plain,
( meet(complement(meet(top,X_261)),X_259) != complement(join(X_261,complement(X_259)))
| meet(complement(meet(top,X_261)),X_259) != meet(complement(X_261),X_259)
| meet(complement(X_261),X_259) = complement(join(X_261,complement(X_259))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(top,X_261)),X_259),complement(join(X_261,complement(X_259)))) ),[0],$fot(meet(complement(X_261),X_259))]]) ).
cnf(refute_0_1819,plain,
( meet(complement(meet(top,X_261)),X_259) != complement(join(X_261,complement(X_259)))
| meet(complement(X_261),X_259) = complement(join(X_261,complement(X_259))) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_261)),X_259),meet(complement(X_261),X_259)) )],[refute_0_1817,refute_0_1818]) ).
cnf(refute_0_1820,plain,
meet(complement(X_261),X_259) = complement(join(X_261,complement(X_259))),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_261)),X_259),complement(join(X_261,complement(X_259)))) )],[refute_0_1809,refute_0_1819]) ).
cnf(refute_0_1821,plain,
meet(complement(X_263),X_262) = complement(join(X_263,complement(X_262))),
inference(subst,[],[refute_0_1820:[bind(X_259,$fot(X_262)),bind(X_261,$fot(X_263))]]) ).
cnf(refute_0_1822,plain,
( meet(complement(X_263),X_262) != complement(join(X_263,complement(X_262)))
| complement(join(X_263,complement(X_262))) = meet(complement(X_263),X_262) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_263),X_262))),bind(Y,$fot(complement(join(X_263,complement(X_262)))))]]) ).
cnf(refute_0_1823,plain,
complement(join(X_263,complement(X_262))) = meet(complement(X_263),X_262),
inference(resolve,[$cnf( $equal(meet(complement(X_263),X_262),complement(join(X_263,complement(X_262)))) )],[refute_0_1821,refute_0_1822]) ).
cnf(refute_0_1824,plain,
( complement(join(X_263,complement(X_262))) != meet(complement(X_263),X_262)
| join(X_263,complement(X_262)) != complement(complement(join(X_263,complement(X_262))))
| join(X_263,complement(X_262)) = complement(meet(complement(X_263),X_262)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_263,complement(X_262)),complement(complement(join(X_263,complement(X_262))))) ),[1,0],$fot(meet(complement(X_263),X_262))]]) ).
cnf(refute_0_1825,plain,
( join(X_263,complement(X_262)) != complement(complement(join(X_263,complement(X_262))))
| join(X_263,complement(X_262)) = complement(meet(complement(X_263),X_262)) ),
inference(resolve,[$cnf( $equal(complement(join(X_263,complement(X_262))),meet(complement(X_263),X_262)) )],[refute_0_1823,refute_0_1824]) ).
cnf(refute_0_1826,plain,
join(X_263,complement(X_262)) = complement(meet(complement(X_263),X_262)),
inference(resolve,[$cnf( $equal(join(X_263,complement(X_262)),complement(complement(join(X_263,complement(X_262))))) )],[refute_0_1793,refute_0_1825]) ).
cnf(refute_0_1827,plain,
( join(X_263,complement(X_262)) != complement(meet(complement(X_263),X_262))
| complement(meet(complement(X_263),X_262)) = join(X_263,complement(X_262)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_263,complement(X_262)))),bind(Y,$fot(complement(meet(complement(X_263),X_262))))]]) ).
cnf(refute_0_1828,plain,
complement(meet(complement(X_263),X_262)) = join(X_263,complement(X_262)),
inference(resolve,[$cnf( $equal(join(X_263,complement(X_262)),complement(meet(complement(X_263),X_262))) )],[refute_0_1826,refute_0_1827]) ).
cnf(refute_0_1829,plain,
complement(meet(complement(X_87),X_267)) = join(X_87,complement(X_267)),
inference(subst,[],[refute_0_1828:[bind(X_262,$fot(X_267)),bind(X_263,$fot(X_87))]]) ).
cnf(refute_0_1830,plain,
meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))) = meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))),
introduced(tautology,[refl,[$fot(meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))))]]) ).
cnf(refute_0_1831,plain,
( complement(meet(complement(X_87),X_267)) != join(X_87,complement(X_267))
| meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))) != meet(join(X_87,X_267),complement(meet(complement(X_87),X_267)))
| meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))) = meet(join(X_87,X_267),join(X_87,complement(X_267))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))),meet(join(X_87,X_267),complement(meet(complement(X_87),X_267)))) ),[1,1],$fot(join(X_87,complement(X_267)))]]) ).
cnf(refute_0_1832,plain,
( complement(meet(complement(X_87),X_267)) != join(X_87,complement(X_267))
| meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))) = meet(join(X_87,X_267),join(X_87,complement(X_267))) ),
inference(resolve,[$cnf( $equal(meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))),meet(join(X_87,X_267),complement(meet(complement(X_87),X_267)))) )],[refute_0_1830,refute_0_1831]) ).
cnf(refute_0_1833,plain,
meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))) = meet(join(X_87,X_267),join(X_87,complement(X_267))),
inference(resolve,[$cnf( $equal(complement(meet(complement(X_87),X_267)),join(X_87,complement(X_267))) )],[refute_0_1829,refute_0_1832]) ).
cnf(refute_0_1834,plain,
meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) = meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))),
inference(subst,[],[refute_0_1273:[bind(X_6,$fot(join(X_87,X_267))),bind(X_7,$fot(complement(meet(complement(X_87),X_267))))]]) ).
cnf(refute_0_1835,plain,
( meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) != meet(join(X_87,X_267),complement(meet(complement(X_87),X_267)))
| meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))) != meet(join(X_87,X_267),join(X_87,complement(X_267)))
| meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) = meet(join(X_87,X_267),join(X_87,complement(X_267))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)))),bind(Y,$fot(meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))))),bind(Z,$fot(meet(join(X_87,X_267),join(X_87,complement(X_267)))))]]) ).
cnf(refute_0_1836,plain,
( meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))) != meet(join(X_87,X_267),join(X_87,complement(X_267)))
| meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) = meet(join(X_87,X_267),join(X_87,complement(X_267))) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)),meet(join(X_87,X_267),complement(meet(complement(X_87),X_267)))) )],[refute_0_1834,refute_0_1835]) ).
cnf(refute_0_1837,plain,
meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) = meet(join(X_87,X_267),join(X_87,complement(X_267))),
inference(resolve,[$cnf( $equal(meet(join(X_87,X_267),complement(meet(complement(X_87),X_267))),meet(join(X_87,X_267),join(X_87,complement(X_267)))) )],[refute_0_1833,refute_0_1836]) ).
cnf(refute_0_1838,plain,
( meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) != complement(complement(X_87))
| meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) != meet(join(X_87,X_267),join(X_87,complement(X_267)))
| meet(join(X_87,X_267),join(X_87,complement(X_267))) = complement(complement(X_87)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)),complement(complement(X_87))) ),[0],$fot(meet(join(X_87,X_267),join(X_87,complement(X_267))))]]) ).
cnf(refute_0_1839,plain,
( meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) != complement(complement(X_87))
| meet(join(X_87,X_267),join(X_87,complement(X_267))) = complement(complement(X_87)) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)),meet(join(X_87,X_267),join(X_87,complement(X_267)))) )],[refute_0_1837,refute_0_1838]) ).
cnf(refute_0_1840,plain,
( complement(complement(X_87)) != X_87
| meet(join(X_87,X_267),join(X_87,complement(X_267))) != complement(complement(X_87))
| meet(join(X_87,X_267),join(X_87,complement(X_267))) = X_87 ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_87,X_267),join(X_87,complement(X_267))),complement(complement(X_87))) ),[1],$fot(X_87)]]) ).
cnf(refute_0_1841,plain,
( meet(join(X_87,X_267),join(X_87,complement(X_267))) != complement(complement(X_87))
| meet(join(X_87,X_267),join(X_87,complement(X_267))) = X_87 ),
inference(resolve,[$cnf( $equal(complement(complement(X_87)),X_87) )],[refute_0_383,refute_0_1840]) ).
cnf(refute_0_1842,plain,
( meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)) != complement(complement(X_87))
| meet(join(X_87,X_267),join(X_87,complement(X_267))) = X_87 ),
inference(resolve,[$cnf( $equal(meet(join(X_87,X_267),join(X_87,complement(X_267))),complement(complement(X_87))) )],[refute_0_1839,refute_0_1841]) ).
cnf(refute_0_1843,plain,
meet(join(X_87,X_267),join(X_87,complement(X_267))) = X_87,
inference(resolve,[$cnf( $equal(meet(complement(meet(complement(X_87),X_267)),join(X_87,X_267)),complement(complement(X_87))) )],[refute_0_1792,refute_0_1842]) ).
cnf(refute_0_1844,plain,
meet(join(X_357,X_356),join(X_357,complement(X_356))) = X_357,
inference(subst,[],[refute_0_1843:[bind(X_267,$fot(X_356)),bind(X_87,$fot(X_357))]]) ).
cnf(refute_0_1845,plain,
( meet(complement(meet(join(X_357,X_356),join(X_357,complement(X_356)))),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) != complement(join(X_357,complement(X_356)))
| meet(join(X_357,X_356),join(X_357,complement(X_356))) != X_357
| meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) = complement(join(X_357,complement(X_356))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(join(X_357,X_356),join(X_357,complement(X_356)))),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))),complement(join(X_357,complement(X_356)))) ),[0,0,0],$fot(X_357)]]) ).
