TSTP Solution File: REL050-3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL050-3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 19:46:25 EDT 2022
% Result : Unsatisfiable 44.66s 44.82s
% Output : CNFRefutation 44.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 155
% Number of leaves : 461
% Syntax : Number of clauses : 1918 ( 960 unt; 0 nHn;1027 RR)
% Number of literals : 3300 (3299 equ;1384 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 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 : 2585 ( 60 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(maddux1_join_commutativity_1,axiom,
join(A,B) = join(B,A) ).
cnf(maddux2_join_associativity_2,axiom,
join(A,join(B,C)) = join(join(A,B),C) ).
cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(A,B) = complement(join(complement(A),complement(B))) ).
cnf(composition_associativity_5,axiom,
composition(A,composition(B,C)) = composition(composition(A,B),C) ).
cnf(composition_identity_6,axiom,
composition(A,one) = A ).
cnf(composition_distributivity_7,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ).
cnf(converse_idempotence_8,axiom,
converse(converse(A)) = A ).
cnf(converse_additivity_9,axiom,
converse(join(A,B)) = join(converse(A),converse(B)) ).
cnf(converse_multiplicativity_10,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ).
cnf(def_top_12,axiom,
top = join(A,complement(A)) ).
cnf(def_zero_13,axiom,
zero = meet(A,complement(A)) ).
cnf(goals_17,negated_conjecture,
complement(composition(sk1,top)) != composition(complement(composition(sk1,top)),top) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_4,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_3]) ).
cnf(refute_0_5,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_6,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) ),[0],$fot(join(complement(B),composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_7,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_7]) ).
cnf(refute_0_9,plain,
join(complement(X_79),composition(converse(converse(A)),complement(composition(converse(A),X_79)))) = complement(X_79),
inference(subst,[],[refute_0_8:[bind(A,$fot(converse(A))),bind(B,$fot(X_79))]]) ).
cnf(refute_0_10,plain,
( converse(converse(A)) != A
| join(complement(X_79),composition(converse(converse(A)),complement(composition(converse(A),X_79)))) != complement(X_79)
| join(complement(X_79),composition(A,complement(composition(converse(A),X_79)))) = complement(X_79) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_79),composition(converse(converse(A)),complement(composition(converse(A),X_79)))),complement(X_79)) ),[0,1,0],$fot(A)]]) ).
cnf(refute_0_11,plain,
( join(complement(X_79),composition(converse(converse(A)),complement(composition(converse(A),X_79)))) != complement(X_79)
| join(complement(X_79),composition(A,complement(composition(converse(A),X_79)))) = complement(X_79) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_10]) ).
cnf(refute_0_12,plain,
join(complement(X_79),composition(A,complement(composition(converse(A),X_79)))) = complement(X_79),
inference(resolve,[$cnf( $equal(join(complement(X_79),composition(converse(converse(A)),complement(composition(converse(A),X_79)))),complement(X_79)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79)))) = complement(X_79),
inference(subst,[],[refute_0_12:[bind(A,$fot(complement(X_79)))]]) ).
cnf(refute_0_14,plain,
converse(converse(join(X_74,composition(X_74,X_75)))) = join(X_74,composition(X_74,X_75)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(join(X_74,composition(X_74,X_75))))]]) ).
cnf(refute_0_15,plain,
composition(join(X_31,one),X_33) = join(composition(X_31,X_33),composition(one,X_33)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_31)),bind(B,$fot(one)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_16,plain,
converse(composition(converse(A),X_15)) = composition(converse(X_15),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_15))]]) ).
cnf(refute_0_17,plain,
( converse(composition(converse(A),X_15)) != composition(converse(X_15),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_15)) = composition(converse(X_15),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_15)),composition(converse(X_15),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_18,plain,
( converse(composition(converse(A),X_15)) != composition(converse(X_15),converse(converse(A)))
| converse(composition(converse(A),X_15)) = composition(converse(X_15),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_17]) ).
cnf(refute_0_19,plain,
converse(composition(converse(A),X_15)) = composition(converse(X_15),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_15)),composition(converse(X_15),converse(converse(A)))) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
converse(composition(converse(X_16),one)) = composition(converse(one),X_16),
inference(subst,[],[refute_0_19:[bind(A,$fot(X_16)),bind(X_15,$fot(one))]]) ).
cnf(refute_0_21,plain,
composition(converse(X_16),one) = converse(X_16),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_16)))]]) ).
cnf(refute_0_22,plain,
( composition(converse(X_16),one) != converse(X_16)
| converse(composition(converse(X_16),one)) != composition(converse(one),X_16)
| converse(converse(X_16)) = composition(converse(one),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_16),one)),composition(converse(one),X_16)) ),[0,0],$fot(converse(X_16))]]) ).
cnf(refute_0_23,plain,
( converse(composition(converse(X_16),one)) != composition(converse(one),X_16)
| converse(converse(X_16)) = composition(converse(one),X_16) ),
inference(resolve,[$cnf( $equal(composition(converse(X_16),one),converse(X_16)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
converse(converse(X_16)) = composition(converse(one),X_16),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_16),one)),composition(converse(one),X_16)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
converse(converse(X_16)) = X_16,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_16))]]) ).
cnf(refute_0_26,plain,
( converse(converse(X_16)) != X_16
| converse(converse(X_16)) != composition(converse(one),X_16)
| X_16 = composition(converse(one),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_16)),composition(converse(one),X_16)) ),[0],$fot(X_16)]]) ).
cnf(refute_0_27,plain,
( converse(converse(X_16)) != composition(converse(one),X_16)
| X_16 = composition(converse(one),X_16) ),
inference(resolve,[$cnf( $equal(converse(converse(X_16)),X_16) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
X_16 = composition(converse(one),X_16),
inference(resolve,[$cnf( $equal(converse(converse(X_16)),composition(converse(one),X_16)) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_30,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_28:[bind(X_16,$fot(one))]]) ).
cnf(refute_0_31,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_32,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_34,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_29,refute_0_34]) ).
cnf(refute_0_36,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_37,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
composition(converse(one),X_16) = composition(converse(one),X_16),
introduced(tautology,[refl,[$fot(composition(converse(one),X_16))]]) ).
cnf(refute_0_39,plain,
( composition(converse(one),X_16) != composition(converse(one),X_16)
| converse(one) != one
| composition(converse(one),X_16) = composition(one,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_16),composition(converse(one),X_16)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_40,plain,
( converse(one) != one
| composition(converse(one),X_16) = composition(one,X_16) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_16),composition(converse(one),X_16)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
composition(converse(one),X_16) = composition(one,X_16),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
( X_16 != composition(converse(one),X_16)
| composition(converse(one),X_16) != composition(one,X_16)
| X_16 = composition(one,X_16) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_16,composition(one,X_16)) ),[0],$fot(composition(converse(one),X_16))]]) ).
cnf(refute_0_43,plain,
( X_16 != composition(converse(one),X_16)
| X_16 = composition(one,X_16) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_16),composition(one,X_16)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
X_16 = composition(one,X_16),
inference(resolve,[$cnf( $equal(X_16,composition(converse(one),X_16)) )],[refute_0_28,refute_0_43]) ).
cnf(refute_0_45,plain,
X_33 = composition(one,X_33),
inference(subst,[],[refute_0_44:[bind(X_16,$fot(X_33))]]) ).
cnf(refute_0_46,plain,
( X_33 != composition(one,X_33)
| composition(one,X_33) = X_33 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_33)),bind(Y,$fot(composition(one,X_33)))]]) ).
cnf(refute_0_47,plain,
composition(one,X_33) = X_33,
inference(resolve,[$cnf( $equal(X_33,composition(one,X_33)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( composition(join(X_31,one),X_33) != join(composition(X_31,X_33),composition(one,X_33))
| composition(one,X_33) != X_33
| composition(join(X_31,one),X_33) = join(composition(X_31,X_33),X_33) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_31,one),X_33),join(composition(X_31,X_33),composition(one,X_33))) ),[1,1],$fot(X_33)]]) ).
cnf(refute_0_49,plain,
( composition(join(X_31,one),X_33) != join(composition(X_31,X_33),composition(one,X_33))
| composition(join(X_31,one),X_33) = join(composition(X_31,X_33),X_33) ),
inference(resolve,[$cnf( $equal(composition(one,X_33),X_33) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
composition(join(X_31,one),X_33) = join(composition(X_31,X_33),X_33),
inference(resolve,[$cnf( $equal(composition(join(X_31,one),X_33),join(composition(X_31,X_33),composition(one,X_33))) )],[refute_0_15,refute_0_49]) ).
cnf(refute_0_51,plain,
join(composition(X_31,X_33),X_33) = join(X_33,composition(X_31,X_33)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_33)),bind(B,$fot(composition(X_31,X_33)))]]) ).
cnf(refute_0_52,plain,
( composition(join(X_31,one),X_33) != join(composition(X_31,X_33),X_33)
| join(composition(X_31,X_33),X_33) != join(X_33,composition(X_31,X_33))
| composition(join(X_31,one),X_33) = join(X_33,composition(X_31,X_33)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_31,one),X_33),join(X_33,composition(X_31,X_33))) ),[0],$fot(join(composition(X_31,X_33),X_33))]]) ).
cnf(refute_0_53,plain,
( composition(join(X_31,one),X_33) != join(composition(X_31,X_33),X_33)
| composition(join(X_31,one),X_33) = join(X_33,composition(X_31,X_33)) ),
inference(resolve,[$cnf( $equal(join(composition(X_31,X_33),X_33),join(X_33,composition(X_31,X_33))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
composition(join(X_31,one),X_33) = join(X_33,composition(X_31,X_33)),
inference(resolve,[$cnf( $equal(composition(join(X_31,one),X_33),join(composition(X_31,X_33),X_33)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
composition(join(converse(B),one),converse(A)) = join(converse(A),composition(converse(B),converse(A))),
inference(subst,[],[refute_0_54:[bind(X_31,$fot(converse(B))),bind(X_33,$fot(converse(A)))]]) ).
cnf(refute_0_56,plain,
( converse(composition(A,B)) != composition(converse(B),converse(A))
| composition(converse(B),converse(A)) = converse(composition(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(A,B)))),bind(Y,$fot(composition(converse(B),converse(A))))]]) ).
cnf(refute_0_57,plain,
composition(converse(B),converse(A)) = converse(composition(A,B)),
inference(resolve,[$cnf( $equal(converse(composition(A,B)),composition(converse(B),converse(A))) )],[converse_multiplicativity_10,refute_0_56]) ).
cnf(refute_0_58,plain,
( composition(converse(B),converse(A)) != converse(composition(A,B))
| composition(join(converse(B),one),converse(A)) != join(converse(A),composition(converse(B),converse(A)))
| composition(join(converse(B),one),converse(A)) = join(converse(A),converse(composition(A,B))) ),
introduced(tautology,[equality,[$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_59,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( $equal(composition(converse(B),converse(A)),converse(composition(A,B))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
composition(join(converse(B),one),converse(A)) = join(converse(A),converse(composition(A,B))),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),join(converse(A),composition(converse(B),converse(A)))) )],[refute_0_55,refute_0_59]) ).
cnf(refute_0_61,plain,
composition(converse(join(B,one)),converse(A)) = converse(composition(A,join(B,one))),
inference(subst,[],[refute_0_57:[bind(B,$fot(join(B,one)))]]) ).
cnf(refute_0_62,plain,
converse(join(X_4,converse(A))) = join(converse(X_4),converse(converse(A))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_4)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_63,plain,
( converse(converse(A)) != A
| converse(join(X_4,converse(A))) != join(converse(X_4),converse(converse(A)))
| converse(join(X_4,converse(A))) = join(converse(X_4),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_4,converse(A))),join(converse(X_4),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_64,plain,
( converse(join(X_4,converse(A))) != join(converse(X_4),converse(converse(A)))
| converse(join(X_4,converse(A))) = join(converse(X_4),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_63]) ).
cnf(refute_0_65,plain,
converse(join(X_4,converse(A))) = join(converse(X_4),A),
inference(resolve,[$cnf( $equal(converse(join(X_4,converse(A))),join(converse(X_4),converse(converse(A)))) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
converse(join(X_4,converse(one))) = join(converse(X_4),one),
inference(subst,[],[refute_0_65:[bind(A,$fot(one))]]) ).
cnf(refute_0_67,plain,
( converse(join(X_4,converse(one))) != join(converse(X_4),one)
| converse(one) != one
| converse(join(X_4,one)) = join(converse(X_4),one) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_4,converse(one))),join(converse(X_4),one)) ),[0,0,1],$fot(one)]]) ).
cnf(refute_0_68,plain,
( converse(join(X_4,converse(one))) != join(converse(X_4),one)
| converse(join(X_4,one)) = join(converse(X_4),one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_37,refute_0_67]) ).
cnf(refute_0_69,plain,
converse(join(X_4,one)) = join(converse(X_4),one),
inference(resolve,[$cnf( $equal(converse(join(X_4,converse(one))),join(converse(X_4),one)) )],[refute_0_66,refute_0_68]) ).
cnf(refute_0_70,plain,
join(converse(X_4),one) = join(one,converse(X_4)),
inference(subst,[],[refute_0_4:[bind(A,$fot(one)),bind(B,$fot(converse(X_4)))]]) ).
cnf(refute_0_71,plain,
( converse(join(X_4,one)) != join(converse(X_4),one)
| join(converse(X_4),one) != join(one,converse(X_4))
| converse(join(X_4,one)) = join(one,converse(X_4)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X_4,one)),join(one,converse(X_4))) ),[0],$fot(join(converse(X_4),one))]]) ).
cnf(refute_0_72,plain,
( converse(join(X_4,one)) != join(converse(X_4),one)
| converse(join(X_4,one)) = join(one,converse(X_4)) ),
inference(resolve,[$cnf( $equal(join(converse(X_4),one),join(one,converse(X_4))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
converse(join(X_4,one)) = join(one,converse(X_4)),
inference(resolve,[$cnf( $equal(converse(join(X_4,one)),join(converse(X_4),one)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
( converse(join(X_4,one)) != join(one,converse(X_4))
| join(one,converse(X_4)) = converse(join(X_4,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_4,one)))),bind(Y,$fot(join(one,converse(X_4))))]]) ).
cnf(refute_0_75,plain,
join(one,converse(X_4)) = converse(join(X_4,one)),
inference(resolve,[$cnf( $equal(converse(join(X_4,one)),join(one,converse(X_4))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
join(one,converse(B)) = converse(join(B,one)),
inference(subst,[],[refute_0_75:[bind(X_4,$fot(B))]]) ).
cnf(refute_0_77,plain,
composition(join(one,converse(B)),converse(A)) = composition(join(one,converse(B)),converse(A)),
introduced(tautology,[refl,[$fot(composition(join(one,converse(B)),converse(A)))]]) ).
cnf(refute_0_78,plain,
( composition(join(one,converse(B)),converse(A)) != composition(join(one,converse(B)),converse(A))
| join(one,converse(B)) != converse(join(B,one))
| composition(join(one,converse(B)),converse(A)) = composition(converse(join(B,one)),converse(A)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(B)),converse(A)),composition(join(one,converse(B)),converse(A))) ),[1,0],$fot(converse(join(B,one)))]]) ).
cnf(refute_0_79,plain,
( join(one,converse(B)) != converse(join(B,one))
| composition(join(one,converse(B)),converse(A)) = composition(converse(join(B,one)),converse(A)) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(B)),converse(A)),composition(join(one,converse(B)),converse(A))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
composition(join(one,converse(B)),converse(A)) = composition(converse(join(B,one)),converse(A)),
inference(resolve,[$cnf( $equal(join(one,converse(B)),converse(join(B,one))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_82,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_81]) ).
cnf(refute_0_83,plain,
( composition(converse(join(B,one)),converse(A)) != converse(composition(A,join(B,one)))
| composition(join(one,converse(B)),converse(A)) != composition(converse(join(B,one)),converse(A))
| composition(join(one,converse(B)),converse(A)) = converse(composition(A,join(B,one))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(composition(join(one,converse(B)),converse(A)))),bind(Y,$fot(composition(converse(join(B,one)),converse(A)))),bind(Z,$fot(converse(composition(A,join(B,one)))))]]) ).
cnf(refute_0_84,plain,
( composition(converse(join(B,one)),converse(A)) != converse(composition(A,join(B,one)))
| composition(join(one,converse(B)),converse(A)) = converse(composition(A,join(B,one))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(B)),converse(A)),composition(converse(join(B,one)),converse(A))) )],[refute_0_80,refute_0_83]) ).
cnf(refute_0_85,plain,
composition(join(one,converse(B)),converse(A)) = converse(composition(A,join(B,one))),
inference(resolve,[$cnf( $equal(composition(converse(join(B,one)),converse(A)),converse(composition(A,join(B,one)))) )],[refute_0_61,refute_0_84]) ).
cnf(refute_0_86,plain,
composition(join(X_34,one),X_35) = join(X_35,composition(X_34,X_35)),
inference(subst,[],[refute_0_54:[bind(X_31,$fot(X_34)),bind(X_33,$fot(X_35))]]) ).
cnf(refute_0_87,plain,
join(one,X_34) = join(X_34,one),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(one)),bind(B,$fot(X_34))]]) ).
cnf(refute_0_88,plain,
( join(one,X_34) != join(X_34,one)
| join(X_34,one) = join(one,X_34) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,X_34))),bind(Y,$fot(join(X_34,one)))]]) ).
cnf(refute_0_89,plain,
join(X_34,one) = join(one,X_34),
inference(resolve,[$cnf( $equal(join(one,X_34),join(X_34,one)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( composition(join(X_34,one),X_35) != join(X_35,composition(X_34,X_35))
| join(X_34,one) != join(one,X_34)
| composition(join(one,X_34),X_35) = join(X_35,composition(X_34,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_34,one),X_35),join(X_35,composition(X_34,X_35))) ),[0,0],$fot(join(one,X_34))]]) ).
cnf(refute_0_91,plain,
( composition(join(X_34,one),X_35) != join(X_35,composition(X_34,X_35))
| composition(join(one,X_34),X_35) = join(X_35,composition(X_34,X_35)) ),
inference(resolve,[$cnf( $equal(join(X_34,one),join(one,X_34)) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
composition(join(one,X_34),X_35) = join(X_35,composition(X_34,X_35)),
inference(resolve,[$cnf( $equal(composition(join(X_34,one),X_35),join(X_35,composition(X_34,X_35))) )],[refute_0_86,refute_0_91]) ).
cnf(refute_0_93,plain,
( composition(join(X_31,one),X_33) != join(X_33,composition(X_31,X_33))
| join(X_33,composition(X_31,X_33)) = composition(join(X_31,one),X_33) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_31,one),X_33))),bind(Y,$fot(join(X_33,composition(X_31,X_33))))]]) ).
cnf(refute_0_94,plain,
join(X_33,composition(X_31,X_33)) = composition(join(X_31,one),X_33),
inference(resolve,[$cnf( $equal(composition(join(X_31,one),X_33),join(X_33,composition(X_31,X_33))) )],[refute_0_54,refute_0_93]) ).
cnf(refute_0_95,plain,
join(X_35,composition(X_34,X_35)) = composition(join(X_34,one),X_35),
inference(subst,[],[refute_0_94:[bind(X_31,$fot(X_34)),bind(X_33,$fot(X_35))]]) ).
cnf(refute_0_96,plain,
( composition(join(one,X_34),X_35) != join(X_35,composition(X_34,X_35))
| join(X_35,composition(X_34,X_35)) != composition(join(X_34,one),X_35)
| composition(join(one,X_34),X_35) = composition(join(X_34,one),X_35) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,X_34),X_35),composition(join(X_34,one),X_35)) ),[0],$fot(join(X_35,composition(X_34,X_35)))]]) ).
cnf(refute_0_97,plain,
( composition(join(one,X_34),X_35) != join(X_35,composition(X_34,X_35))
| composition(join(one,X_34),X_35) = composition(join(X_34,one),X_35) ),
inference(resolve,[$cnf( $equal(join(X_35,composition(X_34,X_35)),composition(join(X_34,one),X_35)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
composition(join(one,X_34),X_35) = composition(join(X_34,one),X_35),
inference(resolve,[$cnf( $equal(composition(join(one,X_34),X_35),join(X_35,composition(X_34,X_35))) )],[refute_0_92,refute_0_97]) ).
cnf(refute_0_99,plain,
( composition(join(one,X_34),X_35) != composition(join(X_34,one),X_35)
| composition(join(X_34,one),X_35) = composition(join(one,X_34),X_35) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,X_34),X_35))),bind(Y,$fot(composition(join(X_34,one),X_35)))]]) ).
cnf(refute_0_100,plain,
composition(join(X_34,one),X_35) = composition(join(one,X_34),X_35),
inference(resolve,[$cnf( $equal(composition(join(one,X_34),X_35),composition(join(X_34,one),X_35)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
composition(join(converse(B),one),converse(A)) = composition(join(one,converse(B)),converse(A)),
inference(subst,[],[refute_0_100:[bind(X_34,$fot(converse(B))),bind(X_35,$fot(converse(A)))]]) ).
cnf(refute_0_102,plain,
( composition(join(converse(B),one),converse(A)) != composition(join(one,converse(B)),converse(A))
| composition(join(one,converse(B)),converse(A)) != converse(composition(A,join(B,one)))
| composition(join(converse(B),one),converse(A)) = converse(composition(A,join(B,one))) ),
inference(subst,[],[refute_0_82:[bind(X,$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(B,one)))))]]) ).
cnf(refute_0_103,plain,
( composition(join(one,converse(B)),converse(A)) != converse(composition(A,join(B,one)))
| composition(join(converse(B),one),converse(A)) = converse(composition(A,join(B,one))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),composition(join(one,converse(B)),converse(A))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
composition(join(converse(B),one),converse(A)) = converse(composition(A,join(B,one))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(B)),converse(A)),converse(composition(A,join(B,one)))) )],[refute_0_85,refute_0_103]) ).
cnf(refute_0_105,plain,
( composition(join(converse(B),one),converse(A)) != converse(composition(A,join(B,one)))
| composition(join(converse(B),one),converse(A)) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(B,one))) = join(converse(A),converse(composition(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(B),one),converse(A)),join(converse(A),converse(composition(A,B)))) ),[0],$fot(converse(composition(A,join(B,one))))]]) ).
cnf(refute_0_106,plain,
( composition(join(converse(B),one),converse(A)) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(B,one))) = join(converse(A),converse(composition(A,B))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),converse(composition(A,join(B,one)))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(join(converse(A),converse(B))))]]) ).
cnf(refute_0_108,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_107]) ).
cnf(refute_0_109,plain,
join(converse(A),converse(composition(A,B))) = converse(join(A,composition(A,B))),
inference(subst,[],[refute_0_108:[bind(B,$fot(composition(A,B)))]]) ).
cnf(refute_0_110,plain,
( converse(composition(A,join(B,one))) != join(converse(A),converse(composition(A,B)))
| join(converse(A),converse(composition(A,B))) != converse(join(A,composition(A,B)))
| converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(composition(A,join(B,one))),converse(join(A,composition(A,B)))) ),[0],$fot(join(converse(A),converse(composition(A,B))))]]) ).
cnf(refute_0_111,plain,
( converse(composition(A,join(B,one))) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(composition(A,B))),converse(join(A,composition(A,B)))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( composition(join(converse(B),one),converse(A)) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))) ),
inference(resolve,[$cnf( $equal(converse(composition(A,join(B,one))),join(converse(A),converse(composition(A,B)))) )],[refute_0_106,refute_0_111]) ).
cnf(refute_0_113,plain,
converse(composition(A,join(B,one))) = converse(join(A,composition(A,B))),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),join(converse(A),converse(composition(A,B)))) )],[refute_0_60,refute_0_112]) ).
cnf(refute_0_114,plain,
converse(composition(X_74,join(X_75,one))) = converse(join(X_74,composition(X_74,X_75))),
inference(subst,[],[refute_0_113:[bind(A,$fot(X_74)),bind(B,$fot(X_75))]]) ).
cnf(refute_0_115,plain,
( converse(composition(X_74,join(X_75,one))) != converse(join(X_74,composition(X_74,X_75)))
| converse(join(X_74,composition(X_74,X_75))) = converse(composition(X_74,join(X_75,one))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(X_74,join(X_75,one))))),bind(Y,$fot(converse(join(X_74,composition(X_74,X_75)))))]]) ).
cnf(refute_0_116,plain,
converse(join(X_74,composition(X_74,X_75))) = converse(composition(X_74,join(X_75,one))),
inference(resolve,[$cnf( $equal(converse(composition(X_74,join(X_75,one))),converse(join(X_74,composition(X_74,X_75)))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
( converse(converse(join(X_74,composition(X_74,X_75)))) != join(X_74,composition(X_74,X_75))
| converse(join(X_74,composition(X_74,X_75))) != converse(composition(X_74,join(X_75,one)))
| converse(converse(composition(X_74,join(X_75,one)))) = join(X_74,composition(X_74,X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(join(X_74,composition(X_74,X_75)))),join(X_74,composition(X_74,X_75))) ),[0,0],$fot(converse(composition(X_74,join(X_75,one))))]]) ).
cnf(refute_0_118,plain,
( converse(converse(join(X_74,composition(X_74,X_75)))) != join(X_74,composition(X_74,X_75))
| converse(converse(composition(X_74,join(X_75,one)))) = join(X_74,composition(X_74,X_75)) ),
inference(resolve,[$cnf( $equal(converse(join(X_74,composition(X_74,X_75))),converse(composition(X_74,join(X_75,one)))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
converse(converse(composition(X_74,join(X_75,one)))) = join(X_74,composition(X_74,X_75)),
inference(resolve,[$cnf( $equal(converse(converse(join(X_74,composition(X_74,X_75)))),join(X_74,composition(X_74,X_75))) )],[refute_0_14,refute_0_118]) ).
cnf(refute_0_120,plain,
converse(converse(composition(X_74,join(X_75,one)))) = composition(X_74,join(X_75,one)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(X_74,join(X_75,one))))]]) ).
cnf(refute_0_121,plain,
( converse(converse(composition(X_74,join(X_75,one)))) != composition(X_74,join(X_75,one))
| converse(converse(composition(X_74,join(X_75,one)))) != join(X_74,composition(X_74,X_75))
| composition(X_74,join(X_75,one)) = join(X_74,composition(X_74,X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(composition(X_74,join(X_75,one)))),join(X_74,composition(X_74,X_75))) ),[0],$fot(composition(X_74,join(X_75,one)))]]) ).
cnf(refute_0_122,plain,
( converse(converse(composition(X_74,join(X_75,one)))) != join(X_74,composition(X_74,X_75))
| composition(X_74,join(X_75,one)) = join(X_74,composition(X_74,X_75)) ),
inference(resolve,[$cnf( $equal(converse(converse(composition(X_74,join(X_75,one)))),composition(X_74,join(X_75,one))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
composition(X_74,join(X_75,one)) = join(X_74,composition(X_74,X_75)),
inference(resolve,[$cnf( $equal(converse(converse(composition(X_74,join(X_75,one)))),join(X_74,composition(X_74,X_75))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) = join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79)))),
inference(subst,[],[refute_0_123:[bind(X_74,$fot(complement(X_79))),bind(X_75,$fot(complement(composition(converse(complement(X_79)),X_79))))]]) ).
cnf(refute_0_125,plain,
( composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) != join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79))))
| join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79)))) = composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)))),bind(Y,$fot(join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79))))))]]) ).
cnf(refute_0_126,plain,
join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79)))) = composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)),
inference(resolve,[$cnf( $equal(composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)),join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79))))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79)))) != complement(X_79)
| join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79)))) != composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one))
| composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) = complement(X_79) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79)))),complement(X_79)) ),[0],$fot(composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)))]]) ).
cnf(refute_0_128,plain,
( join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79)))) != complement(X_79)
| composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) = complement(X_79) ),
inference(resolve,[$cnf( $equal(join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79)))),composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) = complement(X_79),
inference(resolve,[$cnf( $equal(join(complement(X_79),composition(complement(X_79),complement(composition(converse(complement(X_79)),X_79)))),complement(X_79)) )],[refute_0_13,refute_0_128]) ).
cnf(refute_0_130,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_131,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$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_132,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( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_132]) ).
cnf(refute_0_134,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_135,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_136,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_135]) ).
cnf(refute_0_137,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_138,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_139,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_82:[bind(X,$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_142,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_134,refute_0_142]) ).
cnf(refute_0_144,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$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_145,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_133,refute_0_145]) ).
cnf(refute_0_147,plain,
X_107 = join(meet(X_107,X_108),complement(join(complement(X_107),X_108))),
inference(subst,[],[refute_0_146:[bind(A,$fot(X_107)),bind(B,$fot(X_108))]]) ).
cnf(refute_0_148,plain,
meet(X_10,X_11) = complement(join(complement(X_10),complement(X_11))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_10)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_149,plain,
join(complement(X_11),complement(X_10)) = join(complement(X_10),complement(X_11)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_11))),bind(B,$fot(complement(X_10)))]]) ).
cnf(refute_0_150,plain,
( join(complement(X_11),complement(X_10)) != join(complement(X_10),complement(X_11))
| join(complement(X_10),complement(X_11)) = join(complement(X_11),complement(X_10)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_11),complement(X_10)))),bind(Y,$fot(join(complement(X_10),complement(X_11))))]]) ).
cnf(refute_0_151,plain,
join(complement(X_10),complement(X_11)) = join(complement(X_11),complement(X_10)),
inference(resolve,[$cnf( $equal(join(complement(X_11),complement(X_10)),join(complement(X_10),complement(X_11))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
( join(complement(X_10),complement(X_11)) != join(complement(X_11),complement(X_10))
| meet(X_10,X_11) != complement(join(complement(X_10),complement(X_11)))
| meet(X_10,X_11) = complement(join(complement(X_11),complement(X_10))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_10,X_11),complement(join(complement(X_10),complement(X_11)))) ),[1,0],$fot(join(complement(X_11),complement(X_10)))]]) ).
cnf(refute_0_153,plain,
( meet(X_10,X_11) != complement(join(complement(X_10),complement(X_11)))
| meet(X_10,X_11) = complement(join(complement(X_11),complement(X_10))) ),
inference(resolve,[$cnf( $equal(join(complement(X_10),complement(X_11)),join(complement(X_11),complement(X_10))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
meet(X_10,X_11) = complement(join(complement(X_11),complement(X_10))),
inference(resolve,[$cnf( $equal(meet(X_10,X_11),complement(join(complement(X_10),complement(X_11)))) )],[refute_0_148,refute_0_153]) ).
cnf(refute_0_155,plain,
complement(join(complement(X_11),complement(X_10))) = meet(X_11,X_10),
inference(subst,[],[refute_0_136:[bind(A,$fot(X_11)),bind(B,$fot(X_10))]]) ).
cnf(refute_0_156,plain,
( complement(join(complement(X_11),complement(X_10))) != meet(X_11,X_10)
| meet(X_10,X_11) != complement(join(complement(X_11),complement(X_10)))
| meet(X_10,X_11) = meet(X_11,X_10) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_10,X_11),complement(join(complement(X_11),complement(X_10)))) ),[1],$fot(meet(X_11,X_10))]]) ).
cnf(refute_0_157,plain,
( meet(X_10,X_11) != complement(join(complement(X_11),complement(X_10)))
| meet(X_10,X_11) = meet(X_11,X_10) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_11),complement(X_10))),meet(X_11,X_10)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
meet(X_10,X_11) = meet(X_11,X_10),
inference(resolve,[$cnf( $equal(meet(X_10,X_11),complement(join(complement(X_11),complement(X_10)))) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
meet(X_108,X_107) = meet(X_107,X_108),
inference(subst,[],[refute_0_158:[bind(X_10,$fot(X_108)),bind(X_11,$fot(X_107))]]) ).
cnf(refute_0_160,plain,
( meet(X_108,X_107) != meet(X_107,X_108)
| meet(X_107,X_108) = meet(X_108,X_107) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_108,X_107))),bind(Y,$fot(meet(X_107,X_108)))]]) ).
cnf(refute_0_161,plain,
meet(X_107,X_108) = meet(X_108,X_107),
inference(resolve,[$cnf( $equal(meet(X_108,X_107),meet(X_107,X_108)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( X_107 != join(meet(X_107,X_108),complement(join(complement(X_107),X_108)))
| meet(X_107,X_108) != meet(X_108,X_107)
| X_107 = join(meet(X_108,X_107),complement(join(complement(X_107),X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(X_107,join(meet(X_107,X_108),complement(join(complement(X_107),X_108)))) ),[1,0],$fot(meet(X_108,X_107))]]) ).
cnf(refute_0_163,plain,
( X_107 != join(meet(X_107,X_108),complement(join(complement(X_107),X_108)))
| X_107 = join(meet(X_108,X_107),complement(join(complement(X_107),X_108))) ),
inference(resolve,[$cnf( $equal(meet(X_107,X_108),meet(X_108,X_107)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
X_107 = join(meet(X_108,X_107),complement(join(complement(X_107),X_108))),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,X_108),complement(join(complement(X_107),X_108)))) )],[refute_0_147,refute_0_163]) ).
cnf(refute_0_165,plain,
X_107 = join(meet(join(complement(complement(X_107)),X_148),X_107),complement(join(complement(X_107),join(complement(complement(X_107)),X_148)))),
inference(subst,[],[refute_0_164:[bind(X_108,$fot(join(complement(complement(X_107)),X_148)))]]) ).
cnf(refute_0_166,plain,
join(X_41,join(complement(X_41),X_43)) = join(join(X_41,complement(X_41)),X_43),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_41)),bind(B,$fot(complement(X_41))),bind(C,$fot(X_43))]]) ).
cnf(refute_0_167,plain,
top = join(X_41,complement(X_41)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_41))]]) ).
cnf(refute_0_168,plain,
( top != join(X_41,complement(X_41))
| join(X_41,complement(X_41)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(X_41,complement(X_41))))]]) ).
cnf(refute_0_169,plain,
join(X_41,complement(X_41)) = top,
inference(resolve,[$cnf( $equal(top,join(X_41,complement(X_41))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
( join(X_41,complement(X_41)) != top
| join(X_41,join(complement(X_41),X_43)) != join(join(X_41,complement(X_41)),X_43)
| join(X_41,join(complement(X_41),X_43)) = join(top,X_43) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,join(complement(X_41),X_43)),join(join(X_41,complement(X_41)),X_43)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_171,plain,
( join(X_41,join(complement(X_41),X_43)) != join(join(X_41,complement(X_41)),X_43)
| join(X_41,join(complement(X_41),X_43)) = join(top,X_43) ),
inference(resolve,[$cnf( $equal(join(X_41,complement(X_41)),top) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
join(X_41,join(complement(X_41),X_43)) = join(top,X_43),
inference(resolve,[$cnf( $equal(join(X_41,join(complement(X_41),X_43)),join(join(X_41,complement(X_41)),X_43)) )],[refute_0_166,refute_0_171]) ).
cnf(refute_0_173,plain,
join(X_41,join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top)))))) = join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_41)),bind(B,$fot(meet(top,join(zero,zero)))),bind(C,$fot(join(zero,meet(top,join(zero,meet(top,top))))))]]) ).
cnf(refute_0_174,plain,
top = join(join(complement(X_10),complement(X_11)),complement(join(complement(X_10),complement(X_11)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(complement(X_10),complement(X_11))))]]) ).
cnf(refute_0_175,plain,
( meet(X_10,X_11) != complement(join(complement(X_10),complement(X_11)))
| complement(join(complement(X_10),complement(X_11))) = meet(X_10,X_11) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_10,X_11))),bind(Y,$fot(complement(join(complement(X_10),complement(X_11)))))]]) ).
cnf(refute_0_176,plain,
complement(join(complement(X_10),complement(X_11))) = meet(X_10,X_11),
inference(resolve,[$cnf( $equal(meet(X_10,X_11),complement(join(complement(X_10),complement(X_11)))) )],[refute_0_148,refute_0_175]) ).
cnf(refute_0_177,plain,
( complement(join(complement(X_10),complement(X_11))) != meet(X_10,X_11)
| top != join(join(complement(X_10),complement(X_11)),complement(join(complement(X_10),complement(X_11))))
| top = join(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_10),complement(X_11)),complement(join(complement(X_10),complement(X_11))))) ),[1,1],$fot(meet(X_10,X_11))]]) ).
cnf(refute_0_178,plain,
( top != join(join(complement(X_10),complement(X_11)),complement(join(complement(X_10),complement(X_11))))
| top = join(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_10),complement(X_11))),meet(X_10,X_11)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
top = join(join(complement(X_10),complement(X_11)),meet(X_10,X_11)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_10),complement(X_11)),complement(join(complement(X_10),complement(X_11))))) )],[refute_0_174,refute_0_178]) ).
cnf(refute_0_180,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_181,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_180]) ).
cnf(refute_0_182,plain,
join(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) = join(complement(X_10),join(complement(X_11),meet(X_10,X_11))),
inference(subst,[],[refute_0_181:[bind(A,$fot(complement(X_10))),bind(B,$fot(complement(X_11))),bind(C,$fot(meet(X_10,X_11)))]]) ).
cnf(refute_0_183,plain,
( join(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) != join(complement(X_10),join(complement(X_11),meet(X_10,X_11)))
| top != join(join(complement(X_10),complement(X_11)),meet(X_10,X_11))
| top = join(complement(X_10),join(complement(X_11),meet(X_10,X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_10),complement(X_11)),meet(X_10,X_11))) ),[1],$fot(join(complement(X_10),join(complement(X_11),meet(X_10,X_11))))]]) ).
cnf(refute_0_184,plain,
( top != join(join(complement(X_10),complement(X_11)),meet(X_10,X_11))
| top = join(complement(X_10),join(complement(X_11),meet(X_10,X_11))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_10),complement(X_11)),meet(X_10,X_11)),join(complement(X_10),join(complement(X_11),meet(X_10,X_11)))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
top = join(complement(X_10),join(complement(X_11),meet(X_10,X_11))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_10),complement(X_11)),meet(X_10,X_11))) )],[refute_0_179,refute_0_184]) ).
cnf(refute_0_186,plain,
top = join(complement(X_22),join(complement(top),meet(X_22,top))),
inference(subst,[],[refute_0_185:[bind(X_10,$fot(X_22)),bind(X_11,$fot(top))]]) ).
cnf(refute_0_187,plain,
zero = meet(join(complement(X_10),complement(X_11)),complement(join(complement(X_10),complement(X_11)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_10),complement(X_11))))]]) ).
cnf(refute_0_188,plain,
( complement(join(complement(X_10),complement(X_11))) != meet(X_10,X_11)
| zero != meet(join(complement(X_10),complement(X_11)),complement(join(complement(X_10),complement(X_11))))
| zero = meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_10),complement(X_11)),complement(join(complement(X_10),complement(X_11))))) ),[1,1],$fot(meet(X_10,X_11))]]) ).
cnf(refute_0_189,plain,
( zero != meet(join(complement(X_10),complement(X_11)),complement(join(complement(X_10),complement(X_11))))
| zero = meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_10),complement(X_11))),meet(X_10,X_11)) )],[refute_0_176,refute_0_188]) ).
cnf(refute_0_190,plain,
zero = meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_10),complement(X_11)),complement(join(complement(X_10),complement(X_11))))) )],[refute_0_187,refute_0_189]) ).
cnf(refute_0_191,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_192,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_191]) ).
cnf(refute_0_193,plain,
join(meet(X_10,X_11),complement(meet(X_10,X_11))) = top,
inference(subst,[],[refute_0_192:[bind(A,$fot(meet(X_10,X_11)))]]) ).
cnf(refute_0_194,plain,
complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))) = complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))))]]) ).
cnf(refute_0_195,plain,
( complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))) != complement(join(meet(X_10,X_11),complement(meet(X_10,X_11))))
| join(meet(X_10,X_11),complement(meet(X_10,X_11))) != top
| complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))),complement(join(meet(X_10,X_11),complement(meet(X_10,X_11))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_196,plain,
( join(meet(X_10,X_11),complement(meet(X_10,X_11))) != top
| complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))),complement(join(meet(X_10,X_11),complement(meet(X_10,X_11))))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_10,X_11),complement(meet(X_10,X_11))),top) )],[refute_0_193,refute_0_196]) ).
cnf(refute_0_198,plain,
meet(join(complement(X_10),complement(X_11)),B) = complement(join(complement(join(complement(X_10),complement(X_11))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_10),complement(X_11))))]]) ).
cnf(refute_0_199,plain,
( complement(join(complement(X_10),complement(X_11))) != meet(X_10,X_11)
| meet(join(complement(X_10),complement(X_11)),B) != complement(join(complement(join(complement(X_10),complement(X_11))),complement(B)))
| meet(join(complement(X_10),complement(X_11)),B) = complement(join(meet(X_10,X_11),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_10),complement(X_11)),B),complement(join(complement(join(complement(X_10),complement(X_11))),complement(B)))) ),[1,0,0],$fot(meet(X_10,X_11))]]) ).
cnf(refute_0_200,plain,
( meet(join(complement(X_10),complement(X_11)),B) != complement(join(complement(join(complement(X_10),complement(X_11))),complement(B)))
| meet(join(complement(X_10),complement(X_11)),B) = complement(join(meet(X_10,X_11),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_10),complement(X_11))),meet(X_10,X_11)) )],[refute_0_176,refute_0_199]) ).
cnf(refute_0_201,plain,
meet(join(complement(X_10),complement(X_11)),B) = complement(join(meet(X_10,X_11),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_10),complement(X_11)),B),complement(join(complement(join(complement(X_10),complement(X_11))),complement(B)))) )],[refute_0_198,refute_0_200]) ).
cnf(refute_0_202,plain,
meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) = complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))),
inference(subst,[],[refute_0_201:[bind(B,$fot(meet(X_10,X_11)))]]) ).
cnf(refute_0_203,plain,
( complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))) != complement(top)
| meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) != complement(join(meet(X_10,X_11),complement(meet(X_10,X_11))))
| meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) = complement(top) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)))),bind(Y,$fot(complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_204,plain,
( complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))) != complement(top)
| meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)),complement(join(meet(X_10,X_11),complement(meet(X_10,X_11))))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_10,X_11),complement(meet(X_10,X_11)))),complement(top)) )],[refute_0_197,refute_0_204]) ).
cnf(refute_0_206,plain,
( meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)) != complement(top)
| zero != meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_207,plain,
( zero != meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11)),complement(top)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_10),complement(X_11)),meet(X_10,X_11))) )],[refute_0_190,refute_0_207]) ).
cnf(refute_0_209,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_210,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
( complement(top) != zero
| top != join(complement(X_22),join(complement(top),meet(X_22,top)))
| top = join(complement(X_22),join(zero,meet(X_22,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_22),join(complement(top),meet(X_22,top)))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_212,plain,
( top != join(complement(X_22),join(complement(top),meet(X_22,top)))
| top = join(complement(X_22),join(zero,meet(X_22,top))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
top = join(complement(X_22),join(zero,meet(X_22,top))),
inference(resolve,[$cnf( $equal(top,join(complement(X_22),join(complement(top),meet(X_22,top)))) )],[refute_0_186,refute_0_212]) ).
cnf(refute_0_214,plain,
top = join(complement(join(zero,meet(top,top))),join(zero,meet(join(zero,meet(top,top)),top))),
inference(subst,[],[refute_0_213:[bind(X_22,$fot(join(zero,meet(top,top))))]]) ).
cnf(refute_0_215,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_216,plain,
( complement(top) != zero
| meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_0_217,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_216]) ).
cnf(refute_0_218,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_215,refute_0_217]) ).
cnf(refute_0_219,plain,
meet(top,join(zero,zero)) = complement(join(zero,complement(join(zero,zero)))),
inference(subst,[],[refute_0_218:[bind(B,$fot(join(zero,zero)))]]) ).
cnf(refute_0_220,plain,
meet(top,top) = complement(join(zero,complement(top))),
inference(subst,[],[refute_0_218:[bind(B,$fot(top))]]) ).
cnf(refute_0_221,plain,
( complement(top) != zero
| meet(top,top) != complement(join(zero,complement(top)))
| meet(top,top) = complement(join(zero,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,top),complement(join(zero,complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_222,plain,
( meet(top,top) != complement(join(zero,complement(top)))
| meet(top,top) = complement(join(zero,zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_221]) ).
cnf(refute_0_223,plain,
meet(top,top) = complement(join(zero,zero)),
inference(resolve,[$cnf( $equal(meet(top,top),complement(join(zero,complement(top)))) )],[refute_0_220,refute_0_222]) ).
cnf(refute_0_224,plain,
( meet(top,top) != complement(join(zero,zero))
| complement(join(zero,zero)) = meet(top,top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,top))),bind(Y,$fot(complement(join(zero,zero))))]]) ).
cnf(refute_0_225,plain,
complement(join(zero,zero)) = meet(top,top),
inference(resolve,[$cnf( $equal(meet(top,top),complement(join(zero,zero))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
( complement(join(zero,zero)) != meet(top,top)
| meet(top,join(zero,zero)) != complement(join(zero,complement(join(zero,zero))))
| meet(top,join(zero,zero)) = complement(join(zero,meet(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,zero)),complement(join(zero,complement(join(zero,zero))))) ),[1,0,1],$fot(meet(top,top))]]) ).