cnf(refute_0_1846,plain,
( meet(complement(meet(join(X_357,X_356),join(X_357,complement(X_356)))),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) != complement(join(X_357,complement(X_356)))
| meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) = complement(join(X_357,complement(X_356))) ),
inference(resolve,[$cnf( $equal(meet(join(X_357,X_356),join(X_357,complement(X_356))),X_357) )],[refute_0_1844,refute_0_1845]) ).
cnf(refute_0_1847,plain,
meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) = complement(join(X_357,complement(X_356))),
inference(resolve,[$cnf( $equal(meet(complement(meet(join(X_357,X_356),join(X_357,complement(X_356)))),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))),complement(join(X_357,complement(X_356)))) )],[refute_0_1781,refute_0_1846]) ).
cnf(refute_0_1848,plain,
( meet(complement(X_261),X_259) != complement(join(X_261,complement(X_259)))
| complement(join(X_261,complement(X_259))) = meet(complement(X_261),X_259) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_261),X_259))),bind(Y,$fot(complement(join(X_261,complement(X_259)))))]]) ).
cnf(refute_0_1849,plain,
complement(join(X_261,complement(X_259))) = meet(complement(X_261),X_259),
inference(resolve,[$cnf( $equal(meet(complement(X_261),X_259),complement(join(X_261,complement(X_259)))) )],[refute_0_1820,refute_0_1848]) ).
cnf(refute_0_1850,plain,
complement(join(X_357,complement(X_356))) = meet(complement(X_357),X_356),
inference(subst,[],[refute_0_1849:[bind(X_259,$fot(X_356)),bind(X_261,$fot(X_357))]]) ).
cnf(refute_0_1851,plain,
join(X_356,complement(join(X_357,complement(X_356)))) = join(X_356,complement(join(X_357,complement(X_356)))),
introduced(tautology,[refl,[$fot(join(X_356,complement(join(X_357,complement(X_356)))))]]) ).
cnf(refute_0_1852,plain,
( complement(join(X_357,complement(X_356))) != meet(complement(X_357),X_356)
| join(X_356,complement(join(X_357,complement(X_356)))) != join(X_356,complement(join(X_357,complement(X_356))))
| join(X_356,complement(join(X_357,complement(X_356)))) = join(X_356,meet(complement(X_357),X_356)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_356,complement(join(X_357,complement(X_356)))),join(X_356,complement(join(X_357,complement(X_356))))) ),[1,1],$fot(meet(complement(X_357),X_356))]]) ).
cnf(refute_0_1853,plain,
( complement(join(X_357,complement(X_356))) != meet(complement(X_357),X_356)
| join(X_356,complement(join(X_357,complement(X_356)))) = join(X_356,meet(complement(X_357),X_356)) ),
inference(resolve,[$cnf( $equal(join(X_356,complement(join(X_357,complement(X_356)))),join(X_356,complement(join(X_357,complement(X_356))))) )],[refute_0_1851,refute_0_1852]) ).
cnf(refute_0_1854,plain,
join(X_356,complement(join(X_357,complement(X_356)))) = join(X_356,meet(complement(X_357),X_356)),
inference(resolve,[$cnf( $equal(complement(join(X_357,complement(X_356))),meet(complement(X_357),X_356)) )],[refute_0_1850,refute_0_1853]) ).
cnf(refute_0_1855,plain,
join(X_357,join(X_356,complement(join(X_357,complement(X_356))))) = join(X_357,join(X_356,complement(join(X_357,complement(X_356))))),
introduced(tautology,[refl,[$fot(join(X_357,join(X_356,complement(join(X_357,complement(X_356))))))]]) ).
cnf(refute_0_1856,plain,
( join(X_356,complement(join(X_357,complement(X_356)))) != join(X_356,meet(complement(X_357),X_356))
| join(X_357,join(X_356,complement(join(X_357,complement(X_356))))) != join(X_357,join(X_356,complement(join(X_357,complement(X_356)))))
| join(X_357,join(X_356,complement(join(X_357,complement(X_356))))) = join(X_357,join(X_356,meet(complement(X_357),X_356))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_357,join(X_356,complement(join(X_357,complement(X_356))))),join(X_357,join(X_356,complement(join(X_357,complement(X_356)))))) ),[1,1],$fot(join(X_356,meet(complement(X_357),X_356)))]]) ).
cnf(refute_0_1857,plain,
( join(X_356,complement(join(X_357,complement(X_356)))) != join(X_356,meet(complement(X_357),X_356))
| join(X_357,join(X_356,complement(join(X_357,complement(X_356))))) = join(X_357,join(X_356,meet(complement(X_357),X_356))) ),
inference(resolve,[$cnf( $equal(join(X_357,join(X_356,complement(join(X_357,complement(X_356))))),join(X_357,join(X_356,complement(join(X_357,complement(X_356)))))) )],[refute_0_1855,refute_0_1856]) ).
cnf(refute_0_1858,plain,
join(X_357,join(X_356,complement(join(X_357,complement(X_356))))) = join(X_357,join(X_356,meet(complement(X_357),X_356))),
inference(resolve,[$cnf( $equal(join(X_356,complement(join(X_357,complement(X_356)))),join(X_356,meet(complement(X_357),X_356))) )],[refute_0_1854,refute_0_1857]) ).
cnf(refute_0_1859,plain,
converse(join(converse(A),join(converse(B),converse(X_252)))) = join(converse(join(converse(A),converse(B))),X_252),
inference(subst,[],[refute_0_1712:[bind(A,$fot(X_252)),bind(X_35,$fot(converse(A))),bind(X_36,$fot(converse(B)))]]) ).
cnf(refute_0_1860,plain,
( converse(join(converse(A),join(converse(B),converse(X_252)))) != join(converse(join(converse(A),converse(B))),X_252)
| join(converse(A),converse(B)) != converse(join(A,B))
| converse(join(converse(A),join(converse(B),converse(X_252)))) = join(converse(converse(join(A,B))),X_252) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),join(converse(B),converse(X_252)))),join(converse(join(converse(A),converse(B))),X_252)) ),[1,0,0],$fot(converse(join(A,B)))]]) ).
cnf(refute_0_1861,plain,
( converse(join(converse(A),join(converse(B),converse(X_252)))) != join(converse(join(converse(A),converse(B))),X_252)
| converse(join(converse(A),join(converse(B),converse(X_252)))) = join(converse(converse(join(A,B))),X_252) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(B)),converse(join(A,B))) )],[refute_0_544,refute_0_1860]) ).
cnf(refute_0_1862,plain,
converse(join(converse(A),join(converse(B),converse(X_252)))) = join(converse(converse(join(A,B))),X_252),
inference(resolve,[$cnf( $equal(converse(join(converse(A),join(converse(B),converse(X_252)))),join(converse(join(converse(A),converse(B))),X_252)) )],[refute_0_1859,refute_0_1861]) ).
cnf(refute_0_1863,plain,
join(X_252,converse(converse(A))) = join(X_252,converse(converse(A))),
introduced(tautology,[refl,[$fot(join(X_252,converse(converse(A))))]]) ).
cnf(refute_0_1864,plain,
( converse(converse(A)) != A
| join(X_252,converse(converse(A))) != join(X_252,converse(converse(A)))
| join(X_252,converse(converse(A))) = join(X_252,A) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_252,converse(converse(A))),join(X_252,converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_1865,plain,
( converse(converse(A)) != A
| join(X_252,converse(converse(A))) = join(X_252,A) ),
inference(resolve,[$cnf( $equal(join(X_252,converse(converse(A))),join(X_252,converse(converse(A)))) )],[refute_0_1863,refute_0_1864]) ).
cnf(refute_0_1866,plain,
join(X_252,converse(converse(A))) = join(X_252,A),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1865]) ).
cnf(refute_0_1867,plain,
converse(join(converse(X_252),converse(A))) = join(X_252,converse(converse(A))),
inference(subst,[],[refute_0_89:[bind(A,$fot(X_252)),bind(X_13,$fot(converse(A)))]]) ).
cnf(refute_0_1868,plain,
( converse(join(converse(X_252),converse(A))) != join(X_252,converse(converse(A)))
| join(X_252,converse(converse(A))) != join(X_252,A)
| converse(join(converse(X_252),converse(A))) = join(X_252,A) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(converse(X_252),converse(A))))),bind(Y,$fot(join(X_252,converse(converse(A))))),bind(Z,$fot(join(X_252,A)))]]) ).
cnf(refute_0_1869,plain,
( join(X_252,converse(converse(A))) != join(X_252,A)
| converse(join(converse(X_252),converse(A))) = join(X_252,A) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X_252),converse(A))),join(X_252,converse(converse(A)))) )],[refute_0_1867,refute_0_1868]) ).
cnf(refute_0_1870,plain,
converse(join(converse(X_252),converse(A))) = join(X_252,A),
inference(resolve,[$cnf( $equal(join(X_252,converse(converse(A))),join(X_252,A)) )],[refute_0_1866,refute_0_1869]) ).
cnf(refute_0_1871,plain,
join(B,converse(join(converse(X_252),converse(A)))) = join(B,converse(join(converse(X_252),converse(A)))),
introduced(tautology,[refl,[$fot(join(B,converse(join(converse(X_252),converse(A)))))]]) ).
cnf(refute_0_1872,plain,
( converse(join(converse(X_252),converse(A))) != join(X_252,A)
| join(B,converse(join(converse(X_252),converse(A)))) != join(B,converse(join(converse(X_252),converse(A))))
| join(B,converse(join(converse(X_252),converse(A)))) = join(B,join(X_252,A)) ),
introduced(tautology,[equality,[$cnf( $equal(join(B,converse(join(converse(X_252),converse(A)))),join(B,converse(join(converse(X_252),converse(A))))) ),[1,1],$fot(join(X_252,A))]]) ).
cnf(refute_0_1873,plain,
( converse(join(converse(X_252),converse(A))) != join(X_252,A)
| join(B,converse(join(converse(X_252),converse(A)))) = join(B,join(X_252,A)) ),
inference(resolve,[$cnf( $equal(join(B,converse(join(converse(X_252),converse(A)))),join(B,converse(join(converse(X_252),converse(A))))) )],[refute_0_1871,refute_0_1872]) ).
cnf(refute_0_1874,plain,
join(B,converse(join(converse(X_252),converse(A)))) = join(B,join(X_252,A)),
inference(resolve,[$cnf( $equal(converse(join(converse(X_252),converse(A))),join(X_252,A)) )],[refute_0_1870,refute_0_1873]) ).
cnf(refute_0_1875,plain,
join(join(X_193,converse(X_192)),converse(X_191)) = join(converse(X_191),join(X_193,converse(X_192))),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(X_193,converse(X_192)))),bind(B,$fot(converse(X_191)))]]) ).
cnf(refute_0_1876,plain,
converse(join(X_12,converse(join(X_15,converse(X_14))))) = join(converse(X_12),join(X_15,converse(X_14))),
inference(subst,[],[refute_0_567:[bind(A,$fot(join(X_15,converse(X_14))))]]) ).
cnf(refute_0_1877,plain,
converse(join(X_15,converse(X_14))) = join(converse(X_15),X_14),
inference(subst,[],[refute_0_567:[bind(A,$fot(X_14)),bind(X_12,$fot(X_15))]]) ).
cnf(refute_0_1878,plain,
( converse(join(X_12,converse(join(X_15,converse(X_14))))) != join(converse(X_12),join(X_15,converse(X_14)))
| converse(join(X_15,converse(X_14))) != join(converse(X_15),X_14)
| converse(join(X_12,join(converse(X_15),X_14))) = join(converse(X_12),join(X_15,converse(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_12,converse(join(X_15,converse(X_14))))),join(converse(X_12),join(X_15,converse(X_14)))) ),[0,0,1],$fot(join(converse(X_15),X_14))]]) ).
cnf(refute_0_1879,plain,
( converse(join(X_12,converse(join(X_15,converse(X_14))))) != join(converse(X_12),join(X_15,converse(X_14)))
| converse(join(X_12,join(converse(X_15),X_14))) = join(converse(X_12),join(X_15,converse(X_14))) ),
inference(resolve,[$cnf( $equal(converse(join(X_15,converse(X_14))),join(converse(X_15),X_14)) )],[refute_0_1877,refute_0_1878]) ).
cnf(refute_0_1880,plain,
converse(join(X_12,join(converse(X_15),X_14))) = join(converse(X_12),join(X_15,converse(X_14))),
inference(resolve,[$cnf( $equal(converse(join(X_12,converse(join(X_15,converse(X_14))))),join(converse(X_12),join(X_15,converse(X_14)))) )],[refute_0_1876,refute_0_1879]) ).
cnf(refute_0_1881,plain,
converse(join(X_191,join(converse(X_193),X_192))) = join(converse(X_191),join(X_193,converse(X_192))),
inference(subst,[],[refute_0_1880:[bind(X_12,$fot(X_191)),bind(X_14,$fot(X_192)),bind(X_15,$fot(X_193))]]) ).
cnf(refute_0_1882,plain,
( converse(join(X_191,join(converse(X_193),X_192))) != join(converse(X_191),join(X_193,converse(X_192)))
| join(converse(X_191),join(X_193,converse(X_192))) = converse(join(X_191,join(converse(X_193),X_192))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_191,join(converse(X_193),X_192))))),bind(Y,$fot(join(converse(X_191),join(X_193,converse(X_192)))))]]) ).
cnf(refute_0_1883,plain,
join(converse(X_191),join(X_193,converse(X_192))) = converse(join(X_191,join(converse(X_193),X_192))),
inference(resolve,[$cnf( $equal(converse(join(X_191,join(converse(X_193),X_192))),join(converse(X_191),join(X_193,converse(X_192)))) )],[refute_0_1881,refute_0_1882]) ).
cnf(refute_0_1884,plain,
( join(converse(X_191),join(X_193,converse(X_192))) != converse(join(X_191,join(converse(X_193),X_192)))
| join(join(X_193,converse(X_192)),converse(X_191)) != join(converse(X_191),join(X_193,converse(X_192)))
| join(join(X_193,converse(X_192)),converse(X_191)) = converse(join(X_191,join(converse(X_193),X_192))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_193,converse(X_192)),converse(X_191)),join(converse(X_191),join(X_193,converse(X_192)))) ),[1],$fot(converse(join(X_191,join(converse(X_193),X_192))))]]) ).
cnf(refute_0_1885,plain,
( join(join(X_193,converse(X_192)),converse(X_191)) != join(converse(X_191),join(X_193,converse(X_192)))
| join(join(X_193,converse(X_192)),converse(X_191)) = converse(join(X_191,join(converse(X_193),X_192))) ),
inference(resolve,[$cnf( $equal(join(converse(X_191),join(X_193,converse(X_192))),converse(join(X_191,join(converse(X_193),X_192)))) )],[refute_0_1883,refute_0_1884]) ).
cnf(refute_0_1886,plain,
join(join(X_193,converse(X_192)),converse(X_191)) = converse(join(X_191,join(converse(X_193),X_192))),
inference(resolve,[$cnf( $equal(join(join(X_193,converse(X_192)),converse(X_191)),join(converse(X_191),join(X_193,converse(X_192)))) )],[refute_0_1875,refute_0_1885]) ).
cnf(refute_0_1887,plain,
join(converse(X_192),converse(X_191)) = converse(join(X_192,X_191)),
inference(subst,[],[refute_0_544:[bind(A,$fot(X_192)),bind(B,$fot(X_191))]]) ).
cnf(refute_0_1888,plain,
join(X_193,join(converse(X_192),converse(X_191))) = join(X_193,join(converse(X_192),converse(X_191))),
introduced(tautology,[refl,[$fot(join(X_193,join(converse(X_192),converse(X_191))))]]) ).
cnf(refute_0_1889,plain,
( join(X_193,join(converse(X_192),converse(X_191))) != join(X_193,join(converse(X_192),converse(X_191)))
| join(converse(X_192),converse(X_191)) != converse(join(X_192,X_191))
| join(X_193,join(converse(X_192),converse(X_191))) = join(X_193,converse(join(X_192,X_191))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_193,join(converse(X_192),converse(X_191))),join(X_193,join(converse(X_192),converse(X_191)))) ),[1,1],$fot(converse(join(X_192,X_191)))]]) ).
cnf(refute_0_1890,plain,
( join(converse(X_192),converse(X_191)) != converse(join(X_192,X_191))
| join(X_193,join(converse(X_192),converse(X_191))) = join(X_193,converse(join(X_192,X_191))) ),
inference(resolve,[$cnf( $equal(join(X_193,join(converse(X_192),converse(X_191))),join(X_193,join(converse(X_192),converse(X_191)))) )],[refute_0_1888,refute_0_1889]) ).
cnf(refute_0_1891,plain,
join(X_193,join(converse(X_192),converse(X_191))) = join(X_193,converse(join(X_192,X_191))),
inference(resolve,[$cnf( $equal(join(converse(X_192),converse(X_191)),converse(join(X_192,X_191))) )],[refute_0_1887,refute_0_1890]) ).
cnf(refute_0_1892,plain,
join(join(X_193,converse(X_192)),converse(X_191)) = join(X_193,join(converse(X_192),converse(X_191))),
inference(subst,[],[refute_0_440:[bind(A,$fot(X_193)),bind(B,$fot(converse(X_192))),bind(C,$fot(converse(X_191)))]]) ).
cnf(refute_0_1893,plain,
( join(X_193,join(converse(X_192),converse(X_191))) != join(X_193,converse(join(X_192,X_191)))
| join(join(X_193,converse(X_192)),converse(X_191)) != join(X_193,join(converse(X_192),converse(X_191)))
| join(join(X_193,converse(X_192)),converse(X_191)) = join(X_193,converse(join(X_192,X_191))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(join(X_193,converse(X_192)),converse(X_191)))),bind(Y,$fot(join(X_193,join(converse(X_192),converse(X_191))))),bind(Z,$fot(join(X_193,converse(join(X_192,X_191)))))]]) ).
cnf(refute_0_1894,plain,
( join(X_193,join(converse(X_192),converse(X_191))) != join(X_193,converse(join(X_192,X_191)))
| join(join(X_193,converse(X_192)),converse(X_191)) = join(X_193,converse(join(X_192,X_191))) ),
inference(resolve,[$cnf( $equal(join(join(X_193,converse(X_192)),converse(X_191)),join(X_193,join(converse(X_192),converse(X_191)))) )],[refute_0_1892,refute_0_1893]) ).