cnf(refute_0_227,plain,
( meet(top,join(zero,zero)) != complement(join(zero,complement(join(zero,zero))))
| meet(top,join(zero,zero)) = complement(join(zero,meet(top,top))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),meet(top,top)) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
meet(top,join(zero,zero)) = complement(join(zero,meet(top,top))),
inference(resolve,[$cnf( $equal(meet(top,join(zero,zero)),complement(join(zero,complement(join(zero,zero))))) )],[refute_0_219,refute_0_227]) ).
cnf(refute_0_229,plain,
( meet(top,join(zero,zero)) != complement(join(zero,meet(top,top)))
| complement(join(zero,meet(top,top))) = meet(top,join(zero,zero)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,join(zero,zero)))),bind(Y,$fot(complement(join(zero,meet(top,top)))))]]) ).
cnf(refute_0_230,plain,
complement(join(zero,meet(top,top))) = meet(top,join(zero,zero)),
inference(resolve,[$cnf( $equal(meet(top,join(zero,zero)),complement(join(zero,meet(top,top)))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
( complement(join(zero,meet(top,top))) != meet(top,join(zero,zero))
| top != join(complement(join(zero,meet(top,top))),join(zero,meet(join(zero,meet(top,top)),top)))
| top = join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(join(zero,meet(top,top))),join(zero,meet(join(zero,meet(top,top)),top)))) ),[1,0],$fot(meet(top,join(zero,zero)))]]) ).
cnf(refute_0_232,plain,
( top != join(complement(join(zero,meet(top,top))),join(zero,meet(join(zero,meet(top,top)),top)))
| top = join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,top))),meet(top,join(zero,zero))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
top = join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))),
inference(resolve,[$cnf( $equal(top,join(complement(join(zero,meet(top,top))),join(zero,meet(join(zero,meet(top,top)),top)))) )],[refute_0_214,refute_0_232]) ).
cnf(refute_0_234,plain,
meet(A,top) = complement(join(complement(A),complement(top))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(top))]]) ).
cnf(refute_0_235,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_236,plain,
( meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_235]) ).
cnf(refute_0_237,plain,
meet(A,top) = complement(join(complement(A),zero)),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) )],[refute_0_234,refute_0_236]) ).
cnf(refute_0_238,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) = meet(top,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,B))),bind(Y,$fot(complement(join(zero,complement(B)))))]]) ).
cnf(refute_0_239,plain,
complement(join(zero,complement(B))) = meet(top,B),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_218,refute_0_238]) ).
cnf(refute_0_240,plain,
complement(join(zero,complement(A))) = meet(top,A),
inference(subst,[],[refute_0_239:[bind(B,$fot(A))]]) ).
cnf(refute_0_241,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_242,plain,
complement(join(complement(A),zero)) = complement(join(complement(A),zero)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),zero)))]]) ).
cnf(refute_0_243,plain,
( complement(join(complement(A),zero)) != complement(join(complement(A),zero))
| join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) ),[1,0],$fot(join(zero,complement(A)))]]) ).
cnf(refute_0_244,plain,
( join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
complement(join(complement(A),zero)) = complement(join(zero,complement(A))),
inference(resolve,[$cnf( $equal(join(complement(A),zero),join(zero,complement(A))) )],[refute_0_241,refute_0_244]) ).
cnf(refute_0_246,plain,
( complement(join(complement(A),zero)) != complement(join(zero,complement(A)))
| complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(complement(join(complement(A),zero)))),bind(Y,$fot(complement(join(zero,complement(A))))),bind(Z,$fot(meet(top,A)))]]) ).
cnf(refute_0_247,plain,
( complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(zero,complement(A)))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
complement(join(complement(A),zero)) = meet(top,A),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(A))),meet(top,A)) )],[refute_0_240,refute_0_247]) ).
cnf(refute_0_249,plain,
( complement(join(complement(A),zero)) != meet(top,A)
| meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) ),[1],$fot(meet(top,A))]]) ).
cnf(refute_0_250,plain,
( meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),meet(top,A)) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
meet(A,top) = meet(top,A),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) )],[refute_0_237,refute_0_250]) ).
cnf(refute_0_252,plain,
meet(join(zero,meet(top,top)),top) = meet(top,join(zero,meet(top,top))),
inference(subst,[],[refute_0_251:[bind(A,$fot(join(zero,meet(top,top))))]]) ).
cnf(refute_0_253,plain,
join(zero,meet(join(zero,meet(top,top)),top)) = join(zero,meet(join(zero,meet(top,top)),top)),
introduced(tautology,[refl,[$fot(join(zero,meet(join(zero,meet(top,top)),top)))]]) ).
cnf(refute_0_254,plain,
( join(zero,meet(join(zero,meet(top,top)),top)) != join(zero,meet(join(zero,meet(top,top)),top))
| meet(join(zero,meet(top,top)),top) != meet(top,join(zero,meet(top,top)))
| join(zero,meet(join(zero,meet(top,top)),top)) = join(zero,meet(top,join(zero,meet(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(zero,meet(top,top)),top)),join(zero,meet(join(zero,meet(top,top)),top))) ),[1,1],$fot(meet(top,join(zero,meet(top,top))))]]) ).
cnf(refute_0_255,plain,
( meet(join(zero,meet(top,top)),top) != meet(top,join(zero,meet(top,top)))
| join(zero,meet(join(zero,meet(top,top)),top)) = join(zero,meet(top,join(zero,meet(top,top)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,meet(top,top)),top)),join(zero,meet(join(zero,meet(top,top)),top))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
join(zero,meet(join(zero,meet(top,top)),top)) = join(zero,meet(top,join(zero,meet(top,top)))),
inference(resolve,[$cnf( $equal(meet(join(zero,meet(top,top)),top),meet(top,join(zero,meet(top,top)))) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))) = join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))),
introduced(tautology,[refl,[$fot(join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))))]]) ).
cnf(refute_0_258,plain,
( join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))) != join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top)))
| join(zero,meet(join(zero,meet(top,top)),top)) != join(zero,meet(top,join(zero,meet(top,top))))
| join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))) = join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))),join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top)))) ),[1,1],$fot(join(zero,meet(top,join(zero,meet(top,top)))))]]) ).
cnf(refute_0_259,plain,
( join(zero,meet(join(zero,meet(top,top)),top)) != join(zero,meet(top,join(zero,meet(top,top))))
| join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))) = join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top))))) ),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))),join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top)))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))) = join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top))))),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,meet(top,top)),top)),join(zero,meet(top,join(zero,meet(top,top))))) )],[refute_0_256,refute_0_259]) ).
cnf(refute_0_261,plain,
( join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))) != join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top)))))
| top != join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top)))
| top = join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top)))) ),[1],$fot(join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top))))))]]) ).
cnf(refute_0_262,plain,
( top != join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top)))
| top = join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top))))) ),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top))),join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top)))))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
top = join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top))))),
inference(resolve,[$cnf( $equal(top,join(meet(top,join(zero,zero)),join(zero,meet(join(zero,meet(top,top)),top)))) )],[refute_0_233,refute_0_262]) ).
cnf(refute_0_264,plain,
( top != join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top)))))
| join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top))))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top)))))))]]) ).
cnf(refute_0_265,plain,
join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top))))) = top,
inference(resolve,[$cnf( $equal(top,join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top)))))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
( join(X_41,join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top)))))) != join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top)))))
| join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top))))) != top
| join(X_41,top) = join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top)))))),join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top)))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_267,plain,
( join(X_41,join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top)))))) != join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top)))))
| join(X_41,top) = join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))) ),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top))))),top) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
join(X_41,top) = join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))),
inference(resolve,[$cnf( $equal(join(X_41,join(meet(top,join(zero,zero)),join(zero,meet(top,join(zero,meet(top,top)))))),join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top)))))) )],[refute_0_173,refute_0_267]) ).
cnf(refute_0_269,plain,
join(A,join(X_41,X_42)) = join(join(X_41,X_42),A),
inference(subst,[],[maddux1_join_commutativity_1:[bind(B,$fot(join(X_41,X_42)))]]) ).
cnf(refute_0_270,plain,
join(X_41,join(X_42,A)) = join(join(X_41,X_42),A),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_41)),bind(B,$fot(X_42)),bind(C,$fot(A))]]) ).
cnf(refute_0_271,plain,
( join(X_41,join(X_42,A)) != join(join(X_41,X_42),A)
| join(join(X_41,X_42),A) = join(X_41,join(X_42,A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_41,join(X_42,A)))),bind(Y,$fot(join(join(X_41,X_42),A)))]]) ).
cnf(refute_0_272,plain,
join(join(X_41,X_42),A) = join(X_41,join(X_42,A)),
inference(resolve,[$cnf( $equal(join(X_41,join(X_42,A)),join(join(X_41,X_42),A)) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
( join(A,join(X_41,X_42)) != join(join(X_41,X_42),A)
| join(join(X_41,X_42),A) != join(X_41,join(X_42,A))
| join(A,join(X_41,X_42)) = join(X_41,join(X_42,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_41,X_42)),join(X_41,join(X_42,A))) ),[0],$fot(join(join(X_41,X_42),A))]]) ).
cnf(refute_0_274,plain,
( join(A,join(X_41,X_42)) != join(join(X_41,X_42),A)
| join(A,join(X_41,X_42)) = join(X_41,join(X_42,A)) ),
inference(resolve,[$cnf( $equal(join(join(X_41,X_42),A),join(X_41,join(X_42,A))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
join(A,join(X_41,X_42)) = join(X_41,join(X_42,A)),
inference(resolve,[$cnf( $equal(join(A,join(X_41,X_42)),join(join(X_41,X_42),A)) )],[refute_0_269,refute_0_274]) ).
cnf(refute_0_276,plain,
( join(A,join(X_41,X_42)) != join(X_41,join(X_42,A))
| join(X_41,join(X_42,A)) = join(A,join(X_41,X_42)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(X_41,X_42)))),bind(Y,$fot(join(X_41,join(X_42,A))))]]) ).
cnf(refute_0_277,plain,
join(X_41,join(X_42,A)) = join(A,join(X_41,X_42)),
inference(resolve,[$cnf( $equal(join(A,join(X_41,X_42)),join(X_41,join(X_42,A))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero)))) = join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)),
inference(subst,[],[refute_0_277:[bind(A,$fot(meet(top,join(zero,zero)))),bind(X_41,$fot(meet(top,join(zero,meet(top,top))))),bind(X_42,$fot(X_41))]]) ).
cnf(refute_0_279,plain,
join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))) = join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))),
introduced(tautology,[refl,[$fot(join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))))]]) ).
cnf(refute_0_280,plain,
( join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero)))) != join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))
| join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))) != join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero)))))
| join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))) = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))),join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero)))))) ),[1,1],$fot(join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))]]) ).
cnf(refute_0_281,plain,
( join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero)))) != join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))
| join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))) = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))),join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero)))))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))) = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero)))),join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) )],[refute_0_278,refute_0_281]) ).
cnf(refute_0_283,plain,
join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))) = join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))),
inference(subst,[],[refute_0_275:[bind(A,$fot(join(X_41,meet(top,join(zero,zero))))),bind(X_41,$fot(zero)),bind(X_42,$fot(meet(top,join(zero,meet(top,top)))))]]) ).
cnf(refute_0_284,plain,
( join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))) != join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero)))))
| join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))) != join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))
| join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))) = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))))),bind(Y,$fot(join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))))),bind(Z,$fot(join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))))]]) ).
cnf(refute_0_285,plain,
( join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))) != join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))
| join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))) = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) ),
inference(resolve,[$cnf( $equal(join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))),join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero)))))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))) = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,join(zero,meet(top,top))),join(X_41,meet(top,join(zero,zero))))),join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))) )],[refute_0_282,refute_0_285]) ).
cnf(refute_0_287,plain,
( join(X_41,top) != join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top)))))
| join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))) != join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))
| join(X_41,top) = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_41,top),join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))) ),[0],$fot(join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))))]]) ).
cnf(refute_0_288,plain,
( join(X_41,top) != join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top)))))
| join(X_41,top) = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) ),
inference(resolve,[$cnf( $equal(join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top))))),join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
join(X_41,top) = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))),
inference(resolve,[$cnf( $equal(join(X_41,top),join(join(X_41,meet(top,join(zero,zero))),join(zero,meet(top,join(zero,meet(top,top)))))) )],[refute_0_268,refute_0_288]) ).
cnf(refute_0_290,plain,
join(X_51,join(complement(X_51),complement(complement(X_51)))) = join(top,complement(complement(X_51))),
inference(subst,[],[refute_0_172:[bind(X_41,$fot(X_51)),bind(X_43,$fot(complement(complement(X_51))))]]) ).
cnf(refute_0_291,plain,
top = join(complement(X_51),complement(complement(X_51))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_51)))]]) ).
cnf(refute_0_292,plain,
( top != join(complement(X_51),complement(complement(X_51)))
| join(complement(X_51),complement(complement(X_51))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_51),complement(complement(X_51)))))]]) ).
cnf(refute_0_293,plain,
join(complement(X_51),complement(complement(X_51))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_51),complement(complement(X_51)))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
( join(X_51,join(complement(X_51),complement(complement(X_51)))) != join(top,complement(complement(X_51)))
| join(complement(X_51),complement(complement(X_51))) != top
| join(X_51,top) = join(top,complement(complement(X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_51,join(complement(X_51),complement(complement(X_51)))),join(top,complement(complement(X_51)))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_295,plain,
( join(X_51,join(complement(X_51),complement(complement(X_51)))) != join(top,complement(complement(X_51)))
| join(X_51,top) = join(top,complement(complement(X_51))) ),
inference(resolve,[$cnf( $equal(join(complement(X_51),complement(complement(X_51))),top) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
join(X_51,top) = join(top,complement(complement(X_51))),
inference(resolve,[$cnf( $equal(join(X_51,join(complement(X_51),complement(complement(X_51)))),join(top,complement(complement(X_51)))) )],[refute_0_290,refute_0_295]) ).
cnf(refute_0_297,plain,
top = join(complement(X_11),join(complement(X_11),meet(X_11,X_11))),
inference(subst,[],[refute_0_185:[bind(X_10,$fot(X_11))]]) ).
cnf(refute_0_298,plain,
meet(B,B) = complement(join(complement(B),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(B))]]) ).
cnf(refute_0_299,plain,
composition(join(one,one),X_35) = join(X_35,composition(one,X_35)),
inference(subst,[],[refute_0_54:[bind(X_31,$fot(one)),bind(X_33,$fot(X_35))]]) ).
cnf(refute_0_300,plain,
X_35 = composition(one,X_35),
inference(subst,[],[refute_0_44:[bind(X_16,$fot(X_35))]]) ).
cnf(refute_0_301,plain,
( X_35 != composition(one,X_35)
| composition(one,X_35) = X_35 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_35)),bind(Y,$fot(composition(one,X_35)))]]) ).
cnf(refute_0_302,plain,
composition(one,X_35) = X_35,
inference(resolve,[$cnf( $equal(X_35,composition(one,X_35)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
( composition(join(one,one),X_35) != join(X_35,composition(one,X_35))
| composition(one,X_35) != X_35
| composition(join(one,one),X_35) = join(X_35,X_35) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),X_35),join(X_35,composition(one,X_35))) ),[1,1],$fot(X_35)]]) ).
cnf(refute_0_304,plain,
( composition(join(one,one),X_35) != join(X_35,composition(one,X_35))
| composition(join(one,one),X_35) = join(X_35,X_35) ),
inference(resolve,[$cnf( $equal(composition(one,X_35),X_35) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
composition(join(one,one),X_35) = join(X_35,X_35),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_35),join(X_35,composition(one,X_35))) )],[refute_0_299,refute_0_304]) ).
cnf(refute_0_306,plain,
composition(join(one,one),complement(B)) = join(complement(B),complement(B)),
inference(subst,[],[refute_0_305:[bind(X_35,$fot(complement(B)))]]) ).
cnf(refute_0_307,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_308,plain,
join(complement(B),complement(B)) = composition(join(one,one),complement(B)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(B)),join(complement(B),complement(B))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
( join(complement(B),complement(B)) != composition(join(one,one),complement(B))
| meet(B,B) != complement(join(complement(B),complement(B)))
| meet(B,B) = complement(composition(join(one,one),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(B,B),complement(join(complement(B),complement(B)))) ),[1,0],$fot(composition(join(one,one),complement(B)))]]) ).
cnf(refute_0_310,plain,
( meet(B,B) != complement(join(complement(B),complement(B)))
| meet(B,B) = complement(composition(join(one,one),complement(B))) ),
inference(resolve,[$cnf( $equal(join(complement(B),complement(B)),composition(join(one,one),complement(B))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
meet(B,B) = complement(composition(join(one,one),complement(B))),
inference(resolve,[$cnf( $equal(meet(B,B),complement(join(complement(B),complement(B)))) )],[refute_0_298,refute_0_310]) ).
cnf(refute_0_312,plain,
meet(X_11,X_11) = complement(composition(join(one,one),complement(X_11))),
inference(subst,[],[refute_0_311:[bind(B,$fot(X_11))]]) ).
cnf(refute_0_313,plain,
( meet(X_11,X_11) != complement(composition(join(one,one),complement(X_11)))
| top != join(complement(X_11),join(complement(X_11),meet(X_11,X_11)))
| top = join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_11),join(complement(X_11),meet(X_11,X_11)))) ),[1,1,1],$fot(complement(composition(join(one,one),complement(X_11))))]]) ).
cnf(refute_0_314,plain,
( top != join(complement(X_11),join(complement(X_11),meet(X_11,X_11)))
| top = join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) ),
inference(resolve,[$cnf( $equal(meet(X_11,X_11),complement(composition(join(one,one),complement(X_11)))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
top = join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))),
inference(resolve,[$cnf( $equal(top,join(complement(X_11),join(complement(X_11),meet(X_11,X_11)))) )],[refute_0_297,refute_0_314]) ).
cnf(refute_0_316,plain,
join(X_41,join(complement(X_22),join(zero,complement(complement(X_22))))) = join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_41)),bind(B,$fot(complement(X_22))),bind(C,$fot(join(zero,complement(complement(X_22)))))]]) ).
cnf(refute_0_317,plain,
top = join(complement(X_22),join(complement(complement(X_22)),meet(X_22,complement(X_22)))),
inference(subst,[],[refute_0_185:[bind(X_10,$fot(X_22)),bind(X_11,$fot(complement(X_22)))]]) ).
cnf(refute_0_318,plain,
zero = meet(X_22,complement(X_22)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_22))]]) ).
cnf(refute_0_319,plain,
( zero != meet(X_22,complement(X_22))
| meet(X_22,complement(X_22)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_22,complement(X_22))))]]) ).
cnf(refute_0_320,plain,
meet(X_22,complement(X_22)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_22,complement(X_22))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
( meet(X_22,complement(X_22)) != zero
| top != join(complement(X_22),join(complement(complement(X_22)),meet(X_22,complement(X_22))))
| top = join(complement(X_22),join(complement(complement(X_22)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_22),join(complement(complement(X_22)),meet(X_22,complement(X_22))))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_322,plain,
( top != join(complement(X_22),join(complement(complement(X_22)),meet(X_22,complement(X_22))))
| top = join(complement(X_22),join(complement(complement(X_22)),zero)) ),
inference(resolve,[$cnf( $equal(meet(X_22,complement(X_22)),zero) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
top = join(complement(X_22),join(complement(complement(X_22)),zero)),
inference(resolve,[$cnf( $equal(top,join(complement(X_22),join(complement(complement(X_22)),meet(X_22,complement(X_22))))) )],[refute_0_317,refute_0_322]) ).
cnf(refute_0_324,plain,
join(complement(complement(X_22)),zero) = join(zero,complement(complement(X_22))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(complement(X_22))))]]) ).
cnf(refute_0_325,plain,
join(complement(X_22),join(complement(complement(X_22)),zero)) = join(complement(X_22),join(complement(complement(X_22)),zero)),
introduced(tautology,[refl,[$fot(join(complement(X_22),join(complement(complement(X_22)),zero)))]]) ).
cnf(refute_0_326,plain,
( join(complement(X_22),join(complement(complement(X_22)),zero)) != join(complement(X_22),join(complement(complement(X_22)),zero))
| join(complement(complement(X_22)),zero) != join(zero,complement(complement(X_22)))
| join(complement(X_22),join(complement(complement(X_22)),zero)) = join(complement(X_22),join(zero,complement(complement(X_22)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_22),join(complement(complement(X_22)),zero)),join(complement(X_22),join(complement(complement(X_22)),zero))) ),[1,1],$fot(join(zero,complement(complement(X_22))))]]) ).
cnf(refute_0_327,plain,
( join(complement(complement(X_22)),zero) != join(zero,complement(complement(X_22)))
| join(complement(X_22),join(complement(complement(X_22)),zero)) = join(complement(X_22),join(zero,complement(complement(X_22)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_22),join(complement(complement(X_22)),zero)),join(complement(X_22),join(complement(complement(X_22)),zero))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
join(complement(X_22),join(complement(complement(X_22)),zero)) = join(complement(X_22),join(zero,complement(complement(X_22)))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_22)),zero),join(zero,complement(complement(X_22)))) )],[refute_0_324,refute_0_327]) ).
cnf(refute_0_329,plain,
( join(complement(X_22),join(complement(complement(X_22)),zero)) != join(complement(X_22),join(zero,complement(complement(X_22))))
| top != join(complement(X_22),join(complement(complement(X_22)),zero))
| top = join(complement(X_22),join(zero,complement(complement(X_22)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_22),join(complement(complement(X_22)),zero))) ),[1],$fot(join(complement(X_22),join(zero,complement(complement(X_22)))))]]) ).
cnf(refute_0_330,plain,
( top != join(complement(X_22),join(complement(complement(X_22)),zero))
| top = join(complement(X_22),join(zero,complement(complement(X_22)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_22),join(complement(complement(X_22)),zero)),join(complement(X_22),join(zero,complement(complement(X_22))))) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
top = join(complement(X_22),join(zero,complement(complement(X_22)))),
inference(resolve,[$cnf( $equal(top,join(complement(X_22),join(complement(complement(X_22)),zero))) )],[refute_0_323,refute_0_330]) ).
cnf(refute_0_332,plain,
( top != join(complement(X_22),join(zero,complement(complement(X_22))))
| join(complement(X_22),join(zero,complement(complement(X_22)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_22),join(zero,complement(complement(X_22))))))]]) ).
cnf(refute_0_333,plain,
join(complement(X_22),join(zero,complement(complement(X_22)))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_22),join(zero,complement(complement(X_22))))) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
( join(X_41,join(complement(X_22),join(zero,complement(complement(X_22))))) != join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22))))
| join(complement(X_22),join(zero,complement(complement(X_22)))) != top
| join(X_41,top) = join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,join(complement(X_22),join(zero,complement(complement(X_22))))),join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_335,plain,
( join(X_41,join(complement(X_22),join(zero,complement(complement(X_22))))) != join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22))))
| join(X_41,top) = join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_22),join(zero,complement(complement(X_22)))),top) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
join(X_41,top) = join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))),
inference(resolve,[$cnf( $equal(join(X_41,join(complement(X_22),join(zero,complement(complement(X_22))))),join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22))))) )],[refute_0_316,refute_0_335]) ).
cnf(refute_0_337,plain,
join(complement(complement(X_22)),join(X_41,complement(X_22))) = join(complement(X_22),join(complement(complement(X_22)),X_41)),
inference(subst,[],[refute_0_277:[bind(A,$fot(complement(X_22))),bind(X_41,$fot(complement(complement(X_22)))),bind(X_42,$fot(X_41))]]) ).
cnf(refute_0_338,plain,
join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))) = join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))),
introduced(tautology,[refl,[$fot(join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))))]]) ).
cnf(refute_0_339,plain,
( join(complement(complement(X_22)),join(X_41,complement(X_22))) != join(complement(X_22),join(complement(complement(X_22)),X_41))
| join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))) != join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22))))
| join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))) = join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))),join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22))))) ),[1,1],$fot(join(complement(X_22),join(complement(complement(X_22)),X_41)))]]) ).
cnf(refute_0_340,plain,
( join(complement(complement(X_22)),join(X_41,complement(X_22))) != join(complement(X_22),join(complement(complement(X_22)),X_41))
| join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))) = join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))),join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22))))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))) = join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_22)),join(X_41,complement(X_22))),join(complement(X_22),join(complement(complement(X_22)),X_41))) )],[refute_0_337,refute_0_340]) ).
cnf(refute_0_342,plain,
join(complement(complement(X_22)),join(join(X_41,complement(X_22)),zero)) = join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))),
inference(subst,[],[refute_0_277:[bind(A,$fot(zero)),bind(X_41,$fot(complement(complement(X_22)))),bind(X_42,$fot(join(X_41,complement(X_22))))]]) ).
cnf(refute_0_343,plain,
join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) = join(complement(complement(X_22)),join(join(X_41,complement(X_22)),zero)),
inference(subst,[],[refute_0_277:[bind(A,$fot(complement(complement(X_22)))),bind(X_41,$fot(join(X_41,complement(X_22)))),bind(X_42,$fot(zero))]]) ).
cnf(refute_0_344,plain,
( join(complement(complement(X_22)),join(join(X_41,complement(X_22)),zero)) != join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22))))
| join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) != join(complement(complement(X_22)),join(join(X_41,complement(X_22)),zero))
| join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) = join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))))),bind(Y,$fot(join(complement(complement(X_22)),join(join(X_41,complement(X_22)),zero)))),bind(Z,$fot(join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22))))))]]) ).
cnf(refute_0_345,plain,
( join(complement(complement(X_22)),join(join(X_41,complement(X_22)),zero)) != join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22))))
| join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) = join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))) ),
inference(resolve,[$cnf( $equal(join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))),join(complement(complement(X_22)),join(join(X_41,complement(X_22)),zero))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) = join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_22)),join(join(X_41,complement(X_22)),zero)),join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22))))) )],[refute_0_342,refute_0_345]) ).
cnf(refute_0_347,plain,
( join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) != join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22))))
| join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))) != join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))
| join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) = join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))))),bind(Y,$fot(join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))))),bind(Z,$fot(join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))))]]) ).
cnf(refute_0_348,plain,
( join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))) != join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))
| join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) = join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) ),
inference(resolve,[$cnf( $equal(join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))),join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22))))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) = join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))),
inference(resolve,[$cnf( $equal(join(zero,join(complement(complement(X_22)),join(X_41,complement(X_22)))),join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))) )],[refute_0_341,refute_0_348]) ).
cnf(refute_0_350,plain,
( join(X_41,top) != join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22))))
| join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))) != join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))
| join(X_41,top) = join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_41,top),join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))) ),[0],$fot(join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))))]]) ).
cnf(refute_0_351,plain,
( join(X_41,top) != join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22))))
| join(X_41,top) = join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) ),
inference(resolve,[$cnf( $equal(join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22)))),join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
join(X_41,top) = join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))),
inference(resolve,[$cnf( $equal(join(X_41,top),join(join(X_41,complement(X_22)),join(zero,complement(complement(X_22))))) )],[refute_0_336,refute_0_351]) ).
cnf(refute_0_353,plain,
join(top,join(zero,X_43)) = join(join(top,zero),X_43),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(top)),bind(B,$fot(zero)),bind(C,$fot(X_43))]]) ).
cnf(refute_0_354,plain,
top = join(top,complement(top)),
inference(subst,[],[def_top_12:[bind(A,$fot(top))]]) ).
cnf(refute_0_355,plain,
( complement(top) != zero
| top != join(top,complement(top))
| top = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_356,plain,
( top != join(top,complement(top))
| top = join(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_355]) ).
cnf(refute_0_357,plain,
top = join(top,zero),
inference(resolve,[$cnf( $equal(top,join(top,complement(top))) )],[refute_0_354,refute_0_356]) ).
cnf(refute_0_358,plain,
( top != join(top,zero)
| join(top,zero) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,zero)))]]) ).
cnf(refute_0_359,plain,
join(top,zero) = top,
inference(resolve,[$cnf( $equal(top,join(top,zero)) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
( join(top,join(zero,X_43)) != join(join(top,zero),X_43)
| join(top,zero) != top
| join(top,join(zero,X_43)) = join(top,X_43) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,X_43)),join(join(top,zero),X_43)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_361,plain,
( join(top,join(zero,X_43)) != join(join(top,zero),X_43)
| join(top,join(zero,X_43)) = join(top,X_43) ),
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
join(top,join(zero,X_43)) = join(top,X_43),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_43)),join(join(top,zero),X_43)) )],[refute_0_353,refute_0_361]) ).
cnf(refute_0_363,plain,
join(top,join(zero,X_41)) = join(top,X_41),
inference(subst,[],[refute_0_362:[bind(X_43,$fot(X_41))]]) ).
cnf(refute_0_364,plain,
join(X_41,join(X_42,X_43)) = join(join(X_41,X_42),X_43),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_41)),bind(B,$fot(X_42)),bind(C,$fot(X_43))]]) ).
cnf(refute_0_365,plain,
join(X_42,X_41) = join(X_41,X_42),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_42)),bind(B,$fot(X_41))]]) ).
cnf(refute_0_366,plain,
( join(X_42,X_41) != join(X_41,X_42)
| join(X_41,X_42) = join(X_42,X_41) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_42,X_41))),bind(Y,$fot(join(X_41,X_42)))]]) ).
cnf(refute_0_367,plain,
join(X_41,X_42) = join(X_42,X_41),
inference(resolve,[$cnf( $equal(join(X_42,X_41),join(X_41,X_42)) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
( join(X_41,X_42) != join(X_42,X_41)
| join(X_41,join(X_42,X_43)) != join(join(X_41,X_42),X_43)
| join(X_41,join(X_42,X_43)) = join(join(X_42,X_41),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,join(X_42,X_43)),join(join(X_41,X_42),X_43)) ),[1,0],$fot(join(X_42,X_41))]]) ).
cnf(refute_0_369,plain,
( join(X_41,join(X_42,X_43)) != join(join(X_41,X_42),X_43)
| join(X_41,join(X_42,X_43)) = join(join(X_42,X_41),X_43) ),
inference(resolve,[$cnf( $equal(join(X_41,X_42),join(X_42,X_41)) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
join(X_41,join(X_42,X_43)) = join(join(X_42,X_41),X_43),
inference(resolve,[$cnf( $equal(join(X_41,join(X_42,X_43)),join(join(X_41,X_42),X_43)) )],[refute_0_364,refute_0_369]) ).
cnf(refute_0_371,plain,
join(join(X_42,X_41),X_43) = join(X_42,join(X_41,X_43)),
inference(subst,[],[refute_0_181:[bind(A,$fot(X_42)),bind(B,$fot(X_41)),bind(C,$fot(X_43))]]) ).
cnf(refute_0_372,plain,
( join(X_41,join(X_42,X_43)) != join(join(X_42,X_41),X_43)
| join(join(X_42,X_41),X_43) != join(X_42,join(X_41,X_43))
| join(X_41,join(X_42,X_43)) = join(X_42,join(X_41,X_43)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_41,join(X_42,X_43)),join(X_42,join(X_41,X_43))) ),[0],$fot(join(join(X_42,X_41),X_43))]]) ).
cnf(refute_0_373,plain,
( join(X_41,join(X_42,X_43)) != join(join(X_42,X_41),X_43)
| join(X_41,join(X_42,X_43)) = join(X_42,join(X_41,X_43)) ),
inference(resolve,[$cnf( $equal(join(join(X_42,X_41),X_43),join(X_42,join(X_41,X_43))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
join(X_41,join(X_42,X_43)) = join(X_42,join(X_41,X_43)),
inference(resolve,[$cnf( $equal(join(X_41,join(X_42,X_43)),join(join(X_42,X_41),X_43)) )],[refute_0_370,refute_0_373]) ).
cnf(refute_0_375,plain,
( join(X_41,join(X_42,X_43)) != join(X_42,join(X_41,X_43))
| join(X_42,join(X_41,X_43)) = join(X_41,join(X_42,X_43)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_41,join(X_42,X_43)))),bind(Y,$fot(join(X_42,join(X_41,X_43))))]]) ).
cnf(refute_0_376,plain,
join(X_42,join(X_41,X_43)) = join(X_41,join(X_42,X_43)),
inference(resolve,[$cnf( $equal(join(X_41,join(X_42,X_43)),join(X_42,join(X_41,X_43))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
join(zero,join(top,X_41)) = join(top,join(zero,X_41)),
inference(subst,[],[refute_0_376:[bind(X_41,$fot(top)),bind(X_42,$fot(zero)),bind(X_43,$fot(X_41))]]) ).
cnf(refute_0_378,plain,
( join(top,join(zero,X_41)) != join(top,X_41)
| join(zero,join(top,X_41)) != join(top,join(zero,X_41))
| join(zero,join(top,X_41)) = join(top,X_41) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(zero,join(top,X_41)))),bind(Y,$fot(join(top,join(zero,X_41)))),bind(Z,$fot(join(top,X_41)))]]) ).
cnf(refute_0_379,plain,
( join(top,join(zero,X_41)) != join(top,X_41)
| join(zero,join(top,X_41)) = join(top,X_41) ),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_41)),join(top,join(zero,X_41))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
join(zero,join(top,X_41)) = join(top,X_41),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_41)),join(top,X_41)) )],[refute_0_363,refute_0_379]) ).
cnf(refute_0_381,plain,
join(complement(X_22),join(complement(complement(X_22)),X_41)) = join(top,X_41),
inference(subst,[],[refute_0_172:[bind(X_41,$fot(complement(X_22))),bind(X_43,$fot(X_41))]]) ).
cnf(refute_0_382,plain,
join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) = join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))),
introduced(tautology,[refl,[$fot(join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))))]]) ).
cnf(refute_0_383,plain,
( join(complement(X_22),join(complement(complement(X_22)),X_41)) != join(top,X_41)
| join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) != join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))
| join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) = join(zero,join(top,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))),join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))) ),[1,1],$fot(join(top,X_41))]]) ).
cnf(refute_0_384,plain,
( join(complement(X_22),join(complement(complement(X_22)),X_41)) != join(top,X_41)
| join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) = join(zero,join(top,X_41)) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))),join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) = join(zero,join(top,X_41)),
inference(resolve,[$cnf( $equal(join(complement(X_22),join(complement(complement(X_22)),X_41)),join(top,X_41)) )],[refute_0_381,refute_0_384]) ).
cnf(refute_0_386,plain,
( join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) != join(zero,join(top,X_41))
| join(zero,join(top,X_41)) != join(top,X_41)
| join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) = join(top,X_41) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))))),bind(Y,$fot(join(zero,join(top,X_41)))),bind(Z,$fot(join(top,X_41)))]]) ).
cnf(refute_0_387,plain,
( join(zero,join(top,X_41)) != join(top,X_41)
| join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) = join(top,X_41) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))),join(zero,join(top,X_41))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) = join(top,X_41),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_41)),join(top,X_41)) )],[refute_0_380,refute_0_387]) ).
cnf(refute_0_389,plain,
( join(X_41,top) != join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))
| join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))) != join(top,X_41)
| join(X_41,top) = join(top,X_41) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_41,top),join(top,X_41)) ),[0],$fot(join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))))]]) ).
cnf(refute_0_390,plain,
( join(X_41,top) != join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))
| join(X_41,top) = join(top,X_41) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41))),join(top,X_41)) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
join(X_41,top) = join(top,X_41),
inference(resolve,[$cnf( $equal(join(X_41,top),join(zero,join(complement(X_22),join(complement(complement(X_22)),X_41)))) )],[refute_0_352,refute_0_390]) ).
cnf(refute_0_392,plain,
join(complement(X_11),top) = join(top,complement(X_11)),
inference(subst,[],[refute_0_391:[bind(X_41,$fot(complement(X_11)))]]) ).
cnf(refute_0_393,plain,
join(complement(X_11),complement(complement(X_11))) = top,
inference(subst,[],[refute_0_192:[bind(A,$fot(complement(X_11)))]]) ).
cnf(refute_0_394,plain,
join(complement(X_79),composition(converse(one),complement(composition(one,X_79)))) = complement(X_79),
inference(subst,[],[refute_0_8:[bind(A,$fot(one)),bind(B,$fot(X_79))]]) ).
cnf(refute_0_395,plain,
X_79 = composition(one,X_79),
inference(subst,[],[refute_0_44:[bind(X_16,$fot(X_79))]]) ).
cnf(refute_0_396,plain,
( X_79 != composition(one,X_79)
| composition(one,X_79) = X_79 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_79)),bind(Y,$fot(composition(one,X_79)))]]) ).
cnf(refute_0_397,plain,
composition(one,X_79) = X_79,
inference(resolve,[$cnf( $equal(X_79,composition(one,X_79)) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
( composition(one,X_79) != X_79
| join(complement(X_79),composition(converse(one),complement(composition(one,X_79)))) != complement(X_79)
| join(complement(X_79),composition(converse(one),complement(X_79))) = complement(X_79) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_79),composition(converse(one),complement(composition(one,X_79)))),complement(X_79)) ),[0,1,1,0],$fot(X_79)]]) ).
cnf(refute_0_399,plain,
( join(complement(X_79),composition(converse(one),complement(composition(one,X_79)))) != complement(X_79)
| join(complement(X_79),composition(converse(one),complement(X_79))) = complement(X_79) ),
inference(resolve,[$cnf( $equal(composition(one,X_79),X_79) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
join(complement(X_79),composition(converse(one),complement(X_79))) = complement(X_79),
inference(resolve,[$cnf( $equal(join(complement(X_79),composition(converse(one),complement(composition(one,X_79)))),complement(X_79)) )],[refute_0_394,refute_0_399]) ).
cnf(refute_0_401,plain,
converse(join(one,one)) = join(one,converse(one)),
inference(subst,[],[refute_0_73:[bind(X_4,$fot(one))]]) ).
cnf(refute_0_402,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_403,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(join(one,one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_37,refute_0_402]) ).
cnf(refute_0_404,plain,
converse(join(one,one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) )],[refute_0_401,refute_0_403]) ).
cnf(refute_0_405,plain,
join(one,converse(one)) = converse(join(one,one)),
inference(subst,[],[refute_0_75:[bind(X_4,$fot(one))]]) ).
cnf(refute_0_406,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_82:[bind(X,$fot(join(one,converse(one)))),bind(Y,$fot(converse(join(one,one)))),bind(Z,$fot(join(one,one)))]]) ).
cnf(refute_0_407,plain,
( converse(join(one,one)) != join(one,one)
| join(one,converse(one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(join(one,converse(one)),converse(join(one,one))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
join(one,converse(one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_404,refute_0_407]) ).
cnf(refute_0_409,plain,
composition(join(one,converse(one)),complement(X_79)) = composition(join(one,converse(one)),complement(X_79)),
introduced(tautology,[refl,[$fot(composition(join(one,converse(one)),complement(X_79)))]]) ).
cnf(refute_0_410,plain,
( composition(join(one,converse(one)),complement(X_79)) != composition(join(one,converse(one)),complement(X_79))
| join(one,converse(one)) != join(one,one)
| composition(join(one,converse(one)),complement(X_79)) = composition(join(one,one),complement(X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(one)),complement(X_79)),composition(join(one,converse(one)),complement(X_79))) ),[1,0],$fot(join(one,one))]]) ).
cnf(refute_0_411,plain,
( join(one,converse(one)) != join(one,one)
| composition(join(one,converse(one)),complement(X_79)) = composition(join(one,one),complement(X_79)) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(one)),complement(X_79)),composition(join(one,converse(one)),complement(X_79))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
composition(join(one,converse(one)),complement(X_79)) = composition(join(one,one),complement(X_79)),
inference(resolve,[$cnf( $equal(join(one,converse(one)),join(one,one)) )],[refute_0_408,refute_0_411]) ).
cnf(refute_0_413,plain,
composition(join(converse(one),one),complement(X_79)) = composition(join(one,converse(one)),complement(X_79)),
inference(subst,[],[refute_0_100:[bind(X_34,$fot(converse(one))),bind(X_35,$fot(complement(X_79)))]]) ).
cnf(refute_0_414,plain,
join(complement(X_79),composition(converse(one),complement(X_79))) = composition(join(converse(one),one),complement(X_79)),
inference(subst,[],[refute_0_94:[bind(X_31,$fot(converse(one))),bind(X_33,$fot(complement(X_79)))]]) ).
cnf(refute_0_415,plain,
( composition(join(converse(one),one),complement(X_79)) != composition(join(one,converse(one)),complement(X_79))
| join(complement(X_79),composition(converse(one),complement(X_79))) != composition(join(converse(one),one),complement(X_79))
| join(complement(X_79),composition(converse(one),complement(X_79))) = composition(join(one,converse(one)),complement(X_79)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(X_79),composition(converse(one),complement(X_79))))),bind(Y,$fot(composition(join(converse(one),one),complement(X_79)))),bind(Z,$fot(composition(join(one,converse(one)),complement(X_79))))]]) ).
cnf(refute_0_416,plain,
( composition(join(converse(one),one),complement(X_79)) != composition(join(one,converse(one)),complement(X_79))
| join(complement(X_79),composition(converse(one),complement(X_79))) = composition(join(one,converse(one)),complement(X_79)) ),
inference(resolve,[$cnf( $equal(join(complement(X_79),composition(converse(one),complement(X_79))),composition(join(converse(one),one),complement(X_79))) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
join(complement(X_79),composition(converse(one),complement(X_79))) = composition(join(one,converse(one)),complement(X_79)),
inference(resolve,[$cnf( $equal(composition(join(converse(one),one),complement(X_79)),composition(join(one,converse(one)),complement(X_79))) )],[refute_0_413,refute_0_416]) ).
cnf(refute_0_418,plain,
( composition(join(one,converse(one)),complement(X_79)) != composition(join(one,one),complement(X_79))
| join(complement(X_79),composition(converse(one),complement(X_79))) != composition(join(one,converse(one)),complement(X_79))
| join(complement(X_79),composition(converse(one),complement(X_79))) = composition(join(one,one),complement(X_79)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(X_79),composition(converse(one),complement(X_79))))),bind(Y,$fot(composition(join(one,converse(one)),complement(X_79)))),bind(Z,$fot(composition(join(one,one),complement(X_79))))]]) ).
cnf(refute_0_419,plain,
( composition(join(one,converse(one)),complement(X_79)) != composition(join(one,one),complement(X_79))
| join(complement(X_79),composition(converse(one),complement(X_79))) = composition(join(one,one),complement(X_79)) ),
inference(resolve,[$cnf( $equal(join(complement(X_79),composition(converse(one),complement(X_79))),composition(join(one,converse(one)),complement(X_79))) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
join(complement(X_79),composition(converse(one),complement(X_79))) = composition(join(one,one),complement(X_79)),
inference(resolve,[$cnf( $equal(composition(join(one,converse(one)),complement(X_79)),composition(join(one,one),complement(X_79))) )],[refute_0_412,refute_0_419]) ).
cnf(refute_0_421,plain,
( join(complement(X_79),composition(converse(one),complement(X_79))) != complement(X_79)
| join(complement(X_79),composition(converse(one),complement(X_79))) != composition(join(one,one),complement(X_79))
| composition(join(one,one),complement(X_79)) = complement(X_79) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_79),composition(converse(one),complement(X_79))),complement(X_79)) ),[0],$fot(composition(join(one,one),complement(X_79)))]]) ).
cnf(refute_0_422,plain,
( join(complement(X_79),composition(converse(one),complement(X_79))) != complement(X_79)
| composition(join(one,one),complement(X_79)) = complement(X_79) ),
inference(resolve,[$cnf( $equal(join(complement(X_79),composition(converse(one),complement(X_79))),composition(join(one,one),complement(X_79))) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
composition(join(one,one),complement(X_79)) = complement(X_79),
inference(resolve,[$cnf( $equal(join(complement(X_79),composition(converse(one),complement(X_79))),complement(X_79)) )],[refute_0_400,refute_0_422]) ).
cnf(refute_0_424,plain,
composition(join(one,one),complement(X_11)) = complement(X_11),
inference(subst,[],[refute_0_423:[bind(X_79,$fot(X_11))]]) ).
cnf(refute_0_425,plain,
complement(composition(join(one,one),complement(X_11))) = complement(composition(join(one,one),complement(X_11))),
introduced(tautology,[refl,[$fot(complement(composition(join(one,one),complement(X_11))))]]) ).
cnf(refute_0_426,plain,
( complement(composition(join(one,one),complement(X_11))) != complement(composition(join(one,one),complement(X_11)))
| composition(join(one,one),complement(X_11)) != complement(X_11)
| complement(composition(join(one,one),complement(X_11))) = complement(complement(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(join(one,one),complement(X_11))),complement(composition(join(one,one),complement(X_11)))) ),[1,0],$fot(complement(X_11))]]) ).
cnf(refute_0_427,plain,
( composition(join(one,one),complement(X_11)) != complement(X_11)
| complement(composition(join(one,one),complement(X_11))) = complement(complement(X_11)) ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),complement(X_11))),complement(composition(join(one,one),complement(X_11)))) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
complement(composition(join(one,one),complement(X_11))) = complement(complement(X_11)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_11)),complement(X_11)) )],[refute_0_424,refute_0_427]) ).