cnf(refute_0_1895,plain,
join(join(X_193,converse(X_192)),converse(X_191)) = join(X_193,converse(join(X_192,X_191))),
inference(resolve,[$cnf( $equal(join(X_193,join(converse(X_192),converse(X_191))),join(X_193,converse(join(X_192,X_191)))) )],[refute_0_1891,refute_0_1894]) ).
cnf(refute_0_1896,plain,
( join(join(X_193,converse(X_192)),converse(X_191)) != converse(join(X_191,join(converse(X_193),X_192)))
| join(join(X_193,converse(X_192)),converse(X_191)) != join(X_193,converse(join(X_192,X_191)))
| join(X_193,converse(join(X_192,X_191))) = converse(join(X_191,join(converse(X_193),X_192))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_193,converse(X_192)),converse(X_191)),converse(join(X_191,join(converse(X_193),X_192)))) ),[0],$fot(join(X_193,converse(join(X_192,X_191))))]]) ).
cnf(refute_0_1897,plain,
( join(join(X_193,converse(X_192)),converse(X_191)) != converse(join(X_191,join(converse(X_193),X_192)))
| join(X_193,converse(join(X_192,X_191))) = converse(join(X_191,join(converse(X_193),X_192))) ),
inference(resolve,[$cnf( $equal(join(join(X_193,converse(X_192)),converse(X_191)),join(X_193,converse(join(X_192,X_191)))) )],[refute_0_1895,refute_0_1896]) ).
cnf(refute_0_1898,plain,
join(X_193,converse(join(X_192,X_191))) = converse(join(X_191,join(converse(X_193),X_192))),
inference(resolve,[$cnf( $equal(join(join(X_193,converse(X_192)),converse(X_191)),converse(join(X_191,join(converse(X_193),X_192)))) )],[refute_0_1886,refute_0_1897]) ).
cnf(refute_0_1899,plain,
( join(X_193,converse(join(X_192,X_191))) != converse(join(X_191,join(converse(X_193),X_192)))
| converse(join(X_191,join(converse(X_193),X_192))) = join(X_193,converse(join(X_192,X_191))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_193,converse(join(X_192,X_191))))),bind(Y,$fot(converse(join(X_191,join(converse(X_193),X_192)))))]]) ).
cnf(refute_0_1900,plain,
converse(join(X_191,join(converse(X_193),X_192))) = join(X_193,converse(join(X_192,X_191))),
inference(resolve,[$cnf( $equal(join(X_193,converse(join(X_192,X_191))),converse(join(X_191,join(converse(X_193),X_192)))) )],[refute_0_1898,refute_0_1899]) ).
cnf(refute_0_1901,plain,
converse(join(converse(A),join(converse(B),converse(X_252)))) = join(B,converse(join(converse(X_252),converse(A)))),
inference(subst,[],[refute_0_1900:[bind(X_191,$fot(converse(A))),bind(X_192,$fot(converse(X_252))),bind(X_193,$fot(B))]]) ).
cnf(refute_0_1902,plain,
( converse(join(converse(A),join(converse(B),converse(X_252)))) != join(B,converse(join(converse(X_252),converse(A))))
| join(B,converse(join(converse(X_252),converse(A)))) != join(B,join(X_252,A))
| converse(join(converse(A),join(converse(B),converse(X_252)))) = join(B,join(X_252,A)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(converse(A),join(converse(B),converse(X_252)))))),bind(Y,$fot(join(B,converse(join(converse(X_252),converse(A)))))),bind(Z,$fot(join(B,join(X_252,A))))]]) ).
cnf(refute_0_1903,plain,
( join(B,converse(join(converse(X_252),converse(A)))) != join(B,join(X_252,A))
| converse(join(converse(A),join(converse(B),converse(X_252)))) = join(B,join(X_252,A)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(A),join(converse(B),converse(X_252)))),join(B,converse(join(converse(X_252),converse(A))))) )],[refute_0_1901,refute_0_1902]) ).
cnf(refute_0_1904,plain,
converse(join(converse(A),join(converse(B),converse(X_252)))) = join(B,join(X_252,A)),
inference(resolve,[$cnf( $equal(join(B,converse(join(converse(X_252),converse(A)))),join(B,join(X_252,A))) )],[refute_0_1874,refute_0_1903]) ).
cnf(refute_0_1905,plain,
( converse(join(converse(A),join(converse(B),converse(X_252)))) != join(B,join(X_252,A))
| converse(join(converse(A),join(converse(B),converse(X_252)))) != join(converse(converse(join(A,B))),X_252)
| join(B,join(X_252,A)) = join(converse(converse(join(A,B))),X_252) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),join(converse(B),converse(X_252)))),join(converse(converse(join(A,B))),X_252)) ),[0],$fot(join(B,join(X_252,A)))]]) ).
cnf(refute_0_1906,plain,
( converse(join(converse(A),join(converse(B),converse(X_252)))) != join(converse(converse(join(A,B))),X_252)
| join(B,join(X_252,A)) = join(converse(converse(join(A,B))),X_252) ),
inference(resolve,[$cnf( $equal(converse(join(converse(A),join(converse(B),converse(X_252)))),join(B,join(X_252,A))) )],[refute_0_1904,refute_0_1905]) ).
cnf(refute_0_1907,plain,
join(join(A,B),X_252) = join(A,join(B,X_252)),
inference(subst,[],[refute_0_440:[bind(C,$fot(X_252))]]) ).
cnf(refute_0_1908,plain,
converse(converse(join(A,B))) = join(A,B),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(join(A,B)))]]) ).
cnf(refute_0_1909,plain,
join(converse(converse(join(A,B))),X_252) = join(converse(converse(join(A,B))),X_252),
introduced(tautology,[refl,[$fot(join(converse(converse(join(A,B))),X_252))]]) ).
cnf(refute_0_1910,plain,
( converse(converse(join(A,B))) != join(A,B)
| join(converse(converse(join(A,B))),X_252) != join(converse(converse(join(A,B))),X_252)
| join(converse(converse(join(A,B))),X_252) = join(join(A,B),X_252) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(converse(join(A,B))),X_252),join(converse(converse(join(A,B))),X_252)) ),[1,0],$fot(join(A,B))]]) ).
cnf(refute_0_1911,plain,
( converse(converse(join(A,B))) != join(A,B)
| join(converse(converse(join(A,B))),X_252) = join(join(A,B),X_252) ),
inference(resolve,[$cnf( $equal(join(converse(converse(join(A,B))),X_252),join(converse(converse(join(A,B))),X_252)) )],[refute_0_1909,refute_0_1910]) ).
cnf(refute_0_1912,plain,
join(converse(converse(join(A,B))),X_252) = join(join(A,B),X_252),
inference(resolve,[$cnf( $equal(converse(converse(join(A,B))),join(A,B)) )],[refute_0_1908,refute_0_1911]) ).
cnf(refute_0_1913,plain,
( join(converse(converse(join(A,B))),X_252) != join(join(A,B),X_252)
| join(join(A,B),X_252) != join(A,join(B,X_252))
| join(converse(converse(join(A,B))),X_252) = join(A,join(B,X_252)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(converse(converse(join(A,B))),X_252))),bind(Y,$fot(join(join(A,B),X_252))),bind(Z,$fot(join(A,join(B,X_252))))]]) ).
cnf(refute_0_1914,plain,
( join(join(A,B),X_252) != join(A,join(B,X_252))
| join(converse(converse(join(A,B))),X_252) = join(A,join(B,X_252)) ),
inference(resolve,[$cnf( $equal(join(converse(converse(join(A,B))),X_252),join(join(A,B),X_252)) )],[refute_0_1912,refute_0_1913]) ).
cnf(refute_0_1915,plain,
join(converse(converse(join(A,B))),X_252) = join(A,join(B,X_252)),
inference(resolve,[$cnf( $equal(join(join(A,B),X_252),join(A,join(B,X_252))) )],[refute_0_1907,refute_0_1914]) ).
cnf(refute_0_1916,plain,
( join(B,join(X_252,A)) != join(converse(converse(join(A,B))),X_252)
| join(converse(converse(join(A,B))),X_252) != join(A,join(B,X_252))
| join(B,join(X_252,A)) = join(A,join(B,X_252)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(B,join(X_252,A)),join(A,join(B,X_252))) ),[0],$fot(join(converse(converse(join(A,B))),X_252))]]) ).
cnf(refute_0_1917,plain,
( join(B,join(X_252,A)) != join(converse(converse(join(A,B))),X_252)
| join(B,join(X_252,A)) = join(A,join(B,X_252)) ),
inference(resolve,[$cnf( $equal(join(converse(converse(join(A,B))),X_252),join(A,join(B,X_252))) )],[refute_0_1915,refute_0_1916]) ).
cnf(refute_0_1918,plain,
( converse(join(converse(A),join(converse(B),converse(X_252)))) != join(converse(converse(join(A,B))),X_252)
| join(B,join(X_252,A)) = join(A,join(B,X_252)) ),
inference(resolve,[$cnf( $equal(join(B,join(X_252,A)),join(converse(converse(join(A,B))),X_252)) )],[refute_0_1906,refute_0_1917]) ).
cnf(refute_0_1919,plain,
join(B,join(X_252,A)) = join(A,join(B,X_252)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),join(converse(B),converse(X_252)))),join(converse(converse(join(A,B))),X_252)) )],[refute_0_1862,refute_0_1918]) ).
cnf(refute_0_1920,plain,
( join(B,join(X_252,A)) != join(A,join(B,X_252))
| join(A,join(B,X_252)) = join(B,join(X_252,A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(B,join(X_252,A)))),bind(Y,$fot(join(A,join(B,X_252))))]]) ).