cnf(refute_0_429,plain,
join(complement(X_11),complement(composition(join(one,one),complement(X_11)))) = join(complement(X_11),complement(composition(join(one,one),complement(X_11)))),
introduced(tautology,[refl,[$fot(join(complement(X_11),complement(composition(join(one,one),complement(X_11)))))]]) ).
cnf(refute_0_430,plain,
( complement(composition(join(one,one),complement(X_11))) != complement(complement(X_11))
| join(complement(X_11),complement(composition(join(one,one),complement(X_11)))) != join(complement(X_11),complement(composition(join(one,one),complement(X_11))))
| join(complement(X_11),complement(composition(join(one,one),complement(X_11)))) = join(complement(X_11),complement(complement(X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_11),complement(composition(join(one,one),complement(X_11)))),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) ),[1,1],$fot(complement(complement(X_11)))]]) ).
cnf(refute_0_431,plain,
( complement(composition(join(one,one),complement(X_11))) != complement(complement(X_11))
| join(complement(X_11),complement(composition(join(one,one),complement(X_11)))) = join(complement(X_11),complement(complement(X_11))) ),
inference(resolve,[$cnf( $equal(join(complement(X_11),complement(composition(join(one,one),complement(X_11)))),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
join(complement(X_11),complement(composition(join(one,one),complement(X_11)))) = join(complement(X_11),complement(complement(X_11))),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),complement(X_11))),complement(complement(X_11))) )],[refute_0_428,refute_0_431]) ).
cnf(refute_0_433,plain,
( join(complement(X_11),complement(complement(X_11))) != top
| join(complement(X_11),complement(composition(join(one,one),complement(X_11)))) != join(complement(X_11),complement(complement(X_11)))
| join(complement(X_11),complement(composition(join(one,one),complement(X_11)))) = top ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(X_11),complement(composition(join(one,one),complement(X_11)))))),bind(Y,$fot(join(complement(X_11),complement(complement(X_11))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_434,plain,
( join(complement(X_11),complement(complement(X_11))) != top
| join(complement(X_11),complement(composition(join(one,one),complement(X_11)))) = top ),
inference(resolve,[$cnf( $equal(join(complement(X_11),complement(composition(join(one,one),complement(X_11)))),join(complement(X_11),complement(complement(X_11)))) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
join(complement(X_11),complement(composition(join(one,one),complement(X_11)))) = top,
inference(resolve,[$cnf( $equal(join(complement(X_11),complement(complement(X_11))),top) )],[refute_0_393,refute_0_434]) ).
cnf(refute_0_436,plain,
join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) = join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))),
introduced(tautology,[refl,[$fot(join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))))]]) ).
cnf(refute_0_437,plain,
( join(complement(X_11),complement(composition(join(one,one),complement(X_11)))) != top
| join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) != join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11)))))
| join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) = join(complement(X_11),top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))),join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11)))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_438,plain,
( join(complement(X_11),complement(composition(join(one,one),complement(X_11)))) != top
| join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) = join(complement(X_11),top) ),
inference(resolve,[$cnf( $equal(join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))),join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11)))))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) = join(complement(X_11),top),
inference(resolve,[$cnf( $equal(join(complement(X_11),complement(composition(join(one,one),complement(X_11)))),top) )],[refute_0_435,refute_0_438]) ).
cnf(refute_0_440,plain,
( join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) != join(complement(X_11),top)
| join(complement(X_11),top) != join(top,complement(X_11))
| join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) = join(top,complement(X_11)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))))),bind(Y,$fot(join(complement(X_11),top))),bind(Z,$fot(join(top,complement(X_11))))]]) ).
cnf(refute_0_441,plain,
( join(complement(X_11),top) != join(top,complement(X_11))
| join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) = join(top,complement(X_11)) ),
inference(resolve,[$cnf( $equal(join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))),join(complement(X_11),top)) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) = join(top,complement(X_11)),
inference(resolve,[$cnf( $equal(join(complement(X_11),top),join(top,complement(X_11))) )],[refute_0_392,refute_0_441]) ).
cnf(refute_0_443,plain,
( join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))) != join(top,complement(X_11))
| top != join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11)))))
| top = join(top,complement(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11)))))) ),[1],$fot(join(top,complement(X_11)))]]) ).
cnf(refute_0_444,plain,
( top != join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11)))))
| top = join(top,complement(X_11)) ),
inference(resolve,[$cnf( $equal(join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11))))),join(top,complement(X_11))) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
top = join(top,complement(X_11)),
inference(resolve,[$cnf( $equal(top,join(complement(X_11),join(complement(X_11),complement(composition(join(one,one),complement(X_11)))))) )],[refute_0_315,refute_0_444]) ).
cnf(refute_0_446,plain,
( top != join(top,complement(X_11))
| join(top,complement(X_11)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(X_11))))]]) ).
cnf(refute_0_447,plain,
join(top,complement(X_11)) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(X_11))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
join(top,complement(complement(X_51))) = top,
inference(subst,[],[refute_0_447:[bind(X_11,$fot(complement(X_51)))]]) ).
cnf(refute_0_449,plain,
( join(X_51,top) != join(top,complement(complement(X_51)))
| join(top,complement(complement(X_51))) != top
| join(X_51,top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_51,top),top) ),[0],$fot(join(top,complement(complement(X_51))))]]) ).
cnf(refute_0_450,plain,
( join(X_51,top) != join(top,complement(complement(X_51)))
| join(X_51,top) = top ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(X_51))),top) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
join(X_51,top) = top,
inference(resolve,[$cnf( $equal(join(X_51,top),join(top,complement(complement(X_51)))) )],[refute_0_296,refute_0_450]) ).
cnf(refute_0_452,plain,
join(X_41,top) = top,
inference(subst,[],[refute_0_451:[bind(X_51,$fot(X_41))]]) ).
cnf(refute_0_453,plain,
( join(X_41,top) != join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))
| join(X_41,top) != top
| top = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,top),join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))) ),[0],$fot(top)]]) ).
cnf(refute_0_454,plain,
( join(X_41,top) != join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))
| top = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) ),
inference(resolve,[$cnf( $equal(join(X_41,top),top) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
join(top,join(meet(top,join(zero,zero)),C)) = join(join(top,meet(top,join(zero,zero))),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(top)),bind(B,$fot(meet(top,join(zero,zero))))]]) ).
cnf(refute_0_456,plain,
join(X_41,join(zero,join(zero,meet(top,top)))) = join(join(X_41,zero),join(zero,meet(top,top))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_41)),bind(B,$fot(zero)),bind(C,$fot(join(zero,meet(top,top))))]]) ).
cnf(refute_0_457,plain,
top = join(join(zero,zero),complement(join(zero,zero))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(zero,zero)))]]) ).
cnf(refute_0_458,plain,
( complement(join(zero,zero)) != meet(top,top)
| top != join(join(zero,zero),complement(join(zero,zero)))
| top = join(join(zero,zero),meet(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(zero,zero),complement(join(zero,zero)))) ),[1,1],$fot(meet(top,top))]]) ).
cnf(refute_0_459,plain,
( top != join(join(zero,zero),complement(join(zero,zero)))
| top = join(join(zero,zero),meet(top,top)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),meet(top,top)) )],[refute_0_225,refute_0_458]) ).
cnf(refute_0_460,plain,
top = join(join(zero,zero),meet(top,top)),
inference(resolve,[$cnf( $equal(top,join(join(zero,zero),complement(join(zero,zero)))) )],[refute_0_457,refute_0_459]) ).
cnf(refute_0_461,plain,
join(join(zero,zero),meet(top,top)) = join(zero,join(zero,meet(top,top))),
inference(subst,[],[refute_0_181:[bind(A,$fot(zero)),bind(B,$fot(zero)),bind(C,$fot(meet(top,top)))]]) ).
cnf(refute_0_462,plain,
( join(join(zero,zero),meet(top,top)) != join(zero,join(zero,meet(top,top)))
| top != join(join(zero,zero),meet(top,top))
| top = join(zero,join(zero,meet(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(zero,zero),meet(top,top))) ),[1],$fot(join(zero,join(zero,meet(top,top))))]]) ).
cnf(refute_0_463,plain,
( top != join(join(zero,zero),meet(top,top))
| top = join(zero,join(zero,meet(top,top))) ),
inference(resolve,[$cnf( $equal(join(join(zero,zero),meet(top,top)),join(zero,join(zero,meet(top,top)))) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
top = join(zero,join(zero,meet(top,top))),
inference(resolve,[$cnf( $equal(top,join(join(zero,zero),meet(top,top))) )],[refute_0_460,refute_0_463]) ).
cnf(refute_0_465,plain,
( top != join(zero,join(zero,meet(top,top)))
| join(zero,join(zero,meet(top,top))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(zero,join(zero,meet(top,top)))))]]) ).
cnf(refute_0_466,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,join(zero,meet(top,top)))) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
( join(X_41,join(zero,join(zero,meet(top,top)))) != join(join(X_41,zero),join(zero,meet(top,top)))
| join(zero,join(zero,meet(top,top))) != top
| join(X_41,top) = join(join(X_41,zero),join(zero,meet(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,join(zero,join(zero,meet(top,top)))),join(join(X_41,zero),join(zero,meet(top,top)))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_468,plain,
( join(X_41,join(zero,join(zero,meet(top,top)))) != join(join(X_41,zero),join(zero,meet(top,top)))
| join(X_41,top) = join(join(X_41,zero),join(zero,meet(top,top))) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(top,top))),top) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
join(X_41,top) = join(join(X_41,zero),join(zero,meet(top,top))),
inference(resolve,[$cnf( $equal(join(X_41,join(zero,join(zero,meet(top,top)))),join(join(X_41,zero),join(zero,meet(top,top)))) )],[refute_0_456,refute_0_468]) ).
cnf(refute_0_470,plain,
join(meet(top,top),join(X_41,zero)) = join(zero,join(meet(top,top),X_41)),
inference(subst,[],[refute_0_277:[bind(A,$fot(zero)),bind(X_41,$fot(meet(top,top))),bind(X_42,$fot(X_41))]]) ).
cnf(refute_0_471,plain,
join(zero,join(meet(top,top),join(X_41,zero))) = join(zero,join(meet(top,top),join(X_41,zero))),
introduced(tautology,[refl,[$fot(join(zero,join(meet(top,top),join(X_41,zero))))]]) ).
cnf(refute_0_472,plain,
( join(meet(top,top),join(X_41,zero)) != join(zero,join(meet(top,top),X_41))
| join(zero,join(meet(top,top),join(X_41,zero))) != join(zero,join(meet(top,top),join(X_41,zero)))
| join(zero,join(meet(top,top),join(X_41,zero))) = join(zero,join(zero,join(meet(top,top),X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(top,top),join(X_41,zero))),join(zero,join(meet(top,top),join(X_41,zero)))) ),[1,1],$fot(join(zero,join(meet(top,top),X_41)))]]) ).
cnf(refute_0_473,plain,
( join(meet(top,top),join(X_41,zero)) != join(zero,join(meet(top,top),X_41))
| join(zero,join(meet(top,top),join(X_41,zero))) = join(zero,join(zero,join(meet(top,top),X_41))) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,top),join(X_41,zero))),join(zero,join(meet(top,top),join(X_41,zero)))) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
join(zero,join(meet(top,top),join(X_41,zero))) = join(zero,join(zero,join(meet(top,top),X_41))),
inference(resolve,[$cnf( $equal(join(meet(top,top),join(X_41,zero)),join(zero,join(meet(top,top),X_41))) )],[refute_0_470,refute_0_473]) ).
cnf(refute_0_475,plain,
join(join(X_41,zero),join(zero,meet(top,top))) = join(zero,join(meet(top,top),join(X_41,zero))),
inference(subst,[],[refute_0_275:[bind(A,$fot(join(X_41,zero))),bind(X_41,$fot(zero)),bind(X_42,$fot(meet(top,top)))]]) ).
cnf(refute_0_476,plain,
( join(join(X_41,zero),join(zero,meet(top,top))) != join(zero,join(meet(top,top),join(X_41,zero)))
| join(zero,join(meet(top,top),join(X_41,zero))) != join(zero,join(zero,join(meet(top,top),X_41)))
| join(join(X_41,zero),join(zero,meet(top,top))) = join(zero,join(zero,join(meet(top,top),X_41))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(join(X_41,zero),join(zero,meet(top,top))))),bind(Y,$fot(join(zero,join(meet(top,top),join(X_41,zero))))),bind(Z,$fot(join(zero,join(zero,join(meet(top,top),X_41)))))]]) ).
cnf(refute_0_477,plain,
( join(zero,join(meet(top,top),join(X_41,zero))) != join(zero,join(zero,join(meet(top,top),X_41)))
| join(join(X_41,zero),join(zero,meet(top,top))) = join(zero,join(zero,join(meet(top,top),X_41))) ),
inference(resolve,[$cnf( $equal(join(join(X_41,zero),join(zero,meet(top,top))),join(zero,join(meet(top,top),join(X_41,zero)))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
join(join(X_41,zero),join(zero,meet(top,top))) = join(zero,join(zero,join(meet(top,top),X_41))),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,top),join(X_41,zero))),join(zero,join(zero,join(meet(top,top),X_41)))) )],[refute_0_474,refute_0_477]) ).
cnf(refute_0_479,plain,
( join(X_41,top) != join(join(X_41,zero),join(zero,meet(top,top)))
| join(join(X_41,zero),join(zero,meet(top,top))) != join(zero,join(zero,join(meet(top,top),X_41)))
| join(X_41,top) = join(zero,join(zero,join(meet(top,top),X_41))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_41,top),join(zero,join(zero,join(meet(top,top),X_41)))) ),[0],$fot(join(join(X_41,zero),join(zero,meet(top,top))))]]) ).
cnf(refute_0_480,plain,
( join(X_41,top) != join(join(X_41,zero),join(zero,meet(top,top)))
| join(X_41,top) = join(zero,join(zero,join(meet(top,top),X_41))) ),
inference(resolve,[$cnf( $equal(join(join(X_41,zero),join(zero,meet(top,top))),join(zero,join(zero,join(meet(top,top),X_41)))) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
join(X_41,top) = join(zero,join(zero,join(meet(top,top),X_41))),
inference(resolve,[$cnf( $equal(join(X_41,top),join(join(X_41,zero),join(zero,meet(top,top)))) )],[refute_0_469,refute_0_480]) ).
cnf(refute_0_482,plain,
join(meet(top,join(zero,zero)),top) = join(zero,join(zero,join(meet(top,top),meet(top,join(zero,zero))))),
inference(subst,[],[refute_0_481:[bind(X_41,$fot(meet(top,join(zero,zero))))]]) ).
cnf(refute_0_483,plain,
top = join(join(zero,meet(top,top)),complement(join(zero,meet(top,top)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(zero,meet(top,top))))]]) ).
cnf(refute_0_484,plain,
( complement(join(zero,meet(top,top))) != meet(top,join(zero,zero))
| top != join(join(zero,meet(top,top)),complement(join(zero,meet(top,top))))
| top = join(join(zero,meet(top,top)),meet(top,join(zero,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(zero,meet(top,top)),complement(join(zero,meet(top,top))))) ),[1,1],$fot(meet(top,join(zero,zero)))]]) ).
cnf(refute_0_485,plain,
( top != join(join(zero,meet(top,top)),complement(join(zero,meet(top,top))))
| top = join(join(zero,meet(top,top)),meet(top,join(zero,zero))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,top))),meet(top,join(zero,zero))) )],[refute_0_230,refute_0_484]) ).
cnf(refute_0_486,plain,
top = join(join(zero,meet(top,top)),meet(top,join(zero,zero))),
inference(resolve,[$cnf( $equal(top,join(join(zero,meet(top,top)),complement(join(zero,meet(top,top))))) )],[refute_0_483,refute_0_485]) ).
cnf(refute_0_487,plain,
join(join(zero,meet(top,top)),meet(top,join(zero,zero))) = join(zero,join(meet(top,top),meet(top,join(zero,zero)))),
inference(subst,[],[refute_0_181:[bind(A,$fot(zero)),bind(B,$fot(meet(top,top))),bind(C,$fot(meet(top,join(zero,zero))))]]) ).
cnf(refute_0_488,plain,
( join(join(zero,meet(top,top)),meet(top,join(zero,zero))) != join(zero,join(meet(top,top),meet(top,join(zero,zero))))
| top != join(join(zero,meet(top,top)),meet(top,join(zero,zero)))
| top = join(zero,join(meet(top,top),meet(top,join(zero,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(zero,meet(top,top)),meet(top,join(zero,zero)))) ),[1],$fot(join(zero,join(meet(top,top),meet(top,join(zero,zero)))))]]) ).
cnf(refute_0_489,plain,
( top != join(join(zero,meet(top,top)),meet(top,join(zero,zero)))
| top = join(zero,join(meet(top,top),meet(top,join(zero,zero)))) ),
inference(resolve,[$cnf( $equal(join(join(zero,meet(top,top)),meet(top,join(zero,zero))),join(zero,join(meet(top,top),meet(top,join(zero,zero))))) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
top = join(zero,join(meet(top,top),meet(top,join(zero,zero)))),
inference(resolve,[$cnf( $equal(top,join(join(zero,meet(top,top)),meet(top,join(zero,zero)))) )],[refute_0_486,refute_0_489]) ).
cnf(refute_0_491,plain,
( top != join(zero,join(meet(top,top),meet(top,join(zero,zero))))
| join(zero,join(meet(top,top),meet(top,join(zero,zero)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(zero,join(meet(top,top),meet(top,join(zero,zero))))))]]) ).
cnf(refute_0_492,plain,
join(zero,join(meet(top,top),meet(top,join(zero,zero)))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,join(meet(top,top),meet(top,join(zero,zero))))) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
( join(meet(top,join(zero,zero)),top) != join(zero,join(zero,join(meet(top,top),meet(top,join(zero,zero)))))
| join(zero,join(meet(top,top),meet(top,join(zero,zero)))) != top
| join(meet(top,join(zero,zero)),top) = join(zero,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,join(zero,zero)),top),join(zero,join(zero,join(meet(top,top),meet(top,join(zero,zero)))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_494,plain,
( join(meet(top,join(zero,zero)),top) != join(zero,join(zero,join(meet(top,top),meet(top,join(zero,zero)))))
| join(meet(top,join(zero,zero)),top) = join(zero,top) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,top),meet(top,join(zero,zero)))),top) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
join(meet(top,join(zero,zero)),top) = join(zero,top),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),top),join(zero,join(zero,join(meet(top,top),meet(top,join(zero,zero)))))) )],[refute_0_482,refute_0_494]) ).
cnf(refute_0_496,plain,
join(meet(top,join(zero,zero)),top) = join(top,meet(top,join(zero,zero))),
inference(subst,[],[refute_0_391:[bind(X_41,$fot(meet(top,join(zero,zero))))]]) ).
cnf(refute_0_497,plain,
( join(meet(top,join(zero,zero)),top) != join(top,meet(top,join(zero,zero)))
| join(meet(top,join(zero,zero)),top) != join(zero,top)
| join(top,meet(top,join(zero,zero))) = join(zero,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,join(zero,zero)),top),join(zero,top)) ),[0],$fot(join(top,meet(top,join(zero,zero))))]]) ).
cnf(refute_0_498,plain,
( join(meet(top,join(zero,zero)),top) != join(zero,top)
| join(top,meet(top,join(zero,zero))) = join(zero,top) ),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),top),join(top,meet(top,join(zero,zero)))) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
join(zero,top) = join(top,zero),
inference(subst,[],[refute_0_391:[bind(X_41,$fot(zero))]]) ).
cnf(refute_0_500,plain,
( join(top,zero) != top
| join(zero,top) != join(top,zero)
| join(zero,top) = top ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(zero,top))),bind(Y,$fot(join(top,zero))),bind(Z,$fot(top))]]) ).
cnf(refute_0_501,plain,
( join(top,zero) != top
| join(zero,top) = top ),
inference(resolve,[$cnf( $equal(join(zero,top),join(top,zero)) )],[refute_0_499,refute_0_500]) ).
cnf(refute_0_502,plain,
join(zero,top) = top,
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_359,refute_0_501]) ).
cnf(refute_0_503,plain,
( join(top,meet(top,join(zero,zero))) != join(zero,top)
| join(zero,top) != top
| join(top,meet(top,join(zero,zero))) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(top,meet(top,join(zero,zero))),top) ),[0],$fot(join(zero,top))]]) ).
cnf(refute_0_504,plain,
( join(top,meet(top,join(zero,zero))) != join(zero,top)
| join(top,meet(top,join(zero,zero))) = top ),
inference(resolve,[$cnf( $equal(join(zero,top),top) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
( join(meet(top,join(zero,zero)),top) != join(zero,top)
| join(top,meet(top,join(zero,zero))) = top ),
inference(resolve,[$cnf( $equal(join(top,meet(top,join(zero,zero))),join(zero,top)) )],[refute_0_498,refute_0_504]) ).
cnf(refute_0_506,plain,
join(top,meet(top,join(zero,zero))) = top,
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),top),join(zero,top)) )],[refute_0_495,refute_0_505]) ).
cnf(refute_0_507,plain,
( join(top,join(meet(top,join(zero,zero)),C)) != join(join(top,meet(top,join(zero,zero))),C)
| join(top,meet(top,join(zero,zero))) != top
| join(top,join(meet(top,join(zero,zero)),C)) = join(top,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(meet(top,join(zero,zero)),C)),join(join(top,meet(top,join(zero,zero))),C)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_508,plain,
( join(top,join(meet(top,join(zero,zero)),C)) != join(join(top,meet(top,join(zero,zero))),C)
| join(top,join(meet(top,join(zero,zero)),C)) = join(top,C) ),
inference(resolve,[$cnf( $equal(join(top,meet(top,join(zero,zero))),top) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
join(top,join(meet(top,join(zero,zero)),C)) = join(top,C),
inference(resolve,[$cnf( $equal(join(top,join(meet(top,join(zero,zero)),C)),join(join(top,meet(top,join(zero,zero))),C)) )],[refute_0_455,refute_0_508]) ).
cnf(refute_0_510,plain,
join(top,join(meet(top,join(zero,zero)),X_41)) = join(top,X_41),
inference(subst,[],[refute_0_509:[bind(C,$fot(X_41))]]) ).
cnf(refute_0_511,plain,
join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))) = join(top,join(meet(top,join(zero,zero)),X_41)),
inference(subst,[],[refute_0_172:[bind(X_41,$fot(zero)),bind(X_43,$fot(join(meet(top,join(zero,zero)),X_41)))]]) ).
cnf(refute_0_512,plain,
( join(top,join(meet(top,join(zero,zero)),X_41)) != join(top,X_41)
| join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))) != join(top,join(meet(top,join(zero,zero)),X_41))
| join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))) = join(top,X_41) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))))),bind(Y,$fot(join(top,join(meet(top,join(zero,zero)),X_41)))),bind(Z,$fot(join(top,X_41)))]]) ).
cnf(refute_0_513,plain,
( join(top,join(meet(top,join(zero,zero)),X_41)) != join(top,X_41)
| join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))) = join(top,X_41) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))),join(top,join(meet(top,join(zero,zero)),X_41))) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))) = join(top,X_41),
inference(resolve,[$cnf( $equal(join(top,join(meet(top,join(zero,zero)),X_41)),join(top,X_41)) )],[refute_0_510,refute_0_513]) ).
cnf(refute_0_515,plain,
join(meet(top,join(zero,zero)),join(complement(zero),X_41)) = join(complement(zero),join(meet(top,join(zero,zero)),X_41)),
inference(subst,[],[refute_0_376:[bind(X_41,$fot(complement(zero))),bind(X_42,$fot(meet(top,join(zero,zero)))),bind(X_43,$fot(X_41))]]) ).
cnf(refute_0_516,plain,
complement(complement(top)) = complement(complement(top)),
introduced(tautology,[refl,[$fot(complement(complement(top)))]]) ).
cnf(refute_0_517,plain,
( complement(complement(top)) != complement(complement(top))
| complement(top) != zero
| complement(complement(top)) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),complement(complement(top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_518,plain,
( complement(top) != zero
| complement(complement(top)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(complement(top))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
complement(complement(top)) = complement(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_518]) ).
cnf(refute_0_520,plain,
join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) = complement(composition(join(one,one),complement(B))),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_78)),bind(B,$fot(composition(join(one,one),complement(B))))]]) ).
cnf(refute_0_521,plain,
( meet(B,B) != complement(composition(join(one,one),complement(B)))
| complement(composition(join(one,one),complement(B))) = meet(B,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(B,B))),bind(Y,$fot(complement(composition(join(one,one),complement(B)))))]]) ).
cnf(refute_0_522,plain,
complement(composition(join(one,one),complement(B))) = meet(B,B),
inference(resolve,[$cnf( $equal(meet(B,B),complement(composition(join(one,one),complement(B)))) )],[refute_0_311,refute_0_521]) ).
cnf(refute_0_523,plain,
( complement(composition(join(one,one),complement(B))) != meet(B,B)
| join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) != complement(composition(join(one,one),complement(B)))
| join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) = meet(B,B) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))),complement(composition(join(one,one),complement(B)))) ),[1],$fot(meet(B,B))]]) ).
cnf(refute_0_524,plain,
( join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) != complement(composition(join(one,one),complement(B)))
| join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) = meet(B,B) ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),complement(B))),meet(B,B)) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) = meet(B,B),
inference(resolve,[$cnf( $equal(join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))),complement(composition(join(one,one),complement(B)))) )],[refute_0_520,refute_0_524]) ).
cnf(refute_0_526,plain,
composition(join(one,one),complement(B)) = complement(B),
inference(subst,[],[refute_0_423:[bind(X_79,$fot(B))]]) ).
cnf(refute_0_527,plain,
complement(composition(join(one,one),complement(B))) = complement(composition(join(one,one),complement(B))),
introduced(tautology,[refl,[$fot(complement(composition(join(one,one),complement(B))))]]) ).
cnf(refute_0_528,plain,
( complement(composition(join(one,one),complement(B))) != complement(composition(join(one,one),complement(B)))
| composition(join(one,one),complement(B)) != complement(B)
| complement(composition(join(one,one),complement(B))) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(join(one,one),complement(B))),complement(composition(join(one,one),complement(B)))) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_529,plain,
( composition(join(one,one),complement(B)) != complement(B)
| complement(composition(join(one,one),complement(B))) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),complement(B))),complement(composition(join(one,one),complement(B)))) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
complement(composition(join(one,one),complement(B))) = complement(complement(B)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(B)),complement(B)) )],[refute_0_526,refute_0_529]) ).
cnf(refute_0_531,plain,
( complement(composition(join(one,one),complement(B))) != complement(complement(B))
| join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) != complement(composition(join(one,one),complement(B)))
| join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) = complement(complement(B)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))))),bind(Y,$fot(complement(composition(join(one,one),complement(B))))),bind(Z,$fot(complement(complement(B))))]]) ).
cnf(refute_0_532,plain,
( complement(composition(join(one,one),complement(B))) != complement(complement(B))
| join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))),complement(composition(join(one,one),complement(B)))) )],[refute_0_520,refute_0_531]) ).
cnf(refute_0_533,plain,
join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) = complement(complement(B)),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),complement(B))),complement(complement(B))) )],[refute_0_530,refute_0_532]) ).
cnf(refute_0_534,plain,
( join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) != complement(complement(B))
| join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) != meet(B,B)
| complement(complement(B)) = meet(B,B) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))),meet(B,B)) ),[0],$fot(complement(complement(B)))]]) ).
cnf(refute_0_535,plain,
( join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))) != meet(B,B)
| complement(complement(B)) = meet(B,B) ),
inference(resolve,[$cnf( $equal(join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))),complement(complement(B))) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
complement(complement(B)) = meet(B,B),
inference(resolve,[$cnf( $equal(join(complement(composition(join(one,one),complement(B))),composition(converse(X_78),complement(composition(X_78,composition(join(one,one),complement(B)))))),meet(B,B)) )],[refute_0_525,refute_0_535]) ).
cnf(refute_0_537,plain,
( complement(complement(B)) != meet(B,B)
| meet(B,B) = complement(complement(B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(complement(B)))),bind(Y,$fot(meet(B,B)))]]) ).
cnf(refute_0_538,plain,
meet(B,B) = complement(complement(B)),
inference(resolve,[$cnf( $equal(complement(complement(B)),meet(B,B)) )],[refute_0_536,refute_0_537]) ).
cnf(refute_0_539,plain,
meet(top,top) = complement(complement(top)),
inference(subst,[],[refute_0_538:[bind(B,$fot(top))]]) ).
cnf(refute_0_540,plain,
( complement(complement(top)) != complement(zero)
| meet(top,top) != complement(complement(top))
| meet(top,top) = complement(zero) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(meet(top,top))),bind(Y,$fot(complement(complement(top)))),bind(Z,$fot(complement(zero)))]]) ).
cnf(refute_0_541,plain,
( complement(complement(top)) != complement(zero)
| meet(top,top) = complement(zero) ),
inference(resolve,[$cnf( $equal(meet(top,top),complement(complement(top))) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
meet(top,top) = complement(zero),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_519,refute_0_541]) ).
cnf(refute_0_543,plain,
join(zero,complement(zero)) = top,
inference(subst,[],[refute_0_192:[bind(A,$fot(zero))]]) ).
cnf(refute_0_544,plain,
join(zero,meet(top,top)) = join(zero,meet(top,top)),
introduced(tautology,[refl,[$fot(join(zero,meet(top,top)))]]) ).
cnf(refute_0_545,plain,
( join(zero,meet(top,top)) != join(zero,meet(top,top))
| meet(top,top) != complement(zero)
| join(zero,meet(top,top)) = join(zero,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(top,top)),join(zero,meet(top,top))) ),[1,1],$fot(complement(zero))]]) ).
cnf(refute_0_546,plain,
( meet(top,top) != complement(zero)
| join(zero,meet(top,top)) = join(zero,complement(zero)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,top)),join(zero,meet(top,top))) )],[refute_0_544,refute_0_545]) ).
cnf(refute_0_547,plain,
join(zero,meet(top,top)) = join(zero,complement(zero)),
inference(resolve,[$cnf( $equal(meet(top,top),complement(zero)) )],[refute_0_542,refute_0_546]) ).
cnf(refute_0_548,plain,
( join(zero,complement(zero)) != top
| join(zero,meet(top,top)) != join(zero,complement(zero))
| join(zero,meet(top,top)) = top ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(zero,meet(top,top)))),bind(Y,$fot(join(zero,complement(zero)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_549,plain,
( join(zero,complement(zero)) != top
| join(zero,meet(top,top)) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,top)),join(zero,complement(zero))) )],[refute_0_547,refute_0_548]) ).
cnf(refute_0_550,plain,
join(zero,meet(top,top)) = top,
inference(resolve,[$cnf( $equal(join(zero,complement(zero)),top) )],[refute_0_543,refute_0_549]) ).
cnf(refute_0_551,plain,
meet(top,join(zero,meet(top,top))) = meet(top,join(zero,meet(top,top))),
introduced(tautology,[refl,[$fot(meet(top,join(zero,meet(top,top))))]]) ).
cnf(refute_0_552,plain,
( join(zero,meet(top,top)) != top
| meet(top,join(zero,meet(top,top))) != meet(top,join(zero,meet(top,top)))
| meet(top,join(zero,meet(top,top))) = meet(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,meet(top,top))),meet(top,join(zero,meet(top,top)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_553,plain,
( join(zero,meet(top,top)) != top
| meet(top,join(zero,meet(top,top))) = meet(top,top) ),
inference(resolve,[$cnf( $equal(meet(top,join(zero,meet(top,top))),meet(top,join(zero,meet(top,top)))) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
meet(top,join(zero,meet(top,top))) = meet(top,top),
inference(resolve,[$cnf( $equal(join(zero,meet(top,top)),top) )],[refute_0_550,refute_0_553]) ).
cnf(refute_0_555,plain,
( meet(top,join(zero,meet(top,top))) != meet(top,top)
| meet(top,top) != complement(zero)
| meet(top,join(zero,meet(top,top))) = complement(zero) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(meet(top,join(zero,meet(top,top))))),bind(Y,$fot(meet(top,top))),bind(Z,$fot(complement(zero)))]]) ).
cnf(refute_0_556,plain,
( meet(top,top) != complement(zero)
| meet(top,join(zero,meet(top,top))) = complement(zero) ),
inference(resolve,[$cnf( $equal(meet(top,join(zero,meet(top,top))),meet(top,top)) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
meet(top,join(zero,meet(top,top))) = complement(zero),
inference(resolve,[$cnf( $equal(meet(top,top),complement(zero)) )],[refute_0_542,refute_0_556]) ).
cnf(refute_0_558,plain,
join(meet(top,join(zero,meet(top,top))),X_41) = join(meet(top,join(zero,meet(top,top))),X_41),
introduced(tautology,[refl,[$fot(join(meet(top,join(zero,meet(top,top))),X_41))]]) ).
cnf(refute_0_559,plain,
( join(meet(top,join(zero,meet(top,top))),X_41) != join(meet(top,join(zero,meet(top,top))),X_41)
| meet(top,join(zero,meet(top,top))) != complement(zero)
| join(meet(top,join(zero,meet(top,top))),X_41) = join(complement(zero),X_41) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,join(zero,meet(top,top))),X_41),join(meet(top,join(zero,meet(top,top))),X_41)) ),[1,0],$fot(complement(zero))]]) ).
cnf(refute_0_560,plain,
( meet(top,join(zero,meet(top,top))) != complement(zero)
| join(meet(top,join(zero,meet(top,top))),X_41) = join(complement(zero),X_41) ),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,meet(top,top))),X_41),join(meet(top,join(zero,meet(top,top))),X_41)) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
join(meet(top,join(zero,meet(top,top))),X_41) = join(complement(zero),X_41),
inference(resolve,[$cnf( $equal(meet(top,join(zero,meet(top,top))),complement(zero)) )],[refute_0_557,refute_0_560]) ).
cnf(refute_0_562,plain,
join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)) = join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)),
introduced(tautology,[refl,[$fot(join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))]]) ).
cnf(refute_0_563,plain,
( join(meet(top,join(zero,meet(top,top))),X_41) != join(complement(zero),X_41)
| join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)) != join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))
| join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)) = join(meet(top,join(zero,zero)),join(complement(zero),X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)),join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) ),[1,1],$fot(join(complement(zero),X_41))]]) ).
cnf(refute_0_564,plain,
( join(meet(top,join(zero,meet(top,top))),X_41) != join(complement(zero),X_41)
| join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)) = join(meet(top,join(zero,zero)),join(complement(zero),X_41)) ),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)),join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)) = join(meet(top,join(zero,zero)),join(complement(zero),X_41)),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,meet(top,top))),X_41),join(complement(zero),X_41)) )],[refute_0_561,refute_0_564]) ).
cnf(refute_0_566,plain,
( join(meet(top,join(zero,zero)),join(complement(zero),X_41)) != join(complement(zero),join(meet(top,join(zero,zero)),X_41))
| join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)) != join(meet(top,join(zero,zero)),join(complement(zero),X_41))
| join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)) = join(complement(zero),join(meet(top,join(zero,zero)),X_41)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))),bind(Y,$fot(join(meet(top,join(zero,zero)),join(complement(zero),X_41)))),bind(Z,$fot(join(complement(zero),join(meet(top,join(zero,zero)),X_41))))]]) ).
cnf(refute_0_567,plain,
( join(meet(top,join(zero,zero)),join(complement(zero),X_41)) != join(complement(zero),join(meet(top,join(zero,zero)),X_41))
| join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)) = join(complement(zero),join(meet(top,join(zero,zero)),X_41)) ),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)),join(meet(top,join(zero,zero)),join(complement(zero),X_41))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)) = join(complement(zero),join(meet(top,join(zero,zero)),X_41)),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),join(complement(zero),X_41)),join(complement(zero),join(meet(top,join(zero,zero)),X_41))) )],[refute_0_515,refute_0_567]) ).
cnf(refute_0_569,plain,
join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) = join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))),
introduced(tautology,[refl,[$fot(join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))))]]) ).
cnf(refute_0_570,plain,
( join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)) != join(complement(zero),join(meet(top,join(zero,zero)),X_41))
| join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) != join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))
| join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) = join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))),join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))) ),[1,1],$fot(join(complement(zero),join(meet(top,join(zero,zero)),X_41)))]]) ).
cnf(refute_0_571,plain,
( join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)) != join(complement(zero),join(meet(top,join(zero,zero)),X_41))
| join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) = join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))),join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))) )],[refute_0_569,refute_0_570]) ).
cnf(refute_0_572,plain,
join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) = join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))),
inference(resolve,[$cnf( $equal(join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)),join(complement(zero),join(meet(top,join(zero,zero)),X_41))) )],[refute_0_568,refute_0_571]) ).
cnf(refute_0_573,plain,
( join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))) != join(top,X_41)
| join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) != join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41)))
| join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) = join(top,X_41) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))))),bind(Y,$fot(join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))))),bind(Z,$fot(join(top,X_41)))]]) ).
cnf(refute_0_574,plain,
( join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))) != join(top,X_41)
| join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) = join(top,X_41) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))),join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41)))) )],[refute_0_572,refute_0_573]) ).
cnf(refute_0_575,plain,
join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) = join(top,X_41),
inference(resolve,[$cnf( $equal(join(zero,join(complement(zero),join(meet(top,join(zero,zero)),X_41))),join(top,X_41)) )],[refute_0_514,refute_0_574]) ).
cnf(refute_0_576,plain,
( join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))) != join(top,X_41)
| top != join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))
| top = join(top,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))) ),[1],$fot(join(top,X_41))]]) ).
cnf(refute_0_577,plain,
( top != join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))
| top = join(top,X_41) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41))),join(top,X_41)) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
( join(X_41,top) != join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))
| top = join(top,X_41) ),
inference(resolve,[$cnf( $equal(top,join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))) )],[refute_0_454,refute_0_577]) ).
cnf(refute_0_579,plain,
top = join(top,X_41),
inference(resolve,[$cnf( $equal(join(X_41,top),join(zero,join(meet(top,join(zero,zero)),join(meet(top,join(zero,meet(top,top))),X_41)))) )],[refute_0_289,refute_0_578]) ).
cnf(refute_0_580,plain,
( top != join(top,X_41)
| join(top,X_41) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,X_41)))]]) ).
cnf(refute_0_581,plain,
join(top,X_41) = top,
inference(resolve,[$cnf( $equal(top,join(top,X_41)) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
join(top,X_43) = top,
inference(subst,[],[refute_0_581:[bind(X_41,$fot(X_43))]]) ).
cnf(refute_0_583,plain,
( join(X_41,join(complement(X_41),X_43)) != join(top,X_43)
| join(top,X_43) != top
| join(X_41,join(complement(X_41),X_43)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_41,join(complement(X_41),X_43)),top) ),[0],$fot(join(top,X_43))]]) ).
cnf(refute_0_584,plain,
( join(X_41,join(complement(X_41),X_43)) != join(top,X_43)
| join(X_41,join(complement(X_41),X_43)) = top ),
inference(resolve,[$cnf( $equal(join(top,X_43),top) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
join(X_41,join(complement(X_41),X_43)) = top,
inference(resolve,[$cnf( $equal(join(X_41,join(complement(X_41),X_43)),join(top,X_43)) )],[refute_0_172,refute_0_584]) ).
cnf(refute_0_586,plain,
join(complement(X_107),join(complement(complement(X_107)),X_148)) = top,
inference(subst,[],[refute_0_585:[bind(X_41,$fot(complement(X_107))),bind(X_43,$fot(X_148))]]) ).
cnf(refute_0_587,plain,
( X_107 != join(meet(join(complement(complement(X_107)),X_148),X_107),complement(join(complement(X_107),join(complement(complement(X_107)),X_148))))
| join(complement(X_107),join(complement(complement(X_107)),X_148)) != top
| X_107 = join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_107,join(meet(join(complement(complement(X_107)),X_148),X_107),complement(join(complement(X_107),join(complement(complement(X_107)),X_148))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_588,plain,
( X_107 != join(meet(join(complement(complement(X_107)),X_148),X_107),complement(join(complement(X_107),join(complement(complement(X_107)),X_148))))
| X_107 = join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_107),join(complement(complement(X_107)),X_148)),top) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
X_107 = join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)),
inference(resolve,[$cnf( $equal(X_107,join(meet(join(complement(complement(X_107)),X_148),X_107),complement(join(complement(X_107),join(complement(complement(X_107)),X_148))))) )],[refute_0_165,refute_0_588]) ).
cnf(refute_0_590,plain,
X_107 = join(meet(X_107,complement(complement(X_107))),complement(join(complement(X_107),complement(complement(X_107))))),
inference(subst,[],[refute_0_146:[bind(A,$fot(X_107)),bind(B,$fot(complement(complement(X_107))))]]) ).
cnf(refute_0_591,plain,
top = join(complement(X_107),complement(complement(X_107))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_107)))]]) ).
cnf(refute_0_592,plain,
( top != join(complement(X_107),complement(complement(X_107)))
| join(complement(X_107),complement(complement(X_107))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_107),complement(complement(X_107)))))]]) ).
cnf(refute_0_593,plain,
join(complement(X_107),complement(complement(X_107))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_107),complement(complement(X_107)))) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
( X_107 != join(meet(X_107,complement(complement(X_107))),complement(join(complement(X_107),complement(complement(X_107)))))
| join(complement(X_107),complement(complement(X_107))) != top
| X_107 = join(meet(X_107,complement(complement(X_107))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_107,join(meet(X_107,complement(complement(X_107))),complement(join(complement(X_107),complement(complement(X_107)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_595,plain,
( X_107 != join(meet(X_107,complement(complement(X_107))),complement(join(complement(X_107),complement(complement(X_107)))))
| X_107 = join(meet(X_107,complement(complement(X_107))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_107),complement(complement(X_107))),top) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
X_107 = join(meet(X_107,complement(complement(X_107))),complement(top)),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,complement(complement(X_107))),complement(join(complement(X_107),complement(complement(X_107)))))) )],[refute_0_590,refute_0_595]) ).
cnf(refute_0_597,plain,
join(complement(top),meet(X_107,complement(complement(X_107)))) = join(complement(top),meet(X_107,complement(complement(X_107)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_107,complement(complement(X_107)))))]]) ).
cnf(refute_0_598,plain,
( complement(top) != zero
| join(complement(top),meet(X_107,complement(complement(X_107)))) != join(complement(top),meet(X_107,complement(complement(X_107))))
| join(complement(top),meet(X_107,complement(complement(X_107)))) = join(zero,meet(X_107,complement(complement(X_107)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_107,complement(complement(X_107)))),join(complement(top),meet(X_107,complement(complement(X_107))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_599,plain,
( complement(top) != zero
| join(complement(top),meet(X_107,complement(complement(X_107)))) = join(zero,meet(X_107,complement(complement(X_107)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_107,complement(complement(X_107)))),join(complement(top),meet(X_107,complement(complement(X_107))))) )],[refute_0_597,refute_0_598]) ).
cnf(refute_0_600,plain,
join(complement(top),meet(X_107,complement(complement(X_107)))) = join(zero,meet(X_107,complement(complement(X_107)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_599]) ).
cnf(refute_0_601,plain,
join(meet(X_107,complement(complement(X_107))),complement(top)) = join(complement(top),meet(X_107,complement(complement(X_107)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_107,complement(complement(X_107)))))]]) ).
cnf(refute_0_602,plain,
( join(complement(top),meet(X_107,complement(complement(X_107)))) != join(zero,meet(X_107,complement(complement(X_107))))
| join(meet(X_107,complement(complement(X_107))),complement(top)) != join(complement(top),meet(X_107,complement(complement(X_107))))
| join(meet(X_107,complement(complement(X_107))),complement(top)) = join(zero,meet(X_107,complement(complement(X_107)))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(X_107,complement(complement(X_107))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_107,complement(complement(X_107)))))),bind(Z,$fot(join(zero,meet(X_107,complement(complement(X_107))))))]]) ).
cnf(refute_0_603,plain,
( join(complement(top),meet(X_107,complement(complement(X_107)))) != join(zero,meet(X_107,complement(complement(X_107))))
| join(meet(X_107,complement(complement(X_107))),complement(top)) = join(zero,meet(X_107,complement(complement(X_107)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_107,complement(complement(X_107))),complement(top)),join(complement(top),meet(X_107,complement(complement(X_107))))) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
join(meet(X_107,complement(complement(X_107))),complement(top)) = join(zero,meet(X_107,complement(complement(X_107)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_107,complement(complement(X_107)))),join(zero,meet(X_107,complement(complement(X_107))))) )],[refute_0_600,refute_0_603]) ).
cnf(refute_0_605,plain,
( X_107 != join(meet(X_107,complement(complement(X_107))),complement(top))
| join(meet(X_107,complement(complement(X_107))),complement(top)) != join(zero,meet(X_107,complement(complement(X_107))))
| X_107 = join(zero,meet(X_107,complement(complement(X_107)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,join(zero,meet(X_107,complement(complement(X_107))))) ),[0],$fot(join(meet(X_107,complement(complement(X_107))),complement(top)))]]) ).
cnf(refute_0_606,plain,
( X_107 != join(meet(X_107,complement(complement(X_107))),complement(top))
| X_107 = join(zero,meet(X_107,complement(complement(X_107)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_107,complement(complement(X_107))),complement(top)),join(zero,meet(X_107,complement(complement(X_107))))) )],[refute_0_604,refute_0_605]) ).
cnf(refute_0_607,plain,
X_107 = join(zero,meet(X_107,complement(complement(X_107)))),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,complement(complement(X_107))),complement(top))) )],[refute_0_596,refute_0_606]) ).
cnf(refute_0_608,plain,
X_107 = join(meet(X_107,join(complement(X_107),complement(X_107))),complement(join(complement(X_107),join(complement(X_107),complement(X_107))))),
inference(subst,[],[refute_0_146:[bind(A,$fot(X_107)),bind(B,$fot(join(complement(X_107),complement(X_107))))]]) ).
cnf(refute_0_609,plain,
composition(join(join(one,one),one),X_33) = join(X_33,composition(join(one,one),X_33)),
inference(subst,[],[refute_0_54:[bind(X_31,$fot(join(one,one)))]]) ).
cnf(refute_0_610,plain,
composition(join(one,one),X_33) = join(X_33,X_33),
inference(subst,[],[refute_0_305:[bind(X_35,$fot(X_33))]]) ).
cnf(refute_0_611,plain,
( composition(join(join(one,one),one),X_33) != join(X_33,composition(join(one,one),X_33))
| composition(join(one,one),X_33) != join(X_33,X_33)
| composition(join(join(one,one),one),X_33) = join(X_33,join(X_33,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(one,one),one),X_33),join(X_33,composition(join(one,one),X_33))) ),[1,1],$fot(join(X_33,X_33))]]) ).
cnf(refute_0_612,plain,
( composition(join(join(one,one),one),X_33) != join(X_33,composition(join(one,one),X_33))
| composition(join(join(one,one),one),X_33) = join(X_33,join(X_33,X_33)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_33),join(X_33,X_33)) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
composition(join(join(one,one),one),X_33) = join(X_33,join(X_33,X_33)),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),X_33),join(X_33,composition(join(one,one),X_33))) )],[refute_0_609,refute_0_612]) ).
cnf(refute_0_614,plain,
composition(join(join(one,one),one),X_33) = composition(join(one,join(one,one)),X_33),
inference(subst,[],[refute_0_100:[bind(X_34,$fot(join(one,one))),bind(X_35,$fot(X_33))]]) ).
cnf(refute_0_615,plain,
( composition(join(join(one,one),one),X_33) != composition(join(one,join(one,one)),X_33)
| composition(join(join(one,one),one),X_33) != join(X_33,join(X_33,X_33))
| composition(join(one,join(one,one)),X_33) = join(X_33,join(X_33,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(one,one),one),X_33),join(X_33,join(X_33,X_33))) ),[0],$fot(composition(join(one,join(one,one)),X_33))]]) ).
cnf(refute_0_616,plain,
( composition(join(join(one,one),one),X_33) != join(X_33,join(X_33,X_33))
| composition(join(one,join(one,one)),X_33) = join(X_33,join(X_33,X_33)) ),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),X_33),composition(join(one,join(one,one)),X_33)) )],[refute_0_614,refute_0_615]) ).
cnf(refute_0_617,plain,
composition(join(one,join(one,one)),X_33) = join(X_33,join(X_33,X_33)),
inference(resolve,[$cnf( $equal(composition(join(join(one,one),one),X_33),join(X_33,join(X_33,X_33))) )],[refute_0_613,refute_0_616]) ).
cnf(refute_0_618,plain,
composition(join(one,join(one,one)),complement(X_107)) = join(complement(X_107),join(complement(X_107),complement(X_107))),
inference(subst,[],[refute_0_617:[bind(X_33,$fot(complement(X_107)))]]) ).
cnf(refute_0_619,plain,
( composition(join(one,join(one,one)),complement(X_107)) != join(complement(X_107),join(complement(X_107),complement(X_107)))
| join(complement(X_107),join(complement(X_107),complement(X_107))) = composition(join(one,join(one,one)),complement(X_107)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,join(one,one)),complement(X_107)))),bind(Y,$fot(join(complement(X_107),join(complement(X_107),complement(X_107)))))]]) ).
cnf(refute_0_620,plain,
join(complement(X_107),join(complement(X_107),complement(X_107))) = composition(join(one,join(one,one)),complement(X_107)),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),complement(X_107)),join(complement(X_107),join(complement(X_107),complement(X_107)))) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
( X_107 != join(meet(X_107,join(complement(X_107),complement(X_107))),complement(join(complement(X_107),join(complement(X_107),complement(X_107)))))
| join(complement(X_107),join(complement(X_107),complement(X_107))) != composition(join(one,join(one,one)),complement(X_107))
| X_107 = join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_107,join(meet(X_107,join(complement(X_107),complement(X_107))),complement(join(complement(X_107),join(complement(X_107),complement(X_107)))))) ),[1,1,0],$fot(composition(join(one,join(one,one)),complement(X_107)))]]) ).
cnf(refute_0_622,plain,
( X_107 != join(meet(X_107,join(complement(X_107),complement(X_107))),complement(join(complement(X_107),join(complement(X_107),complement(X_107)))))
| X_107 = join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_107),join(complement(X_107),complement(X_107))),composition(join(one,join(one,one)),complement(X_107))) )],[refute_0_620,refute_0_621]) ).
cnf(refute_0_623,plain,
X_107 = join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,join(complement(X_107),complement(X_107))),complement(join(complement(X_107),join(complement(X_107),complement(X_107)))))) )],[refute_0_608,refute_0_622]) ).
cnf(refute_0_624,plain,
( X_16 != composition(one,X_16)
| composition(one,X_16) = X_16 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_16)),bind(Y,$fot(composition(one,X_16)))]]) ).
cnf(refute_0_625,plain,
composition(one,X_16) = X_16,
inference(resolve,[$cnf( $equal(X_16,composition(one,X_16)) )],[refute_0_44,refute_0_624]) ).
cnf(refute_0_626,plain,
composition(one,complement(X_107)) = complement(X_107),
inference(subst,[],[refute_0_625:[bind(X_16,$fot(complement(X_107)))]]) ).
cnf(refute_0_627,plain,
composition(X_46,composition(join(one,one),X_48)) = composition(composition(X_46,join(one,one)),X_48),
inference(subst,[],[composition_associativity_5:[bind(A,$fot(X_46)),bind(B,$fot(join(one,one))),bind(C,$fot(X_48))]]) ).
cnf(refute_0_628,plain,
converse(join(converse(A),converse(A))) = join(converse(converse(A)),A),
inference(subst,[],[refute_0_65:[bind(X_4,$fot(converse(A)))]]) ).
cnf(refute_0_629,plain,
composition(join(one,one),converse(A)) = join(converse(A),converse(A)),
inference(subst,[],[refute_0_305:[bind(X_35,$fot(converse(A)))]]) ).
cnf(refute_0_630,plain,
( composition(join(one,one),converse(A)) != join(converse(A),converse(A))
| join(converse(A),converse(A)) = composition(join(one,one),converse(A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),converse(A)))),bind(Y,$fot(join(converse(A),converse(A))))]]) ).
cnf(refute_0_631,plain,
join(converse(A),converse(A)) = composition(join(one,one),converse(A)),
inference(resolve,[$cnf( $equal(composition(join(one,one),converse(A)),join(converse(A),converse(A))) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
( converse(join(converse(A),converse(A))) != join(converse(converse(A)),A)
| join(converse(A),converse(A)) != composition(join(one,one),converse(A))
| converse(composition(join(one,one),converse(A))) = join(converse(converse(A)),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),converse(A))),join(converse(converse(A)),A)) ),[0,0],$fot(composition(join(one,one),converse(A)))]]) ).
cnf(refute_0_633,plain,
( converse(join(converse(A),converse(A))) != join(converse(converse(A)),A)
| converse(composition(join(one,one),converse(A))) = join(converse(converse(A)),A) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(A)),composition(join(one,one),converse(A))) )],[refute_0_631,refute_0_632]) ).
cnf(refute_0_634,plain,
converse(composition(join(one,one),converse(A))) = join(converse(converse(A)),A),
inference(resolve,[$cnf( $equal(converse(join(converse(A),converse(A))),join(converse(converse(A)),A)) )],[refute_0_628,refute_0_633]) ).
cnf(refute_0_635,plain,
composition(A,converse(join(one,one))) = composition(A,converse(join(one,one))),
introduced(tautology,[refl,[$fot(composition(A,converse(join(one,one))))]]) ).
cnf(refute_0_636,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_637,plain,
( converse(join(one,one)) != join(one,one)
| composition(A,converse(join(one,one))) = composition(A,join(one,one)) ),
inference(resolve,[$cnf( $equal(composition(A,converse(join(one,one))),composition(A,converse(join(one,one)))) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
composition(A,converse(join(one,one))) = composition(A,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_404,refute_0_637]) ).
cnf(refute_0_639,plain,
converse(composition(X_14,converse(A))) = composition(converse(converse(A)),converse(X_14)),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(X_14)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_640,plain,
( converse(composition(X_14,converse(A))) != composition(converse(converse(A)),converse(X_14))
| converse(converse(A)) != A
| converse(composition(X_14,converse(A))) = composition(A,converse(X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_14,converse(A))),composition(converse(converse(A)),converse(X_14))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_641,plain,
( converse(composition(X_14,converse(A))) != composition(converse(converse(A)),converse(X_14))
| converse(composition(X_14,converse(A))) = composition(A,converse(X_14)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_640]) ).
cnf(refute_0_642,plain,
converse(composition(X_14,converse(A))) = composition(A,converse(X_14)),
inference(resolve,[$cnf( $equal(converse(composition(X_14,converse(A))),composition(converse(converse(A)),converse(X_14))) )],[refute_0_639,refute_0_641]) ).
cnf(refute_0_643,plain,
converse(composition(join(one,one),converse(A))) = composition(A,converse(join(one,one))),
inference(subst,[],[refute_0_642:[bind(X_14,$fot(join(one,one)))]]) ).
cnf(refute_0_644,plain,
( composition(A,converse(join(one,one))) != composition(A,join(one,one))
| converse(composition(join(one,one),converse(A))) != composition(A,converse(join(one,one)))
| converse(composition(join(one,one),converse(A))) = composition(A,join(one,one)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(converse(composition(join(one,one),converse(A))))),bind(Y,$fot(composition(A,converse(join(one,one))))),bind(Z,$fot(composition(A,join(one,one))))]]) ).
cnf(refute_0_645,plain,
( composition(A,converse(join(one,one))) != composition(A,join(one,one))
| converse(composition(join(one,one),converse(A))) = composition(A,join(one,one)) ),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),converse(A))),composition(A,converse(join(one,one)))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
converse(composition(join(one,one),converse(A))) = composition(A,join(one,one)),
inference(resolve,[$cnf( $equal(composition(A,converse(join(one,one))),composition(A,join(one,one))) )],[refute_0_638,refute_0_645]) ).
cnf(refute_0_647,plain,
( converse(composition(join(one,one),converse(A))) != composition(A,join(one,one))
| converse(composition(join(one,one),converse(A))) != join(converse(converse(A)),A)
| composition(A,join(one,one)) = join(converse(converse(A)),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(one,one),converse(A))),join(converse(converse(A)),A)) ),[0],$fot(composition(A,join(one,one)))]]) ).
cnf(refute_0_648,plain,
( converse(composition(join(one,one),converse(A))) != join(converse(converse(A)),A)
| composition(A,join(one,one)) = join(converse(converse(A)),A) ),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),converse(A))),composition(A,join(one,one))) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
join(A,converse(converse(A))) = join(A,converse(converse(A))),
introduced(tautology,[refl,[$fot(join(A,converse(converse(A))))]]) ).
cnf(refute_0_650,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_651,plain,
( converse(converse(A)) != A
| join(A,converse(converse(A))) = join(A,A) ),
inference(resolve,[$cnf( $equal(join(A,converse(converse(A))),join(A,converse(converse(A)))) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
join(A,converse(converse(A))) = join(A,A),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_651]) ).
cnf(refute_0_653,plain,
join(converse(converse(A)),A) = join(A,converse(converse(A))),
inference(subst,[],[refute_0_4:[bind(B,$fot(converse(converse(A))))]]) ).
cnf(refute_0_654,plain,
( join(A,converse(converse(A))) != join(A,A)
| join(converse(converse(A)),A) != join(A,converse(converse(A)))
| join(converse(converse(A)),A) = join(A,A) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(converse(converse(A)),A))),bind(Y,$fot(join(A,converse(converse(A))))),bind(Z,$fot(join(A,A)))]]) ).
cnf(refute_0_655,plain,
( join(A,converse(converse(A))) != join(A,A)
| join(converse(converse(A)),A) = join(A,A) ),
inference(resolve,[$cnf( $equal(join(converse(converse(A)),A),join(A,converse(converse(A)))) )],[refute_0_653,refute_0_654]) ).
cnf(refute_0_656,plain,
join(converse(converse(A)),A) = join(A,A),
inference(resolve,[$cnf( $equal(join(A,converse(converse(A))),join(A,A)) )],[refute_0_652,refute_0_655]) ).
cnf(refute_0_657,plain,
( composition(A,join(one,one)) != join(converse(converse(A)),A)
| join(converse(converse(A)),A) != join(A,A)
| composition(A,join(one,one)) = join(A,A) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(A,join(one,one)),join(A,A)) ),[0],$fot(join(converse(converse(A)),A))]]) ).
cnf(refute_0_658,plain,
( composition(A,join(one,one)) != join(converse(converse(A)),A)
| composition(A,join(one,one)) = join(A,A) ),
inference(resolve,[$cnf( $equal(join(converse(converse(A)),A),join(A,A)) )],[refute_0_656,refute_0_657]) ).
cnf(refute_0_659,plain,
( converse(composition(join(one,one),converse(A))) != join(converse(converse(A)),A)
| composition(A,join(one,one)) = join(A,A) ),
inference(resolve,[$cnf( $equal(composition(A,join(one,one)),join(converse(converse(A)),A)) )],[refute_0_648,refute_0_658]) ).
cnf(refute_0_660,plain,
composition(A,join(one,one)) = join(A,A),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),converse(A))),join(converse(converse(A)),A)) )],[refute_0_634,refute_0_659]) ).
cnf(refute_0_661,plain,
composition(X_46,join(one,one)) = join(X_46,X_46),
inference(subst,[],[refute_0_660:[bind(A,$fot(X_46))]]) ).
cnf(refute_0_662,plain,
( composition(X_46,composition(join(one,one),X_48)) != composition(composition(X_46,join(one,one)),X_48)
| composition(X_46,join(one,one)) != join(X_46,X_46)
| composition(X_46,composition(join(one,one),X_48)) = composition(join(X_46,X_46),X_48) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_46,composition(join(one,one),X_48)),composition(composition(X_46,join(one,one)),X_48)) ),[1,0],$fot(join(X_46,X_46))]]) ).
cnf(refute_0_663,plain,
( composition(X_46,composition(join(one,one),X_48)) != composition(composition(X_46,join(one,one)),X_48)
| composition(X_46,composition(join(one,one),X_48)) = composition(join(X_46,X_46),X_48) ),
inference(resolve,[$cnf( $equal(composition(X_46,join(one,one)),join(X_46,X_46)) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
composition(X_46,composition(join(one,one),X_48)) = composition(join(X_46,X_46),X_48),
inference(resolve,[$cnf( $equal(composition(X_46,composition(join(one,one),X_48)),composition(composition(X_46,join(one,one)),X_48)) )],[refute_0_627,refute_0_663]) ).
cnf(refute_0_665,plain,
composition(X_46,composition(join(one,one),complement(X_84))) = composition(join(X_46,X_46),complement(X_84)),
inference(subst,[],[refute_0_664:[bind(X_48,$fot(complement(X_84)))]]) ).
cnf(refute_0_666,plain,
composition(join(one,one),complement(X_84)) = complement(X_84),
inference(subst,[],[refute_0_423:[bind(X_79,$fot(X_84))]]) ).
cnf(refute_0_667,plain,
( composition(X_46,composition(join(one,one),complement(X_84))) != composition(join(X_46,X_46),complement(X_84))
| composition(join(one,one),complement(X_84)) != complement(X_84)
| composition(X_46,complement(X_84)) = composition(join(X_46,X_46),complement(X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_46,composition(join(one,one),complement(X_84))),composition(join(X_46,X_46),complement(X_84))) ),[0,1],$fot(complement(X_84))]]) ).
cnf(refute_0_668,plain,
( composition(X_46,composition(join(one,one),complement(X_84))) != composition(join(X_46,X_46),complement(X_84))
| composition(X_46,complement(X_84)) = composition(join(X_46,X_46),complement(X_84)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_84)),complement(X_84)) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
composition(X_46,complement(X_84)) = composition(join(X_46,X_46),complement(X_84)),
inference(resolve,[$cnf( $equal(composition(X_46,composition(join(one,one),complement(X_84))),composition(join(X_46,X_46),complement(X_84))) )],[refute_0_665,refute_0_668]) ).
cnf(refute_0_670,plain,
( composition(X_46,complement(X_84)) != composition(join(X_46,X_46),complement(X_84))
| composition(join(X_46,X_46),complement(X_84)) = composition(X_46,complement(X_84)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(X_46,complement(X_84)))),bind(Y,$fot(composition(join(X_46,X_46),complement(X_84))))]]) ).
cnf(refute_0_671,plain,
composition(join(X_46,X_46),complement(X_84)) = composition(X_46,complement(X_84)),
inference(resolve,[$cnf( $equal(composition(X_46,complement(X_84)),composition(join(X_46,X_46),complement(X_84))) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
composition(join(one,one),complement(X_107)) = composition(one,complement(X_107)),
inference(subst,[],[refute_0_671:[bind(X_46,$fot(one)),bind(X_84,$fot(X_107))]]) ).
cnf(refute_0_673,plain,
( composition(join(one,one),complement(X_107)) != composition(one,complement(X_107))
| composition(one,complement(X_107)) != complement(X_107)
| composition(join(one,one),complement(X_107)) = complement(X_107) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(composition(join(one,one),complement(X_107)))),bind(Y,$fot(composition(one,complement(X_107)))),bind(Z,$fot(complement(X_107)))]]) ).
cnf(refute_0_674,plain,
( composition(one,complement(X_107)) != complement(X_107)
| composition(join(one,one),complement(X_107)) = complement(X_107) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_107)),composition(one,complement(X_107))) )],[refute_0_672,refute_0_673]) ).
cnf(refute_0_675,plain,
composition(join(one,one),complement(X_107)) = complement(X_107),
inference(resolve,[$cnf( $equal(composition(one,complement(X_107)),complement(X_107)) )],[refute_0_626,refute_0_674]) ).
cnf(refute_0_676,plain,
composition(join(A,join(one,one)),complement(X_84)) = join(composition(A,complement(X_84)),composition(join(one,one),complement(X_84))),
inference(subst,[],[composition_distributivity_7:[bind(B,$fot(join(one,one))),bind(C,$fot(complement(X_84)))]]) ).
cnf(refute_0_677,plain,
( composition(join(A,join(one,one)),complement(X_84)) != join(composition(A,complement(X_84)),composition(join(one,one),complement(X_84)))
| composition(join(one,one),complement(X_84)) != complement(X_84)
| composition(join(A,join(one,one)),complement(X_84)) = join(composition(A,complement(X_84)),complement(X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(A,join(one,one)),complement(X_84)),join(composition(A,complement(X_84)),composition(join(one,one),complement(X_84)))) ),[1,1],$fot(complement(X_84))]]) ).
cnf(refute_0_678,plain,
( composition(join(A,join(one,one)),complement(X_84)) != join(composition(A,complement(X_84)),composition(join(one,one),complement(X_84)))
| composition(join(A,join(one,one)),complement(X_84)) = join(composition(A,complement(X_84)),complement(X_84)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_84)),complement(X_84)) )],[refute_0_666,refute_0_677]) ).
cnf(refute_0_679,plain,
composition(join(A,join(one,one)),complement(X_84)) = join(composition(A,complement(X_84)),complement(X_84)),
inference(resolve,[$cnf( $equal(composition(join(A,join(one,one)),complement(X_84)),join(composition(A,complement(X_84)),composition(join(one,one),complement(X_84)))) )],[refute_0_676,refute_0_678]) ).
cnf(refute_0_680,plain,
join(complement(X_84),composition(A,complement(X_84))) = composition(join(A,one),complement(X_84)),
inference(subst,[],[refute_0_94:[bind(X_31,$fot(A)),bind(X_33,$fot(complement(X_84)))]]) ).
cnf(refute_0_681,plain,
join(composition(A,complement(X_84)),complement(X_84)) = join(complement(X_84),composition(A,complement(X_84))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_84))),bind(B,$fot(composition(A,complement(X_84))))]]) ).
cnf(refute_0_682,plain,
( join(complement(X_84),composition(A,complement(X_84))) != composition(join(A,one),complement(X_84))
| join(composition(A,complement(X_84)),complement(X_84)) != join(complement(X_84),composition(A,complement(X_84)))
| join(composition(A,complement(X_84)),complement(X_84)) = composition(join(A,one),complement(X_84)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(composition(A,complement(X_84)),complement(X_84)))),bind(Y,$fot(join(complement(X_84),composition(A,complement(X_84))))),bind(Z,$fot(composition(join(A,one),complement(X_84))))]]) ).
cnf(refute_0_683,plain,
( join(complement(X_84),composition(A,complement(X_84))) != composition(join(A,one),complement(X_84))
| join(composition(A,complement(X_84)),complement(X_84)) = composition(join(A,one),complement(X_84)) ),
inference(resolve,[$cnf( $equal(join(composition(A,complement(X_84)),complement(X_84)),join(complement(X_84),composition(A,complement(X_84)))) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
join(composition(A,complement(X_84)),complement(X_84)) = composition(join(A,one),complement(X_84)),
inference(resolve,[$cnf( $equal(join(complement(X_84),composition(A,complement(X_84))),composition(join(A,one),complement(X_84))) )],[refute_0_680,refute_0_683]) ).
cnf(refute_0_685,plain,
( composition(join(A,join(one,one)),complement(X_84)) != join(composition(A,complement(X_84)),complement(X_84))
| join(composition(A,complement(X_84)),complement(X_84)) != composition(join(A,one),complement(X_84))
| composition(join(A,join(one,one)),complement(X_84)) = composition(join(A,one),complement(X_84)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(A,join(one,one)),complement(X_84)),composition(join(A,one),complement(X_84))) ),[0],$fot(join(composition(A,complement(X_84)),complement(X_84)))]]) ).
cnf(refute_0_686,plain,
( composition(join(A,join(one,one)),complement(X_84)) != join(composition(A,complement(X_84)),complement(X_84))
| composition(join(A,join(one,one)),complement(X_84)) = composition(join(A,one),complement(X_84)) ),
inference(resolve,[$cnf( $equal(join(composition(A,complement(X_84)),complement(X_84)),composition(join(A,one),complement(X_84))) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
composition(join(A,join(one,one)),complement(X_84)) = composition(join(A,one),complement(X_84)),
inference(resolve,[$cnf( $equal(composition(join(A,join(one,one)),complement(X_84)),join(composition(A,complement(X_84)),complement(X_84))) )],[refute_0_679,refute_0_686]) ).
cnf(refute_0_688,plain,
composition(join(one,join(one,one)),complement(X_107)) = composition(join(one,one),complement(X_107)),
inference(subst,[],[refute_0_687:[bind(A,$fot(one)),bind(X_84,$fot(X_107))]]) ).
cnf(refute_0_689,plain,
( composition(join(one,join(one,one)),complement(X_107)) != composition(join(one,one),complement(X_107))
| composition(join(one,one),complement(X_107)) != complement(X_107)
| composition(join(one,join(one,one)),complement(X_107)) = complement(X_107) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(composition(join(one,join(one,one)),complement(X_107)))),bind(Y,$fot(composition(join(one,one),complement(X_107)))),bind(Z,$fot(complement(X_107)))]]) ).
cnf(refute_0_690,plain,
( composition(join(one,one),complement(X_107)) != complement(X_107)
| composition(join(one,join(one,one)),complement(X_107)) = complement(X_107) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),complement(X_107)),composition(join(one,one),complement(X_107))) )],[refute_0_688,refute_0_689]) ).
cnf(refute_0_691,plain,
composition(join(one,join(one,one)),complement(X_107)) = complement(X_107),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_107)),complement(X_107)) )],[refute_0_675,refute_0_690]) ).
cnf(refute_0_692,plain,
complement(composition(join(one,join(one,one)),complement(X_107))) = complement(composition(join(one,join(one,one)),complement(X_107))),
introduced(tautology,[refl,[$fot(complement(composition(join(one,join(one,one)),complement(X_107))))]]) ).
cnf(refute_0_693,plain,
( complement(composition(join(one,join(one,one)),complement(X_107))) != complement(composition(join(one,join(one,one)),complement(X_107)))
| composition(join(one,join(one,one)),complement(X_107)) != complement(X_107)
| complement(composition(join(one,join(one,one)),complement(X_107))) = complement(complement(X_107)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(join(one,join(one,one)),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) ),[1,0],$fot(complement(X_107))]]) ).
cnf(refute_0_694,plain,
( composition(join(one,join(one,one)),complement(X_107)) != complement(X_107)
| complement(composition(join(one,join(one,one)),complement(X_107))) = complement(complement(X_107)) ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,join(one,one)),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
complement(composition(join(one,join(one,one)),complement(X_107))) = complement(complement(X_107)),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),complement(X_107)),complement(X_107)) )],[refute_0_691,refute_0_694]) ).
cnf(refute_0_696,plain,
join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))) = join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))),
introduced(tautology,[refl,[$fot(join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))))]]) ).
cnf(refute_0_697,plain,
( complement(composition(join(one,join(one,one)),complement(X_107))) != complement(complement(X_107))
| join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))) != join(zero,complement(composition(join(one,join(one,one)),complement(X_107))))
| join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))) = join(zero,complement(complement(X_107))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))),join(zero,complement(composition(join(one,join(one,one)),complement(X_107))))) ),[1,1],$fot(complement(complement(X_107)))]]) ).
cnf(refute_0_698,plain,
( complement(composition(join(one,join(one,one)),complement(X_107))) != complement(complement(X_107))
| join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))) = join(zero,complement(complement(X_107))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))),join(zero,complement(composition(join(one,join(one,one)),complement(X_107))))) )],[refute_0_696,refute_0_697]) ).
cnf(refute_0_699,plain,
join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))) = join(zero,complement(complement(X_107))),
inference(resolve,[$cnf( $equal(complement(composition(join(one,join(one,one)),complement(X_107))),complement(complement(X_107))) )],[refute_0_695,refute_0_698]) ).
cnf(refute_0_700,plain,
meet(X_107,X_107) = complement(complement(X_107)),
inference(subst,[],[refute_0_538:[bind(B,$fot(X_107))]]) ).
cnf(refute_0_701,plain,
join(complement(X_107),meet(X_107,X_107)) = join(complement(X_107),meet(X_107,X_107)),
introduced(tautology,[refl,[$fot(join(complement(X_107),meet(X_107,X_107)))]]) ).
cnf(refute_0_702,plain,
( join(complement(X_107),meet(X_107,X_107)) != join(complement(X_107),meet(X_107,X_107))
| meet(X_107,X_107) != complement(complement(X_107))
| join(complement(X_107),meet(X_107,X_107)) = join(complement(X_107),complement(complement(X_107))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_107),meet(X_107,X_107)),join(complement(X_107),meet(X_107,X_107))) ),[1,1],$fot(complement(complement(X_107)))]]) ).
cnf(refute_0_703,plain,
( meet(X_107,X_107) != complement(complement(X_107))
| join(complement(X_107),meet(X_107,X_107)) = join(complement(X_107),complement(complement(X_107))) ),
inference(resolve,[$cnf( $equal(join(complement(X_107),meet(X_107,X_107)),join(complement(X_107),meet(X_107,X_107))) )],[refute_0_701,refute_0_702]) ).
cnf(refute_0_704,plain,
join(complement(X_107),meet(X_107,X_107)) = join(complement(X_107),complement(complement(X_107))),
inference(resolve,[$cnf( $equal(meet(X_107,X_107),complement(complement(X_107))) )],[refute_0_700,refute_0_703]) ).
cnf(refute_0_705,plain,
( join(complement(X_107),complement(complement(X_107))) != top
| join(complement(X_107),meet(X_107,X_107)) != join(complement(X_107),complement(complement(X_107)))
| join(complement(X_107),meet(X_107,X_107)) = top ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(X_107),meet(X_107,X_107)))),bind(Y,$fot(join(complement(X_107),complement(complement(X_107))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_706,plain,
( join(complement(X_107),complement(complement(X_107))) != top
| join(complement(X_107),meet(X_107,X_107)) = top ),
inference(resolve,[$cnf( $equal(join(complement(X_107),meet(X_107,X_107)),join(complement(X_107),complement(complement(X_107)))) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
join(complement(X_107),meet(X_107,X_107)) = top,
inference(resolve,[$cnf( $equal(join(complement(X_107),complement(complement(X_107))),top) )],[refute_0_593,refute_0_706]) ).
cnf(refute_0_708,plain,
complement(join(complement(X_107),meet(X_107,X_107))) = complement(join(complement(X_107),meet(X_107,X_107))),
introduced(tautology,[refl,[$fot(complement(join(complement(X_107),meet(X_107,X_107))))]]) ).
cnf(refute_0_709,plain,
( complement(join(complement(X_107),meet(X_107,X_107))) != complement(join(complement(X_107),meet(X_107,X_107)))
| join(complement(X_107),meet(X_107,X_107)) != top
| complement(join(complement(X_107),meet(X_107,X_107))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X_107),meet(X_107,X_107))),complement(join(complement(X_107),meet(X_107,X_107)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_710,plain,
( join(complement(X_107),meet(X_107,X_107)) != top
| complement(join(complement(X_107),meet(X_107,X_107))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_107),meet(X_107,X_107))),complement(join(complement(X_107),meet(X_107,X_107)))) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
complement(join(complement(X_107),meet(X_107,X_107))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(X_107),meet(X_107,X_107)),top) )],[refute_0_707,refute_0_710]) ).
cnf(refute_0_712,plain,
( complement(join(complement(X_107),meet(X_107,X_107))) != complement(top)
| complement(top) != zero
| complement(join(complement(X_107),meet(X_107,X_107))) = zero ),
inference(subst,[],[refute_0_82:[bind(X,$fot(complement(join(complement(X_107),meet(X_107,X_107))))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_713,plain,
( complement(top) != zero
| complement(join(complement(X_107),meet(X_107,X_107))) = zero ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_107),meet(X_107,X_107))),complement(top)) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
complement(join(complement(X_107),meet(X_107,X_107))) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_713]) ).
cnf(refute_0_715,plain,
meet(A,join(complement(X_10),complement(X_11))) = complement(join(complement(A),complement(join(complement(X_10),complement(X_11))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(complement(X_10),complement(X_11))))]]) ).
cnf(refute_0_716,plain,
( complement(join(complement(X_10),complement(X_11))) != meet(X_10,X_11)
| meet(A,join(complement(X_10),complement(X_11))) != complement(join(complement(A),complement(join(complement(X_10),complement(X_11)))))
| meet(A,join(complement(X_10),complement(X_11))) = complement(join(complement(A),meet(X_10,X_11))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_10),complement(X_11))),complement(join(complement(A),complement(join(complement(X_10),complement(X_11)))))) ),[1,0,1],$fot(meet(X_10,X_11))]]) ).
cnf(refute_0_717,plain,
( meet(A,join(complement(X_10),complement(X_11))) != complement(join(complement(A),complement(join(complement(X_10),complement(X_11)))))
| meet(A,join(complement(X_10),complement(X_11))) = complement(join(complement(A),meet(X_10,X_11))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_10),complement(X_11))),meet(X_10,X_11)) )],[refute_0_176,refute_0_716]) ).
cnf(refute_0_718,plain,
meet(A,join(complement(X_10),complement(X_11))) = complement(join(complement(A),meet(X_10,X_11))),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_10),complement(X_11))),complement(join(complement(A),complement(join(complement(X_10),complement(X_11)))))) )],[refute_0_715,refute_0_717]) ).
cnf(refute_0_719,plain,
meet(X_107,join(complement(X_107),complement(X_107))) = complement(join(complement(X_107),meet(X_107,X_107))),
inference(subst,[],[refute_0_718:[bind(A,$fot(X_107)),bind(X_10,$fot(X_107)),bind(X_11,$fot(X_107))]]) ).
cnf(refute_0_720,plain,
( complement(join(complement(X_107),meet(X_107,X_107))) != zero
| meet(X_107,join(complement(X_107),complement(X_107))) != complement(join(complement(X_107),meet(X_107,X_107)))
| meet(X_107,join(complement(X_107),complement(X_107))) = zero ),
inference(subst,[],[refute_0_82:[bind(X,$fot(meet(X_107,join(complement(X_107),complement(X_107))))),bind(Y,$fot(complement(join(complement(X_107),meet(X_107,X_107))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_721,plain,
( complement(join(complement(X_107),meet(X_107,X_107))) != zero
| meet(X_107,join(complement(X_107),complement(X_107))) = zero ),
inference(resolve,[$cnf( $equal(meet(X_107,join(complement(X_107),complement(X_107))),complement(join(complement(X_107),meet(X_107,X_107)))) )],[refute_0_719,refute_0_720]) ).
cnf(refute_0_722,plain,
meet(X_107,join(complement(X_107),complement(X_107))) = zero,
inference(resolve,[$cnf( $equal(complement(join(complement(X_107),meet(X_107,X_107))),zero) )],[refute_0_714,refute_0_721]) ).
cnf(refute_0_723,plain,
join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) = join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))),
introduced(tautology,[refl,[$fot(join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))))]]) ).
cnf(refute_0_724,plain,
( join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) != join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107))))
| meet(X_107,join(complement(X_107),complement(X_107))) != zero
| join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) = join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))),join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_725,plain,
( meet(X_107,join(complement(X_107),complement(X_107))) != zero
| join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) = join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))),join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107))))) )],[refute_0_723,refute_0_724]) ).
cnf(refute_0_726,plain,
join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) = join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))),
inference(resolve,[$cnf( $equal(meet(X_107,join(complement(X_107),complement(X_107))),zero) )],[refute_0_722,refute_0_725]) ).
cnf(refute_0_727,plain,
( join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) != join(zero,complement(composition(join(one,join(one,one)),complement(X_107))))
| join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))) != join(zero,complement(complement(X_107)))
| join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) = join(zero,complement(complement(X_107))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))))),bind(Y,$fot(join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))))),bind(Z,$fot(join(zero,complement(complement(X_107)))))]]) ).
cnf(refute_0_728,plain,
( join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))) != join(zero,complement(complement(X_107)))
| join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) = join(zero,complement(complement(X_107))) ),
inference(resolve,[$cnf( $equal(join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))),join(zero,complement(composition(join(one,join(one,one)),complement(X_107))))) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) = join(zero,complement(complement(X_107))),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(join(one,join(one,one)),complement(X_107)))),join(zero,complement(complement(X_107)))) )],[refute_0_699,refute_0_728]) ).
cnf(refute_0_730,plain,
( X_107 != join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107))))
| join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))) != join(zero,complement(complement(X_107)))
| X_107 = join(zero,complement(complement(X_107))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,join(zero,complement(complement(X_107)))) ),[0],$fot(join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))))]]) ).
cnf(refute_0_731,plain,
( X_107 != join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107))))
| X_107 = join(zero,complement(complement(X_107))) ),
inference(resolve,[$cnf( $equal(join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107)))),join(zero,complement(complement(X_107)))) )],[refute_0_729,refute_0_730]) ).
cnf(refute_0_732,plain,
X_107 = join(zero,complement(complement(X_107))),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,join(complement(X_107),complement(X_107))),complement(composition(join(one,join(one,one)),complement(X_107))))) )],[refute_0_623,refute_0_731]) ).
cnf(refute_0_733,plain,
join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_108),complement(join(complement(join(zero,complement(B))),X_108))),
inference(subst,[],[refute_0_146:[bind(A,$fot(join(zero,complement(B)))),bind(B,$fot(X_108))]]) ).
cnf(refute_0_734,plain,
( complement(join(zero,complement(B))) != meet(top,B)
| join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_108),complement(join(complement(join(zero,complement(B))),X_108)))
| join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_108),complement(join(meet(top,B),X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_108),complement(join(complement(join(zero,complement(B))),X_108)))) ),[1,1,0,0],$fot(meet(top,B))]]) ).
cnf(refute_0_735,plain,
( join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_108),complement(join(complement(join(zero,complement(B))),X_108)))
| join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_108),complement(join(meet(top,B),X_108))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),meet(top,B)) )],[refute_0_239,refute_0_734]) ).
cnf(refute_0_736,plain,
join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_108),complement(join(meet(top,B),X_108))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_108),complement(join(complement(join(zero,complement(B))),X_108)))) )],[refute_0_733,refute_0_735]) ).
cnf(refute_0_737,plain,
join(meet(join(zero,complement(B)),X_108),complement(join(meet(top,B),X_108))) = join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(meet(top,B),X_108)))),bind(B,$fot(meet(join(zero,complement(B)),X_108)))]]) ).
cnf(refute_0_738,plain,
( join(meet(join(zero,complement(B)),X_108),complement(join(meet(top,B),X_108))) != join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108))
| join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_108),complement(join(meet(top,B),X_108)))
| join(zero,complement(B)) = join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_108),complement(join(meet(top,B),X_108)))) ),[1],$fot(join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)))]]) ).
cnf(refute_0_739,plain,
( join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_108),complement(join(meet(top,B),X_108)))
| join(zero,complement(B)) = join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) ),
inference(resolve,[$cnf( $equal(join(meet(join(zero,complement(B)),X_108),complement(join(meet(top,B),X_108))),join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108))) )],[refute_0_737,refute_0_738]) ).
cnf(refute_0_740,plain,
join(zero,complement(B)) = join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_108),complement(join(meet(top,B),X_108)))) )],[refute_0_736,refute_0_739]) ).
cnf(refute_0_741,plain,
( A != join(meet(A,B),complement(join(complement(A),B)))
| join(meet(A,B),complement(join(complement(A),B))) = A ),
inference(subst,[],[refute_0_2:[bind(X,$fot(A)),bind(Y,$fot(join(meet(A,B),complement(join(complement(A),B)))))]]) ).
cnf(refute_0_742,plain,
join(meet(A,B),complement(join(complement(A),B))) = A,
inference(resolve,[$cnf( $equal(A,join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_146,refute_0_741]) ).
cnf(refute_0_743,plain,
join(meet(complement(B),X_108),complement(join(complement(complement(B)),X_108))) = complement(B),
inference(subst,[],[refute_0_742:[bind(A,$fot(complement(B))),bind(B,$fot(X_108))]]) ).
cnf(refute_0_744,plain,
join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)) = join(meet(complement(B),X_108),complement(join(complement(complement(B)),X_108))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(complement(B),X_108))),bind(B,$fot(complement(join(complement(complement(B)),X_108))))]]) ).
cnf(refute_0_745,plain,
( join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)) != join(meet(complement(B),X_108),complement(join(complement(complement(B)),X_108)))
| join(meet(complement(B),X_108),complement(join(complement(complement(B)),X_108))) != complement(B)
| join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)) = complement(B) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)))),bind(Y,$fot(join(meet(complement(B),X_108),complement(join(complement(complement(B)),X_108))))),bind(Z,$fot(complement(B)))]]) ).
cnf(refute_0_746,plain,
( join(meet(complement(B),X_108),complement(join(complement(complement(B)),X_108))) != complement(B)
| join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)) = complement(B) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)),join(meet(complement(B),X_108),complement(join(complement(complement(B)),X_108)))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)) = complement(B),
inference(resolve,[$cnf( $equal(join(meet(complement(B),X_108),complement(join(complement(complement(B)),X_108))),complement(B)) )],[refute_0_743,refute_0_746]) ).
cnf(refute_0_748,plain,
meet(join(zero,complement(X_13)),B) = complement(join(complement(join(zero,complement(X_13))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(zero,complement(X_13))))]]) ).
cnf(refute_0_749,plain,
meet(top,X_13) = complement(join(zero,complement(X_13))),
inference(subst,[],[refute_0_218:[bind(B,$fot(X_13))]]) ).
cnf(refute_0_750,plain,
( meet(top,X_13) != complement(join(zero,complement(X_13)))
| complement(join(zero,complement(X_13))) = meet(top,X_13) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,X_13))),bind(Y,$fot(complement(join(zero,complement(X_13)))))]]) ).
cnf(refute_0_751,plain,
complement(join(zero,complement(X_13))) = meet(top,X_13),
inference(resolve,[$cnf( $equal(meet(top,X_13),complement(join(zero,complement(X_13)))) )],[refute_0_749,refute_0_750]) ).
cnf(refute_0_752,plain,
( complement(join(zero,complement(X_13))) != meet(top,X_13)
| meet(join(zero,complement(X_13)),B) != complement(join(complement(join(zero,complement(X_13))),complement(B)))
| meet(join(zero,complement(X_13)),B) = complement(join(meet(top,X_13),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_13)),B),complement(join(complement(join(zero,complement(X_13))),complement(B)))) ),[1,0,0],$fot(meet(top,X_13))]]) ).
cnf(refute_0_753,plain,
( meet(join(zero,complement(X_13)),B) != complement(join(complement(join(zero,complement(X_13))),complement(B)))
| meet(join(zero,complement(X_13)),B) = complement(join(meet(top,X_13),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_13))),meet(top,X_13)) )],[refute_0_751,refute_0_752]) ).
cnf(refute_0_754,plain,
meet(join(zero,complement(X_13)),B) = complement(join(meet(top,X_13),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_13)),B),complement(join(complement(join(zero,complement(X_13))),complement(B)))) )],[refute_0_748,refute_0_753]) ).
cnf(refute_0_755,plain,
complement(join(complement(complement(X_13)),complement(B))) = meet(complement(X_13),B),
inference(subst,[],[refute_0_136:[bind(A,$fot(complement(X_13)))]]) ).
cnf(refute_0_756,plain,
meet(top,join(zero,complement(X_13))) = complement(join(zero,complement(join(zero,complement(X_13))))),
inference(subst,[],[refute_0_218:[bind(B,$fot(join(zero,complement(X_13))))]]) ).
cnf(refute_0_757,plain,
( complement(join(zero,complement(X_13))) != meet(top,X_13)
| meet(top,join(zero,complement(X_13))) != complement(join(zero,complement(join(zero,complement(X_13)))))
| meet(top,join(zero,complement(X_13))) = complement(join(zero,meet(top,X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,complement(X_13))),complement(join(zero,complement(join(zero,complement(X_13)))))) ),[1,0,1],$fot(meet(top,X_13))]]) ).
cnf(refute_0_758,plain,
( meet(top,join(zero,complement(X_13))) != complement(join(zero,complement(join(zero,complement(X_13)))))
| meet(top,join(zero,complement(X_13))) = complement(join(zero,meet(top,X_13))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_13))),meet(top,X_13)) )],[refute_0_751,refute_0_757]) ).
cnf(refute_0_759,plain,
meet(top,join(zero,complement(X_13))) = complement(join(zero,meet(top,X_13))),
inference(resolve,[$cnf( $equal(meet(top,join(zero,complement(X_13))),complement(join(zero,complement(join(zero,complement(X_13)))))) )],[refute_0_756,refute_0_758]) ).
cnf(refute_0_760,plain,
X_107 = join(meet(X_107,top),complement(join(complement(X_107),top))),
inference(subst,[],[refute_0_146:[bind(A,$fot(X_107)),bind(B,$fot(top))]]) ).
cnf(refute_0_761,plain,
meet(X_107,top) = meet(top,X_107),
inference(subst,[],[refute_0_251:[bind(A,$fot(X_107))]]) ).
cnf(refute_0_762,plain,
( X_107 != join(meet(X_107,top),complement(join(complement(X_107),top)))
| meet(X_107,top) != meet(top,X_107)
| X_107 = join(meet(top,X_107),complement(join(complement(X_107),top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_107,join(meet(X_107,top),complement(join(complement(X_107),top)))) ),[1,0],$fot(meet(top,X_107))]]) ).
cnf(refute_0_763,plain,
( X_107 != join(meet(X_107,top),complement(join(complement(X_107),top)))
| X_107 = join(meet(top,X_107),complement(join(complement(X_107),top))) ),
inference(resolve,[$cnf( $equal(meet(X_107,top),meet(top,X_107)) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
X_107 = join(meet(top,X_107),complement(join(complement(X_107),top))),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,top),complement(join(complement(X_107),top)))) )],[refute_0_760,refute_0_763]) ).
cnf(refute_0_765,plain,
join(meet(top,X_107),zero) = join(zero,meet(top,X_107)),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(meet(top,X_107)))]]) ).
cnf(refute_0_766,plain,
join(complement(X_107),top) = top,
inference(subst,[],[refute_0_451:[bind(X_51,$fot(complement(X_107)))]]) ).
cnf(refute_0_767,plain,
complement(join(complement(X_107),top)) = complement(join(complement(X_107),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(X_107),top)))]]) ).
cnf(refute_0_768,plain,
( complement(join(complement(X_107),top)) != complement(join(complement(X_107),top))
| join(complement(X_107),top) != top
| complement(join(complement(X_107),top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X_107),top)),complement(join(complement(X_107),top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_769,plain,
( join(complement(X_107),top) != top
| complement(join(complement(X_107),top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_107),top)),complement(join(complement(X_107),top))) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
complement(join(complement(X_107),top)) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(X_107),top),top) )],[refute_0_766,refute_0_769]) ).