cnf(refute_0_1921,plain,
join(A,join(B,X_252)) = join(B,join(X_252,A)),
inference(resolve,[$cnf( $equal(join(B,join(X_252,A)),join(A,join(B,X_252))) )],[refute_0_1919,refute_0_1920]) ).
cnf(refute_0_1922,plain,
join(complement(join(X_357,complement(X_356))),join(X_357,X_356)) = join(X_357,join(X_356,complement(join(X_357,complement(X_356))))),
inference(subst,[],[refute_0_1921:[bind(A,$fot(complement(join(X_357,complement(X_356))))),bind(B,$fot(X_357)),bind(X_252,$fot(X_356))]]) ).
cnf(refute_0_1923,plain,
( join(X_357,join(X_356,complement(join(X_357,complement(X_356))))) != join(X_357,join(X_356,meet(complement(X_357),X_356)))
| join(complement(join(X_357,complement(X_356))),join(X_357,X_356)) != join(X_357,join(X_356,complement(join(X_357,complement(X_356)))))
| join(complement(join(X_357,complement(X_356))),join(X_357,X_356)) = join(X_357,join(X_356,meet(complement(X_357),X_356))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(join(X_357,complement(X_356))),join(X_357,X_356)))),bind(Y,$fot(join(X_357,join(X_356,complement(join(X_357,complement(X_356))))))),bind(Z,$fot(join(X_357,join(X_356,meet(complement(X_357),X_356)))))]]) ).
cnf(refute_0_1924,plain,
( join(X_357,join(X_356,complement(join(X_357,complement(X_356))))) != join(X_357,join(X_356,meet(complement(X_357),X_356)))
| join(complement(join(X_357,complement(X_356))),join(X_357,X_356)) = join(X_357,join(X_356,meet(complement(X_357),X_356))) ),
inference(resolve,[$cnf( $equal(join(complement(join(X_357,complement(X_356))),join(X_357,X_356)),join(X_357,join(X_356,complement(join(X_357,complement(X_356)))))) )],[refute_0_1922,refute_0_1923]) ).
cnf(refute_0_1925,plain,
join(complement(join(X_357,complement(X_356))),join(X_357,X_356)) = join(X_357,join(X_356,meet(complement(X_357),X_356))),
inference(resolve,[$cnf( $equal(join(X_357,join(X_356,complement(join(X_357,complement(X_356))))),join(X_357,join(X_356,meet(complement(X_357),X_356)))) )],[refute_0_1858,refute_0_1924]) ).
cnf(refute_0_1926,plain,
meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) = meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))),
introduced(tautology,[refl,[$fot(meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))))]]) ).
cnf(refute_0_1927,plain,
( join(complement(join(X_357,complement(X_356))),join(X_357,X_356)) != join(X_357,join(X_356,meet(complement(X_357),X_356)))
| meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) != meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356)))
| meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) = meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))),meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356)))) ),[1,1],$fot(join(X_357,join(X_356,meet(complement(X_357),X_356))))]]) ).
cnf(refute_0_1928,plain,
( join(complement(join(X_357,complement(X_356))),join(X_357,X_356)) != join(X_357,join(X_356,meet(complement(X_357),X_356)))
| meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) = meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))),meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356)))) )],[refute_0_1926,refute_0_1927]) ).
cnf(refute_0_1929,plain,
meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) = meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))),
inference(resolve,[$cnf( $equal(join(complement(join(X_357,complement(X_356))),join(X_357,X_356)),join(X_357,join(X_356,meet(complement(X_357),X_356)))) )],[refute_0_1925,refute_0_1928]) ).
cnf(refute_0_1930,plain,
( meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) != complement(join(X_357,complement(X_356)))
| meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) != meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356))))
| meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) = complement(join(X_357,complement(X_356))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))),complement(join(X_357,complement(X_356)))) ),[0],$fot(meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))))]]) ).
cnf(refute_0_1931,plain,
( meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) != complement(join(X_357,complement(X_356)))
| meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) = complement(join(X_357,complement(X_356))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))),meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356))))) )],[refute_0_1929,refute_0_1930]) ).
cnf(refute_0_1932,plain,
( complement(join(X_357,complement(X_356))) != meet(complement(X_357),X_356)
| meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) != complement(join(X_357,complement(X_356)))
| meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) = meet(complement(X_357),X_356) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))),complement(join(X_357,complement(X_356)))) ),[1],$fot(meet(complement(X_357),X_356))]]) ).
cnf(refute_0_1933,plain,
( meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) != complement(join(X_357,complement(X_356)))
| meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) = meet(complement(X_357),X_356) ),
inference(resolve,[$cnf( $equal(complement(join(X_357,complement(X_356))),meet(complement(X_357),X_356)) )],[refute_0_1850,refute_0_1932]) ).
cnf(refute_0_1934,plain,
( meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))) != complement(join(X_357,complement(X_356)))
| meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) = meet(complement(X_357),X_356) ),
inference(resolve,[$cnf( $equal(meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))),complement(join(X_357,complement(X_356)))) )],[refute_0_1931,refute_0_1933]) ).
cnf(refute_0_1935,plain,
meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) = meet(complement(X_357),X_356),
inference(resolve,[$cnf( $equal(meet(complement(X_357),join(complement(join(X_357,complement(X_356))),join(X_357,X_356))),complement(join(X_357,complement(X_356)))) )],[refute_0_1847,refute_0_1934]) ).
cnf(refute_0_1936,plain,
meet(join(X_357,join(complement(X_357),X_37)),join(X_357,complement(join(complement(X_357),X_37)))) = X_357,
inference(subst,[],[refute_0_1843:[bind(X_267,$fot(join(complement(X_357),X_37))),bind(X_87,$fot(X_357))]]) ).
cnf(refute_0_1937,plain,
join(X_357,join(complement(X_357),X_37)) = top,
inference(subst,[],[refute_0_634:[bind(X_35,$fot(X_357))]]) ).
cnf(refute_0_1938,plain,
( join(X_357,join(complement(X_357),X_37)) != top
| meet(join(X_357,join(complement(X_357),X_37)),join(X_357,complement(join(complement(X_357),X_37)))) != X_357
| meet(top,join(X_357,complement(join(complement(X_357),X_37)))) = X_357 ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_357,join(complement(X_357),X_37)),join(X_357,complement(join(complement(X_357),X_37)))),X_357) ),[0,0],$fot(top)]]) ).
cnf(refute_0_1939,plain,
( meet(join(X_357,join(complement(X_357),X_37)),join(X_357,complement(join(complement(X_357),X_37)))) != X_357
| meet(top,join(X_357,complement(join(complement(X_357),X_37)))) = X_357 ),
inference(resolve,[$cnf( $equal(join(X_357,join(complement(X_357),X_37)),top) )],[refute_0_1937,refute_0_1938]) ).
cnf(refute_0_1940,plain,
meet(top,join(X_357,complement(join(complement(X_357),X_37)))) = X_357,
inference(resolve,[$cnf( $equal(meet(join(X_357,join(complement(X_357),X_37)),join(X_357,complement(join(complement(X_357),X_37)))),X_357) )],[refute_0_1936,refute_0_1939]) ).
cnf(refute_0_1941,plain,
join(complement(X_262),X_263) = join(X_263,complement(X_262)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_262))),bind(B,$fot(X_263))]]) ).
cnf(refute_0_1942,plain,
( join(complement(X_262),X_263) != join(X_263,complement(X_262))
| join(X_263,complement(X_262)) = join(complement(X_262),X_263) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_262),X_263))),bind(Y,$fot(join(X_263,complement(X_262))))]]) ).
cnf(refute_0_1943,plain,
join(X_263,complement(X_262)) = join(complement(X_262),X_263),
inference(resolve,[$cnf( $equal(join(complement(X_262),X_263),join(X_263,complement(X_262))) )],[refute_0_1941,refute_0_1942]) ).
cnf(refute_0_1944,plain,
( join(X_263,complement(X_262)) != join(complement(X_262),X_263)
| meet(complement(X_263),X_262) != complement(join(X_263,complement(X_262)))
| meet(complement(X_263),X_262) = complement(join(complement(X_262),X_263)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_263),X_262),complement(join(X_263,complement(X_262)))) ),[1,0],$fot(join(complement(X_262),X_263))]]) ).
cnf(refute_0_1945,plain,
( meet(complement(X_263),X_262) != complement(join(X_263,complement(X_262)))
| meet(complement(X_263),X_262) = complement(join(complement(X_262),X_263)) ),
inference(resolve,[$cnf( $equal(join(X_263,complement(X_262)),join(complement(X_262),X_263)) )],[refute_0_1943,refute_0_1944]) ).
cnf(refute_0_1946,plain,
meet(complement(X_263),X_262) = complement(join(complement(X_262),X_263)),
inference(resolve,[$cnf( $equal(meet(complement(X_263),X_262),complement(join(X_263,complement(X_262)))) )],[refute_0_1821,refute_0_1945]) ).
cnf(refute_0_1947,plain,
( meet(complement(X_263),X_262) != complement(join(complement(X_262),X_263))
| complement(join(complement(X_262),X_263)) = meet(complement(X_263),X_262) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_263),X_262))),bind(Y,$fot(complement(join(complement(X_262),X_263))))]]) ).