cnf(refute_0_771,plain,
( complement(join(complement(X_107),top)) != complement(top)
| complement(top) != zero
| complement(join(complement(X_107),top)) = zero ),
inference(subst,[],[refute_0_82:[bind(X,$fot(complement(join(complement(X_107),top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_772,plain,
( complement(top) != zero
| complement(join(complement(X_107),top)) = zero ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_107),top)),complement(top)) )],[refute_0_770,refute_0_771]) ).
cnf(refute_0_773,plain,
complement(join(complement(X_107),top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_772]) ).
cnf(refute_0_774,plain,
join(meet(top,X_107),complement(join(complement(X_107),top))) = join(meet(top,X_107),complement(join(complement(X_107),top))),
introduced(tautology,[refl,[$fot(join(meet(top,X_107),complement(join(complement(X_107),top))))]]) ).
cnf(refute_0_775,plain,
( complement(join(complement(X_107),top)) != zero
| join(meet(top,X_107),complement(join(complement(X_107),top))) != join(meet(top,X_107),complement(join(complement(X_107),top)))
| join(meet(top,X_107),complement(join(complement(X_107),top))) = join(meet(top,X_107),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_107),complement(join(complement(X_107),top))),join(meet(top,X_107),complement(join(complement(X_107),top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_776,plain,
( complement(join(complement(X_107),top)) != zero
| join(meet(top,X_107),complement(join(complement(X_107),top))) = join(meet(top,X_107),zero) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_107),complement(join(complement(X_107),top))),join(meet(top,X_107),complement(join(complement(X_107),top)))) )],[refute_0_774,refute_0_775]) ).
cnf(refute_0_777,plain,
join(meet(top,X_107),complement(join(complement(X_107),top))) = join(meet(top,X_107),zero),
inference(resolve,[$cnf( $equal(complement(join(complement(X_107),top)),zero) )],[refute_0_773,refute_0_776]) ).
cnf(refute_0_778,plain,
( join(meet(top,X_107),complement(join(complement(X_107),top))) != join(meet(top,X_107),zero)
| join(meet(top,X_107),zero) != join(zero,meet(top,X_107))
| join(meet(top,X_107),complement(join(complement(X_107),top))) = join(zero,meet(top,X_107)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(top,X_107),complement(join(complement(X_107),top))))),bind(Y,$fot(join(meet(top,X_107),zero))),bind(Z,$fot(join(zero,meet(top,X_107))))]]) ).
cnf(refute_0_779,plain,
( join(meet(top,X_107),zero) != join(zero,meet(top,X_107))
| join(meet(top,X_107),complement(join(complement(X_107),top))) = join(zero,meet(top,X_107)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_107),complement(join(complement(X_107),top))),join(meet(top,X_107),zero)) )],[refute_0_777,refute_0_778]) ).
cnf(refute_0_780,plain,
join(meet(top,X_107),complement(join(complement(X_107),top))) = join(zero,meet(top,X_107)),
inference(resolve,[$cnf( $equal(join(meet(top,X_107),zero),join(zero,meet(top,X_107))) )],[refute_0_765,refute_0_779]) ).
cnf(refute_0_781,plain,
( X_107 != join(meet(top,X_107),complement(join(complement(X_107),top)))
| join(meet(top,X_107),complement(join(complement(X_107),top))) != join(zero,meet(top,X_107))
| X_107 = join(zero,meet(top,X_107)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,join(zero,meet(top,X_107))) ),[0],$fot(join(meet(top,X_107),complement(join(complement(X_107),top))))]]) ).
cnf(refute_0_782,plain,
( X_107 != join(meet(top,X_107),complement(join(complement(X_107),top)))
| X_107 = join(zero,meet(top,X_107)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_107),complement(join(complement(X_107),top))),join(zero,meet(top,X_107))) )],[refute_0_780,refute_0_781]) ).
cnf(refute_0_783,plain,
X_107 = join(zero,meet(top,X_107)),
inference(resolve,[$cnf( $equal(X_107,join(meet(top,X_107),complement(join(complement(X_107),top)))) )],[refute_0_764,refute_0_782]) ).
cnf(refute_0_784,plain,
( X_107 != join(zero,meet(top,X_107))
| join(zero,meet(top,X_107)) = X_107 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_107)),bind(Y,$fot(join(zero,meet(top,X_107))))]]) ).
cnf(refute_0_785,plain,
join(zero,meet(top,X_107)) = X_107,
inference(resolve,[$cnf( $equal(X_107,join(zero,meet(top,X_107))) )],[refute_0_783,refute_0_784]) ).
cnf(refute_0_786,plain,
join(zero,meet(top,X_13)) = X_13,
inference(subst,[],[refute_0_785:[bind(X_107,$fot(X_13))]]) ).
cnf(refute_0_787,plain,
complement(join(zero,meet(top,X_13))) = complement(join(zero,meet(top,X_13))),
introduced(tautology,[refl,[$fot(complement(join(zero,meet(top,X_13))))]]) ).
cnf(refute_0_788,plain,
( complement(join(zero,meet(top,X_13))) != complement(join(zero,meet(top,X_13)))
| join(zero,meet(top,X_13)) != X_13
| complement(join(zero,meet(top,X_13))) = complement(X_13) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,meet(top,X_13))),complement(join(zero,meet(top,X_13)))) ),[1,0],$fot(X_13)]]) ).
cnf(refute_0_789,plain,
( join(zero,meet(top,X_13)) != X_13
| complement(join(zero,meet(top,X_13))) = complement(X_13) ),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,X_13))),complement(join(zero,meet(top,X_13)))) )],[refute_0_787,refute_0_788]) ).
cnf(refute_0_790,plain,
complement(join(zero,meet(top,X_13))) = complement(X_13),
inference(resolve,[$cnf( $equal(join(zero,meet(top,X_13)),X_13) )],[refute_0_786,refute_0_789]) ).
cnf(refute_0_791,plain,
( complement(join(zero,meet(top,X_13))) != complement(X_13)
| meet(top,join(zero,complement(X_13))) != complement(join(zero,meet(top,X_13)))
| meet(top,join(zero,complement(X_13))) = complement(X_13) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,complement(X_13))),complement(join(zero,meet(top,X_13)))) ),[1],$fot(complement(X_13))]]) ).
cnf(refute_0_792,plain,
( meet(top,join(zero,complement(X_13))) != complement(join(zero,meet(top,X_13)))
| meet(top,join(zero,complement(X_13))) = complement(X_13) ),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,X_13))),complement(X_13)) )],[refute_0_790,refute_0_791]) ).
cnf(refute_0_793,plain,
meet(top,join(zero,complement(X_13))) = complement(X_13),
inference(resolve,[$cnf( $equal(meet(top,join(zero,complement(X_13))),complement(join(zero,meet(top,X_13)))) )],[refute_0_759,refute_0_792]) ).
cnf(refute_0_794,plain,
meet(top,join(zero,complement(complement(X_115)))) = complement(complement(X_115)),
inference(subst,[],[refute_0_793:[bind(X_13,$fot(complement(X_115)))]]) ).
cnf(refute_0_795,plain,
X_115 = join(zero,complement(complement(X_115))),
inference(subst,[],[refute_0_732:[bind(X_107,$fot(X_115))]]) ).
cnf(refute_0_796,plain,
( X_115 != join(zero,complement(complement(X_115)))
| join(zero,complement(complement(X_115))) = X_115 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_115)),bind(Y,$fot(join(zero,complement(complement(X_115)))))]]) ).
cnf(refute_0_797,plain,
join(zero,complement(complement(X_115))) = X_115,
inference(resolve,[$cnf( $equal(X_115,join(zero,complement(complement(X_115)))) )],[refute_0_795,refute_0_796]) ).
cnf(refute_0_798,plain,
( join(zero,complement(complement(X_115))) != X_115
| meet(top,join(zero,complement(complement(X_115)))) != complement(complement(X_115))
| meet(top,X_115) = complement(complement(X_115)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,complement(complement(X_115)))),complement(complement(X_115))) ),[0,1],$fot(X_115)]]) ).
cnf(refute_0_799,plain,
( meet(top,join(zero,complement(complement(X_115)))) != complement(complement(X_115))
| meet(top,X_115) = complement(complement(X_115)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_115))),X_115) )],[refute_0_797,refute_0_798]) ).
cnf(refute_0_800,plain,
meet(top,X_115) = complement(complement(X_115)),
inference(resolve,[$cnf( $equal(meet(top,join(zero,complement(complement(X_115)))),complement(complement(X_115))) )],[refute_0_794,refute_0_799]) ).
cnf(refute_0_801,plain,
meet(top,X_13) = complement(complement(X_13)),
inference(subst,[],[refute_0_800:[bind(X_115,$fot(X_13))]]) ).
cnf(refute_0_802,plain,
join(meet(top,X_13),complement(B)) = join(meet(top,X_13),complement(B)),
introduced(tautology,[refl,[$fot(join(meet(top,X_13),complement(B)))]]) ).
cnf(refute_0_803,plain,
( join(meet(top,X_13),complement(B)) != join(meet(top,X_13),complement(B))
| meet(top,X_13) != complement(complement(X_13))
| join(meet(top,X_13),complement(B)) = join(complement(complement(X_13)),complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_13),complement(B)),join(meet(top,X_13),complement(B))) ),[1,0],$fot(complement(complement(X_13)))]]) ).
cnf(refute_0_804,plain,
( meet(top,X_13) != complement(complement(X_13))
| join(meet(top,X_13),complement(B)) = join(complement(complement(X_13)),complement(B)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_13),complement(B)),join(meet(top,X_13),complement(B))) )],[refute_0_802,refute_0_803]) ).
cnf(refute_0_805,plain,
join(meet(top,X_13),complement(B)) = join(complement(complement(X_13)),complement(B)),
inference(resolve,[$cnf( $equal(meet(top,X_13),complement(complement(X_13))) )],[refute_0_801,refute_0_804]) ).
cnf(refute_0_806,plain,
complement(join(meet(top,X_13),complement(B))) = complement(join(meet(top,X_13),complement(B))),
introduced(tautology,[refl,[$fot(complement(join(meet(top,X_13),complement(B))))]]) ).
cnf(refute_0_807,plain,
( complement(join(meet(top,X_13),complement(B))) != complement(join(meet(top,X_13),complement(B)))
| join(meet(top,X_13),complement(B)) != join(complement(complement(X_13)),complement(B))
| complement(join(meet(top,X_13),complement(B))) = complement(join(complement(complement(X_13)),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(top,X_13),complement(B))),complement(join(meet(top,X_13),complement(B)))) ),[1,0],$fot(join(complement(complement(X_13)),complement(B)))]]) ).
cnf(refute_0_808,plain,
( join(meet(top,X_13),complement(B)) != join(complement(complement(X_13)),complement(B))
| complement(join(meet(top,X_13),complement(B))) = complement(join(complement(complement(X_13)),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,X_13),complement(B))),complement(join(meet(top,X_13),complement(B)))) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
complement(join(meet(top,X_13),complement(B))) = complement(join(complement(complement(X_13)),complement(B))),
inference(resolve,[$cnf( $equal(join(meet(top,X_13),complement(B)),join(complement(complement(X_13)),complement(B))) )],[refute_0_805,refute_0_808]) ).
cnf(refute_0_810,plain,
( complement(join(complement(complement(X_13)),complement(B))) != meet(complement(X_13),B)
| complement(join(meet(top,X_13),complement(B))) != complement(join(complement(complement(X_13)),complement(B)))
| complement(join(meet(top,X_13),complement(B))) = meet(complement(X_13),B) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(complement(join(meet(top,X_13),complement(B))))),bind(Y,$fot(complement(join(complement(complement(X_13)),complement(B))))),bind(Z,$fot(meet(complement(X_13),B)))]]) ).
cnf(refute_0_811,plain,
( complement(join(complement(complement(X_13)),complement(B))) != meet(complement(X_13),B)
| complement(join(meet(top,X_13),complement(B))) = meet(complement(X_13),B) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,X_13),complement(B))),complement(join(complement(complement(X_13)),complement(B)))) )],[refute_0_809,refute_0_810]) ).
cnf(refute_0_812,plain,
complement(join(meet(top,X_13),complement(B))) = meet(complement(X_13),B),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_13)),complement(B))),meet(complement(X_13),B)) )],[refute_0_755,refute_0_811]) ).
cnf(refute_0_813,plain,
( complement(join(meet(top,X_13),complement(B))) != meet(complement(X_13),B)
| meet(join(zero,complement(X_13)),B) != complement(join(meet(top,X_13),complement(B)))
| meet(join(zero,complement(X_13)),B) = meet(complement(X_13),B) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_13)),B),complement(join(meet(top,X_13),complement(B)))) ),[1],$fot(meet(complement(X_13),B))]]) ).
cnf(refute_0_814,plain,
( meet(join(zero,complement(X_13)),B) != complement(join(meet(top,X_13),complement(B)))
| meet(join(zero,complement(X_13)),B) = meet(complement(X_13),B) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,X_13),complement(B))),meet(complement(X_13),B)) )],[refute_0_812,refute_0_813]) ).
cnf(refute_0_815,plain,
meet(join(zero,complement(X_13)),B) = meet(complement(X_13),B),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_13)),B),complement(join(meet(top,X_13),complement(B)))) )],[refute_0_754,refute_0_814]) ).
cnf(refute_0_816,plain,
meet(join(zero,complement(B)),X_108) = meet(complement(B),X_108),
inference(subst,[],[refute_0_815:[bind(B,$fot(X_108)),bind(X_13,$fot(B))]]) ).
cnf(refute_0_817,plain,
join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)) = join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)),
introduced(tautology,[refl,[$fot(join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)))]]) ).
cnf(refute_0_818,plain,
( join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)) != join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108))
| meet(join(zero,complement(B)),X_108) != meet(complement(B),X_108)
| join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)) = join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)),join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108))) ),[1,1],$fot(meet(complement(B),X_108))]]) ).
cnf(refute_0_819,plain,
( meet(join(zero,complement(B)),X_108) != meet(complement(B),X_108)
| join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)) = join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)),join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108))) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)) = join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(B)),X_108),meet(complement(B),X_108)) )],[refute_0_816,refute_0_819]) ).
cnf(refute_0_821,plain,
meet(top,B) = complement(complement(B)),
inference(subst,[],[refute_0_800:[bind(X_115,$fot(B))]]) ).
cnf(refute_0_822,plain,
join(meet(top,B),X_108) = join(meet(top,B),X_108),
introduced(tautology,[refl,[$fot(join(meet(top,B),X_108))]]) ).
cnf(refute_0_823,plain,
( join(meet(top,B),X_108) != join(meet(top,B),X_108)
| meet(top,B) != complement(complement(B))
| join(meet(top,B),X_108) = join(complement(complement(B)),X_108) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,B),X_108),join(meet(top,B),X_108)) ),[1,0],$fot(complement(complement(B)))]]) ).
cnf(refute_0_824,plain,
( meet(top,B) != complement(complement(B))
| join(meet(top,B),X_108) = join(complement(complement(B)),X_108) ),
inference(resolve,[$cnf( $equal(join(meet(top,B),X_108),join(meet(top,B),X_108)) )],[refute_0_822,refute_0_823]) ).
cnf(refute_0_825,plain,
join(meet(top,B),X_108) = join(complement(complement(B)),X_108),
inference(resolve,[$cnf( $equal(meet(top,B),complement(complement(B))) )],[refute_0_821,refute_0_824]) ).
cnf(refute_0_826,plain,
complement(join(meet(top,B),X_108)) = complement(join(meet(top,B),X_108)),
introduced(tautology,[refl,[$fot(complement(join(meet(top,B),X_108)))]]) ).
cnf(refute_0_827,plain,
( complement(join(meet(top,B),X_108)) != complement(join(meet(top,B),X_108))
| join(meet(top,B),X_108) != join(complement(complement(B)),X_108)
| complement(join(meet(top,B),X_108)) = complement(join(complement(complement(B)),X_108)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(top,B),X_108)),complement(join(meet(top,B),X_108))) ),[1,0],$fot(join(complement(complement(B)),X_108))]]) ).
cnf(refute_0_828,plain,
( join(meet(top,B),X_108) != join(complement(complement(B)),X_108)
| complement(join(meet(top,B),X_108)) = complement(join(complement(complement(B)),X_108)) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,B),X_108)),complement(join(meet(top,B),X_108))) )],[refute_0_826,refute_0_827]) ).
cnf(refute_0_829,plain,
complement(join(meet(top,B),X_108)) = complement(join(complement(complement(B)),X_108)),
inference(resolve,[$cnf( $equal(join(meet(top,B),X_108),join(complement(complement(B)),X_108)) )],[refute_0_825,refute_0_828]) ).
cnf(refute_0_830,plain,
join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) = join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)),
introduced(tautology,[refl,[$fot(join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)))]]) ).
cnf(refute_0_831,plain,
( complement(join(meet(top,B),X_108)) != complement(join(complement(complement(B)),X_108))
| join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) != join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108))
| join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) = join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)),join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108))) ),[1,0],$fot(complement(join(complement(complement(B)),X_108)))]]) ).
cnf(refute_0_832,plain,
( complement(join(meet(top,B),X_108)) != complement(join(complement(complement(B)),X_108))
| join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) = join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)),join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108))) )],[refute_0_830,refute_0_831]) ).
cnf(refute_0_833,plain,
join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) = join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)),
inference(resolve,[$cnf( $equal(complement(join(meet(top,B),X_108)),complement(join(complement(complement(B)),X_108))) )],[refute_0_829,refute_0_832]) ).
cnf(refute_0_834,plain,
( join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)) != join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108))
| join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) != join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108))
| join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) = join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)))),bind(Y,$fot(join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)))),bind(Z,$fot(join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108))))]]) ).
cnf(refute_0_835,plain,
( join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)) != join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108))
| join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) = join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)),join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108))) )],[refute_0_833,refute_0_834]) ).
cnf(refute_0_836,plain,
join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) = join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)),
inference(resolve,[$cnf( $equal(join(complement(join(complement(complement(B)),X_108)),meet(join(zero,complement(B)),X_108)),join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108))) )],[refute_0_820,refute_0_835]) ).
cnf(refute_0_837,plain,
( join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)) != complement(B)
| join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) != join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108))
| join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) = complement(B) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)))),bind(Y,$fot(join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)))),bind(Z,$fot(complement(B)))]]) ).
cnf(refute_0_838,plain,
( join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)) != complement(B)
| join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) = complement(B) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)),join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108))) )],[refute_0_836,refute_0_837]) ).
cnf(refute_0_839,plain,
join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) = complement(B),
inference(resolve,[$cnf( $equal(join(complement(join(complement(complement(B)),X_108)),meet(complement(B),X_108)),complement(B)) )],[refute_0_747,refute_0_838]) ).
cnf(refute_0_840,plain,
( join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)) != complement(B)
| join(zero,complement(B)) != join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108))
| join(zero,complement(B)) = complement(B) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108))) ),[1],$fot(complement(B))]]) ).
cnf(refute_0_841,plain,
( join(zero,complement(B)) != join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108))
| join(zero,complement(B)) = complement(B) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108)),complement(B)) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
join(zero,complement(B)) = complement(B),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(complement(join(meet(top,B),X_108)),meet(join(zero,complement(B)),X_108))) )],[refute_0_740,refute_0_841]) ).
cnf(refute_0_843,plain,
join(zero,complement(complement(X_107))) = complement(complement(X_107)),
inference(subst,[],[refute_0_842:[bind(B,$fot(complement(X_107)))]]) ).
cnf(refute_0_844,plain,
( X_107 != join(zero,complement(complement(X_107)))
| join(zero,complement(complement(X_107))) != complement(complement(X_107))
| X_107 = complement(complement(X_107)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,complement(complement(X_107))) ),[0],$fot(join(zero,complement(complement(X_107))))]]) ).
cnf(refute_0_845,plain,
( X_107 != join(zero,complement(complement(X_107)))
| X_107 = complement(complement(X_107)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_107))),complement(complement(X_107))) )],[refute_0_843,refute_0_844]) ).
cnf(refute_0_846,plain,
X_107 = complement(complement(X_107)),
inference(resolve,[$cnf( $equal(X_107,join(zero,complement(complement(X_107)))) )],[refute_0_732,refute_0_845]) ).
cnf(refute_0_847,plain,
( X_107 != complement(complement(X_107))
| complement(complement(X_107)) = X_107 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_107)),bind(Y,$fot(complement(complement(X_107))))]]) ).
cnf(refute_0_848,plain,
complement(complement(X_107)) = X_107,
inference(resolve,[$cnf( $equal(X_107,complement(complement(X_107))) )],[refute_0_846,refute_0_847]) ).
cnf(refute_0_849,plain,
complement(complement(B)) = B,
inference(subst,[],[refute_0_848:[bind(X_107,$fot(B))]]) ).
cnf(refute_0_850,plain,
( complement(complement(B)) != B
| complement(complement(B)) != meet(B,B)
| B = meet(B,B) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(B)),meet(B,B)) ),[0],$fot(B)]]) ).
cnf(refute_0_851,plain,
( complement(complement(B)) != meet(B,B)
| B = meet(B,B) ),
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_849,refute_0_850]) ).
cnf(refute_0_852,plain,
B = meet(B,B),
inference(resolve,[$cnf( $equal(complement(complement(B)),meet(B,B)) )],[refute_0_536,refute_0_851]) ).
cnf(refute_0_853,plain,
( B != meet(B,B)
| meet(B,B) = B ),
inference(subst,[],[refute_0_2:[bind(X,$fot(B)),bind(Y,$fot(meet(B,B)))]]) ).
cnf(refute_0_854,plain,
meet(B,B) = B,
inference(resolve,[$cnf( $equal(B,meet(B,B)) )],[refute_0_852,refute_0_853]) ).
cnf(refute_0_855,plain,
meet(X_107,X_107) = X_107,
inference(subst,[],[refute_0_854:[bind(B,$fot(X_107))]]) ).
cnf(refute_0_856,plain,
meet(X_107,complement(complement(X_107))) = meet(X_107,complement(complement(X_107))),
introduced(tautology,[refl,[$fot(meet(X_107,complement(complement(X_107))))]]) ).
cnf(refute_0_857,plain,
( complement(complement(X_107)) != X_107
| meet(X_107,complement(complement(X_107))) != meet(X_107,complement(complement(X_107)))
| meet(X_107,complement(complement(X_107))) = meet(X_107,X_107) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_107,complement(complement(X_107))),meet(X_107,complement(complement(X_107)))) ),[1,1],$fot(X_107)]]) ).
cnf(refute_0_858,plain,
( complement(complement(X_107)) != X_107
| meet(X_107,complement(complement(X_107))) = meet(X_107,X_107) ),
inference(resolve,[$cnf( $equal(meet(X_107,complement(complement(X_107))),meet(X_107,complement(complement(X_107)))) )],[refute_0_856,refute_0_857]) ).
cnf(refute_0_859,plain,
meet(X_107,complement(complement(X_107))) = meet(X_107,X_107),
inference(resolve,[$cnf( $equal(complement(complement(X_107)),X_107) )],[refute_0_848,refute_0_858]) ).
cnf(refute_0_860,plain,
( meet(X_107,X_107) != X_107
| meet(X_107,complement(complement(X_107))) != meet(X_107,X_107)
| meet(X_107,complement(complement(X_107))) = X_107 ),
inference(subst,[],[refute_0_82:[bind(X,$fot(meet(X_107,complement(complement(X_107))))),bind(Y,$fot(meet(X_107,X_107))),bind(Z,$fot(X_107))]]) ).
cnf(refute_0_861,plain,
( meet(X_107,X_107) != X_107
| meet(X_107,complement(complement(X_107))) = X_107 ),
inference(resolve,[$cnf( $equal(meet(X_107,complement(complement(X_107))),meet(X_107,X_107)) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
meet(X_107,complement(complement(X_107))) = X_107,
inference(resolve,[$cnf( $equal(meet(X_107,X_107),X_107) )],[refute_0_855,refute_0_861]) ).
cnf(refute_0_863,plain,
join(zero,meet(X_107,complement(complement(X_107)))) = join(zero,meet(X_107,complement(complement(X_107)))),
introduced(tautology,[refl,[$fot(join(zero,meet(X_107,complement(complement(X_107)))))]]) ).
cnf(refute_0_864,plain,
( join(zero,meet(X_107,complement(complement(X_107)))) != join(zero,meet(X_107,complement(complement(X_107))))
| meet(X_107,complement(complement(X_107))) != X_107
| join(zero,meet(X_107,complement(complement(X_107)))) = join(zero,X_107) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_107,complement(complement(X_107)))),join(zero,meet(X_107,complement(complement(X_107))))) ),[1,1],$fot(X_107)]]) ).
cnf(refute_0_865,plain,
( meet(X_107,complement(complement(X_107))) != X_107
| join(zero,meet(X_107,complement(complement(X_107)))) = join(zero,X_107) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_107,complement(complement(X_107)))),join(zero,meet(X_107,complement(complement(X_107))))) )],[refute_0_863,refute_0_864]) ).
cnf(refute_0_866,plain,
join(zero,meet(X_107,complement(complement(X_107)))) = join(zero,X_107),
inference(resolve,[$cnf( $equal(meet(X_107,complement(complement(X_107))),X_107) )],[refute_0_862,refute_0_865]) ).
cnf(refute_0_867,plain,
( X_107 != join(zero,meet(X_107,complement(complement(X_107))))
| join(zero,meet(X_107,complement(complement(X_107)))) != join(zero,X_107)
| X_107 = join(zero,X_107) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,join(zero,X_107)) ),[0],$fot(join(zero,meet(X_107,complement(complement(X_107)))))]]) ).
cnf(refute_0_868,plain,
( X_107 != join(zero,meet(X_107,complement(complement(X_107))))
| X_107 = join(zero,X_107) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_107,complement(complement(X_107)))),join(zero,X_107)) )],[refute_0_866,refute_0_867]) ).
cnf(refute_0_869,plain,
X_107 = join(zero,X_107),
inference(resolve,[$cnf( $equal(X_107,join(zero,meet(X_107,complement(complement(X_107))))) )],[refute_0_607,refute_0_868]) ).
cnf(refute_0_870,plain,
( X_107 != join(zero,X_107)
| join(zero,X_107) = X_107 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_107)),bind(Y,$fot(join(zero,X_107)))]]) ).
cnf(refute_0_871,plain,
join(zero,X_107) = X_107,
inference(resolve,[$cnf( $equal(X_107,join(zero,X_107)) )],[refute_0_869,refute_0_870]) ).
cnf(refute_0_872,plain,
join(zero,meet(X_107,join(X_107,X_148))) = meet(X_107,join(X_107,X_148)),
inference(subst,[],[refute_0_871:[bind(X_107,$fot(meet(X_107,join(X_107,X_148))))]]) ).
cnf(refute_0_873,plain,
join(complement(complement(X_107)),X_148) = join(complement(complement(X_107)),X_148),
introduced(tautology,[refl,[$fot(join(complement(complement(X_107)),X_148))]]) ).
cnf(refute_0_874,plain,
( complement(complement(X_107)) != X_107
| join(complement(complement(X_107)),X_148) != join(complement(complement(X_107)),X_148)
| join(complement(complement(X_107)),X_148) = join(X_107,X_148) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_107)),X_148),join(complement(complement(X_107)),X_148)) ),[1,0],$fot(X_107)]]) ).
cnf(refute_0_875,plain,
( complement(complement(X_107)) != X_107
| join(complement(complement(X_107)),X_148) = join(X_107,X_148) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_107)),X_148),join(complement(complement(X_107)),X_148)) )],[refute_0_873,refute_0_874]) ).
cnf(refute_0_876,plain,
join(complement(complement(X_107)),X_148) = join(X_107,X_148),
inference(resolve,[$cnf( $equal(complement(complement(X_107)),X_107) )],[refute_0_848,refute_0_875]) ).
cnf(refute_0_877,plain,
meet(X_107,join(complement(complement(X_107)),X_148)) = meet(X_107,join(complement(complement(X_107)),X_148)),
introduced(tautology,[refl,[$fot(meet(X_107,join(complement(complement(X_107)),X_148)))]]) ).
cnf(refute_0_878,plain,
( join(complement(complement(X_107)),X_148) != join(X_107,X_148)
| meet(X_107,join(complement(complement(X_107)),X_148)) != meet(X_107,join(complement(complement(X_107)),X_148))
| meet(X_107,join(complement(complement(X_107)),X_148)) = meet(X_107,join(X_107,X_148)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_107,join(complement(complement(X_107)),X_148)),meet(X_107,join(complement(complement(X_107)),X_148))) ),[1,1],$fot(join(X_107,X_148))]]) ).
cnf(refute_0_879,plain,
( join(complement(complement(X_107)),X_148) != join(X_107,X_148)
| meet(X_107,join(complement(complement(X_107)),X_148)) = meet(X_107,join(X_107,X_148)) ),
inference(resolve,[$cnf( $equal(meet(X_107,join(complement(complement(X_107)),X_148)),meet(X_107,join(complement(complement(X_107)),X_148))) )],[refute_0_877,refute_0_878]) ).
cnf(refute_0_880,plain,
meet(X_107,join(complement(complement(X_107)),X_148)) = meet(X_107,join(X_107,X_148)),
inference(resolve,[$cnf( $equal(join(complement(complement(X_107)),X_148),join(X_107,X_148)) )],[refute_0_876,refute_0_879]) ).
cnf(refute_0_881,plain,
( meet(X_10,X_11) != meet(X_11,X_10)
| meet(X_11,X_10) = meet(X_10,X_11) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_10,X_11))),bind(Y,$fot(meet(X_11,X_10)))]]) ).
cnf(refute_0_882,plain,
meet(X_11,X_10) = meet(X_10,X_11),
inference(resolve,[$cnf( $equal(meet(X_10,X_11),meet(X_11,X_10)) )],[refute_0_158,refute_0_881]) ).
cnf(refute_0_883,plain,
meet(join(complement(complement(X_107)),X_148),X_107) = meet(X_107,join(complement(complement(X_107)),X_148)),
inference(subst,[],[refute_0_882:[bind(X_10,$fot(X_107)),bind(X_11,$fot(join(complement(complement(X_107)),X_148)))]]) ).
cnf(refute_0_884,plain,
( meet(X_107,join(complement(complement(X_107)),X_148)) != meet(X_107,join(X_107,X_148))
| meet(join(complement(complement(X_107)),X_148),X_107) != meet(X_107,join(complement(complement(X_107)),X_148))
| meet(join(complement(complement(X_107)),X_148),X_107) = meet(X_107,join(X_107,X_148)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(meet(join(complement(complement(X_107)),X_148),X_107))),bind(Y,$fot(meet(X_107,join(complement(complement(X_107)),X_148)))),bind(Z,$fot(meet(X_107,join(X_107,X_148))))]]) ).
cnf(refute_0_885,plain,
( meet(X_107,join(complement(complement(X_107)),X_148)) != meet(X_107,join(X_107,X_148))
| meet(join(complement(complement(X_107)),X_148),X_107) = meet(X_107,join(X_107,X_148)) ),
inference(resolve,[$cnf( $equal(meet(join(complement(complement(X_107)),X_148),X_107),meet(X_107,join(complement(complement(X_107)),X_148))) )],[refute_0_883,refute_0_884]) ).
cnf(refute_0_886,plain,
meet(join(complement(complement(X_107)),X_148),X_107) = meet(X_107,join(X_107,X_148)),
inference(resolve,[$cnf( $equal(meet(X_107,join(complement(complement(X_107)),X_148)),meet(X_107,join(X_107,X_148))) )],[refute_0_880,refute_0_885]) ).
cnf(refute_0_887,plain,
join(zero,meet(join(complement(complement(X_107)),X_148),X_107)) = join(zero,meet(join(complement(complement(X_107)),X_148),X_107)),
introduced(tautology,[refl,[$fot(join(zero,meet(join(complement(complement(X_107)),X_148),X_107)))]]) ).
cnf(refute_0_888,plain,
( join(zero,meet(join(complement(complement(X_107)),X_148),X_107)) != join(zero,meet(join(complement(complement(X_107)),X_148),X_107))
| meet(join(complement(complement(X_107)),X_148),X_107) != meet(X_107,join(X_107,X_148))
| join(zero,meet(join(complement(complement(X_107)),X_148),X_107)) = join(zero,meet(X_107,join(X_107,X_148))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(complement(complement(X_107)),X_148),X_107)),join(zero,meet(join(complement(complement(X_107)),X_148),X_107))) ),[1,1],$fot(meet(X_107,join(X_107,X_148)))]]) ).
cnf(refute_0_889,plain,
( meet(join(complement(complement(X_107)),X_148),X_107) != meet(X_107,join(X_107,X_148))
| join(zero,meet(join(complement(complement(X_107)),X_148),X_107)) = join(zero,meet(X_107,join(X_107,X_148))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(complement(X_107)),X_148),X_107)),join(zero,meet(join(complement(complement(X_107)),X_148),X_107))) )],[refute_0_887,refute_0_888]) ).
cnf(refute_0_890,plain,
join(zero,meet(join(complement(complement(X_107)),X_148),X_107)) = join(zero,meet(X_107,join(X_107,X_148))),
inference(resolve,[$cnf( $equal(meet(join(complement(complement(X_107)),X_148),X_107),meet(X_107,join(X_107,X_148))) )],[refute_0_886,refute_0_889]) ).
cnf(refute_0_891,plain,
join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) = join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)))]]) ).
cnf(refute_0_892,plain,
( complement(top) != zero
| join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) != join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107))
| join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) = join(zero,meet(join(complement(complement(X_107)),X_148),X_107)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)),join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_893,plain,
( complement(top) != zero
| join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) = join(zero,meet(join(complement(complement(X_107)),X_148),X_107)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)),join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107))) )],[refute_0_891,refute_0_892]) ).
cnf(refute_0_894,plain,
join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) = join(zero,meet(join(complement(complement(X_107)),X_148),X_107)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_893]) ).
cnf(refute_0_895,plain,
( join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) != join(zero,meet(join(complement(complement(X_107)),X_148),X_107))
| join(zero,meet(join(complement(complement(X_107)),X_148),X_107)) != join(zero,meet(X_107,join(X_107,X_148)))
| join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) = join(zero,meet(X_107,join(X_107,X_148))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)))),bind(Y,$fot(join(zero,meet(join(complement(complement(X_107)),X_148),X_107)))),bind(Z,$fot(join(zero,meet(X_107,join(X_107,X_148)))))]]) ).
cnf(refute_0_896,plain,
( join(zero,meet(join(complement(complement(X_107)),X_148),X_107)) != join(zero,meet(X_107,join(X_107,X_148)))
| join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) = join(zero,meet(X_107,join(X_107,X_148))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)),join(zero,meet(join(complement(complement(X_107)),X_148),X_107))) )],[refute_0_894,refute_0_895]) ).
cnf(refute_0_897,plain,
join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) = join(zero,meet(X_107,join(X_107,X_148))),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(complement(X_107)),X_148),X_107)),join(zero,meet(X_107,join(X_107,X_148)))) )],[refute_0_890,refute_0_896]) ).
cnf(refute_0_898,plain,
( join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) != join(zero,meet(X_107,join(X_107,X_148)))
| join(zero,meet(X_107,join(X_107,X_148))) != meet(X_107,join(X_107,X_148))
| join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) = meet(X_107,join(X_107,X_148)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)))),bind(Y,$fot(join(zero,meet(X_107,join(X_107,X_148))))),bind(Z,$fot(meet(X_107,join(X_107,X_148))))]]) ).
cnf(refute_0_899,plain,
( join(zero,meet(X_107,join(X_107,X_148))) != meet(X_107,join(X_107,X_148))
| join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) = meet(X_107,join(X_107,X_148)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)),join(zero,meet(X_107,join(X_107,X_148)))) )],[refute_0_897,refute_0_898]) ).
cnf(refute_0_900,plain,
join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) = meet(X_107,join(X_107,X_148)),
inference(resolve,[$cnf( $equal(join(zero,meet(X_107,join(X_107,X_148))),meet(X_107,join(X_107,X_148))) )],[refute_0_872,refute_0_899]) ).
cnf(refute_0_901,plain,
join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)) = join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(join(complement(complement(X_107)),X_148),X_107)))]]) ).
cnf(refute_0_902,plain,
( join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) != meet(X_107,join(X_107,X_148))
| join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)) != join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107))
| join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)) = meet(X_107,join(X_107,X_148)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)))),bind(Y,$fot(join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)))),bind(Z,$fot(meet(X_107,join(X_107,X_148))))]]) ).
cnf(refute_0_903,plain,
( join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)) != meet(X_107,join(X_107,X_148))
| join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)) = meet(X_107,join(X_107,X_148)) ),
inference(resolve,[$cnf( $equal(join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)),join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107))) )],[refute_0_901,refute_0_902]) ).
cnf(refute_0_904,plain,
join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)) = meet(X_107,join(X_107,X_148)),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_107)),X_148),X_107)),meet(X_107,join(X_107,X_148))) )],[refute_0_900,refute_0_903]) ).
cnf(refute_0_905,plain,
( X_107 != join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top))
| join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)) != meet(X_107,join(X_107,X_148))
| X_107 = meet(X_107,join(X_107,X_148)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,meet(X_107,join(X_107,X_148))) ),[0],$fot(join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)))]]) ).
cnf(refute_0_906,plain,
( X_107 != join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top))
| X_107 = meet(X_107,join(X_107,X_148)) ),
inference(resolve,[$cnf( $equal(join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top)),meet(X_107,join(X_107,X_148))) )],[refute_0_904,refute_0_905]) ).
cnf(refute_0_907,plain,
X_107 = meet(X_107,join(X_107,X_148)),
inference(resolve,[$cnf( $equal(X_107,join(meet(join(complement(complement(X_107)),X_148),X_107),complement(top))) )],[refute_0_589,refute_0_906]) ).
cnf(refute_0_908,plain,
converse(A) = meet(converse(A),join(converse(A),converse(B))),
inference(subst,[],[refute_0_907:[bind(X_107,$fot(converse(A))),bind(X_148,$fot(converse(B)))]]) ).
cnf(refute_0_909,plain,
( converse(A) != meet(converse(A),join(converse(A),converse(B)))
| join(converse(A),converse(B)) != converse(join(A,B))
| converse(A) = meet(converse(A),converse(join(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(A),meet(converse(A),join(converse(A),converse(B)))) ),[1,1],$fot(converse(join(A,B)))]]) ).
cnf(refute_0_910,plain,
( converse(A) != meet(converse(A),join(converse(A),converse(B)))
| converse(A) = meet(converse(A),converse(join(A,B))) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(B)),converse(join(A,B))) )],[refute_0_108,refute_0_909]) ).
cnf(refute_0_911,plain,
converse(A) = meet(converse(A),converse(join(A,B))),
inference(resolve,[$cnf( $equal(converse(A),meet(converse(A),join(converse(A),converse(B)))) )],[refute_0_908,refute_0_910]) ).
cnf(refute_0_912,plain,
converse(A) = meet(converse(A),converse(join(A,complement(join(A,complement(converse(complement(converse(complement(A)))))))))),
inference(subst,[],[refute_0_911:[bind(B,$fot(complement(join(A,complement(converse(complement(converse(complement(A)))))))))]]) ).
cnf(refute_0_913,plain,
converse(complement(converse(complement(X_133)))) = join(meet(X_133,converse(complement(converse(complement(X_133))))),complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))),
inference(subst,[],[refute_0_164:[bind(X_107,$fot(converse(complement(converse(complement(X_133)))))),bind(X_108,$fot(X_133))]]) ).
cnf(refute_0_914,plain,
X_107 = join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(join(complement(X_107),converse(complement(converse(complement(X_107))))))),
inference(subst,[],[refute_0_146:[bind(A,$fot(X_107)),bind(B,$fot(converse(complement(converse(complement(X_107))))))]]) ).
cnf(refute_0_915,plain,
converse(join(converse(A),X_5)) = join(converse(converse(A)),converse(X_5)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(A))),bind(B,$fot(X_5))]]) ).
cnf(refute_0_916,plain,
( converse(converse(A)) != A
| converse(join(converse(A),X_5)) != join(converse(converse(A)),converse(X_5))
| converse(join(converse(A),X_5)) = join(A,converse(X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),X_5)),join(converse(converse(A)),converse(X_5))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_917,plain,
( converse(join(converse(A),X_5)) != join(converse(converse(A)),converse(X_5))
| converse(join(converse(A),X_5)) = join(A,converse(X_5)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_916]) ).
cnf(refute_0_918,plain,
converse(join(converse(A),X_5)) = join(A,converse(X_5)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_5)),join(converse(converse(A)),converse(X_5))) )],[refute_0_915,refute_0_917]) ).
cnf(refute_0_919,plain,
converse(join(converse(X_66),complement(converse(X_66)))) = join(X_66,converse(complement(converse(X_66)))),
inference(subst,[],[refute_0_918:[bind(A,$fot(X_66)),bind(X_5,$fot(complement(converse(X_66))))]]) ).
cnf(refute_0_920,plain,
top = join(converse(X_66),complement(converse(X_66))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_66)))]]) ).
cnf(refute_0_921,plain,
( top != join(converse(X_66),complement(converse(X_66)))
| join(converse(X_66),complement(converse(X_66))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_66),complement(converse(X_66)))))]]) ).
cnf(refute_0_922,plain,
join(converse(X_66),complement(converse(X_66))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_66),complement(converse(X_66)))) )],[refute_0_920,refute_0_921]) ).
cnf(refute_0_923,plain,
( converse(join(converse(X_66),complement(converse(X_66)))) != join(X_66,converse(complement(converse(X_66))))
| join(converse(X_66),complement(converse(X_66))) != top
| converse(top) = join(X_66,converse(complement(converse(X_66)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_66),complement(converse(X_66)))),join(X_66,converse(complement(converse(X_66))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_924,plain,
( converse(join(converse(X_66),complement(converse(X_66)))) != join(X_66,converse(complement(converse(X_66))))
| converse(top) = join(X_66,converse(complement(converse(X_66)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_66),complement(converse(X_66))),top) )],[refute_0_922,refute_0_923]) ).
cnf(refute_0_925,plain,
converse(top) = join(X_66,converse(complement(converse(X_66)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_66),complement(converse(X_66)))),join(X_66,converse(complement(converse(X_66))))) )],[refute_0_919,refute_0_924]) ).
cnf(refute_0_926,plain,
converse(join(converse(A),converse(top))) = join(A,converse(converse(top))),
inference(subst,[],[refute_0_918:[bind(X_5,$fot(converse(top)))]]) ).
cnf(refute_0_927,plain,
join(X_41,join(complement(X_41),converse(complement(converse(complement(X_41)))))) = join(top,converse(complement(converse(complement(X_41))))),
inference(subst,[],[refute_0_172:[bind(X_43,$fot(converse(complement(converse(complement(X_41))))))]]) ).
cnf(refute_0_928,plain,
converse(top) = join(complement(X_41),converse(complement(converse(complement(X_41))))),
inference(subst,[],[refute_0_925:[bind(X_66,$fot(complement(X_41)))]]) ).
cnf(refute_0_929,plain,
( converse(top) != join(complement(X_41),converse(complement(converse(complement(X_41)))))
| join(complement(X_41),converse(complement(converse(complement(X_41))))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(complement(X_41),converse(complement(converse(complement(X_41)))))))]]) ).
cnf(refute_0_930,plain,
join(complement(X_41),converse(complement(converse(complement(X_41))))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(complement(X_41),converse(complement(converse(complement(X_41)))))) )],[refute_0_928,refute_0_929]) ).
cnf(refute_0_931,plain,
( join(X_41,join(complement(X_41),converse(complement(converse(complement(X_41)))))) != join(top,converse(complement(converse(complement(X_41)))))
| join(complement(X_41),converse(complement(converse(complement(X_41))))) != converse(top)
| join(X_41,converse(top)) = join(top,converse(complement(converse(complement(X_41))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,join(complement(X_41),converse(complement(converse(complement(X_41)))))),join(top,converse(complement(converse(complement(X_41)))))) ),[0,1],$fot(converse(top))]]) ).
cnf(refute_0_932,plain,
( join(X_41,join(complement(X_41),converse(complement(converse(complement(X_41)))))) != join(top,converse(complement(converse(complement(X_41)))))
| join(X_41,converse(top)) = join(top,converse(complement(converse(complement(X_41))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_41),converse(complement(converse(complement(X_41))))),converse(top)) )],[refute_0_930,refute_0_931]) ).
cnf(refute_0_933,plain,
join(X_41,converse(top)) = join(top,converse(complement(converse(complement(X_41))))),
inference(resolve,[$cnf( $equal(join(X_41,join(complement(X_41),converse(complement(converse(complement(X_41)))))),join(top,converse(complement(converse(complement(X_41)))))) )],[refute_0_927,refute_0_932]) ).
cnf(refute_0_934,plain,
join(top,converse(complement(converse(complement(X_41))))) = top,
inference(subst,[],[refute_0_581:[bind(X_41,$fot(converse(complement(converse(complement(X_41))))))]]) ).
cnf(refute_0_935,plain,
( join(X_41,converse(top)) != join(top,converse(complement(converse(complement(X_41)))))
| join(top,converse(complement(converse(complement(X_41))))) != top
| join(X_41,converse(top)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_41,converse(top)),top) ),[0],$fot(join(top,converse(complement(converse(complement(X_41))))))]]) ).
cnf(refute_0_936,plain,
( join(X_41,converse(top)) != join(top,converse(complement(converse(complement(X_41)))))
| join(X_41,converse(top)) = top ),
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(complement(X_41))))),top) )],[refute_0_934,refute_0_935]) ).
cnf(refute_0_937,plain,
join(X_41,converse(top)) = top,
inference(resolve,[$cnf( $equal(join(X_41,converse(top)),join(top,converse(complement(converse(complement(X_41)))))) )],[refute_0_933,refute_0_936]) ).
cnf(refute_0_938,plain,
join(converse(A),converse(top)) = top,
inference(subst,[],[refute_0_937:[bind(X_41,$fot(converse(A)))]]) ).
cnf(refute_0_939,plain,
( converse(join(converse(A),converse(top))) != join(A,converse(converse(top)))
| join(converse(A),converse(top)) != top
| converse(top) = join(A,converse(converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),converse(top))),join(A,converse(converse(top)))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_940,plain,
( converse(join(converse(A),converse(top))) != join(A,converse(converse(top)))
| converse(top) = join(A,converse(converse(top))) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(top)),top) )],[refute_0_938,refute_0_939]) ).
cnf(refute_0_941,plain,
converse(top) = join(A,converse(converse(top))),
inference(resolve,[$cnf( $equal(converse(join(converse(A),converse(top))),join(A,converse(converse(top)))) )],[refute_0_926,refute_0_940]) ).
cnf(refute_0_942,plain,
join(A,top) = top,
inference(subst,[],[refute_0_451:[bind(X_51,$fot(A))]]) ).
cnf(refute_0_943,plain,
converse(converse(top)) = top,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(top))]]) ).
cnf(refute_0_944,plain,
join(A,converse(converse(top))) = join(A,converse(converse(top))),
introduced(tautology,[refl,[$fot(join(A,converse(converse(top))))]]) ).
cnf(refute_0_945,plain,
( converse(converse(top)) != top
| join(A,converse(converse(top))) != join(A,converse(converse(top)))
| join(A,converse(converse(top))) = join(A,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,converse(converse(top))),join(A,converse(converse(top)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_946,plain,
( converse(converse(top)) != top
| join(A,converse(converse(top))) = join(A,top) ),
inference(resolve,[$cnf( $equal(join(A,converse(converse(top))),join(A,converse(converse(top)))) )],[refute_0_944,refute_0_945]) ).
cnf(refute_0_947,plain,
join(A,converse(converse(top))) = join(A,top),
inference(resolve,[$cnf( $equal(converse(converse(top)),top) )],[refute_0_943,refute_0_946]) ).
cnf(refute_0_948,plain,
( join(A,converse(converse(top))) != join(A,top)
| join(A,top) != top
| join(A,converse(converse(top))) = top ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(A,converse(converse(top))))),bind(Y,$fot(join(A,top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_949,plain,
( join(A,top) != top
| join(A,converse(converse(top))) = top ),
inference(resolve,[$cnf( $equal(join(A,converse(converse(top))),join(A,top)) )],[refute_0_947,refute_0_948]) ).
cnf(refute_0_950,plain,
join(A,converse(converse(top))) = top,
inference(resolve,[$cnf( $equal(join(A,top),top) )],[refute_0_942,refute_0_949]) ).
cnf(refute_0_951,plain,
( converse(top) != join(A,converse(converse(top)))
| join(A,converse(converse(top))) != top
| converse(top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),top) ),[0],$fot(join(A,converse(converse(top))))]]) ).
cnf(refute_0_952,plain,
( converse(top) != join(A,converse(converse(top)))
| converse(top) = top ),
inference(resolve,[$cnf( $equal(join(A,converse(converse(top))),top) )],[refute_0_950,refute_0_951]) ).
cnf(refute_0_953,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(converse(top),join(A,converse(converse(top)))) )],[refute_0_941,refute_0_952]) ).
cnf(refute_0_954,plain,
( converse(top) != join(X_66,converse(complement(converse(X_66))))
| converse(top) != top
| top = join(X_66,converse(complement(converse(X_66)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_66,converse(complement(converse(X_66))))) ),[0],$fot(top)]]) ).
cnf(refute_0_955,plain,
( converse(top) != join(X_66,converse(complement(converse(X_66))))
| top = join(X_66,converse(complement(converse(X_66)))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
top = join(X_66,converse(complement(converse(X_66)))),
inference(resolve,[$cnf( $equal(converse(top),join(X_66,converse(complement(converse(X_66))))) )],[refute_0_925,refute_0_955]) ).
cnf(refute_0_957,plain,
top = join(complement(X_107),converse(complement(converse(complement(X_107))))),
inference(subst,[],[refute_0_956:[bind(X_66,$fot(complement(X_107)))]]) ).
cnf(refute_0_958,plain,
( top != join(complement(X_107),converse(complement(converse(complement(X_107)))))
| join(complement(X_107),converse(complement(converse(complement(X_107))))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_107),converse(complement(converse(complement(X_107)))))))]]) ).
cnf(refute_0_959,plain,
join(complement(X_107),converse(complement(converse(complement(X_107))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_107),converse(complement(converse(complement(X_107)))))) )],[refute_0_957,refute_0_958]) ).
cnf(refute_0_960,plain,
( X_107 != join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(join(complement(X_107),converse(complement(converse(complement(X_107)))))))
| join(complement(X_107),converse(complement(converse(complement(X_107))))) != top
| X_107 = join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_107,join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(join(complement(X_107),converse(complement(converse(complement(X_107)))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_961,plain,
( X_107 != join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(join(complement(X_107),converse(complement(converse(complement(X_107)))))))
| X_107 = join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_107),converse(complement(converse(complement(X_107))))),top) )],[refute_0_959,refute_0_960]) ).
cnf(refute_0_962,plain,
X_107 = join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(join(complement(X_107),converse(complement(converse(complement(X_107)))))))) )],[refute_0_914,refute_0_961]) ).
cnf(refute_0_963,plain,
join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))) = join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))))]]) ).
cnf(refute_0_964,plain,
( complement(top) != zero
| join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))) != join(complement(top),meet(X_107,converse(complement(converse(complement(X_107))))))
| join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))) = join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))),join(complement(top),meet(X_107,converse(complement(converse(complement(X_107))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_965,plain,
( complement(top) != zero
| join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))) = join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))),join(complement(top),meet(X_107,converse(complement(converse(complement(X_107))))))) )],[refute_0_963,refute_0_964]) ).
cnf(refute_0_966,plain,
join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))) = join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_965]) ).
cnf(refute_0_967,plain,
join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)) = join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_107,converse(complement(converse(complement(X_107)))))))]]) ).
cnf(refute_0_968,plain,
( join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))) != join(zero,meet(X_107,converse(complement(converse(complement(X_107))))))
| join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)) != join(complement(top),meet(X_107,converse(complement(converse(complement(X_107))))))
| join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)) = join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))))),bind(Z,$fot(join(zero,meet(X_107,converse(complement(converse(complement(X_107))))))))]]) ).
cnf(refute_0_969,plain,
( join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))) != join(zero,meet(X_107,converse(complement(converse(complement(X_107))))))
| join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)) = join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)),join(complement(top),meet(X_107,converse(complement(converse(complement(X_107))))))) )],[refute_0_967,refute_0_968]) ).
cnf(refute_0_970,plain,
join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)) = join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_107,converse(complement(converse(complement(X_107)))))),join(zero,meet(X_107,converse(complement(converse(complement(X_107))))))) )],[refute_0_966,refute_0_969]) ).
cnf(refute_0_971,plain,
( X_107 != join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top))
| join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)) != join(zero,meet(X_107,converse(complement(converse(complement(X_107))))))
| X_107 = join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,join(zero,meet(X_107,converse(complement(converse(complement(X_107))))))) ),[0],$fot(join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)))]]) ).
cnf(refute_0_972,plain,
( X_107 != join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top))
| X_107 = join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top)),join(zero,meet(X_107,converse(complement(converse(complement(X_107))))))) )],[refute_0_970,refute_0_971]) ).
cnf(refute_0_973,plain,
X_107 = join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,converse(complement(converse(complement(X_107))))),complement(top))) )],[refute_0_962,refute_0_972]) ).
cnf(refute_0_974,plain,
join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))) = meet(X_107,converse(complement(converse(complement(X_107))))),
inference(subst,[],[refute_0_871:[bind(X_107,$fot(meet(X_107,converse(complement(converse(complement(X_107)))))))]]) ).
cnf(refute_0_975,plain,
( X_107 != join(zero,meet(X_107,converse(complement(converse(complement(X_107))))))
| join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))) != meet(X_107,converse(complement(converse(complement(X_107)))))
| X_107 = meet(X_107,converse(complement(converse(complement(X_107))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,meet(X_107,converse(complement(converse(complement(X_107)))))) ),[0],$fot(join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))))]]) ).
cnf(refute_0_976,plain,
( X_107 != join(zero,meet(X_107,converse(complement(converse(complement(X_107))))))
| X_107 = meet(X_107,converse(complement(converse(complement(X_107))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_107,converse(complement(converse(complement(X_107)))))),meet(X_107,converse(complement(converse(complement(X_107)))))) )],[refute_0_974,refute_0_975]) ).
cnf(refute_0_977,plain,
X_107 = meet(X_107,converse(complement(converse(complement(X_107))))),
inference(resolve,[$cnf( $equal(X_107,join(zero,meet(X_107,converse(complement(converse(complement(X_107))))))) )],[refute_0_973,refute_0_976]) ).
cnf(refute_0_978,plain,
X_133 = meet(X_133,converse(complement(converse(complement(X_133))))),
inference(subst,[],[refute_0_977:[bind(X_107,$fot(X_133))]]) ).
cnf(refute_0_979,plain,
( X_133 != meet(X_133,converse(complement(converse(complement(X_133)))))
| meet(X_133,converse(complement(converse(complement(X_133))))) = X_133 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_133)),bind(Y,$fot(meet(X_133,converse(complement(converse(complement(X_133)))))))]]) ).
cnf(refute_0_980,plain,
meet(X_133,converse(complement(converse(complement(X_133))))) = X_133,
inference(resolve,[$cnf( $equal(X_133,meet(X_133,converse(complement(converse(complement(X_133)))))) )],[refute_0_978,refute_0_979]) ).
cnf(refute_0_981,plain,
( converse(complement(converse(complement(X_133)))) != join(meet(X_133,converse(complement(converse(complement(X_133))))),complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)))
| meet(X_133,converse(complement(converse(complement(X_133))))) != X_133
| converse(complement(converse(complement(X_133)))) = join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(X_133)))),join(meet(X_133,converse(complement(converse(complement(X_133))))),complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)))) ),[1,0],$fot(X_133)]]) ).
cnf(refute_0_982,plain,
( converse(complement(converse(complement(X_133)))) != join(meet(X_133,converse(complement(converse(complement(X_133))))),complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)))
| converse(complement(converse(complement(X_133)))) = join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))) ),
inference(resolve,[$cnf( $equal(meet(X_133,converse(complement(converse(complement(X_133))))),X_133) )],[refute_0_980,refute_0_981]) ).
cnf(refute_0_983,plain,
converse(complement(converse(complement(X_133)))) = join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(X_133)))),join(meet(X_133,converse(complement(converse(complement(X_133))))),complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)))) )],[refute_0_913,refute_0_982]) ).
cnf(refute_0_984,plain,
join(complement(converse(complement(converse(complement(X_133))))),X_133) = join(X_133,complement(converse(complement(converse(complement(X_133)))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_133)),bind(B,$fot(complement(converse(complement(converse(complement(X_133)))))))]]) ).
cnf(refute_0_985,plain,
complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)) = complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)),
introduced(tautology,[refl,[$fot(complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)))]]) ).
cnf(refute_0_986,plain,
( complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)) != complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))
| join(complement(converse(complement(converse(complement(X_133))))),X_133) != join(X_133,complement(converse(complement(converse(complement(X_133))))))
| complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)) = complement(join(X_133,complement(converse(complement(converse(complement(X_133))))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)),complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))) ),[1,0],$fot(join(X_133,complement(converse(complement(converse(complement(X_133)))))))]]) ).
cnf(refute_0_987,plain,
( join(complement(converse(complement(converse(complement(X_133))))),X_133) != join(X_133,complement(converse(complement(converse(complement(X_133))))))
| complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)) = complement(join(X_133,complement(converse(complement(converse(complement(X_133))))))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)),complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))) )],[refute_0_985,refute_0_986]) ).
cnf(refute_0_988,plain,
complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)) = complement(join(X_133,complement(converse(complement(converse(complement(X_133))))))),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(complement(X_133))))),X_133),join(X_133,complement(converse(complement(converse(complement(X_133))))))) )],[refute_0_984,refute_0_987]) ).
cnf(refute_0_989,plain,
join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))) = join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))),
introduced(tautology,[refl,[$fot(join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))))]]) ).
cnf(refute_0_990,plain,
( complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)) != complement(join(X_133,complement(converse(complement(converse(complement(X_133)))))))
| join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))) != join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)))
| join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))) = join(X_133,complement(join(X_133,complement(converse(complement(converse(complement(X_133)))))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))),join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)))) ),[1,1],$fot(complement(join(X_133,complement(converse(complement(converse(complement(X_133))))))))]]) ).
cnf(refute_0_991,plain,
( complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)) != complement(join(X_133,complement(converse(complement(converse(complement(X_133)))))))
| join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))) = join(X_133,complement(join(X_133,complement(converse(complement(converse(complement(X_133)))))))) ),
inference(resolve,[$cnf( $equal(join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))),join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)))) )],[refute_0_989,refute_0_990]) ).
cnf(refute_0_992,plain,
join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))) = join(X_133,complement(join(X_133,complement(converse(complement(converse(complement(X_133)))))))),
inference(resolve,[$cnf( $equal(complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)),complement(join(X_133,complement(converse(complement(converse(complement(X_133)))))))) )],[refute_0_988,refute_0_991]) ).
cnf(refute_0_993,plain,
( converse(complement(converse(complement(X_133)))) != join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)))
| join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))) != join(X_133,complement(join(X_133,complement(converse(complement(converse(complement(X_133))))))))
| converse(complement(converse(complement(X_133)))) = join(X_133,complement(join(X_133,complement(converse(complement(converse(complement(X_133)))))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(converse(complement(X_133)))),join(X_133,complement(join(X_133,complement(converse(complement(converse(complement(X_133))))))))) ),[0],$fot(join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))))]]) ).
cnf(refute_0_994,plain,
( converse(complement(converse(complement(X_133)))) != join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)))
| converse(complement(converse(complement(X_133)))) = join(X_133,complement(join(X_133,complement(converse(complement(converse(complement(X_133)))))))) ),
inference(resolve,[$cnf( $equal(join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133))),join(X_133,complement(join(X_133,complement(converse(complement(converse(complement(X_133))))))))) )],[refute_0_992,refute_0_993]) ).
cnf(refute_0_995,plain,
converse(complement(converse(complement(X_133)))) = join(X_133,complement(join(X_133,complement(converse(complement(converse(complement(X_133)))))))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(X_133)))),join(X_133,complement(join(complement(converse(complement(converse(complement(X_133))))),X_133)))) )],[refute_0_983,refute_0_994]) ).
cnf(refute_0_996,plain,
converse(complement(converse(complement(A)))) = join(A,complement(join(A,complement(converse(complement(converse(complement(A)))))))),
inference(subst,[],[refute_0_995:[bind(X_133,$fot(A))]]) ).
cnf(refute_0_997,plain,
( converse(complement(converse(complement(A)))) != join(A,complement(join(A,complement(converse(complement(converse(complement(A))))))))
| join(A,complement(join(A,complement(converse(complement(converse(complement(A)))))))) = converse(complement(converse(complement(A)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(complement(converse(complement(A)))))),bind(Y,$fot(join(A,complement(join(A,complement(converse(complement(converse(complement(A))))))))))]]) ).
cnf(refute_0_998,plain,
join(A,complement(join(A,complement(converse(complement(converse(complement(A)))))))) = converse(complement(converse(complement(A)))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(A)))),join(A,complement(join(A,complement(converse(complement(converse(complement(A))))))))) )],[refute_0_996,refute_0_997]) ).
cnf(refute_0_999,plain,
( converse(A) != meet(converse(A),converse(join(A,complement(join(A,complement(converse(complement(converse(complement(A))))))))))
| join(A,complement(join(A,complement(converse(complement(converse(complement(A)))))))) != converse(complement(converse(complement(A))))
| converse(A) = meet(converse(A),converse(converse(complement(converse(complement(A)))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(A),meet(converse(A),converse(join(A,complement(join(A,complement(converse(complement(converse(complement(A))))))))))) ),[1,1,0],$fot(converse(complement(converse(complement(A)))))]]) ).
cnf(refute_0_1000,plain,
( converse(A) != meet(converse(A),converse(join(A,complement(join(A,complement(converse(complement(converse(complement(A))))))))))
| converse(A) = meet(converse(A),converse(converse(complement(converse(complement(A)))))) ),
inference(resolve,[$cnf( $equal(join(A,complement(join(A,complement(converse(complement(converse(complement(A)))))))),converse(complement(converse(complement(A))))) )],[refute_0_998,refute_0_999]) ).
cnf(refute_0_1001,plain,
converse(A) = meet(converse(A),converse(converse(complement(converse(complement(A)))))),
inference(resolve,[$cnf( $equal(converse(A),meet(converse(A),converse(join(A,complement(join(A,complement(converse(complement(converse(complement(A))))))))))) )],[refute_0_912,refute_0_1000]) ).
cnf(refute_0_1002,plain,
converse(converse(complement(converse(complement(A))))) = complement(converse(complement(A))),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(converse(complement(A)))))]]) ).
cnf(refute_0_1003,plain,
meet(converse(A),converse(converse(complement(converse(complement(A)))))) = meet(converse(A),converse(converse(complement(converse(complement(A)))))),
introduced(tautology,[refl,[$fot(meet(converse(A),converse(converse(complement(converse(complement(A)))))))]]) ).
cnf(refute_0_1004,plain,
( converse(converse(complement(converse(complement(A))))) != complement(converse(complement(A)))
| meet(converse(A),converse(converse(complement(converse(complement(A)))))) != meet(converse(A),converse(converse(complement(converse(complement(A))))))
| meet(converse(A),converse(converse(complement(converse(complement(A)))))) = meet(converse(A),complement(converse(complement(A)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(converse(A),converse(converse(complement(converse(complement(A)))))),meet(converse(A),converse(converse(complement(converse(complement(A))))))) ),[1,1],$fot(complement(converse(complement(A))))]]) ).
cnf(refute_0_1005,plain,
( converse(converse(complement(converse(complement(A))))) != complement(converse(complement(A)))
| meet(converse(A),converse(converse(complement(converse(complement(A)))))) = meet(converse(A),complement(converse(complement(A)))) ),
inference(resolve,[$cnf( $equal(meet(converse(A),converse(converse(complement(converse(complement(A)))))),meet(converse(A),converse(converse(complement(converse(complement(A))))))) )],[refute_0_1003,refute_0_1004]) ).
cnf(refute_0_1006,plain,
meet(converse(A),converse(converse(complement(converse(complement(A)))))) = meet(converse(A),complement(converse(complement(A)))),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(complement(A))))),complement(converse(complement(A)))) )],[refute_0_1002,refute_0_1005]) ).
cnf(refute_0_1007,plain,
( converse(A) != meet(converse(A),converse(converse(complement(converse(complement(A))))))
| meet(converse(A),converse(converse(complement(converse(complement(A)))))) != meet(converse(A),complement(converse(complement(A))))
| converse(A) = meet(converse(A),complement(converse(complement(A)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(A),meet(converse(A),complement(converse(complement(A))))) ),[0],$fot(meet(converse(A),converse(converse(complement(converse(complement(A)))))))]]) ).
cnf(refute_0_1008,plain,
( converse(A) != meet(converse(A),converse(converse(complement(converse(complement(A))))))
| converse(A) = meet(converse(A),complement(converse(complement(A)))) ),
inference(resolve,[$cnf( $equal(meet(converse(A),converse(converse(complement(converse(complement(A)))))),meet(converse(A),complement(converse(complement(A))))) )],[refute_0_1006,refute_0_1007]) ).
cnf(refute_0_1009,plain,
converse(A) = meet(converse(A),complement(converse(complement(A)))),
inference(resolve,[$cnf( $equal(converse(A),meet(converse(A),converse(converse(complement(converse(complement(A))))))) )],[refute_0_1001,refute_0_1008]) ).
cnf(refute_0_1010,plain,
converse(complement(X_107)) = meet(converse(complement(X_107)),complement(converse(complement(complement(X_107))))),
inference(subst,[],[refute_0_1009:[bind(A,$fot(complement(X_107)))]]) ).
cnf(refute_0_1011,plain,
( complement(complement(X_107)) != X_107
| converse(complement(X_107)) != meet(converse(complement(X_107)),complement(converse(complement(complement(X_107)))))
| converse(complement(X_107)) = meet(converse(complement(X_107)),complement(converse(X_107))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(X_107)),meet(converse(complement(X_107)),complement(converse(complement(complement(X_107)))))) ),[1,1,0,0],$fot(X_107)]]) ).
cnf(refute_0_1012,plain,
( converse(complement(X_107)) != meet(converse(complement(X_107)),complement(converse(complement(complement(X_107)))))
| converse(complement(X_107)) = meet(converse(complement(X_107)),complement(converse(X_107))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_107)),X_107) )],[refute_0_848,refute_0_1011]) ).
cnf(refute_0_1013,plain,
converse(complement(X_107)) = meet(converse(complement(X_107)),complement(converse(X_107))),
inference(resolve,[$cnf( $equal(converse(complement(X_107)),meet(converse(complement(X_107)),complement(converse(complement(complement(X_107)))))) )],[refute_0_1010,refute_0_1012]) ).
cnf(refute_0_1014,plain,
complement(X_125) = meet(complement(X_125),converse(complement(converse(complement(complement(X_125)))))),
inference(subst,[],[refute_0_977:[bind(X_107,$fot(complement(X_125)))]]) ).
cnf(refute_0_1015,plain,
X_125 = complement(complement(X_125)),
inference(subst,[],[refute_0_846:[bind(X_107,$fot(X_125))]]) ).
cnf(refute_0_1016,plain,
( X_125 != complement(complement(X_125))
| complement(complement(X_125)) = X_125 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_125)),bind(Y,$fot(complement(complement(X_125))))]]) ).
cnf(refute_0_1017,plain,
complement(complement(X_125)) = X_125,
inference(resolve,[$cnf( $equal(X_125,complement(complement(X_125))) )],[refute_0_1015,refute_0_1016]) ).
cnf(refute_0_1018,plain,
( complement(X_125) != meet(complement(X_125),converse(complement(converse(complement(complement(X_125))))))
| complement(complement(X_125)) != X_125
| complement(X_125) = meet(complement(X_125),converse(complement(converse(X_125)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_125),meet(complement(X_125),converse(complement(converse(complement(complement(X_125))))))) ),[1,1,0,0,0],$fot(X_125)]]) ).
cnf(refute_0_1019,plain,
( complement(X_125) != meet(complement(X_125),converse(complement(converse(complement(complement(X_125))))))
| complement(X_125) = meet(complement(X_125),converse(complement(converse(X_125)))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_125)),X_125) )],[refute_0_1017,refute_0_1018]) ).
cnf(refute_0_1020,plain,
complement(X_125) = meet(complement(X_125),converse(complement(converse(X_125)))),
inference(resolve,[$cnf( $equal(complement(X_125),meet(complement(X_125),converse(complement(converse(complement(complement(X_125))))))) )],[refute_0_1014,refute_0_1019]) ).
cnf(refute_0_1021,plain,
complement(converse(A)) = meet(complement(converse(A)),converse(complement(converse(converse(A))))),
inference(subst,[],[refute_0_1020:[bind(X_125,$fot(converse(A)))]]) ).
cnf(refute_0_1022,plain,
( complement(converse(A)) != meet(complement(converse(A)),converse(complement(converse(converse(A)))))
| converse(converse(A)) != A
| complement(converse(A)) = meet(complement(converse(A)),converse(complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(A)),meet(complement(converse(A)),converse(complement(converse(converse(A)))))) ),[1,1,0,0],$fot(A)]]) ).
cnf(refute_0_1023,plain,
( complement(converse(A)) != meet(complement(converse(A)),converse(complement(converse(converse(A)))))
| complement(converse(A)) = meet(complement(converse(A)),converse(complement(A))) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1022]) ).
cnf(refute_0_1024,plain,
complement(converse(A)) = meet(complement(converse(A)),converse(complement(A))),
inference(resolve,[$cnf( $equal(complement(converse(A)),meet(complement(converse(A)),converse(complement(converse(converse(A)))))) )],[refute_0_1021,refute_0_1023]) ).
cnf(refute_0_1025,plain,
( complement(converse(A)) != meet(complement(converse(A)),converse(complement(A)))
| meet(complement(converse(A)),converse(complement(A))) = complement(converse(A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(converse(A)))),bind(Y,$fot(meet(complement(converse(A)),converse(complement(A)))))]]) ).
cnf(refute_0_1026,plain,
meet(complement(converse(A)),converse(complement(A))) = complement(converse(A)),
inference(resolve,[$cnf( $equal(complement(converse(A)),meet(complement(converse(A)),converse(complement(A)))) )],[refute_0_1024,refute_0_1025]) ).
cnf(refute_0_1027,plain,
meet(complement(converse(X_107)),converse(complement(X_107))) = complement(converse(X_107)),
inference(subst,[],[refute_0_1026:[bind(A,$fot(X_107))]]) ).
cnf(refute_0_1028,plain,
meet(converse(complement(X_107)),complement(converse(X_107))) = meet(complement(converse(X_107)),converse(complement(X_107))),
inference(subst,[],[refute_0_882:[bind(X_10,$fot(complement(converse(X_107)))),bind(X_11,$fot(converse(complement(X_107))))]]) ).
cnf(refute_0_1029,plain,
( meet(complement(converse(X_107)),converse(complement(X_107))) != complement(converse(X_107))
| meet(converse(complement(X_107)),complement(converse(X_107))) != meet(complement(converse(X_107)),converse(complement(X_107)))
| meet(converse(complement(X_107)),complement(converse(X_107))) = complement(converse(X_107)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(meet(converse(complement(X_107)),complement(converse(X_107))))),bind(Y,$fot(meet(complement(converse(X_107)),converse(complement(X_107))))),bind(Z,$fot(complement(converse(X_107))))]]) ).
cnf(refute_0_1030,plain,
( meet(complement(converse(X_107)),converse(complement(X_107))) != complement(converse(X_107))
| meet(converse(complement(X_107)),complement(converse(X_107))) = complement(converse(X_107)) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(X_107)),complement(converse(X_107))),meet(complement(converse(X_107)),converse(complement(X_107)))) )],[refute_0_1028,refute_0_1029]) ).
cnf(refute_0_1031,plain,
meet(converse(complement(X_107)),complement(converse(X_107))) = complement(converse(X_107)),
inference(resolve,[$cnf( $equal(meet(complement(converse(X_107)),converse(complement(X_107))),complement(converse(X_107))) )],[refute_0_1027,refute_0_1030]) ).
cnf(refute_0_1032,plain,
( converse(complement(X_107)) != meet(converse(complement(X_107)),complement(converse(X_107)))
| meet(converse(complement(X_107)),complement(converse(X_107))) != complement(converse(X_107))
| converse(complement(X_107)) = complement(converse(X_107)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(X_107)),complement(converse(X_107))) ),[0],$fot(meet(converse(complement(X_107)),complement(converse(X_107))))]]) ).
cnf(refute_0_1033,plain,
( converse(complement(X_107)) != meet(converse(complement(X_107)),complement(converse(X_107)))
| converse(complement(X_107)) = complement(converse(X_107)) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(X_107)),complement(converse(X_107))),complement(converse(X_107))) )],[refute_0_1031,refute_0_1032]) ).
cnf(refute_0_1034,plain,
converse(complement(X_107)) = complement(converse(X_107)),
inference(resolve,[$cnf( $equal(converse(complement(X_107)),meet(converse(complement(X_107)),complement(converse(X_107)))) )],[refute_0_1013,refute_0_1033]) ).
cnf(refute_0_1035,plain,
converse(complement(X_79)) = complement(converse(X_79)),
inference(subst,[],[refute_0_1034:[bind(X_107,$fot(X_79))]]) ).
cnf(refute_0_1036,plain,
composition(converse(complement(X_79)),X_79) = composition(converse(complement(X_79)),X_79),
introduced(tautology,[refl,[$fot(composition(converse(complement(X_79)),X_79))]]) ).
cnf(refute_0_1037,plain,
( composition(converse(complement(X_79)),X_79) != composition(converse(complement(X_79)),X_79)
| converse(complement(X_79)) != complement(converse(X_79))
| composition(converse(complement(X_79)),X_79) = composition(complement(converse(X_79)),X_79) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(X_79)),X_79),composition(converse(complement(X_79)),X_79)) ),[1,0],$fot(complement(converse(X_79)))]]) ).
cnf(refute_0_1038,plain,
( converse(complement(X_79)) != complement(converse(X_79))
| composition(converse(complement(X_79)),X_79) = composition(complement(converse(X_79)),X_79) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(X_79)),X_79),composition(converse(complement(X_79)),X_79)) )],[refute_0_1036,refute_0_1037]) ).
cnf(refute_0_1039,plain,
composition(converse(complement(X_79)),X_79) = composition(complement(converse(X_79)),X_79),
inference(resolve,[$cnf( $equal(converse(complement(X_79)),complement(converse(X_79))) )],[refute_0_1035,refute_0_1038]) ).
cnf(refute_0_1040,plain,
complement(composition(converse(complement(X_79)),X_79)) = complement(composition(converse(complement(X_79)),X_79)),
introduced(tautology,[refl,[$fot(complement(composition(converse(complement(X_79)),X_79)))]]) ).
cnf(refute_0_1041,plain,
( complement(composition(converse(complement(X_79)),X_79)) != complement(composition(converse(complement(X_79)),X_79))
| composition(converse(complement(X_79)),X_79) != composition(complement(converse(X_79)),X_79)
| complement(composition(converse(complement(X_79)),X_79)) = complement(composition(complement(converse(X_79)),X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(converse(complement(X_79)),X_79)),complement(composition(converse(complement(X_79)),X_79))) ),[1,0],$fot(composition(complement(converse(X_79)),X_79))]]) ).
cnf(refute_0_1042,plain,
( composition(converse(complement(X_79)),X_79) != composition(complement(converse(X_79)),X_79)
| complement(composition(converse(complement(X_79)),X_79)) = complement(composition(complement(converse(X_79)),X_79)) ),
inference(resolve,[$cnf( $equal(complement(composition(converse(complement(X_79)),X_79)),complement(composition(converse(complement(X_79)),X_79))) )],[refute_0_1040,refute_0_1041]) ).
cnf(refute_0_1043,plain,
complement(composition(converse(complement(X_79)),X_79)) = complement(composition(complement(converse(X_79)),X_79)),
inference(resolve,[$cnf( $equal(composition(converse(complement(X_79)),X_79),composition(complement(converse(X_79)),X_79)) )],[refute_0_1039,refute_0_1042]) ).
cnf(refute_0_1044,plain,
join(one,complement(composition(converse(complement(X_79)),X_79))) = join(one,complement(composition(converse(complement(X_79)),X_79))),
introduced(tautology,[refl,[$fot(join(one,complement(composition(converse(complement(X_79)),X_79))))]]) ).
cnf(refute_0_1045,plain,
( complement(composition(converse(complement(X_79)),X_79)) != complement(composition(complement(converse(X_79)),X_79))
| join(one,complement(composition(converse(complement(X_79)),X_79))) != join(one,complement(composition(converse(complement(X_79)),X_79)))
| join(one,complement(composition(converse(complement(X_79)),X_79))) = join(one,complement(composition(complement(converse(X_79)),X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,complement(composition(converse(complement(X_79)),X_79))),join(one,complement(composition(converse(complement(X_79)),X_79)))) ),[1,1],$fot(complement(composition(complement(converse(X_79)),X_79)))]]) ).
cnf(refute_0_1046,plain,
( complement(composition(converse(complement(X_79)),X_79)) != complement(composition(complement(converse(X_79)),X_79))
| join(one,complement(composition(converse(complement(X_79)),X_79))) = join(one,complement(composition(complement(converse(X_79)),X_79))) ),
inference(resolve,[$cnf( $equal(join(one,complement(composition(converse(complement(X_79)),X_79))),join(one,complement(composition(converse(complement(X_79)),X_79)))) )],[refute_0_1044,refute_0_1045]) ).
cnf(refute_0_1047,plain,
join(one,complement(composition(converse(complement(X_79)),X_79))) = join(one,complement(composition(complement(converse(X_79)),X_79))),
inference(resolve,[$cnf( $equal(complement(composition(converse(complement(X_79)),X_79)),complement(composition(complement(converse(X_79)),X_79))) )],[refute_0_1043,refute_0_1046]) ).
cnf(refute_0_1048,plain,
composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))) = composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))),
introduced(tautology,[refl,[$fot(composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))))]]) ).
cnf(refute_0_1049,plain,
( composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))) != composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79))))
| join(one,complement(composition(converse(complement(X_79)),X_79))) != join(one,complement(composition(complement(converse(X_79)),X_79)))
| composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))) = composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))),composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79))))) ),[1,1],$fot(join(one,complement(composition(complement(converse(X_79)),X_79))))]]) ).
cnf(refute_0_1050,plain,
( join(one,complement(composition(converse(complement(X_79)),X_79))) != join(one,complement(composition(complement(converse(X_79)),X_79)))
| composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))) = composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) ),
inference(resolve,[$cnf( $equal(composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))),composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79))))) )],[refute_0_1048,refute_0_1049]) ).
cnf(refute_0_1051,plain,
composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))) = composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))),
inference(resolve,[$cnf( $equal(join(one,complement(composition(converse(complement(X_79)),X_79))),join(one,complement(composition(complement(converse(X_79)),X_79)))) )],[refute_0_1047,refute_0_1050]) ).
cnf(refute_0_1052,plain,
converse(converse(composition(X_186,join(one,X_187)))) = composition(X_186,join(one,X_187)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(X_186,join(one,X_187))))]]) ).
cnf(refute_0_1053,plain,
composition(join(one,converse(X_171)),converse(X_170)) = composition(join(converse(X_171),one),converse(X_170)),
inference(subst,[],[refute_0_98:[bind(X_34,$fot(converse(X_171))),bind(X_35,$fot(converse(X_170)))]]) ).
cnf(refute_0_1054,plain,
converse(composition(X_14,join(X_4,converse(A)))) = composition(converse(join(X_4,converse(A))),converse(X_14)),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(X_14)),bind(B,$fot(join(X_4,converse(A))))]]) ).
cnf(refute_0_1055,plain,
( converse(composition(X_14,join(X_4,converse(A)))) != composition(converse(join(X_4,converse(A))),converse(X_14))
| converse(join(X_4,converse(A))) != join(converse(X_4),A)
| converse(composition(X_14,join(X_4,converse(A)))) = composition(join(converse(X_4),A),converse(X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_14,join(X_4,converse(A)))),composition(converse(join(X_4,converse(A))),converse(X_14))) ),[1,0],$fot(join(converse(X_4),A))]]) ).
cnf(refute_0_1056,plain,
( converse(composition(X_14,join(X_4,converse(A)))) != composition(converse(join(X_4,converse(A))),converse(X_14))
| converse(composition(X_14,join(X_4,converse(A)))) = composition(join(converse(X_4),A),converse(X_14)) ),
inference(resolve,[$cnf( $equal(converse(join(X_4,converse(A))),join(converse(X_4),A)) )],[refute_0_65,refute_0_1055]) ).
cnf(refute_0_1057,plain,
converse(composition(X_14,join(X_4,converse(A)))) = composition(join(converse(X_4),A),converse(X_14)),
inference(resolve,[$cnf( $equal(converse(composition(X_14,join(X_4,converse(A)))),composition(converse(join(X_4,converse(A))),converse(X_14))) )],[refute_0_1054,refute_0_1056]) ).
cnf(refute_0_1058,plain,
converse(composition(X_170,join(X_171,converse(one)))) = composition(join(converse(X_171),one),converse(X_170)),
inference(subst,[],[refute_0_1057:[bind(A,$fot(one)),bind(X_14,$fot(X_170)),bind(X_4,$fot(X_171))]]) ).
cnf(refute_0_1059,plain,
( converse(composition(X_170,join(X_171,converse(one)))) != composition(join(converse(X_171),one),converse(X_170))
| composition(join(converse(X_171),one),converse(X_170)) = converse(composition(X_170,join(X_171,converse(one)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(X_170,join(X_171,converse(one)))))),bind(Y,$fot(composition(join(converse(X_171),one),converse(X_170))))]]) ).
cnf(refute_0_1060,plain,
composition(join(converse(X_171),one),converse(X_170)) = converse(composition(X_170,join(X_171,converse(one)))),
inference(resolve,[$cnf( $equal(converse(composition(X_170,join(X_171,converse(one)))),composition(join(converse(X_171),one),converse(X_170))) )],[refute_0_1058,refute_0_1059]) ).
cnf(refute_0_1061,plain,
( composition(join(converse(X_171),one),converse(X_170)) != converse(composition(X_170,join(X_171,converse(one))))
| composition(join(one,converse(X_171)),converse(X_170)) != composition(join(converse(X_171),one),converse(X_170))
| composition(join(one,converse(X_171)),converse(X_170)) = converse(composition(X_170,join(X_171,converse(one)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(X_171)),converse(X_170)),composition(join(converse(X_171),one),converse(X_170))) ),[1],$fot(converse(composition(X_170,join(X_171,converse(one)))))]]) ).
cnf(refute_0_1062,plain,
( composition(join(one,converse(X_171)),converse(X_170)) != composition(join(converse(X_171),one),converse(X_170))
| composition(join(one,converse(X_171)),converse(X_170)) = converse(composition(X_170,join(X_171,converse(one)))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(X_171),one),converse(X_170)),converse(composition(X_170,join(X_171,converse(one))))) )],[refute_0_1060,refute_0_1061]) ).
cnf(refute_0_1063,plain,
composition(join(one,converse(X_171)),converse(X_170)) = converse(composition(X_170,join(X_171,converse(one)))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(X_171)),converse(X_170)),composition(join(converse(X_171),one),converse(X_170))) )],[refute_0_1053,refute_0_1062]) ).
cnf(refute_0_1064,plain,
join(converse(one),X_171) = join(converse(one),X_171),
introduced(tautology,[refl,[$fot(join(converse(one),X_171))]]) ).
cnf(refute_0_1065,plain,
( converse(one) != one
| join(converse(one),X_171) != join(converse(one),X_171)
| join(converse(one),X_171) = join(one,X_171) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(one),X_171),join(converse(one),X_171)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1066,plain,
( converse(one) != one
| join(converse(one),X_171) = join(one,X_171) ),
inference(resolve,[$cnf( $equal(join(converse(one),X_171),join(converse(one),X_171)) )],[refute_0_1064,refute_0_1065]) ).
cnf(refute_0_1067,plain,
join(converse(one),X_171) = join(one,X_171),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_37,refute_0_1066]) ).
cnf(refute_0_1068,plain,
composition(X_170,join(converse(one),X_171)) = composition(X_170,join(converse(one),X_171)),
introduced(tautology,[refl,[$fot(composition(X_170,join(converse(one),X_171)))]]) ).
cnf(refute_0_1069,plain,
( composition(X_170,join(converse(one),X_171)) != composition(X_170,join(converse(one),X_171))
| join(converse(one),X_171) != join(one,X_171)
| composition(X_170,join(converse(one),X_171)) = composition(X_170,join(one,X_171)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_170,join(converse(one),X_171)),composition(X_170,join(converse(one),X_171))) ),[1,1],$fot(join(one,X_171))]]) ).
cnf(refute_0_1070,plain,
( join(converse(one),X_171) != join(one,X_171)
| composition(X_170,join(converse(one),X_171)) = composition(X_170,join(one,X_171)) ),
inference(resolve,[$cnf( $equal(composition(X_170,join(converse(one),X_171)),composition(X_170,join(converse(one),X_171))) )],[refute_0_1068,refute_0_1069]) ).
cnf(refute_0_1071,plain,
composition(X_170,join(converse(one),X_171)) = composition(X_170,join(one,X_171)),
inference(resolve,[$cnf( $equal(join(converse(one),X_171),join(one,X_171)) )],[refute_0_1067,refute_0_1070]) ).
cnf(refute_0_1072,plain,
converse(composition(X_170,join(converse(one),X_171))) = converse(composition(X_170,join(converse(one),X_171))),
introduced(tautology,[refl,[$fot(converse(composition(X_170,join(converse(one),X_171))))]]) ).
cnf(refute_0_1073,plain,
( composition(X_170,join(converse(one),X_171)) != composition(X_170,join(one,X_171))
| converse(composition(X_170,join(converse(one),X_171))) != converse(composition(X_170,join(converse(one),X_171)))
| converse(composition(X_170,join(converse(one),X_171))) = converse(composition(X_170,join(one,X_171))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_170,join(converse(one),X_171))),converse(composition(X_170,join(converse(one),X_171)))) ),[1,0],$fot(composition(X_170,join(one,X_171)))]]) ).
cnf(refute_0_1074,plain,
( composition(X_170,join(converse(one),X_171)) != composition(X_170,join(one,X_171))
| converse(composition(X_170,join(converse(one),X_171))) = converse(composition(X_170,join(one,X_171))) ),
inference(resolve,[$cnf( $equal(converse(composition(X_170,join(converse(one),X_171))),converse(composition(X_170,join(converse(one),X_171)))) )],[refute_0_1072,refute_0_1073]) ).
cnf(refute_0_1075,plain,
converse(composition(X_170,join(converse(one),X_171))) = converse(composition(X_170,join(one,X_171))),
inference(resolve,[$cnf( $equal(composition(X_170,join(converse(one),X_171)),composition(X_170,join(one,X_171))) )],[refute_0_1071,refute_0_1074]) ).
cnf(refute_0_1076,plain,
converse(composition(X_56,converse(join(X_4,converse(A))))) = composition(join(X_4,converse(A)),converse(X_56)),
inference(subst,[],[refute_0_642:[bind(A,$fot(join(X_4,converse(A)))),bind(X_14,$fot(X_56))]]) ).
cnf(refute_0_1077,plain,
( converse(composition(X_56,converse(join(X_4,converse(A))))) != composition(join(X_4,converse(A)),converse(X_56))
| converse(join(X_4,converse(A))) != join(converse(X_4),A)
| converse(composition(X_56,join(converse(X_4),A))) = composition(join(X_4,converse(A)),converse(X_56)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_56,converse(join(X_4,converse(A))))),composition(join(X_4,converse(A)),converse(X_56))) ),[0,0,1],$fot(join(converse(X_4),A))]]) ).
cnf(refute_0_1078,plain,
( converse(composition(X_56,converse(join(X_4,converse(A))))) != composition(join(X_4,converse(A)),converse(X_56))
| converse(composition(X_56,join(converse(X_4),A))) = composition(join(X_4,converse(A)),converse(X_56)) ),
inference(resolve,[$cnf( $equal(converse(join(X_4,converse(A))),join(converse(X_4),A)) )],[refute_0_65,refute_0_1077]) ).
cnf(refute_0_1079,plain,
converse(composition(X_56,join(converse(X_4),A))) = composition(join(X_4,converse(A)),converse(X_56)),
inference(resolve,[$cnf( $equal(converse(composition(X_56,converse(join(X_4,converse(A))))),composition(join(X_4,converse(A)),converse(X_56))) )],[refute_0_1076,refute_0_1078]) ).
cnf(refute_0_1080,plain,
( converse(composition(X_56,join(converse(X_4),A))) != composition(join(X_4,converse(A)),converse(X_56))
| composition(join(X_4,converse(A)),converse(X_56)) = converse(composition(X_56,join(converse(X_4),A))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(X_56,join(converse(X_4),A))))),bind(Y,$fot(composition(join(X_4,converse(A)),converse(X_56))))]]) ).
cnf(refute_0_1081,plain,
composition(join(X_4,converse(A)),converse(X_56)) = converse(composition(X_56,join(converse(X_4),A))),
inference(resolve,[$cnf( $equal(converse(composition(X_56,join(converse(X_4),A))),composition(join(X_4,converse(A)),converse(X_56))) )],[refute_0_1079,refute_0_1080]) ).
cnf(refute_0_1082,plain,
composition(join(one,converse(X_171)),converse(X_170)) = converse(composition(X_170,join(converse(one),X_171))),
inference(subst,[],[refute_0_1081:[bind(A,$fot(X_171)),bind(X_4,$fot(one)),bind(X_56,$fot(X_170))]]) ).