cnf(refute_0_1948,plain,
complement(join(complement(X_262),X_263)) = meet(complement(X_263),X_262),
inference(resolve,[$cnf( $equal(meet(complement(X_263),X_262),complement(join(complement(X_262),X_263))) )],[refute_0_1946,refute_0_1947]) ).
cnf(refute_0_1949,plain,
complement(join(complement(X_357),X_37)) = meet(complement(X_37),X_357),
inference(subst,[],[refute_0_1948:[bind(X_262,$fot(X_357)),bind(X_263,$fot(X_37))]]) ).
cnf(refute_0_1950,plain,
join(X_357,complement(join(complement(X_357),X_37))) = join(X_357,complement(join(complement(X_357),X_37))),
introduced(tautology,[refl,[$fot(join(X_357,complement(join(complement(X_357),X_37))))]]) ).
cnf(refute_0_1951,plain,
( complement(join(complement(X_357),X_37)) != meet(complement(X_37),X_357)
| join(X_357,complement(join(complement(X_357),X_37))) != join(X_357,complement(join(complement(X_357),X_37)))
| join(X_357,complement(join(complement(X_357),X_37))) = join(X_357,meet(complement(X_37),X_357)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_357,complement(join(complement(X_357),X_37))),join(X_357,complement(join(complement(X_357),X_37)))) ),[1,1],$fot(meet(complement(X_37),X_357))]]) ).
cnf(refute_0_1952,plain,
( complement(join(complement(X_357),X_37)) != meet(complement(X_37),X_357)
| join(X_357,complement(join(complement(X_357),X_37))) = join(X_357,meet(complement(X_37),X_357)) ),
inference(resolve,[$cnf( $equal(join(X_357,complement(join(complement(X_357),X_37))),join(X_357,complement(join(complement(X_357),X_37)))) )],[refute_0_1950,refute_0_1951]) ).
cnf(refute_0_1953,plain,
join(X_357,complement(join(complement(X_357),X_37))) = join(X_357,meet(complement(X_37),X_357)),
inference(resolve,[$cnf( $equal(complement(join(complement(X_357),X_37)),meet(complement(X_37),X_357)) )],[refute_0_1949,refute_0_1952]) ).
cnf(refute_0_1954,plain,
meet(top,join(X_357,complement(join(complement(X_357),X_37)))) = join(X_357,complement(join(complement(X_357),X_37))),
inference(subst,[],[refute_0_1805:[bind(B,$fot(join(X_357,complement(join(complement(X_357),X_37)))))]]) ).
cnf(refute_0_1955,plain,
( join(X_357,complement(join(complement(X_357),X_37))) != join(X_357,meet(complement(X_37),X_357))
| meet(top,join(X_357,complement(join(complement(X_357),X_37)))) != join(X_357,complement(join(complement(X_357),X_37)))
| meet(top,join(X_357,complement(join(complement(X_357),X_37)))) = join(X_357,meet(complement(X_37),X_357)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(top,join(X_357,complement(join(complement(X_357),X_37)))))),bind(Y,$fot(join(X_357,complement(join(complement(X_357),X_37))))),bind(Z,$fot(join(X_357,meet(complement(X_37),X_357))))]]) ).
cnf(refute_0_1956,plain,
( join(X_357,complement(join(complement(X_357),X_37))) != join(X_357,meet(complement(X_37),X_357))
| meet(top,join(X_357,complement(join(complement(X_357),X_37)))) = join(X_357,meet(complement(X_37),X_357)) ),
inference(resolve,[$cnf( $equal(meet(top,join(X_357,complement(join(complement(X_357),X_37)))),join(X_357,complement(join(complement(X_357),X_37)))) )],[refute_0_1954,refute_0_1955]) ).
cnf(refute_0_1957,plain,
meet(top,join(X_357,complement(join(complement(X_357),X_37)))) = join(X_357,meet(complement(X_37),X_357)),
inference(resolve,[$cnf( $equal(join(X_357,complement(join(complement(X_357),X_37))),join(X_357,meet(complement(X_37),X_357))) )],[refute_0_1953,refute_0_1956]) ).
cnf(refute_0_1958,plain,
( meet(top,join(X_357,complement(join(complement(X_357),X_37)))) != X_357
| meet(top,join(X_357,complement(join(complement(X_357),X_37)))) != join(X_357,meet(complement(X_37),X_357))
| join(X_357,meet(complement(X_37),X_357)) = X_357 ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(X_357,complement(join(complement(X_357),X_37)))),X_357) ),[0],$fot(join(X_357,meet(complement(X_37),X_357)))]]) ).
cnf(refute_0_1959,plain,
( meet(top,join(X_357,complement(join(complement(X_357),X_37)))) != X_357
| join(X_357,meet(complement(X_37),X_357)) = X_357 ),
inference(resolve,[$cnf( $equal(meet(top,join(X_357,complement(join(complement(X_357),X_37)))),join(X_357,meet(complement(X_37),X_357))) )],[refute_0_1957,refute_0_1958]) ).
cnf(refute_0_1960,plain,
join(X_357,meet(complement(X_37),X_357)) = X_357,
inference(resolve,[$cnf( $equal(meet(top,join(X_357,complement(join(complement(X_357),X_37)))),X_357) )],[refute_0_1940,refute_0_1959]) ).
cnf(refute_0_1961,plain,
join(X_356,meet(complement(X_357),X_356)) = X_356,
inference(subst,[],[refute_0_1960:[bind(X_357,$fot(X_356)),bind(X_37,$fot(X_357))]]) ).
cnf(refute_0_1962,plain,
join(X_357,join(X_356,meet(complement(X_357),X_356))) = join(X_357,join(X_356,meet(complement(X_357),X_356))),
introduced(tautology,[refl,[$fot(join(X_357,join(X_356,meet(complement(X_357),X_356))))]]) ).
cnf(refute_0_1963,plain,
( join(X_356,meet(complement(X_357),X_356)) != X_356
| join(X_357,join(X_356,meet(complement(X_357),X_356))) != join(X_357,join(X_356,meet(complement(X_357),X_356)))
| join(X_357,join(X_356,meet(complement(X_357),X_356))) = join(X_357,X_356) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_357,join(X_356,meet(complement(X_357),X_356))),join(X_357,join(X_356,meet(complement(X_357),X_356)))) ),[1,1],$fot(X_356)]]) ).
cnf(refute_0_1964,plain,
( join(X_356,meet(complement(X_357),X_356)) != X_356
| join(X_357,join(X_356,meet(complement(X_357),X_356))) = join(X_357,X_356) ),
inference(resolve,[$cnf( $equal(join(X_357,join(X_356,meet(complement(X_357),X_356))),join(X_357,join(X_356,meet(complement(X_357),X_356)))) )],[refute_0_1962,refute_0_1963]) ).
cnf(refute_0_1965,plain,
join(X_357,join(X_356,meet(complement(X_357),X_356))) = join(X_357,X_356),
inference(resolve,[$cnf( $equal(join(X_356,meet(complement(X_357),X_356)),X_356) )],[refute_0_1961,refute_0_1964]) ).
cnf(refute_0_1966,plain,
meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) = meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))),
introduced(tautology,[refl,[$fot(meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))))]]) ).
cnf(refute_0_1967,plain,
( join(X_357,join(X_356,meet(complement(X_357),X_356))) != join(X_357,X_356)
| meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) != meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356))))
| meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) = meet(complement(X_357),join(X_357,X_356)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))),meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356))))) ),[1,1],$fot(join(X_357,X_356))]]) ).
cnf(refute_0_1968,plain,
( join(X_357,join(X_356,meet(complement(X_357),X_356))) != join(X_357,X_356)
| meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) = meet(complement(X_357),join(X_357,X_356)) ),
inference(resolve,[$cnf( $equal(meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))),meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356))))) )],[refute_0_1966,refute_0_1967]) ).
cnf(refute_0_1969,plain,
meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) = meet(complement(X_357),join(X_357,X_356)),
inference(resolve,[$cnf( $equal(join(X_357,join(X_356,meet(complement(X_357),X_356))),join(X_357,X_356)) )],[refute_0_1965,refute_0_1968]) ).
cnf(refute_0_1970,plain,
( meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) != meet(complement(X_357),X_356)
| meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) != meet(complement(X_357),join(X_357,X_356))
| meet(complement(X_357),join(X_357,X_356)) = meet(complement(X_357),X_356) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))),meet(complement(X_357),X_356)) ),[0],$fot(meet(complement(X_357),join(X_357,X_356)))]]) ).
cnf(refute_0_1971,plain,
( meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))) != meet(complement(X_357),X_356)
| meet(complement(X_357),join(X_357,X_356)) = meet(complement(X_357),X_356) ),
inference(resolve,[$cnf( $equal(meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))),meet(complement(X_357),join(X_357,X_356))) )],[refute_0_1969,refute_0_1970]) ).
cnf(refute_0_1972,plain,
meet(complement(X_357),join(X_357,X_356)) = meet(complement(X_357),X_356),
inference(resolve,[$cnf( $equal(meet(complement(X_357),join(X_357,join(X_356,meet(complement(X_357),X_356)))),meet(complement(X_357),X_356)) )],[refute_0_1935,refute_0_1971]) ).
cnf(refute_0_1973,plain,
meet(complement(X_233),join(X_233,X_37)) = meet(complement(X_233),X_37),
inference(subst,[],[refute_0_1972:[bind(X_356,$fot(X_37)),bind(X_357,$fot(X_233))]]) ).
cnf(refute_0_1974,plain,
join(X_233,meet(complement(X_233),join(X_233,X_37))) = join(X_233,meet(complement(X_233),join(X_233,X_37))),
introduced(tautology,[refl,[$fot(join(X_233,meet(complement(X_233),join(X_233,X_37))))]]) ).
cnf(refute_0_1975,plain,
( join(X_233,meet(complement(X_233),join(X_233,X_37))) != join(X_233,meet(complement(X_233),join(X_233,X_37)))
| meet(complement(X_233),join(X_233,X_37)) != meet(complement(X_233),X_37)
| join(X_233,meet(complement(X_233),join(X_233,X_37))) = join(X_233,meet(complement(X_233),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_233,meet(complement(X_233),join(X_233,X_37))),join(X_233,meet(complement(X_233),join(X_233,X_37)))) ),[1,1],$fot(meet(complement(X_233),X_37))]]) ).
cnf(refute_0_1976,plain,
( meet(complement(X_233),join(X_233,X_37)) != meet(complement(X_233),X_37)
| join(X_233,meet(complement(X_233),join(X_233,X_37))) = join(X_233,meet(complement(X_233),X_37)) ),
inference(resolve,[$cnf( $equal(join(X_233,meet(complement(X_233),join(X_233,X_37))),join(X_233,meet(complement(X_233),join(X_233,X_37)))) )],[refute_0_1974,refute_0_1975]) ).
cnf(refute_0_1977,plain,
join(X_233,meet(complement(X_233),join(X_233,X_37))) = join(X_233,meet(complement(X_233),X_37)),
inference(resolve,[$cnf( $equal(meet(complement(X_233),join(X_233,X_37)),meet(complement(X_233),X_37)) )],[refute_0_1973,refute_0_1976]) ).
cnf(refute_0_1978,plain,
( join(X_233,X_37) != join(X_233,meet(complement(X_233),join(X_233,X_37)))
| join(X_233,meet(complement(X_233),join(X_233,X_37))) != join(X_233,meet(complement(X_233),X_37))
| join(X_233,X_37) = join(X_233,meet(complement(X_233),X_37)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_233,X_37),join(X_233,meet(complement(X_233),X_37))) ),[0],$fot(join(X_233,meet(complement(X_233),join(X_233,X_37))))]]) ).
cnf(refute_0_1979,plain,
( join(X_233,X_37) != join(X_233,meet(complement(X_233),join(X_233,X_37)))
| join(X_233,X_37) = join(X_233,meet(complement(X_233),X_37)) ),
inference(resolve,[$cnf( $equal(join(X_233,meet(complement(X_233),join(X_233,X_37))),join(X_233,meet(complement(X_233),X_37))) )],[refute_0_1977,refute_0_1978]) ).
cnf(refute_0_1980,plain,
join(X_233,X_37) = join(X_233,meet(complement(X_233),X_37)),
inference(resolve,[$cnf( $equal(join(X_233,X_37),join(X_233,meet(complement(X_233),join(X_233,X_37)))) )],[refute_0_1765,refute_0_1979]) ).
cnf(refute_0_1981,plain,
( join(X_233,X_37) != join(X_233,meet(complement(X_233),X_37))
| join(X_233,meet(complement(X_233),X_37)) = join(X_233,X_37) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_233,X_37))),bind(Y,$fot(join(X_233,meet(complement(X_233),X_37))))]]) ).
cnf(refute_0_1982,plain,
join(X_233,meet(complement(X_233),X_37)) = join(X_233,X_37),
inference(resolve,[$cnf( $equal(join(X_233,X_37),join(X_233,meet(complement(X_233),X_37))) )],[refute_0_1980,refute_0_1981]) ).
cnf(refute_0_1983,plain,
join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) = join(X_233,composition(join(X_32,one),X_233)),
inference(subst,[],[refute_0_1982:[bind(X_37,$fot(composition(join(X_32,one),X_233)))]]) ).
cnf(refute_0_1984,plain,
( join(X_233,composition(join(X_32,one),X_233)) != composition(join(one,join(X_32,one)),X_233)
| join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) != join(X_233,composition(join(X_32,one),X_233))
| join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) = composition(join(one,join(X_32,one)),X_233) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))))),bind(Y,$fot(join(X_233,composition(join(X_32,one),X_233)))),bind(Z,$fot(composition(join(one,join(X_32,one)),X_233)))]]) ).
cnf(refute_0_1985,plain,
( join(X_233,composition(join(X_32,one),X_233)) != composition(join(one,join(X_32,one)),X_233)
| join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) = composition(join(one,join(X_32,one)),X_233) ),
inference(resolve,[$cnf( $equal(join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))),join(X_233,composition(join(X_32,one),X_233))) )],[refute_0_1983,refute_0_1984]) ).
cnf(refute_0_1986,plain,
join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) = composition(join(one,join(X_32,one)),X_233),
inference(resolve,[$cnf( $equal(join(X_233,composition(join(X_32,one),X_233)),composition(join(one,join(X_32,one)),X_233)) )],[refute_0_1758,refute_0_1985]) ).
cnf(refute_0_1987,plain,
( composition(join(one,join(X_32,one)),X_233) != composition(join(one,X_32),X_233)
| join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) != composition(join(one,join(X_32,one)),X_233)
| join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) = composition(join(one,X_32),X_233) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))))),bind(Y,$fot(composition(join(one,join(X_32,one)),X_233))),bind(Z,$fot(composition(join(one,X_32),X_233)))]]) ).
cnf(refute_0_1988,plain,
( composition(join(one,join(X_32,one)),X_233) != composition(join(one,X_32),X_233)
| join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) = composition(join(one,X_32),X_233) ),
inference(resolve,[$cnf( $equal(join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))),composition(join(one,join(X_32,one)),X_233)) )],[refute_0_1986,refute_0_1987]) ).
cnf(refute_0_1989,plain,
join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) = composition(join(one,X_32),X_233),
inference(resolve,[$cnf( $equal(composition(join(one,join(X_32,one)),X_233),composition(join(one,X_32),X_233)) )],[refute_0_1753,refute_0_1988]) ).
cnf(refute_0_1990,plain,
( composition(join(X_32,one),X_233) != join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233)))
| join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))) != composition(join(one,X_32),X_233)
| composition(join(X_32,one),X_233) = composition(join(one,X_32),X_233) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_32,one),X_233),composition(join(one,X_32),X_233)) ),[0],$fot(join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))))]]) ).
cnf(refute_0_1991,plain,
( composition(join(X_32,one),X_233) != join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233)))
| composition(join(X_32,one),X_233) = composition(join(one,X_32),X_233) ),
inference(resolve,[$cnf( $equal(join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233))),composition(join(one,X_32),X_233)) )],[refute_0_1989,refute_0_1990]) ).
cnf(refute_0_1992,plain,
composition(join(X_32,one),X_233) = composition(join(one,X_32),X_233),
inference(resolve,[$cnf( $equal(composition(join(X_32,one),X_233),join(X_233,meet(complement(X_233),composition(join(X_32,one),X_233)))) )],[refute_0_1644,refute_0_1991]) ).
cnf(refute_0_1993,plain,
composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))) = composition(join(one,converse(complement(meet(one,composition(top,complement(one)))))),complement(converse(composition(X_475,top)))),
inference(subst,[],[refute_0_1992:[bind(X_233,$fot(complement(converse(composition(X_475,top))))),bind(X_32,$fot(converse(complement(meet(one,composition(top,complement(one)))))))]]) ).
cnf(refute_0_1994,plain,
( composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))) != composition(join(one,converse(complement(meet(one,composition(top,complement(one)))))),complement(converse(composition(X_475,top))))
| composition(join(one,converse(complement(meet(one,composition(top,complement(one)))))),complement(converse(composition(X_475,top)))) != converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))
| composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))) = converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))))),bind(Y,$fot(composition(join(one,converse(complement(meet(one,composition(top,complement(one)))))),complement(converse(composition(X_475,top)))))),bind(Z,$fot(converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))))]]) ).
cnf(refute_0_1995,plain,
( composition(join(one,converse(complement(meet(one,composition(top,complement(one)))))),complement(converse(composition(X_475,top)))) != converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))
| composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))) = converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))),composition(join(one,converse(complement(meet(one,composition(top,complement(one)))))),complement(converse(composition(X_475,top))))) )],[refute_0_1993,refute_0_1994]) ).
cnf(refute_0_1996,plain,
composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))) = converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(complement(meet(one,composition(top,complement(one)))))),complement(converse(composition(X_475,top)))),converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))) )],[refute_0_1630,refute_0_1995]) ).
cnf(refute_0_1997,plain,
join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) = composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))),
inference(subst,[],[refute_0_116:[bind(X_32,$fot(converse(complement(meet(one,composition(top,complement(one))))))),bind(X_34,$fot(complement(converse(composition(X_475,top)))))]]) ).
cnf(refute_0_1998,plain,
( composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))) != converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))
| join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) != composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top))))
| join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) = converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))))),bind(Y,$fot(composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))))),bind(Z,$fot(converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))))]]) ).
cnf(refute_0_1999,plain,
( composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))) != converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))
| join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) = converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))),composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top))))) )],[refute_0_1997,refute_0_1998]) ).
cnf(refute_0_2000,plain,
join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) = converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))),
inference(resolve,[$cnf( $equal(composition(join(converse(complement(meet(one,composition(top,complement(one))))),one),complement(converse(composition(X_475,top)))),converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))) )],[refute_0_1996,refute_0_1999]) ).