cnf(refute_0_1083,plain,
( composition(join(one,converse(X_171)),converse(X_170)) != converse(composition(X_170,join(converse(one),X_171)))
| converse(composition(X_170,join(converse(one),X_171))) != converse(composition(X_170,join(one,X_171)))
| composition(join(one,converse(X_171)),converse(X_170)) = converse(composition(X_170,join(one,X_171))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(composition(join(one,converse(X_171)),converse(X_170)))),bind(Y,$fot(converse(composition(X_170,join(converse(one),X_171))))),bind(Z,$fot(converse(composition(X_170,join(one,X_171)))))]]) ).
cnf(refute_0_1084,plain,
( converse(composition(X_170,join(converse(one),X_171))) != converse(composition(X_170,join(one,X_171)))
| composition(join(one,converse(X_171)),converse(X_170)) = converse(composition(X_170,join(one,X_171))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(X_171)),converse(X_170)),converse(composition(X_170,join(converse(one),X_171)))) )],[refute_0_1082,refute_0_1083]) ).
cnf(refute_0_1085,plain,
composition(join(one,converse(X_171)),converse(X_170)) = converse(composition(X_170,join(one,X_171))),
inference(resolve,[$cnf( $equal(converse(composition(X_170,join(converse(one),X_171))),converse(composition(X_170,join(one,X_171)))) )],[refute_0_1075,refute_0_1084]) ).
cnf(refute_0_1086,plain,
( composition(join(one,converse(X_171)),converse(X_170)) != converse(composition(X_170,join(X_171,converse(one))))
| composition(join(one,converse(X_171)),converse(X_170)) != converse(composition(X_170,join(one,X_171)))
| converse(composition(X_170,join(one,X_171))) = converse(composition(X_170,join(X_171,converse(one)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(X_171)),converse(X_170)),converse(composition(X_170,join(X_171,converse(one))))) ),[0],$fot(converse(composition(X_170,join(one,X_171))))]]) ).
cnf(refute_0_1087,plain,
( composition(join(one,converse(X_171)),converse(X_170)) != converse(composition(X_170,join(X_171,converse(one))))
| converse(composition(X_170,join(one,X_171))) = converse(composition(X_170,join(X_171,converse(one)))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(X_171)),converse(X_170)),converse(composition(X_170,join(one,X_171)))) )],[refute_0_1085,refute_0_1086]) ).
cnf(refute_0_1088,plain,
join(X_171,converse(one)) = join(X_171,converse(one)),
introduced(tautology,[refl,[$fot(join(X_171,converse(one)))]]) ).
cnf(refute_0_1089,plain,
( converse(one) != one
| join(X_171,converse(one)) != join(X_171,converse(one))
| join(X_171,converse(one)) = join(X_171,one) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_171,converse(one)),join(X_171,converse(one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1090,plain,
( converse(one) != one
| join(X_171,converse(one)) = join(X_171,one) ),
inference(resolve,[$cnf( $equal(join(X_171,converse(one)),join(X_171,converse(one))) )],[refute_0_1088,refute_0_1089]) ).
cnf(refute_0_1091,plain,
join(X_171,converse(one)) = join(X_171,one),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_37,refute_0_1090]) ).
cnf(refute_0_1092,plain,
composition(X_170,join(X_171,converse(one))) = composition(X_170,join(X_171,converse(one))),
introduced(tautology,[refl,[$fot(composition(X_170,join(X_171,converse(one))))]]) ).
cnf(refute_0_1093,plain,
( composition(X_170,join(X_171,converse(one))) != composition(X_170,join(X_171,converse(one)))
| join(X_171,converse(one)) != join(X_171,one)
| composition(X_170,join(X_171,converse(one))) = composition(X_170,join(X_171,one)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_170,join(X_171,converse(one))),composition(X_170,join(X_171,converse(one)))) ),[1,1],$fot(join(X_171,one))]]) ).
cnf(refute_0_1094,plain,
( join(X_171,converse(one)) != join(X_171,one)
| composition(X_170,join(X_171,converse(one))) = composition(X_170,join(X_171,one)) ),
inference(resolve,[$cnf( $equal(composition(X_170,join(X_171,converse(one))),composition(X_170,join(X_171,converse(one)))) )],[refute_0_1092,refute_0_1093]) ).
cnf(refute_0_1095,plain,
composition(X_170,join(X_171,converse(one))) = composition(X_170,join(X_171,one)),
inference(resolve,[$cnf( $equal(join(X_171,converse(one)),join(X_171,one)) )],[refute_0_1091,refute_0_1094]) ).
cnf(refute_0_1096,plain,
converse(composition(X_170,join(X_171,converse(one)))) = converse(composition(X_170,join(X_171,converse(one)))),
introduced(tautology,[refl,[$fot(converse(composition(X_170,join(X_171,converse(one)))))]]) ).
cnf(refute_0_1097,plain,
( composition(X_170,join(X_171,converse(one))) != composition(X_170,join(X_171,one))
| converse(composition(X_170,join(X_171,converse(one)))) != converse(composition(X_170,join(X_171,converse(one))))
| converse(composition(X_170,join(X_171,converse(one)))) = converse(composition(X_170,join(X_171,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_170,join(X_171,converse(one)))),converse(composition(X_170,join(X_171,converse(one))))) ),[1,0],$fot(composition(X_170,join(X_171,one)))]]) ).
cnf(refute_0_1098,plain,
( composition(X_170,join(X_171,converse(one))) != composition(X_170,join(X_171,one))
| converse(composition(X_170,join(X_171,converse(one)))) = converse(composition(X_170,join(X_171,one))) ),
inference(resolve,[$cnf( $equal(converse(composition(X_170,join(X_171,converse(one)))),converse(composition(X_170,join(X_171,converse(one))))) )],[refute_0_1096,refute_0_1097]) ).
cnf(refute_0_1099,plain,
converse(composition(X_170,join(X_171,converse(one)))) = converse(composition(X_170,join(X_171,one))),
inference(resolve,[$cnf( $equal(composition(X_170,join(X_171,converse(one))),composition(X_170,join(X_171,one))) )],[refute_0_1095,refute_0_1098]) ).
cnf(refute_0_1100,plain,
( converse(composition(X_170,join(X_171,converse(one)))) != converse(composition(X_170,join(X_171,one)))
| converse(composition(X_170,join(one,X_171))) != converse(composition(X_170,join(X_171,converse(one))))
| converse(composition(X_170,join(one,X_171))) = converse(composition(X_170,join(X_171,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_170,join(one,X_171))),converse(composition(X_170,join(X_171,converse(one))))) ),[1],$fot(converse(composition(X_170,join(X_171,one))))]]) ).
cnf(refute_0_1101,plain,
( converse(composition(X_170,join(one,X_171))) != converse(composition(X_170,join(X_171,converse(one))))
| converse(composition(X_170,join(one,X_171))) = converse(composition(X_170,join(X_171,one))) ),
inference(resolve,[$cnf( $equal(converse(composition(X_170,join(X_171,converse(one)))),converse(composition(X_170,join(X_171,one)))) )],[refute_0_1099,refute_0_1100]) ).
cnf(refute_0_1102,plain,
( composition(join(one,converse(X_171)),converse(X_170)) != converse(composition(X_170,join(X_171,converse(one))))
| converse(composition(X_170,join(one,X_171))) = converse(composition(X_170,join(X_171,one))) ),
inference(resolve,[$cnf( $equal(converse(composition(X_170,join(one,X_171))),converse(composition(X_170,join(X_171,converse(one))))) )],[refute_0_1087,refute_0_1101]) ).
cnf(refute_0_1103,plain,
converse(composition(X_170,join(one,X_171))) = converse(composition(X_170,join(X_171,one))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(X_171)),converse(X_170)),converse(composition(X_170,join(X_171,converse(one))))) )],[refute_0_1063,refute_0_1102]) ).
cnf(refute_0_1104,plain,
converse(composition(X_186,join(one,X_187))) = converse(composition(X_186,join(X_187,one))),
inference(subst,[],[refute_0_1103:[bind(X_170,$fot(X_186)),bind(X_171,$fot(X_187))]]) ).
cnf(refute_0_1105,plain,
( converse(composition(X_186,join(one,X_187))) != converse(composition(X_186,join(X_187,one)))
| converse(converse(composition(X_186,join(one,X_187)))) != composition(X_186,join(one,X_187))
| converse(converse(composition(X_186,join(X_187,one)))) = composition(X_186,join(one,X_187)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(composition(X_186,join(one,X_187)))),composition(X_186,join(one,X_187))) ),[0,0],$fot(converse(composition(X_186,join(X_187,one))))]]) ).
cnf(refute_0_1106,plain,
( converse(converse(composition(X_186,join(one,X_187)))) != composition(X_186,join(one,X_187))
| converse(converse(composition(X_186,join(X_187,one)))) = composition(X_186,join(one,X_187)) ),
inference(resolve,[$cnf( $equal(converse(composition(X_186,join(one,X_187))),converse(composition(X_186,join(X_187,one)))) )],[refute_0_1104,refute_0_1105]) ).
cnf(refute_0_1107,plain,
converse(converse(composition(X_186,join(X_187,one)))) = composition(X_186,join(one,X_187)),
inference(resolve,[$cnf( $equal(converse(converse(composition(X_186,join(one,X_187)))),composition(X_186,join(one,X_187))) )],[refute_0_1052,refute_0_1106]) ).
cnf(refute_0_1108,plain,
converse(converse(composition(X_186,join(X_187,one)))) = composition(X_186,join(X_187,one)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(X_186,join(X_187,one))))]]) ).
cnf(refute_0_1109,plain,
( converse(converse(composition(X_186,join(X_187,one)))) != composition(X_186,join(X_187,one))
| converse(converse(composition(X_186,join(X_187,one)))) != composition(X_186,join(one,X_187))
| composition(X_186,join(X_187,one)) = composition(X_186,join(one,X_187)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(composition(X_186,join(X_187,one)))),composition(X_186,join(one,X_187))) ),[0],$fot(composition(X_186,join(X_187,one)))]]) ).
cnf(refute_0_1110,plain,
( converse(converse(composition(X_186,join(X_187,one)))) != composition(X_186,join(one,X_187))
| composition(X_186,join(X_187,one)) = composition(X_186,join(one,X_187)) ),
inference(resolve,[$cnf( $equal(converse(converse(composition(X_186,join(X_187,one)))),composition(X_186,join(X_187,one))) )],[refute_0_1108,refute_0_1109]) ).
cnf(refute_0_1111,plain,
composition(X_186,join(X_187,one)) = composition(X_186,join(one,X_187)),
inference(resolve,[$cnf( $equal(converse(converse(composition(X_186,join(X_187,one)))),composition(X_186,join(one,X_187))) )],[refute_0_1107,refute_0_1110]) ).
cnf(refute_0_1112,plain,
composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) = composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))),
inference(subst,[],[refute_0_1111:[bind(X_186,$fot(complement(X_79))),bind(X_187,$fot(complement(composition(converse(complement(X_79)),X_79))))]]) ).
cnf(refute_0_1113,plain,
( composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) != composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79))))
| composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))) != composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79))))
| composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) = composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)))),bind(Y,$fot(composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))))),bind(Z,$fot(composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79))))))]]) ).
cnf(refute_0_1114,plain,
( composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))) != composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79))))
| composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) = composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) ),
inference(resolve,[$cnf( $equal(composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)),composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79))))) )],[refute_0_1112,refute_0_1113]) ).
cnf(refute_0_1115,plain,
composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) = composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))),
inference(resolve,[$cnf( $equal(composition(complement(X_79),join(one,complement(composition(converse(complement(X_79)),X_79)))),composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79))))) )],[refute_0_1051,refute_0_1114]) ).
cnf(refute_0_1116,plain,
( composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) != complement(X_79)
| composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) != composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79))))
| composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) = complement(X_79) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)),complement(X_79)) ),[0],$fot(composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))))]]) ).
cnf(refute_0_1117,plain,
( composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)) != complement(X_79)
| composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) = complement(X_79) ),
inference(resolve,[$cnf( $equal(composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)),composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79))))) )],[refute_0_1115,refute_0_1116]) ).
cnf(refute_0_1118,plain,
composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) = complement(X_79),
inference(resolve,[$cnf( $equal(composition(complement(X_79),join(complement(composition(converse(complement(X_79)),X_79)),one)),complement(X_79)) )],[refute_0_129,refute_0_1117]) ).
cnf(refute_0_1119,plain,
join(X_108,complement(X_107)) = join(complement(X_107),X_108),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_108)),bind(B,$fot(complement(X_107)))]]) ).
cnf(refute_0_1120,plain,
( join(X_108,complement(X_107)) != join(complement(X_107),X_108)
| join(complement(X_107),X_108) = join(X_108,complement(X_107)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_108,complement(X_107)))),bind(Y,$fot(join(complement(X_107),X_108)))]]) ).
cnf(refute_0_1121,plain,
join(complement(X_107),X_108) = join(X_108,complement(X_107)),
inference(resolve,[$cnf( $equal(join(X_108,complement(X_107)),join(complement(X_107),X_108)) )],[refute_0_1119,refute_0_1120]) ).
cnf(refute_0_1122,plain,
( X_107 != join(meet(X_107,X_108),complement(join(complement(X_107),X_108)))
| join(complement(X_107),X_108) != join(X_108,complement(X_107))
| X_107 = join(meet(X_107,X_108),complement(join(X_108,complement(X_107)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_107,join(meet(X_107,X_108),complement(join(complement(X_107),X_108)))) ),[1,1,0],$fot(join(X_108,complement(X_107)))]]) ).
cnf(refute_0_1123,plain,
( X_107 != join(meet(X_107,X_108),complement(join(complement(X_107),X_108)))
| X_107 = join(meet(X_107,X_108),complement(join(X_108,complement(X_107)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_107),X_108),join(X_108,complement(X_107))) )],[refute_0_1121,refute_0_1122]) ).
cnf(refute_0_1124,plain,
X_107 = join(meet(X_107,X_108),complement(join(X_108,complement(X_107)))),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,X_108),complement(join(complement(X_107),X_108)))) )],[refute_0_147,refute_0_1123]) ).
cnf(refute_0_1125,plain,
complement(X_107) = join(meet(complement(X_107),X_262),complement(join(X_262,complement(complement(X_107))))),
inference(subst,[],[refute_0_1124:[bind(X_107,$fot(complement(X_107))),bind(X_108,$fot(X_262))]]) ).
cnf(refute_0_1126,plain,
( complement(X_107) != join(meet(complement(X_107),X_262),complement(join(X_262,complement(complement(X_107)))))
| complement(complement(X_107)) != X_107
| complement(X_107) = join(meet(complement(X_107),X_262),complement(join(X_262,X_107))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_107),join(meet(complement(X_107),X_262),complement(join(X_262,complement(complement(X_107)))))) ),[1,1,0,1],$fot(X_107)]]) ).
cnf(refute_0_1127,plain,
( complement(X_107) != join(meet(complement(X_107),X_262),complement(join(X_262,complement(complement(X_107)))))
| complement(X_107) = join(meet(complement(X_107),X_262),complement(join(X_262,X_107))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_107)),X_107) )],[refute_0_848,refute_0_1126]) ).
cnf(refute_0_1128,plain,
complement(X_107) = join(meet(complement(X_107),X_262),complement(join(X_262,X_107))),
inference(resolve,[$cnf( $equal(complement(X_107),join(meet(complement(X_107),X_262),complement(join(X_262,complement(complement(X_107)))))) )],[refute_0_1125,refute_0_1127]) ).
cnf(refute_0_1129,plain,
join(meet(complement(X_107),X_262),complement(join(X_262,X_107))) = join(complement(join(X_262,X_107)),meet(complement(X_107),X_262)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(X_262,X_107)))),bind(B,$fot(meet(complement(X_107),X_262)))]]) ).
cnf(refute_0_1130,plain,
( complement(X_107) != join(meet(complement(X_107),X_262),complement(join(X_262,X_107)))
| join(meet(complement(X_107),X_262),complement(join(X_262,X_107))) != join(complement(join(X_262,X_107)),meet(complement(X_107),X_262))
| complement(X_107) = join(complement(join(X_262,X_107)),meet(complement(X_107),X_262)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_107),join(complement(join(X_262,X_107)),meet(complement(X_107),X_262))) ),[0],$fot(join(meet(complement(X_107),X_262),complement(join(X_262,X_107))))]]) ).
cnf(refute_0_1131,plain,
( complement(X_107) != join(meet(complement(X_107),X_262),complement(join(X_262,X_107)))
| complement(X_107) = join(complement(join(X_262,X_107)),meet(complement(X_107),X_262)) ),
inference(resolve,[$cnf( $equal(join(meet(complement(X_107),X_262),complement(join(X_262,X_107))),join(complement(join(X_262,X_107)),meet(complement(X_107),X_262))) )],[refute_0_1129,refute_0_1130]) ).
cnf(refute_0_1132,plain,
complement(X_107) = join(complement(join(X_262,X_107)),meet(complement(X_107),X_262)),
inference(resolve,[$cnf( $equal(complement(X_107),join(meet(complement(X_107),X_262),complement(join(X_262,X_107)))) )],[refute_0_1128,refute_0_1131]) ).
cnf(refute_0_1133,plain,
complement(composition(complement(converse(X_125)),X_125)) = join(complement(join(complement(one),composition(complement(converse(X_125)),X_125))),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),
inference(subst,[],[refute_0_1132:[bind(X_107,$fot(composition(complement(converse(X_125)),X_125))),bind(X_262,$fot(complement(one)))]]) ).
cnf(refute_0_1134,plain,
join(complement(one),composition(converse(X_78),complement(composition(X_78,one)))) = complement(one),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_78)),bind(B,$fot(one))]]) ).
cnf(refute_0_1135,plain,
composition(X_78,one) = X_78,
inference(subst,[],[composition_identity_6:[bind(A,$fot(X_78))]]) ).
cnf(refute_0_1136,plain,
( composition(X_78,one) != X_78
| join(complement(one),composition(converse(X_78),complement(composition(X_78,one)))) != complement(one)
| join(complement(one),composition(converse(X_78),complement(X_78))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(X_78),complement(composition(X_78,one)))),complement(one)) ),[0,1,1,0],$fot(X_78)]]) ).
cnf(refute_0_1137,plain,
( join(complement(one),composition(converse(X_78),complement(composition(X_78,one)))) != complement(one)
| join(complement(one),composition(converse(X_78),complement(X_78))) = complement(one) ),
inference(resolve,[$cnf( $equal(composition(X_78,one),X_78) )],[refute_0_1135,refute_0_1136]) ).
cnf(refute_0_1138,plain,
join(complement(one),composition(converse(X_78),complement(X_78))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(X_78),complement(composition(X_78,one)))),complement(one)) )],[refute_0_1134,refute_0_1137]) ).
cnf(refute_0_1139,plain,
join(complement(one),composition(converse(complement(X_125)),complement(complement(X_125)))) = complement(one),
inference(subst,[],[refute_0_1138:[bind(X_78,$fot(complement(X_125)))]]) ).
cnf(refute_0_1140,plain,
( complement(complement(X_125)) != X_125
| join(complement(one),composition(converse(complement(X_125)),complement(complement(X_125)))) != complement(one)
| join(complement(one),composition(converse(complement(X_125)),X_125)) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(complement(X_125)),complement(complement(X_125)))),complement(one)) ),[0,1,1],$fot(X_125)]]) ).
cnf(refute_0_1141,plain,
( join(complement(one),composition(converse(complement(X_125)),complement(complement(X_125)))) != complement(one)
| join(complement(one),composition(converse(complement(X_125)),X_125)) = complement(one) ),
inference(resolve,[$cnf( $equal(complement(complement(X_125)),X_125) )],[refute_0_1017,refute_0_1140]) ).
cnf(refute_0_1142,plain,
join(complement(one),composition(converse(complement(X_125)),X_125)) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(complement(X_125)),complement(complement(X_125)))),complement(one)) )],[refute_0_1139,refute_0_1141]) ).
cnf(refute_0_1143,plain,
converse(complement(X_125)) = complement(converse(X_125)),
inference(subst,[],[refute_0_1034:[bind(X_107,$fot(X_125))]]) ).
cnf(refute_0_1144,plain,
composition(converse(complement(X_125)),X_125) = composition(converse(complement(X_125)),X_125),
introduced(tautology,[refl,[$fot(composition(converse(complement(X_125)),X_125))]]) ).
cnf(refute_0_1145,plain,
( composition(converse(complement(X_125)),X_125) != composition(converse(complement(X_125)),X_125)
| converse(complement(X_125)) != complement(converse(X_125))
| composition(converse(complement(X_125)),X_125) = composition(complement(converse(X_125)),X_125) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(X_125)),X_125),composition(converse(complement(X_125)),X_125)) ),[1,0],$fot(complement(converse(X_125)))]]) ).
cnf(refute_0_1146,plain,
( converse(complement(X_125)) != complement(converse(X_125))
| composition(converse(complement(X_125)),X_125) = composition(complement(converse(X_125)),X_125) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(X_125)),X_125),composition(converse(complement(X_125)),X_125)) )],[refute_0_1144,refute_0_1145]) ).
cnf(refute_0_1147,plain,
composition(converse(complement(X_125)),X_125) = composition(complement(converse(X_125)),X_125),
inference(resolve,[$cnf( $equal(converse(complement(X_125)),complement(converse(X_125))) )],[refute_0_1143,refute_0_1146]) ).
cnf(refute_0_1148,plain,
join(complement(one),composition(converse(complement(X_125)),X_125)) = join(complement(one),composition(converse(complement(X_125)),X_125)),
introduced(tautology,[refl,[$fot(join(complement(one),composition(converse(complement(X_125)),X_125)))]]) ).
cnf(refute_0_1149,plain,
( composition(converse(complement(X_125)),X_125) != composition(complement(converse(X_125)),X_125)
| join(complement(one),composition(converse(complement(X_125)),X_125)) != join(complement(one),composition(converse(complement(X_125)),X_125))
| join(complement(one),composition(converse(complement(X_125)),X_125)) = join(complement(one),composition(complement(converse(X_125)),X_125)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(complement(X_125)),X_125)),join(complement(one),composition(converse(complement(X_125)),X_125))) ),[1,1],$fot(composition(complement(converse(X_125)),X_125))]]) ).
cnf(refute_0_1150,plain,
( composition(converse(complement(X_125)),X_125) != composition(complement(converse(X_125)),X_125)
| join(complement(one),composition(converse(complement(X_125)),X_125)) = join(complement(one),composition(complement(converse(X_125)),X_125)) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(complement(X_125)),X_125)),join(complement(one),composition(converse(complement(X_125)),X_125))) )],[refute_0_1148,refute_0_1149]) ).
cnf(refute_0_1151,plain,
join(complement(one),composition(converse(complement(X_125)),X_125)) = join(complement(one),composition(complement(converse(X_125)),X_125)),
inference(resolve,[$cnf( $equal(composition(converse(complement(X_125)),X_125),composition(complement(converse(X_125)),X_125)) )],[refute_0_1147,refute_0_1150]) ).
cnf(refute_0_1152,plain,
( join(complement(one),composition(converse(complement(X_125)),X_125)) != complement(one)
| join(complement(one),composition(converse(complement(X_125)),X_125)) != join(complement(one),composition(complement(converse(X_125)),X_125))
| join(complement(one),composition(complement(converse(X_125)),X_125)) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(complement(X_125)),X_125)),complement(one)) ),[0],$fot(join(complement(one),composition(complement(converse(X_125)),X_125)))]]) ).
cnf(refute_0_1153,plain,
( join(complement(one),composition(converse(complement(X_125)),X_125)) != complement(one)
| join(complement(one),composition(complement(converse(X_125)),X_125)) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(complement(X_125)),X_125)),join(complement(one),composition(complement(converse(X_125)),X_125))) )],[refute_0_1151,refute_0_1152]) ).
cnf(refute_0_1154,plain,
join(complement(one),composition(complement(converse(X_125)),X_125)) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(complement(X_125)),X_125)),complement(one)) )],[refute_0_1142,refute_0_1153]) ).
cnf(refute_0_1155,plain,
( complement(composition(complement(converse(X_125)),X_125)) != join(complement(join(complement(one),composition(complement(converse(X_125)),X_125))),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))
| join(complement(one),composition(complement(converse(X_125)),X_125)) != complement(one)
| complement(composition(complement(converse(X_125)),X_125)) = join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(complement(converse(X_125)),X_125)),join(complement(join(complement(one),composition(complement(converse(X_125)),X_125))),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))) ),[1,0,0],$fot(complement(one))]]) ).
cnf(refute_0_1156,plain,
( complement(composition(complement(converse(X_125)),X_125)) != join(complement(join(complement(one),composition(complement(converse(X_125)),X_125))),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))
| complement(composition(complement(converse(X_125)),X_125)) = join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(complement(converse(X_125)),X_125)),complement(one)) )],[refute_0_1154,refute_0_1155]) ).
cnf(refute_0_1157,plain,
complement(composition(complement(converse(X_125)),X_125)) = join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),
inference(resolve,[$cnf( $equal(complement(composition(complement(converse(X_125)),X_125)),join(complement(join(complement(one),composition(complement(converse(X_125)),X_125))),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))) )],[refute_0_1133,refute_0_1156]) ).
cnf(refute_0_1158,plain,
meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)) = meet(complement(one),complement(composition(complement(converse(X_125)),X_125))),
inference(subst,[],[refute_0_882:[bind(X_10,$fot(complement(one))),bind(X_11,$fot(complement(composition(complement(converse(X_125)),X_125))))]]) ).
cnf(refute_0_1159,plain,
join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) = join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),
introduced(tautology,[refl,[$fot(join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))))]]) ).
cnf(refute_0_1160,plain,
( join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) != join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))
| meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)) != meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))
| join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) = join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))) ),[1,1],$fot(meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))]]) ).
cnf(refute_0_1161,plain,
( meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)) != meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))
| join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) = join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) ),
inference(resolve,[$cnf( $equal(join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))) )],[refute_0_1159,refute_0_1160]) ).
cnf(refute_0_1162,plain,
join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) = join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))),
inference(resolve,[$cnf( $equal(meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)),meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) )],[refute_0_1158,refute_0_1161]) ).
cnf(refute_0_1163,plain,
complement(complement(one)) = one,
inference(subst,[],[refute_0_848:[bind(X_107,$fot(one))]]) ).
cnf(refute_0_1164,plain,
join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) = join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),
introduced(tautology,[refl,[$fot(join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))))]]) ).
cnf(refute_0_1165,plain,
( complement(complement(one)) != one
| join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) != join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))
| join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) = join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1166,plain,
( complement(complement(one)) != one
| join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) = join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))) )],[refute_0_1164,refute_0_1165]) ).
cnf(refute_0_1167,plain,
join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) = join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_1163,refute_0_1166]) ).
cnf(refute_0_1168,plain,
( join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) != join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))
| join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) != join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))
| join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) = join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))))),bind(Y,$fot(join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))))),bind(Z,$fot(join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))))]]) ).
cnf(refute_0_1169,plain,
( join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) != join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))
| join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) = join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))) )],[refute_0_1167,refute_0_1168]) ).
cnf(refute_0_1170,plain,
join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) = join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))),
inference(resolve,[$cnf( $equal(join(one,meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))) )],[refute_0_1162,refute_0_1169]) ).
cnf(refute_0_1171,plain,
( complement(composition(complement(converse(X_125)),X_125)) != join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))
| join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))) != join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))
| complement(composition(complement(converse(X_125)),X_125)) = join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(complement(converse(X_125)),X_125)),join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))) ),[0],$fot(join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))))]]) ).
cnf(refute_0_1172,plain,
( complement(composition(complement(converse(X_125)),X_125)) != join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))
| complement(composition(complement(converse(X_125)),X_125)) = join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one))),join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))) )],[refute_0_1170,refute_0_1171]) ).
cnf(refute_0_1173,plain,
complement(composition(complement(converse(X_125)),X_125)) = join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))),
inference(resolve,[$cnf( $equal(complement(composition(complement(converse(X_125)),X_125)),join(complement(complement(one)),meet(complement(composition(complement(converse(X_125)),X_125)),complement(one)))) )],[refute_0_1157,refute_0_1172]) ).
cnf(refute_0_1174,plain,
join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B)))))),
inference(subst,[],[refute_0_607:[bind(X_107,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_1175,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))
| join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))) ),[1,1,1,0],$fot(meet(A,B))]]) ).
cnf(refute_0_1176,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))
| join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_136,refute_0_1175]) ).
cnf(refute_0_1177,plain,
join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))) )],[refute_0_1174,refute_0_1176]) ).
cnf(refute_0_1178,plain,
join(complement(complement(meet(A,B))),meet(A,B)) = join(meet(A,B),complement(complement(meet(A,B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(complement(meet(A,B)))))]]) ).
cnf(refute_0_1179,plain,
complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(meet(A,B))),meet(A,B))))]]) ).
cnf(refute_0_1180,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| join(complement(complement(meet(A,B))),meet(A,B)) != join(meet(A,B),complement(complement(meet(A,B))))
| complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) ),[1,0],$fot(join(meet(A,B),complement(complement(meet(A,B)))))]]) ).
cnf(refute_0_1181,plain,
( join(complement(complement(meet(A,B))),meet(A,B)) != join(meet(A,B),complement(complement(meet(A,B))))
| complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_1179,refute_0_1180]) ).
cnf(refute_0_1182,plain,
complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))),
inference(resolve,[$cnf( $equal(join(complement(complement(meet(A,B))),meet(A,B)),join(meet(A,B),complement(complement(meet(A,B))))) )],[refute_0_1178,refute_0_1181]) ).
cnf(refute_0_1183,plain,
meet(complement(meet(A,B)),join(complement(A),complement(B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
inference(subst,[],[refute_0_718:[bind(A,$fot(complement(meet(A,B)))),bind(X_10,$fot(A)),bind(X_11,$fot(B))]]) ).
cnf(refute_0_1184,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = meet(complement(meet(A,B)),join(complement(A),complement(B))),
inference(subst,[],[refute_0_882:[bind(X_10,$fot(complement(meet(A,B)))),bind(X_11,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_1185,plain,
( meet(complement(meet(A,B)),join(complement(A),complement(B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != meet(complement(meet(A,B)),join(complement(A),complement(B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(meet(join(complement(A),complement(B)),complement(meet(A,B))))),bind(Y,$fot(meet(complement(meet(A,B)),join(complement(A),complement(B))))),bind(Z,$fot(complement(join(complement(complement(meet(A,B))),meet(A,B)))))]]) ).
cnf(refute_0_1186,plain,
( meet(complement(meet(A,B)),join(complement(A),complement(B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),meet(complement(meet(A,B)),join(complement(A),complement(B)))) )],[refute_0_1184,refute_0_1185]) ).
cnf(refute_0_1187,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
inference(resolve,[$cnf( $equal(meet(complement(meet(A,B)),join(complement(A),complement(B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_1183,refute_0_1186]) ).
cnf(refute_0_1188,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(meet(join(complement(A),complement(B)),complement(meet(A,B))))),bind(Y,$fot(complement(join(complement(complement(meet(A,B))),meet(A,B))))),bind(Z,$fot(complement(join(meet(A,B),complement(complement(meet(A,B)))))))]]) ).
cnf(refute_0_1189,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_1187,refute_0_1188]) ).
cnf(refute_0_1190,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(meet(A,B),complement(complement(meet(A,B)))))) )],[refute_0_1182,refute_0_1189]) ).
cnf(refute_0_1191,plain,
join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))))]]) ).
cnf(refute_0_1192,plain,
( join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) ),[1,1],$fot(complement(join(meet(A,B),complement(complement(meet(A,B))))))]]) ).
cnf(refute_0_1193,plain,
( meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) )],[refute_0_1191,refute_0_1192]) ).
cnf(refute_0_1194,plain,
join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),complement(join(meet(A,B),complement(complement(meet(A,B)))))) )],[refute_0_1190,refute_0_1193]) ).
cnf(refute_0_1195,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) ),[0],$fot(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))))]]) ).
cnf(refute_0_1196,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) )],[refute_0_1194,refute_0_1195]) ).
cnf(refute_0_1197,plain,
join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) )],[refute_0_1177,refute_0_1196]) ).
cnf(refute_0_1198,plain,
composition(join(one,one),complement(join(complement(A),complement(B)))) = complement(join(complement(A),complement(B))),
inference(subst,[],[refute_0_423:[bind(X_79,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_1199,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| composition(join(one,one),complement(join(complement(A),complement(B)))) != complement(join(complement(A),complement(B)))
| composition(join(one,one),meet(A,B)) = complement(join(complement(A),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),complement(join(complement(A),complement(B)))),complement(join(complement(A),complement(B)))) ),[0,1],$fot(meet(A,B))]]) ).
cnf(refute_0_1200,plain,
( composition(join(one,one),complement(join(complement(A),complement(B)))) != complement(join(complement(A),complement(B)))
| composition(join(one,one),meet(A,B)) = complement(join(complement(A),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_136,refute_0_1199]) ).
cnf(refute_0_1201,plain,
composition(join(one,one),meet(A,B)) = complement(join(complement(A),complement(B))),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(join(complement(A),complement(B)))),complement(join(complement(A),complement(B)))) )],[refute_0_1198,refute_0_1200]) ).
cnf(refute_0_1202,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| composition(join(one,one),meet(A,B)) != complement(join(complement(A),complement(B)))
| composition(join(one,one),meet(A,B)) = meet(A,B) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),meet(A,B)),complement(join(complement(A),complement(B)))) ),[1],$fot(meet(A,B))]]) ).
cnf(refute_0_1203,plain,
( composition(join(one,one),meet(A,B)) != complement(join(complement(A),complement(B)))
| composition(join(one,one),meet(A,B)) = meet(A,B) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_136,refute_0_1202]) ).
cnf(refute_0_1204,plain,
composition(join(one,one),meet(A,B)) = meet(A,B),
inference(resolve,[$cnf( $equal(composition(join(one,one),meet(A,B)),complement(join(complement(A),complement(B)))) )],[refute_0_1201,refute_0_1203]) ).
cnf(refute_0_1205,plain,
composition(X_35,join(one,one)) = join(X_35,X_35),
inference(subst,[],[refute_0_660:[bind(A,$fot(X_35))]]) ).
cnf(refute_0_1206,plain,
( composition(X_35,join(one,one)) != join(X_35,X_35)
| join(X_35,X_35) = composition(X_35,join(one,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(X_35,join(one,one)))),bind(Y,$fot(join(X_35,X_35)))]]) ).
cnf(refute_0_1207,plain,
join(X_35,X_35) = composition(X_35,join(one,one)),
inference(resolve,[$cnf( $equal(composition(X_35,join(one,one)),join(X_35,X_35)) )],[refute_0_1205,refute_0_1206]) ).
cnf(refute_0_1208,plain,
( composition(join(one,one),X_35) != join(X_35,X_35)
| join(X_35,X_35) != composition(X_35,join(one,one))
| composition(join(one,one),X_35) = composition(X_35,join(one,one)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,one),X_35),composition(X_35,join(one,one))) ),[0],$fot(join(X_35,X_35))]]) ).
cnf(refute_0_1209,plain,
( composition(join(one,one),X_35) != join(X_35,X_35)
| composition(join(one,one),X_35) = composition(X_35,join(one,one)) ),
inference(resolve,[$cnf( $equal(join(X_35,X_35),composition(X_35,join(one,one))) )],[refute_0_1207,refute_0_1208]) ).
cnf(refute_0_1210,plain,
composition(join(one,one),X_35) = composition(X_35,join(one,one)),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_35),join(X_35,X_35)) )],[refute_0_305,refute_0_1209]) ).
cnf(refute_0_1211,plain,
( composition(join(one,one),X_35) != composition(X_35,join(one,one))
| composition(X_35,join(one,one)) = composition(join(one,one),X_35) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),X_35))),bind(Y,$fot(composition(X_35,join(one,one))))]]) ).
cnf(refute_0_1212,plain,
composition(X_35,join(one,one)) = composition(join(one,one),X_35),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_35),composition(X_35,join(one,one))) )],[refute_0_1210,refute_0_1211]) ).
cnf(refute_0_1213,plain,
composition(meet(A,B),join(one,one)) = composition(join(one,one),meet(A,B)),
inference(subst,[],[refute_0_1212:[bind(X_35,$fot(meet(A,B)))]]) ).
cnf(refute_0_1214,plain,
( composition(join(one,one),meet(A,B)) != meet(A,B)
| composition(meet(A,B),join(one,one)) != composition(join(one,one),meet(A,B))
| composition(meet(A,B),join(one,one)) = meet(A,B) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(composition(meet(A,B),join(one,one)))),bind(Y,$fot(composition(join(one,one),meet(A,B)))),bind(Z,$fot(meet(A,B)))]]) ).
cnf(refute_0_1215,plain,
( composition(join(one,one),meet(A,B)) != meet(A,B)
| composition(meet(A,B),join(one,one)) = meet(A,B) ),
inference(resolve,[$cnf( $equal(composition(meet(A,B),join(one,one)),composition(join(one,one),meet(A,B))) )],[refute_0_1213,refute_0_1214]) ).
cnf(refute_0_1216,plain,
composition(meet(A,B),join(one,one)) = meet(A,B),
inference(resolve,[$cnf( $equal(composition(join(one,one),meet(A,B)),meet(A,B)) )],[refute_0_1204,refute_0_1215]) ).
cnf(refute_0_1217,plain,
( composition(A,join(one,one)) != join(A,A)
| join(A,A) = composition(A,join(one,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(A,join(one,one)))),bind(Y,$fot(join(A,A)))]]) ).
cnf(refute_0_1218,plain,
join(A,A) = composition(A,join(one,one)),
inference(resolve,[$cnf( $equal(composition(A,join(one,one)),join(A,A)) )],[refute_0_660,refute_0_1217]) ).
cnf(refute_0_1219,plain,
join(meet(A,B),meet(A,B)) = composition(meet(A,B),join(one,one)),
inference(subst,[],[refute_0_1218:[bind(A,$fot(meet(A,B)))]]) ).
cnf(refute_0_1220,plain,
( composition(meet(A,B),join(one,one)) != meet(A,B)
| join(meet(A,B),meet(A,B)) != composition(meet(A,B),join(one,one))
| join(meet(A,B),meet(A,B)) = meet(A,B) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(A,B),meet(A,B)))),bind(Y,$fot(composition(meet(A,B),join(one,one)))),bind(Z,$fot(meet(A,B)))]]) ).
cnf(refute_0_1221,plain,
( composition(meet(A,B),join(one,one)) != meet(A,B)
| join(meet(A,B),meet(A,B)) = meet(A,B) ),
inference(resolve,[$cnf( $equal(join(meet(A,B),meet(A,B)),composition(meet(A,B),join(one,one))) )],[refute_0_1219,refute_0_1220]) ).
cnf(refute_0_1222,plain,
join(meet(A,B),meet(A,B)) = meet(A,B),
inference(resolve,[$cnf( $equal(composition(meet(A,B),join(one,one)),meet(A,B)) )],[refute_0_1216,refute_0_1221]) ).
cnf(refute_0_1223,plain,
complement(complement(meet(A,B))) = meet(A,B),
inference(subst,[],[refute_0_848:[bind(X_107,$fot(meet(A,B)))]]) ).
cnf(refute_0_1224,plain,
join(meet(A,B),complement(complement(meet(A,B)))) = join(meet(A,B),complement(complement(meet(A,B)))),
introduced(tautology,[refl,[$fot(join(meet(A,B),complement(complement(meet(A,B)))))]]) ).
cnf(refute_0_1225,plain,
( complement(complement(meet(A,B))) != meet(A,B)
| join(meet(A,B),complement(complement(meet(A,B)))) != join(meet(A,B),complement(complement(meet(A,B))))
| join(meet(A,B),complement(complement(meet(A,B)))) = join(meet(A,B),meet(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(A,B),complement(complement(meet(A,B)))),join(meet(A,B),complement(complement(meet(A,B))))) ),[1,1],$fot(meet(A,B))]]) ).
cnf(refute_0_1226,plain,
( complement(complement(meet(A,B))) != meet(A,B)
| join(meet(A,B),complement(complement(meet(A,B)))) = join(meet(A,B),meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(meet(A,B),complement(complement(meet(A,B)))),join(meet(A,B),complement(complement(meet(A,B))))) )],[refute_0_1224,refute_0_1225]) ).
cnf(refute_0_1227,plain,
join(meet(A,B),complement(complement(meet(A,B)))) = join(meet(A,B),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(complement(meet(A,B))),meet(A,B)) )],[refute_0_1223,refute_0_1226]) ).
cnf(refute_0_1228,plain,
( join(meet(A,B),complement(complement(meet(A,B)))) != join(meet(A,B),meet(A,B))
| join(meet(A,B),meet(A,B)) != meet(A,B)
| join(meet(A,B),complement(complement(meet(A,B)))) = meet(A,B) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(A,B),complement(complement(meet(A,B)))))),bind(Y,$fot(join(meet(A,B),meet(A,B)))),bind(Z,$fot(meet(A,B)))]]) ).
cnf(refute_0_1229,plain,
( join(meet(A,B),meet(A,B)) != meet(A,B)
| join(meet(A,B),complement(complement(meet(A,B)))) = meet(A,B) ),
inference(resolve,[$cnf( $equal(join(meet(A,B),complement(complement(meet(A,B)))),join(meet(A,B),meet(A,B))) )],[refute_0_1227,refute_0_1228]) ).
cnf(refute_0_1230,plain,
join(meet(A,B),complement(complement(meet(A,B)))) = meet(A,B),
inference(resolve,[$cnf( $equal(join(meet(A,B),meet(A,B)),meet(A,B)) )],[refute_0_1222,refute_0_1229]) ).
cnf(refute_0_1231,plain,
complement(join(meet(A,B),complement(complement(meet(A,B))))) = complement(join(meet(A,B),complement(complement(meet(A,B))))),
introduced(tautology,[refl,[$fot(complement(join(meet(A,B),complement(complement(meet(A,B))))))]]) ).
cnf(refute_0_1232,plain,
( complement(join(meet(A,B),complement(complement(meet(A,B))))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| join(meet(A,B),complement(complement(meet(A,B)))) != meet(A,B)
| complement(join(meet(A,B),complement(complement(meet(A,B))))) = complement(meet(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(A,B),complement(complement(meet(A,B))))),complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),[1,0],$fot(meet(A,B))]]) ).
cnf(refute_0_1233,plain,
( join(meet(A,B),complement(complement(meet(A,B)))) != meet(A,B)
| complement(join(meet(A,B),complement(complement(meet(A,B))))) = complement(meet(A,B)) ),
inference(resolve,[$cnf( $equal(complement(join(meet(A,B),complement(complement(meet(A,B))))),complement(join(meet(A,B),complement(complement(meet(A,B)))))) )],[refute_0_1231,refute_0_1232]) ).
cnf(refute_0_1234,plain,
complement(join(meet(A,B),complement(complement(meet(A,B))))) = complement(meet(A,B)),
inference(resolve,[$cnf( $equal(join(meet(A,B),complement(complement(meet(A,B)))),meet(A,B)) )],[refute_0_1230,refute_0_1233]) ).
cnf(refute_0_1235,plain,
join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) = complement(join(meet(A,B),complement(complement(meet(A,B))))),
inference(subst,[],[refute_0_871:[bind(X_107,$fot(complement(join(meet(A,B),complement(complement(meet(A,B)))))))]]) ).
cnf(refute_0_1236,plain,
( complement(join(meet(A,B),complement(complement(meet(A,B))))) != complement(meet(A,B))
| join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) = complement(meet(A,B)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))))),bind(Y,$fot(complement(join(meet(A,B),complement(complement(meet(A,B))))))),bind(Z,$fot(complement(meet(A,B))))]]) ).
cnf(refute_0_1237,plain,
( complement(join(meet(A,B),complement(complement(meet(A,B))))) != complement(meet(A,B))
| join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) = complement(meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),complement(join(meet(A,B),complement(complement(meet(A,B)))))) )],[refute_0_1235,refute_0_1236]) ).
cnf(refute_0_1238,plain,
join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) = complement(meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(meet(A,B),complement(complement(meet(A,B))))),complement(meet(A,B))) )],[refute_0_1234,refute_0_1237]) ).
cnf(refute_0_1239,plain,
( join(complement(A),complement(B)) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) != complement(meet(A,B))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),complement(meet(A,B))) ),[0],$fot(join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))))]]) ).
cnf(refute_0_1240,plain,
( join(complement(A),complement(B)) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),complement(meet(A,B))) )],[refute_0_1238,refute_0_1239]) ).
cnf(refute_0_1241,plain,
join(complement(A),complement(B)) = complement(meet(A,B)),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) )],[refute_0_1197,refute_0_1240]) ).
cnf(refute_0_1242,plain,
join(complement(X_10),complement(X_11)) = complement(meet(X_10,X_11)),
inference(subst,[],[refute_0_1241:[bind(A,$fot(X_10)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_1243,plain,
meet(join(complement(X_10),complement(X_11)),B) = meet(join(complement(X_10),complement(X_11)),B),
introduced(tautology,[refl,[$fot(meet(join(complement(X_10),complement(X_11)),B))]]) ).