cnf(refute_0_2001,plain,
( converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) != converse(composition(complement(composition(X_475,top)),top))
| join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) != converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))
| join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) = converse(composition(complement(composition(X_475,top)),top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))))),bind(Y,$fot(converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))))),bind(Z,$fot(converse(composition(complement(composition(X_475,top)),top))))]]) ).
cnf(refute_0_2002,plain,
( converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))) != converse(composition(complement(composition(X_475,top)),top))
| join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) = converse(composition(complement(composition(X_475,top)),top)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))),converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one)))))))) )],[refute_0_2000,refute_0_2001]) ).
cnf(refute_0_2003,plain,
join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) = converse(composition(complement(composition(X_475,top)),top)),
inference(resolve,[$cnf( $equal(converse(composition(complement(composition(X_475,top)),join(converse(one),complement(meet(one,composition(top,complement(one))))))),converse(composition(complement(composition(X_475,top)),top))) )],[refute_0_1189,refute_0_2002]) ).
cnf(refute_0_2004,plain,
( join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) != complement(converse(composition(X_475,top)))
| join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) != converse(composition(complement(composition(X_475,top)),top))
| converse(composition(complement(composition(X_475,top)),top)) = complement(converse(composition(X_475,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))),complement(converse(composition(X_475,top)))) ),[0],$fot(converse(composition(complement(composition(X_475,top)),top)))]]) ).
cnf(refute_0_2005,plain,
( join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))) != complement(converse(composition(X_475,top)))
| converse(composition(complement(composition(X_475,top)),top)) = complement(converse(composition(X_475,top))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))),converse(composition(complement(composition(X_475,top)),top))) )],[refute_0_2003,refute_0_2004]) ).
cnf(refute_0_2006,plain,
converse(composition(complement(composition(X_475,top)),top)) = complement(converse(composition(X_475,top))),
inference(resolve,[$cnf( $equal(join(complement(converse(composition(X_475,top))),composition(converse(complement(meet(one,composition(top,complement(one))))),complement(converse(composition(X_475,top))))),complement(converse(composition(X_475,top)))) )],[refute_0_1168,refute_0_2005]) ).
cnf(refute_0_2007,plain,
converse(composition(complement(composition(X_512,top)),top)) = complement(converse(composition(X_512,top))),
inference(subst,[],[refute_0_2006:[bind(X_475,$fot(X_512))]]) ).
cnf(refute_0_2008,plain,
( converse(composition(complement(composition(X_512,top)),top)) != complement(converse(composition(X_512,top)))
| converse(converse(composition(complement(composition(X_512,top)),top))) != composition(complement(composition(X_512,top)),top)
| converse(complement(converse(composition(X_512,top)))) = composition(complement(composition(X_512,top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(composition(complement(composition(X_512,top)),top))),composition(complement(composition(X_512,top)),top)) ),[0,0],$fot(complement(converse(composition(X_512,top))))]]) ).
cnf(refute_0_2009,plain,
( converse(converse(composition(complement(composition(X_512,top)),top))) != composition(complement(composition(X_512,top)),top)
| converse(complement(converse(composition(X_512,top)))) = composition(complement(composition(X_512,top)),top) ),
inference(resolve,[$cnf( $equal(converse(composition(complement(composition(X_512,top)),top)),complement(converse(composition(X_512,top)))) )],[refute_0_2007,refute_0_2008]) ).
cnf(refute_0_2010,plain,
converse(complement(converse(composition(X_512,top)))) = composition(complement(composition(X_512,top)),top),
inference(resolve,[$cnf( $equal(converse(converse(composition(complement(composition(X_512,top)),top))),composition(complement(composition(X_512,top)),top)) )],[refute_0_410,refute_0_2009]) ).
cnf(refute_0_2011,plain,
converse(converse(composition(X_512,top))) = composition(X_512,top),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(X_512,top)))]]) ).
cnf(refute_0_2012,plain,
complement(converse(converse(composition(X_512,top)))) = complement(converse(converse(composition(X_512,top)))),
introduced(tautology,[refl,[$fot(complement(converse(converse(composition(X_512,top)))))]]) ).
cnf(refute_0_2013,plain,
( complement(converse(converse(composition(X_512,top)))) != complement(converse(converse(composition(X_512,top))))
| converse(converse(composition(X_512,top))) != composition(X_512,top)
| complement(converse(converse(composition(X_512,top)))) = complement(composition(X_512,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(converse(composition(X_512,top)))),complement(converse(converse(composition(X_512,top))))) ),[1,0],$fot(composition(X_512,top))]]) ).
cnf(refute_0_2014,plain,
( converse(converse(composition(X_512,top))) != composition(X_512,top)
| complement(converse(converse(composition(X_512,top)))) = complement(composition(X_512,top)) ),
inference(resolve,[$cnf( $equal(complement(converse(converse(composition(X_512,top)))),complement(converse(converse(composition(X_512,top))))) )],[refute_0_2012,refute_0_2013]) ).
cnf(refute_0_2015,plain,
complement(converse(converse(composition(X_512,top)))) = complement(composition(X_512,top)),
inference(resolve,[$cnf( $equal(converse(converse(composition(X_512,top))),composition(X_512,top)) )],[refute_0_2011,refute_0_2014]) ).
cnf(refute_0_2016,plain,
converse(complement(converse(composition(X_512,top)))) = complement(converse(converse(composition(X_512,top)))),
inference(subst,[],[refute_0_1624:[bind(X_208,$fot(converse(composition(X_512,top))))]]) ).
cnf(refute_0_2017,plain,
( complement(converse(converse(composition(X_512,top)))) != complement(composition(X_512,top))
| converse(complement(converse(composition(X_512,top)))) != complement(converse(converse(composition(X_512,top))))
| converse(complement(converse(composition(X_512,top)))) = complement(composition(X_512,top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(complement(converse(composition(X_512,top)))))),bind(Y,$fot(complement(converse(converse(composition(X_512,top)))))),bind(Z,$fot(complement(composition(X_512,top))))]]) ).
cnf(refute_0_2018,plain,
( complement(converse(converse(composition(X_512,top)))) != complement(composition(X_512,top))
| converse(complement(converse(composition(X_512,top)))) = complement(composition(X_512,top)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(X_512,top)))),complement(converse(converse(composition(X_512,top))))) )],[refute_0_2016,refute_0_2017]) ).
cnf(refute_0_2019,plain,
converse(complement(converse(composition(X_512,top)))) = complement(composition(X_512,top)),
inference(resolve,[$cnf( $equal(complement(converse(converse(composition(X_512,top)))),complement(composition(X_512,top))) )],[refute_0_2015,refute_0_2018]) ).
cnf(refute_0_2020,plain,
( converse(complement(converse(composition(X_512,top)))) != complement(composition(X_512,top))
| converse(complement(converse(composition(X_512,top)))) != composition(complement(composition(X_512,top)),top)
| complement(composition(X_512,top)) = composition(complement(composition(X_512,top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(composition(X_512,top)))),composition(complement(composition(X_512,top)),top)) ),[0],$fot(complement(composition(X_512,top)))]]) ).
cnf(refute_0_2021,plain,
( converse(complement(converse(composition(X_512,top)))) != composition(complement(composition(X_512,top)),top)
| complement(composition(X_512,top)) = composition(complement(composition(X_512,top)),top) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(X_512,top)))),complement(composition(X_512,top))) )],[refute_0_2019,refute_0_2020]) ).
cnf(refute_0_2022,plain,
complement(composition(X_512,top)) = composition(complement(composition(X_512,top)),top),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(X_512,top)))),composition(complement(composition(X_512,top)),top)) )],[refute_0_2010,refute_0_2021]) ).
cnf(refute_0_2023,plain,
( complement(composition(X_512,top)) != composition(complement(composition(X_512,top)),top)
| composition(complement(composition(X_512,top)),top) = complement(composition(X_512,top)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(composition(X_512,top)))),bind(Y,$fot(composition(complement(composition(X_512,top)),top)))]]) ).
cnf(refute_0_2024,plain,
composition(complement(composition(X_512,top)),top) = complement(composition(X_512,top)),
inference(resolve,[$cnf( $equal(complement(composition(X_512,top)),composition(complement(composition(X_512,top)),top)) )],[refute_0_2022,refute_0_2023]) ).
cnf(refute_0_2025,plain,
composition(complement(composition(sk1,top)),top) = complement(composition(sk1,top)),
inference(subst,[],[refute_0_2024:[bind(X_512,$fot(sk1))]]) ).
cnf(refute_0_2026,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) = complement(composition(sk1,top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) ),[0,0],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_2027,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) = complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) )],[refute_0_2025,refute_0_2026]) ).
cnf(refute_0_2028,plain,
complement(composition(sk1,top)) != complement(composition(sk1,top)),
inference(resolve,[$cnf( $equal(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) )],[refute_0_2027,refute_0_409]) ).
cnf(refute_0_2029,plain,
$false,
inference(resolve,[$cnf( $equal(complement(composition(sk1,top)),complement(composition(sk1,top))) )],[refute_0_408,refute_0_2028]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : REL050-2 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.10 % Command : metis --show proof --show saturation %s
% 0.09/0.30 % Computer : n004.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Fri Jul 8 07:40:37 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 12.25/12.69 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.25/12.69
% 12.25/12.69 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.46/12.90
%------------------------------------------------------------------------------