cnf(refute_0_1244,plain,
( join(complement(X_10),complement(X_11)) != complement(meet(X_10,X_11))
| meet(join(complement(X_10),complement(X_11)),B) != meet(join(complement(X_10),complement(X_11)),B)
| meet(join(complement(X_10),complement(X_11)),B) = meet(complement(meet(X_10,X_11)),B) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_10),complement(X_11)),B),meet(join(complement(X_10),complement(X_11)),B)) ),[1,0],$fot(complement(meet(X_10,X_11)))]]) ).
cnf(refute_0_1245,plain,
( join(complement(X_10),complement(X_11)) != complement(meet(X_10,X_11))
| meet(join(complement(X_10),complement(X_11)),B) = meet(complement(meet(X_10,X_11)),B) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_10),complement(X_11)),B),meet(join(complement(X_10),complement(X_11)),B)) )],[refute_0_1243,refute_0_1244]) ).
cnf(refute_0_1246,plain,
meet(join(complement(X_10),complement(X_11)),B) = meet(complement(meet(X_10,X_11)),B),
inference(resolve,[$cnf( $equal(join(complement(X_10),complement(X_11)),complement(meet(X_10,X_11))) )],[refute_0_1242,refute_0_1245]) ).
cnf(refute_0_1247,plain,
( meet(join(complement(X_10),complement(X_11)),B) != complement(join(meet(X_10,X_11),complement(B)))
| meet(join(complement(X_10),complement(X_11)),B) != meet(complement(meet(X_10,X_11)),B)
| meet(complement(meet(X_10,X_11)),B) = complement(join(meet(X_10,X_11),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_10),complement(X_11)),B),complement(join(meet(X_10,X_11),complement(B)))) ),[0],$fot(meet(complement(meet(X_10,X_11)),B))]]) ).
cnf(refute_0_1248,plain,
( meet(join(complement(X_10),complement(X_11)),B) != complement(join(meet(X_10,X_11),complement(B)))
| meet(complement(meet(X_10,X_11)),B) = complement(join(meet(X_10,X_11),complement(B))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_10),complement(X_11)),B),meet(complement(meet(X_10,X_11)),B)) )],[refute_0_1246,refute_0_1247]) ).
cnf(refute_0_1249,plain,
meet(complement(meet(X_10,X_11)),B) = complement(join(meet(X_10,X_11),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_10),complement(X_11)),B),complement(join(meet(X_10,X_11),complement(B)))) )],[refute_0_201,refute_0_1248]) ).
cnf(refute_0_1250,plain,
meet(complement(meet(top,X_298)),X_296) = complement(join(meet(top,X_298),complement(X_296))),
inference(subst,[],[refute_0_1249:[bind(B,$fot(X_296)),bind(X_10,$fot(top)),bind(X_11,$fot(X_298))]]) ).
cnf(refute_0_1251,plain,
complement(complement(X_115)) = X_115,
inference(subst,[],[refute_0_848:[bind(X_107,$fot(X_115))]]) ).
cnf(refute_0_1252,plain,
( complement(complement(X_115)) != X_115
| meet(top,X_115) != complement(complement(X_115))
| meet(top,X_115) = X_115 ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,X_115),complement(complement(X_115))) ),[1],$fot(X_115)]]) ).
cnf(refute_0_1253,plain,
( meet(top,X_115) != complement(complement(X_115))
| meet(top,X_115) = X_115 ),
inference(resolve,[$cnf( $equal(complement(complement(X_115)),X_115) )],[refute_0_1251,refute_0_1252]) ).
cnf(refute_0_1254,plain,
meet(top,X_115) = X_115,
inference(resolve,[$cnf( $equal(meet(top,X_115),complement(complement(X_115))) )],[refute_0_800,refute_0_1253]) ).
cnf(refute_0_1255,plain,
meet(top,X_298) = X_298,
inference(subst,[],[refute_0_1254:[bind(X_115,$fot(X_298))]]) ).
cnf(refute_0_1256,plain,
( meet(complement(meet(top,X_298)),X_296) != complement(join(meet(top,X_298),complement(X_296)))
| meet(top,X_298) != X_298
| meet(complement(meet(top,X_298)),X_296) = complement(join(X_298,complement(X_296))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(top,X_298)),X_296),complement(join(meet(top,X_298),complement(X_296)))) ),[1,0,0],$fot(X_298)]]) ).
cnf(refute_0_1257,plain,
( meet(complement(meet(top,X_298)),X_296) != complement(join(meet(top,X_298),complement(X_296)))
| meet(complement(meet(top,X_298)),X_296) = complement(join(X_298,complement(X_296))) ),
inference(resolve,[$cnf( $equal(meet(top,X_298),X_298) )],[refute_0_1255,refute_0_1256]) ).
cnf(refute_0_1258,plain,
meet(complement(meet(top,X_298)),X_296) = complement(join(X_298,complement(X_296))),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_298)),X_296),complement(join(meet(top,X_298),complement(X_296)))) )],[refute_0_1250,refute_0_1257]) ).
cnf(refute_0_1259,plain,
complement(meet(top,X_298)) = complement(meet(top,X_298)),
introduced(tautology,[refl,[$fot(complement(meet(top,X_298)))]]) ).
cnf(refute_0_1260,plain,
( complement(meet(top,X_298)) != complement(meet(top,X_298))
| meet(top,X_298) != X_298
| complement(meet(top,X_298)) = complement(X_298) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,X_298)),complement(meet(top,X_298))) ),[1,0],$fot(X_298)]]) ).
cnf(refute_0_1261,plain,
( meet(top,X_298) != X_298
| complement(meet(top,X_298)) = complement(X_298) ),
inference(resolve,[$cnf( $equal(complement(meet(top,X_298)),complement(meet(top,X_298))) )],[refute_0_1259,refute_0_1260]) ).
cnf(refute_0_1262,plain,
complement(meet(top,X_298)) = complement(X_298),
inference(resolve,[$cnf( $equal(meet(top,X_298),X_298) )],[refute_0_1255,refute_0_1261]) ).
cnf(refute_0_1263,plain,
meet(complement(meet(top,X_298)),X_296) = meet(complement(meet(top,X_298)),X_296),
introduced(tautology,[refl,[$fot(meet(complement(meet(top,X_298)),X_296))]]) ).
cnf(refute_0_1264,plain,
( complement(meet(top,X_298)) != complement(X_298)
| meet(complement(meet(top,X_298)),X_296) != meet(complement(meet(top,X_298)),X_296)
| meet(complement(meet(top,X_298)),X_296) = meet(complement(X_298),X_296) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(top,X_298)),X_296),meet(complement(meet(top,X_298)),X_296)) ),[1,0],$fot(complement(X_298))]]) ).
cnf(refute_0_1265,plain,
( complement(meet(top,X_298)) != complement(X_298)
| meet(complement(meet(top,X_298)),X_296) = meet(complement(X_298),X_296) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_298)),X_296),meet(complement(meet(top,X_298)),X_296)) )],[refute_0_1263,refute_0_1264]) ).
cnf(refute_0_1266,plain,
meet(complement(meet(top,X_298)),X_296) = meet(complement(X_298),X_296),
inference(resolve,[$cnf( $equal(complement(meet(top,X_298)),complement(X_298)) )],[refute_0_1262,refute_0_1265]) ).
cnf(refute_0_1267,plain,
( meet(complement(meet(top,X_298)),X_296) != complement(join(X_298,complement(X_296)))
| meet(complement(meet(top,X_298)),X_296) != meet(complement(X_298),X_296)
| meet(complement(X_298),X_296) = complement(join(X_298,complement(X_296))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(meet(top,X_298)),X_296),complement(join(X_298,complement(X_296)))) ),[0],$fot(meet(complement(X_298),X_296))]]) ).
cnf(refute_0_1268,plain,
( meet(complement(meet(top,X_298)),X_296) != complement(join(X_298,complement(X_296)))
| meet(complement(X_298),X_296) = complement(join(X_298,complement(X_296))) ),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_298)),X_296),meet(complement(X_298),X_296)) )],[refute_0_1266,refute_0_1267]) ).
cnf(refute_0_1269,plain,
meet(complement(X_298),X_296) = complement(join(X_298,complement(X_296))),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,X_298)),X_296),complement(join(X_298,complement(X_296)))) )],[refute_0_1258,refute_0_1268]) ).
cnf(refute_0_1270,plain,
meet(complement(X_300),complement(X_107)) = complement(join(X_300,complement(complement(X_107)))),
inference(subst,[],[refute_0_1269:[bind(X_296,$fot(complement(X_107))),bind(X_298,$fot(X_300))]]) ).
cnf(refute_0_1271,plain,
( complement(complement(X_107)) != X_107
| meet(complement(X_300),complement(X_107)) != complement(join(X_300,complement(complement(X_107))))
| meet(complement(X_300),complement(X_107)) = complement(join(X_300,X_107)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_300),complement(X_107)),complement(join(X_300,complement(complement(X_107))))) ),[1,0,1],$fot(X_107)]]) ).
cnf(refute_0_1272,plain,
( meet(complement(X_300),complement(X_107)) != complement(join(X_300,complement(complement(X_107))))
| meet(complement(X_300),complement(X_107)) = complement(join(X_300,X_107)) ),
inference(resolve,[$cnf( $equal(complement(complement(X_107)),X_107) )],[refute_0_848,refute_0_1271]) ).
cnf(refute_0_1273,plain,
meet(complement(X_300),complement(X_107)) = complement(join(X_300,X_107)),
inference(resolve,[$cnf( $equal(meet(complement(X_300),complement(X_107)),complement(join(X_300,complement(complement(X_107))))) )],[refute_0_1270,refute_0_1272]) ).
cnf(refute_0_1274,plain,
meet(complement(one),complement(composition(complement(converse(X_125)),X_125))) = complement(join(one,composition(complement(converse(X_125)),X_125))),
inference(subst,[],[refute_0_1273:[bind(X_107,$fot(composition(complement(converse(X_125)),X_125))),bind(X_300,$fot(one))]]) ).
cnf(refute_0_1275,plain,
join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) = join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))),
introduced(tautology,[refl,[$fot(join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))))]]) ).
cnf(refute_0_1276,plain,
( join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) != join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))
| meet(complement(one),complement(composition(complement(converse(X_125)),X_125))) != complement(join(one,composition(complement(converse(X_125)),X_125)))
| join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) = join(one,complement(join(one,composition(complement(converse(X_125)),X_125)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))),join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))) ),[1,1],$fot(complement(join(one,composition(complement(converse(X_125)),X_125))))]]) ).
cnf(refute_0_1277,plain,
( meet(complement(one),complement(composition(complement(converse(X_125)),X_125))) != complement(join(one,composition(complement(converse(X_125)),X_125)))
| join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) = join(one,complement(join(one,composition(complement(converse(X_125)),X_125)))) ),
inference(resolve,[$cnf( $equal(join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))),join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))) )],[refute_0_1275,refute_0_1276]) ).
cnf(refute_0_1278,plain,
join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) = join(one,complement(join(one,composition(complement(converse(X_125)),X_125)))),
inference(resolve,[$cnf( $equal(meet(complement(one),complement(composition(complement(converse(X_125)),X_125))),complement(join(one,composition(complement(converse(X_125)),X_125)))) )],[refute_0_1274,refute_0_1277]) ).
cnf(refute_0_1279,plain,
( complement(composition(complement(converse(X_125)),X_125)) != join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))
| join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))) != join(one,complement(join(one,composition(complement(converse(X_125)),X_125))))
| complement(composition(complement(converse(X_125)),X_125)) = join(one,complement(join(one,composition(complement(converse(X_125)),X_125)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(complement(converse(X_125)),X_125)),join(one,complement(join(one,composition(complement(converse(X_125)),X_125))))) ),[0],$fot(join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))))]]) ).
cnf(refute_0_1280,plain,
( complement(composition(complement(converse(X_125)),X_125)) != join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))
| complement(composition(complement(converse(X_125)),X_125)) = join(one,complement(join(one,composition(complement(converse(X_125)),X_125)))) ),
inference(resolve,[$cnf( $equal(join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125)))),join(one,complement(join(one,composition(complement(converse(X_125)),X_125))))) )],[refute_0_1278,refute_0_1279]) ).
cnf(refute_0_1281,plain,
complement(composition(complement(converse(X_125)),X_125)) = join(one,complement(join(one,composition(complement(converse(X_125)),X_125)))),
inference(resolve,[$cnf( $equal(complement(composition(complement(converse(X_125)),X_125)),join(one,meet(complement(one),complement(composition(complement(converse(X_125)),X_125))))) )],[refute_0_1173,refute_0_1280]) ).
cnf(refute_0_1282,plain,
join(X_300,complement(X_299)) = complement(complement(join(X_300,complement(X_299)))),
inference(subst,[],[refute_0_846:[bind(X_107,$fot(join(X_300,complement(X_299))))]]) ).
cnf(refute_0_1283,plain,
meet(complement(X_300),X_299) = complement(join(X_300,complement(X_299))),
inference(subst,[],[refute_0_1269:[bind(X_296,$fot(X_299)),bind(X_298,$fot(X_300))]]) ).
cnf(refute_0_1284,plain,
( meet(complement(X_300),X_299) != complement(join(X_300,complement(X_299)))
| complement(join(X_300,complement(X_299))) = meet(complement(X_300),X_299) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_300),X_299))),bind(Y,$fot(complement(join(X_300,complement(X_299)))))]]) ).
cnf(refute_0_1285,plain,
complement(join(X_300,complement(X_299))) = meet(complement(X_300),X_299),
inference(resolve,[$cnf( $equal(meet(complement(X_300),X_299),complement(join(X_300,complement(X_299)))) )],[refute_0_1283,refute_0_1284]) ).
cnf(refute_0_1286,plain,
( complement(join(X_300,complement(X_299))) != meet(complement(X_300),X_299)
| join(X_300,complement(X_299)) != complement(complement(join(X_300,complement(X_299))))
| join(X_300,complement(X_299)) = complement(meet(complement(X_300),X_299)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_300,complement(X_299)),complement(complement(join(X_300,complement(X_299))))) ),[1,0],$fot(meet(complement(X_300),X_299))]]) ).
cnf(refute_0_1287,plain,
( join(X_300,complement(X_299)) != complement(complement(join(X_300,complement(X_299))))
| join(X_300,complement(X_299)) = complement(meet(complement(X_300),X_299)) ),
inference(resolve,[$cnf( $equal(complement(join(X_300,complement(X_299))),meet(complement(X_300),X_299)) )],[refute_0_1285,refute_0_1286]) ).
cnf(refute_0_1288,plain,
join(X_300,complement(X_299)) = complement(meet(complement(X_300),X_299)),
inference(resolve,[$cnf( $equal(join(X_300,complement(X_299)),complement(complement(join(X_300,complement(X_299))))) )],[refute_0_1282,refute_0_1287]) ).
cnf(refute_0_1289,plain,
join(X_444,complement(join(X_150,complement(X_444)))) = complement(meet(complement(X_444),join(X_150,complement(X_444)))),
inference(subst,[],[refute_0_1288:[bind(X_299,$fot(join(X_150,complement(X_444)))),bind(X_300,$fot(X_444))]]) ).
cnf(refute_0_1290,plain,
X_149 = meet(X_149,join(X_149,X_150)),
inference(subst,[],[refute_0_907:[bind(X_107,$fot(X_149)),bind(X_148,$fot(X_150))]]) ).
cnf(refute_0_1291,plain,
join(X_150,X_149) = join(X_149,X_150),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_150)),bind(B,$fot(X_149))]]) ).
cnf(refute_0_1292,plain,
( join(X_150,X_149) != join(X_149,X_150)
| join(X_149,X_150) = join(X_150,X_149) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_150,X_149))),bind(Y,$fot(join(X_149,X_150)))]]) ).
cnf(refute_0_1293,plain,
join(X_149,X_150) = join(X_150,X_149),
inference(resolve,[$cnf( $equal(join(X_150,X_149),join(X_149,X_150)) )],[refute_0_1291,refute_0_1292]) ).
cnf(refute_0_1294,plain,
( X_149 != meet(X_149,join(X_149,X_150))
| join(X_149,X_150) != join(X_150,X_149)
| X_149 = meet(X_149,join(X_150,X_149)) ),
introduced(tautology,[equality,[$cnf( $equal(X_149,meet(X_149,join(X_149,X_150))) ),[1,1],$fot(join(X_150,X_149))]]) ).
cnf(refute_0_1295,plain,
( X_149 != meet(X_149,join(X_149,X_150))
| X_149 = meet(X_149,join(X_150,X_149)) ),
inference(resolve,[$cnf( $equal(join(X_149,X_150),join(X_150,X_149)) )],[refute_0_1293,refute_0_1294]) ).
cnf(refute_0_1296,plain,
X_149 = meet(X_149,join(X_150,X_149)),
inference(resolve,[$cnf( $equal(X_149,meet(X_149,join(X_149,X_150))) )],[refute_0_1290,refute_0_1295]) ).
cnf(refute_0_1297,plain,
complement(X_444) = meet(complement(X_444),join(X_150,complement(X_444))),
inference(subst,[],[refute_0_1296:[bind(X_149,$fot(complement(X_444)))]]) ).
cnf(refute_0_1298,plain,
( complement(X_444) != meet(complement(X_444),join(X_150,complement(X_444)))
| meet(complement(X_444),join(X_150,complement(X_444))) = complement(X_444) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_444))),bind(Y,$fot(meet(complement(X_444),join(X_150,complement(X_444)))))]]) ).
cnf(refute_0_1299,plain,
meet(complement(X_444),join(X_150,complement(X_444))) = complement(X_444),
inference(resolve,[$cnf( $equal(complement(X_444),meet(complement(X_444),join(X_150,complement(X_444)))) )],[refute_0_1297,refute_0_1298]) ).
cnf(refute_0_1300,plain,
( join(X_444,complement(join(X_150,complement(X_444)))) != complement(meet(complement(X_444),join(X_150,complement(X_444))))
| meet(complement(X_444),join(X_150,complement(X_444))) != complement(X_444)
| join(X_444,complement(join(X_150,complement(X_444)))) = complement(complement(X_444)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_444,complement(join(X_150,complement(X_444)))),complement(meet(complement(X_444),join(X_150,complement(X_444))))) ),[1,0],$fot(complement(X_444))]]) ).
cnf(refute_0_1301,plain,
( join(X_444,complement(join(X_150,complement(X_444)))) != complement(meet(complement(X_444),join(X_150,complement(X_444))))
| join(X_444,complement(join(X_150,complement(X_444)))) = complement(complement(X_444)) ),
inference(resolve,[$cnf( $equal(meet(complement(X_444),join(X_150,complement(X_444))),complement(X_444)) )],[refute_0_1299,refute_0_1300]) ).
cnf(refute_0_1302,plain,
join(X_444,complement(join(X_150,complement(X_444)))) = complement(complement(X_444)),
inference(resolve,[$cnf( $equal(join(X_444,complement(join(X_150,complement(X_444)))),complement(meet(complement(X_444),join(X_150,complement(X_444))))) )],[refute_0_1289,refute_0_1301]) ).
cnf(refute_0_1303,plain,
( meet(complement(X_298),X_296) != complement(join(X_298,complement(X_296)))
| complement(join(X_298,complement(X_296))) = meet(complement(X_298),X_296) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_298),X_296))),bind(Y,$fot(complement(join(X_298,complement(X_296)))))]]) ).
cnf(refute_0_1304,plain,
complement(join(X_298,complement(X_296))) = meet(complement(X_298),X_296),
inference(resolve,[$cnf( $equal(meet(complement(X_298),X_296),complement(join(X_298,complement(X_296)))) )],[refute_0_1269,refute_0_1303]) ).
cnf(refute_0_1305,plain,
complement(join(X_150,complement(X_444))) = meet(complement(X_150),X_444),
inference(subst,[],[refute_0_1304:[bind(X_296,$fot(X_444)),bind(X_298,$fot(X_150))]]) ).
cnf(refute_0_1306,plain,
join(X_444,complement(join(X_150,complement(X_444)))) = join(X_444,complement(join(X_150,complement(X_444)))),
introduced(tautology,[refl,[$fot(join(X_444,complement(join(X_150,complement(X_444)))))]]) ).
cnf(refute_0_1307,plain,
( complement(join(X_150,complement(X_444))) != meet(complement(X_150),X_444)
| join(X_444,complement(join(X_150,complement(X_444)))) != join(X_444,complement(join(X_150,complement(X_444))))
| join(X_444,complement(join(X_150,complement(X_444)))) = join(X_444,meet(complement(X_150),X_444)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_444,complement(join(X_150,complement(X_444)))),join(X_444,complement(join(X_150,complement(X_444))))) ),[1,1],$fot(meet(complement(X_150),X_444))]]) ).
cnf(refute_0_1308,plain,
( complement(join(X_150,complement(X_444))) != meet(complement(X_150),X_444)
| join(X_444,complement(join(X_150,complement(X_444)))) = join(X_444,meet(complement(X_150),X_444)) ),
inference(resolve,[$cnf( $equal(join(X_444,complement(join(X_150,complement(X_444)))),join(X_444,complement(join(X_150,complement(X_444))))) )],[refute_0_1306,refute_0_1307]) ).
cnf(refute_0_1309,plain,
join(X_444,complement(join(X_150,complement(X_444)))) = join(X_444,meet(complement(X_150),X_444)),
inference(resolve,[$cnf( $equal(complement(join(X_150,complement(X_444))),meet(complement(X_150),X_444)) )],[refute_0_1305,refute_0_1308]) ).
cnf(refute_0_1310,plain,
( join(X_444,complement(join(X_150,complement(X_444)))) != complement(complement(X_444))
| join(X_444,complement(join(X_150,complement(X_444)))) != join(X_444,meet(complement(X_150),X_444))
| join(X_444,meet(complement(X_150),X_444)) = complement(complement(X_444)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_444,complement(join(X_150,complement(X_444)))),complement(complement(X_444))) ),[0],$fot(join(X_444,meet(complement(X_150),X_444)))]]) ).
cnf(refute_0_1311,plain,
( join(X_444,complement(join(X_150,complement(X_444)))) != complement(complement(X_444))
| join(X_444,meet(complement(X_150),X_444)) = complement(complement(X_444)) ),
inference(resolve,[$cnf( $equal(join(X_444,complement(join(X_150,complement(X_444)))),join(X_444,meet(complement(X_150),X_444))) )],[refute_0_1309,refute_0_1310]) ).
cnf(refute_0_1312,plain,
complement(complement(X_444)) = X_444,
inference(subst,[],[refute_0_848:[bind(X_107,$fot(X_444))]]) ).
cnf(refute_0_1313,plain,
( complement(complement(X_444)) != X_444
| join(X_444,meet(complement(X_150),X_444)) != complement(complement(X_444))
| join(X_444,meet(complement(X_150),X_444)) = X_444 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_444,meet(complement(X_150),X_444)),complement(complement(X_444))) ),[1],$fot(X_444)]]) ).
cnf(refute_0_1314,plain,
( join(X_444,meet(complement(X_150),X_444)) != complement(complement(X_444))
| join(X_444,meet(complement(X_150),X_444)) = X_444 ),
inference(resolve,[$cnf( $equal(complement(complement(X_444)),X_444) )],[refute_0_1312,refute_0_1313]) ).
cnf(refute_0_1315,plain,
( join(X_444,complement(join(X_150,complement(X_444)))) != complement(complement(X_444))
| join(X_444,meet(complement(X_150),X_444)) = X_444 ),
inference(resolve,[$cnf( $equal(join(X_444,meet(complement(X_150),X_444)),complement(complement(X_444))) )],[refute_0_1311,refute_0_1314]) ).
cnf(refute_0_1316,plain,
join(X_444,meet(complement(X_150),X_444)) = X_444,
inference(resolve,[$cnf( $equal(join(X_444,complement(join(X_150,complement(X_444)))),complement(complement(X_444))) )],[refute_0_1302,refute_0_1315]) ).
cnf(refute_0_1317,plain,
join(join(X_107,meet(complement(X_107),complement(X_583))),meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583))))) = join(X_107,meet(complement(X_107),complement(X_583))),
inference(subst,[],[refute_0_1316:[bind(X_150,$fot(X_583)),bind(X_444,$fot(join(X_107,meet(complement(X_107),complement(X_583)))))]]) ).
cnf(refute_0_1318,plain,
X_107 = join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(join(complement(X_107),join(complement(X_22),meet(X_22,X_107))))),
inference(subst,[],[refute_0_146:[bind(A,$fot(X_107)),bind(B,$fot(join(complement(X_22),meet(X_22,X_107))))]]) ).
cnf(refute_0_1319,plain,
join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) = join(complement(X_22),join(complement(X_23),meet(X_22,X_23))),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(complement(X_23),meet(X_22,X_23)))),bind(B,$fot(complement(X_22)))]]) ).
cnf(refute_0_1320,plain,
top = join(complement(X_22),join(complement(X_23),meet(X_22,X_23))),
inference(subst,[],[refute_0_185:[bind(X_10,$fot(X_22)),bind(X_11,$fot(X_23))]]) ).
cnf(refute_0_1321,plain,
( top != join(complement(X_22),join(complement(X_23),meet(X_22,X_23)))
| join(complement(X_22),join(complement(X_23),meet(X_22,X_23))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_22),join(complement(X_23),meet(X_22,X_23)))))]]) ).
cnf(refute_0_1322,plain,
join(complement(X_22),join(complement(X_23),meet(X_22,X_23))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_22),join(complement(X_23),meet(X_22,X_23)))) )],[refute_0_1320,refute_0_1321]) ).
cnf(refute_0_1323,plain,
( join(complement(X_22),join(complement(X_23),meet(X_22,X_23))) != top
| join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) != join(complement(X_22),join(complement(X_23),meet(X_22,X_23)))
| join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)),join(complement(X_22),join(complement(X_23),meet(X_22,X_23)))) ),[1],$fot(top)]]) ).
cnf(refute_0_1324,plain,
( join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) != join(complement(X_22),join(complement(X_23),meet(X_22,X_23)))
| join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) = top ),
inference(resolve,[$cnf( $equal(join(complement(X_22),join(complement(X_23),meet(X_22,X_23))),top) )],[refute_0_1322,refute_0_1323]) ).
cnf(refute_0_1325,plain,
join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) = top,
inference(resolve,[$cnf( $equal(join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)),join(complement(X_22),join(complement(X_23),meet(X_22,X_23)))) )],[refute_0_1319,refute_0_1324]) ).
cnf(refute_0_1326,plain,
join(meet(X_22,X_23),complement(X_22)) = join(complement(X_22),meet(X_22,X_23)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_22))),bind(B,$fot(meet(X_22,X_23)))]]) ).
cnf(refute_0_1327,plain,
join(complement(X_23),join(meet(X_22,X_23),complement(X_22))) = join(complement(X_23),join(meet(X_22,X_23),complement(X_22))),
introduced(tautology,[refl,[$fot(join(complement(X_23),join(meet(X_22,X_23),complement(X_22))))]]) ).
cnf(refute_0_1328,plain,
( join(complement(X_23),join(meet(X_22,X_23),complement(X_22))) != join(complement(X_23),join(meet(X_22,X_23),complement(X_22)))
| join(meet(X_22,X_23),complement(X_22)) != join(complement(X_22),meet(X_22,X_23))
| join(complement(X_23),join(meet(X_22,X_23),complement(X_22))) = join(complement(X_23),join(complement(X_22),meet(X_22,X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_23),join(meet(X_22,X_23),complement(X_22))),join(complement(X_23),join(meet(X_22,X_23),complement(X_22)))) ),[1,1],$fot(join(complement(X_22),meet(X_22,X_23)))]]) ).
cnf(refute_0_1329,plain,
( join(meet(X_22,X_23),complement(X_22)) != join(complement(X_22),meet(X_22,X_23))
| join(complement(X_23),join(meet(X_22,X_23),complement(X_22))) = join(complement(X_23),join(complement(X_22),meet(X_22,X_23))) ),
inference(resolve,[$cnf( $equal(join(complement(X_23),join(meet(X_22,X_23),complement(X_22))),join(complement(X_23),join(meet(X_22,X_23),complement(X_22)))) )],[refute_0_1327,refute_0_1328]) ).
cnf(refute_0_1330,plain,
join(complement(X_23),join(meet(X_22,X_23),complement(X_22))) = join(complement(X_23),join(complement(X_22),meet(X_22,X_23))),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_23),complement(X_22)),join(complement(X_22),meet(X_22,X_23))) )],[refute_0_1326,refute_0_1329]) ).
cnf(refute_0_1331,plain,
join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) = join(complement(X_23),join(meet(X_22,X_23),complement(X_22))),
inference(subst,[],[refute_0_181:[bind(A,$fot(complement(X_23))),bind(B,$fot(meet(X_22,X_23))),bind(C,$fot(complement(X_22)))]]) ).
cnf(refute_0_1332,plain,
( join(complement(X_23),join(meet(X_22,X_23),complement(X_22))) != join(complement(X_23),join(complement(X_22),meet(X_22,X_23)))
| join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) != join(complement(X_23),join(meet(X_22,X_23),complement(X_22)))
| join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) = join(complement(X_23),join(complement(X_22),meet(X_22,X_23))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)))),bind(Y,$fot(join(complement(X_23),join(meet(X_22,X_23),complement(X_22))))),bind(Z,$fot(join(complement(X_23),join(complement(X_22),meet(X_22,X_23)))))]]) ).
cnf(refute_0_1333,plain,
( join(complement(X_23),join(meet(X_22,X_23),complement(X_22))) != join(complement(X_23),join(complement(X_22),meet(X_22,X_23)))
| join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) = join(complement(X_23),join(complement(X_22),meet(X_22,X_23))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)),join(complement(X_23),join(meet(X_22,X_23),complement(X_22)))) )],[refute_0_1331,refute_0_1332]) ).
cnf(refute_0_1334,plain,
join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) = join(complement(X_23),join(complement(X_22),meet(X_22,X_23))),
inference(resolve,[$cnf( $equal(join(complement(X_23),join(meet(X_22,X_23),complement(X_22))),join(complement(X_23),join(complement(X_22),meet(X_22,X_23)))) )],[refute_0_1330,refute_0_1333]) ).
cnf(refute_0_1335,plain,
( join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) != join(complement(X_23),join(complement(X_22),meet(X_22,X_23)))
| join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) != top
| join(complement(X_23),join(complement(X_22),meet(X_22,X_23))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)),top) ),[0],$fot(join(complement(X_23),join(complement(X_22),meet(X_22,X_23))))]]) ).
cnf(refute_0_1336,plain,
( join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)) != top
| join(complement(X_23),join(complement(X_22),meet(X_22,X_23))) = top ),
inference(resolve,[$cnf( $equal(join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)),join(complement(X_23),join(complement(X_22),meet(X_22,X_23)))) )],[refute_0_1334,refute_0_1335]) ).
cnf(refute_0_1337,plain,
join(complement(X_23),join(complement(X_22),meet(X_22,X_23))) = top,
inference(resolve,[$cnf( $equal(join(join(complement(X_23),meet(X_22,X_23)),complement(X_22)),top) )],[refute_0_1325,refute_0_1336]) ).
cnf(refute_0_1338,plain,
join(complement(X_107),join(complement(X_22),meet(X_22,X_107))) = top,
inference(subst,[],[refute_0_1337:[bind(X_23,$fot(X_107))]]) ).
cnf(refute_0_1339,plain,
( X_107 != join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(join(complement(X_107),join(complement(X_22),meet(X_22,X_107)))))
| join(complement(X_107),join(complement(X_22),meet(X_22,X_107))) != top
| X_107 = join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_107,join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(join(complement(X_107),join(complement(X_22),meet(X_22,X_107)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_1340,plain,
( X_107 != join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(join(complement(X_107),join(complement(X_22),meet(X_22,X_107)))))
| X_107 = join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_107),join(complement(X_22),meet(X_22,X_107))),top) )],[refute_0_1338,refute_0_1339]) ).
cnf(refute_0_1341,plain,
X_107 = join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(join(complement(X_107),join(complement(X_22),meet(X_22,X_107)))))) )],[refute_0_1318,refute_0_1340]) ).
cnf(refute_0_1342,plain,
join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))) = join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))))]]) ).
cnf(refute_0_1343,plain,
( complement(top) != zero
| join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))) != join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107))))
| join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))) = join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))),join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1344,plain,
( complement(top) != zero
| join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))) = join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))),join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107))))) )],[refute_0_1342,refute_0_1343]) ).
cnf(refute_0_1345,plain,
join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))) = join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_1344]) ).
cnf(refute_0_1346,plain,
join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)) = join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_107,join(complement(X_22),meet(X_22,X_107)))))]]) ).
cnf(refute_0_1347,plain,
( join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))) != join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107))))
| join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)) != join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107))))
| join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)) = join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))))),bind(Z,$fot(join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107))))))]]) ).
cnf(refute_0_1348,plain,
( join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))) != join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107))))
| join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)) = join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)),join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107))))) )],[refute_0_1346,refute_0_1347]) ).
cnf(refute_0_1349,plain,
join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)) = join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_107,join(complement(X_22),meet(X_22,X_107)))),join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107))))) )],[refute_0_1345,refute_0_1348]) ).
cnf(refute_0_1350,plain,
( X_107 != join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top))
| join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)) != join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107))))
| X_107 = join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107))))) ),[0],$fot(join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)))]]) ).
cnf(refute_0_1351,plain,
( X_107 != join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top))
| X_107 = join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top)),join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107))))) )],[refute_0_1349,refute_0_1350]) ).
cnf(refute_0_1352,plain,
X_107 = join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,join(complement(X_22),meet(X_22,X_107))),complement(top))) )],[refute_0_1341,refute_0_1351]) ).
cnf(refute_0_1353,plain,
join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))) = meet(X_107,join(complement(X_22),meet(X_22,X_107))),
inference(subst,[],[refute_0_871:[bind(X_107,$fot(meet(X_107,join(complement(X_22),meet(X_22,X_107)))))]]) ).
cnf(refute_0_1354,plain,
( X_107 != join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107))))
| join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))) != meet(X_107,join(complement(X_22),meet(X_22,X_107)))
| X_107 = meet(X_107,join(complement(X_22),meet(X_22,X_107))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,meet(X_107,join(complement(X_22),meet(X_22,X_107)))) ),[0],$fot(join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))))]]) ).
cnf(refute_0_1355,plain,
( X_107 != join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107))))
| X_107 = meet(X_107,join(complement(X_22),meet(X_22,X_107))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107)))),meet(X_107,join(complement(X_22),meet(X_22,X_107)))) )],[refute_0_1353,refute_0_1354]) ).
cnf(refute_0_1356,plain,
X_107 = meet(X_107,join(complement(X_22),meet(X_22,X_107))),
inference(resolve,[$cnf( $equal(X_107,join(zero,meet(X_107,join(complement(X_22),meet(X_22,X_107))))) )],[refute_0_1352,refute_0_1355]) ).
cnf(refute_0_1357,plain,
X_134 = meet(X_134,join(complement(complement(X_107)),meet(complement(X_107),X_134))),
inference(subst,[],[refute_0_1356:[bind(X_107,$fot(X_134)),bind(X_22,$fot(complement(X_107)))]]) ).
cnf(refute_0_1358,plain,
( X_134 != meet(X_134,join(complement(complement(X_107)),meet(complement(X_107),X_134)))
| complement(complement(X_107)) != X_107
| X_134 = meet(X_134,join(X_107,meet(complement(X_107),X_134))) ),
introduced(tautology,[equality,[$cnf( $equal(X_134,meet(X_134,join(complement(complement(X_107)),meet(complement(X_107),X_134)))) ),[1,1,0],$fot(X_107)]]) ).
cnf(refute_0_1359,plain,
( X_134 != meet(X_134,join(complement(complement(X_107)),meet(complement(X_107),X_134)))
| X_134 = meet(X_134,join(X_107,meet(complement(X_107),X_134))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_107)),X_107) )],[refute_0_848,refute_0_1358]) ).
cnf(refute_0_1360,plain,
X_134 = meet(X_134,join(X_107,meet(complement(X_107),X_134))),
inference(resolve,[$cnf( $equal(X_134,meet(X_134,join(complement(complement(X_107)),meet(complement(X_107),X_134)))) )],[refute_0_1357,refute_0_1359]) ).
cnf(refute_0_1361,plain,
complement(X_583) = meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583)))),
inference(subst,[],[refute_0_1360:[bind(X_134,$fot(complement(X_583)))]]) ).
cnf(refute_0_1362,plain,
( complement(X_583) != meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583))))
| meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583)))) = complement(X_583) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_583))),bind(Y,$fot(meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583))))))]]) ).
cnf(refute_0_1363,plain,
meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583)))) = complement(X_583),
inference(resolve,[$cnf( $equal(complement(X_583),meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583))))) )],[refute_0_1361,refute_0_1362]) ).
cnf(refute_0_1364,plain,
( join(join(X_107,meet(complement(X_107),complement(X_583))),meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583))))) != join(X_107,meet(complement(X_107),complement(X_583)))
| meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583)))) != complement(X_583)
| join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) = join(X_107,meet(complement(X_107),complement(X_583))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_107,meet(complement(X_107),complement(X_583))),meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583))))),join(X_107,meet(complement(X_107),complement(X_583)))) ),[0,1],$fot(complement(X_583))]]) ).
cnf(refute_0_1365,plain,
( join(join(X_107,meet(complement(X_107),complement(X_583))),meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583))))) != join(X_107,meet(complement(X_107),complement(X_583)))
| join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) = join(X_107,meet(complement(X_107),complement(X_583))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583)))),complement(X_583)) )],[refute_0_1363,refute_0_1364]) ).
cnf(refute_0_1366,plain,
join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) = join(X_107,meet(complement(X_107),complement(X_583))),
inference(resolve,[$cnf( $equal(join(join(X_107,meet(complement(X_107),complement(X_583))),meet(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583))))),join(X_107,meet(complement(X_107),complement(X_583)))) )],[refute_0_1317,refute_0_1365]) ).
cnf(refute_0_1367,plain,
join(X_41,join(X_42,meet(complement(X_583),X_41))) = join(X_42,join(X_41,meet(complement(X_583),X_41))),
inference(subst,[],[refute_0_374:[bind(X_43,$fot(meet(complement(X_583),X_41)))]]) ).
cnf(refute_0_1368,plain,
join(X_41,meet(complement(X_583),X_41)) = X_41,
inference(subst,[],[refute_0_1316:[bind(X_150,$fot(X_583)),bind(X_444,$fot(X_41))]]) ).
cnf(refute_0_1369,plain,
( join(X_41,join(X_42,meet(complement(X_583),X_41))) != join(X_42,join(X_41,meet(complement(X_583),X_41)))
| join(X_41,meet(complement(X_583),X_41)) != X_41
| join(X_41,join(X_42,meet(complement(X_583),X_41))) = join(X_42,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,join(X_42,meet(complement(X_583),X_41))),join(X_42,join(X_41,meet(complement(X_583),X_41)))) ),[1,1],$fot(X_41)]]) ).
cnf(refute_0_1370,plain,
( join(X_41,join(X_42,meet(complement(X_583),X_41))) != join(X_42,join(X_41,meet(complement(X_583),X_41)))
| join(X_41,join(X_42,meet(complement(X_583),X_41))) = join(X_42,X_41) ),
inference(resolve,[$cnf( $equal(join(X_41,meet(complement(X_583),X_41)),X_41) )],[refute_0_1368,refute_0_1369]) ).
cnf(refute_0_1371,plain,
join(X_41,join(X_42,meet(complement(X_583),X_41))) = join(X_42,X_41),
inference(resolve,[$cnf( $equal(join(X_41,join(X_42,meet(complement(X_583),X_41))),join(X_42,join(X_41,meet(complement(X_583),X_41)))) )],[refute_0_1367,refute_0_1370]) ).
cnf(refute_0_1372,plain,
join(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583)))) = join(X_107,complement(X_583)),
inference(subst,[],[refute_0_1371:[bind(X_41,$fot(complement(X_583))),bind(X_42,$fot(X_107)),bind(X_583,$fot(X_107))]]) ).
cnf(refute_0_1373,plain,
join(X_444,complement(composition(complement(X_444),top))) = complement(meet(complement(X_444),composition(complement(X_444),top))),
inference(subst,[],[refute_0_1288:[bind(X_299,$fot(composition(complement(X_444),top))),bind(X_300,$fot(X_444))]]) ).
cnf(refute_0_1374,plain,
X_107 = join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205)))))),
inference(subst,[],[refute_0_164:[bind(X_108,$fot(join(X_205,complement(join(complement(X_107),X_205)))))]]) ).
cnf(refute_0_1375,plain,
top = join(join(X_41,X_42),complement(join(X_41,X_42))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(X_41,X_42)))]]) ).
cnf(refute_0_1376,plain,
join(X_41,join(X_42,complement(join(X_41,X_42)))) = join(join(X_41,X_42),complement(join(X_41,X_42))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_41)),bind(B,$fot(X_42)),bind(C,$fot(complement(join(X_41,X_42))))]]) ).
cnf(refute_0_1377,plain,
( join(X_41,join(X_42,complement(join(X_41,X_42)))) != join(join(X_41,X_42),complement(join(X_41,X_42)))
| join(join(X_41,X_42),complement(join(X_41,X_42))) = join(X_41,join(X_42,complement(join(X_41,X_42)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_41,join(X_42,complement(join(X_41,X_42)))))),bind(Y,$fot(join(join(X_41,X_42),complement(join(X_41,X_42)))))]]) ).
cnf(refute_0_1378,plain,
join(join(X_41,X_42),complement(join(X_41,X_42))) = join(X_41,join(X_42,complement(join(X_41,X_42)))),
inference(resolve,[$cnf( $equal(join(X_41,join(X_42,complement(join(X_41,X_42)))),join(join(X_41,X_42),complement(join(X_41,X_42)))) )],[refute_0_1376,refute_0_1377]) ).
cnf(refute_0_1379,plain,
( join(join(X_41,X_42),complement(join(X_41,X_42))) != join(X_41,join(X_42,complement(join(X_41,X_42))))
| top != join(join(X_41,X_42),complement(join(X_41,X_42)))
| top = join(X_41,join(X_42,complement(join(X_41,X_42)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(X_41,X_42),complement(join(X_41,X_42)))) ),[1],$fot(join(X_41,join(X_42,complement(join(X_41,X_42)))))]]) ).
cnf(refute_0_1380,plain,
( top != join(join(X_41,X_42),complement(join(X_41,X_42)))
| top = join(X_41,join(X_42,complement(join(X_41,X_42)))) ),
inference(resolve,[$cnf( $equal(join(join(X_41,X_42),complement(join(X_41,X_42))),join(X_41,join(X_42,complement(join(X_41,X_42))))) )],[refute_0_1378,refute_0_1379]) ).
cnf(refute_0_1381,plain,
top = join(X_41,join(X_42,complement(join(X_41,X_42)))),
inference(resolve,[$cnf( $equal(top,join(join(X_41,X_42),complement(join(X_41,X_42)))) )],[refute_0_1375,refute_0_1380]) ).
cnf(refute_0_1382,plain,
top = join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205)))),
inference(subst,[],[refute_0_1381:[bind(X_41,$fot(complement(X_107))),bind(X_42,$fot(X_205))]]) ).
cnf(refute_0_1383,plain,
( top != join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205))))
| join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205))))))]]) ).
cnf(refute_0_1384,plain,
join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205)))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205))))) )],[refute_0_1382,refute_0_1383]) ).
cnf(refute_0_1385,plain,
( X_107 != join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205))))))
| join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205)))) != top
| X_107 = join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_107,join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_1386,plain,
( X_107 != join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205))))))
| X_107 = join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205)))),top) )],[refute_0_1384,refute_0_1385]) ).
cnf(refute_0_1387,plain,
X_107 = join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)),
inference(resolve,[$cnf( $equal(X_107,join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(join(complement(X_107),join(X_205,complement(join(complement(X_107),X_205))))))) )],[refute_0_1374,refute_0_1386]) ).
cnf(refute_0_1388,plain,
join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) = meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))),
inference(subst,[],[refute_0_871:[bind(X_107,$fot(meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))))]]) ).
cnf(refute_0_1389,plain,
meet(join(X_205,complement(join(complement(X_107),X_205))),X_107) = meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))),
inference(subst,[],[refute_0_882:[bind(X_10,$fot(X_107)),bind(X_11,$fot(join(X_205,complement(join(complement(X_107),X_205)))))]]) ).
cnf(refute_0_1390,plain,
join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),
introduced(tautology,[refl,[$fot(join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)))]]) ).
cnf(refute_0_1391,plain,
( join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) != join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107))
| meet(join(X_205,complement(join(complement(X_107),X_205))),X_107) != meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))
| join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107))) ),[1,1],$fot(meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))))]]) ).
cnf(refute_0_1392,plain,
( meet(join(X_205,complement(join(complement(X_107),X_205))),X_107) != meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))
| join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107))) )],[refute_0_1390,refute_0_1391]) ).
cnf(refute_0_1393,plain,
join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))),
inference(resolve,[$cnf( $equal(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) )],[refute_0_1389,refute_0_1392]) ).
cnf(refute_0_1394,plain,
join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)))]]) ).
cnf(refute_0_1395,plain,
( complement(top) != zero
| join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) != join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107))
| join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1396,plain,
( complement(top) != zero
| join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107))) )],[refute_0_1394,refute_0_1395]) ).
cnf(refute_0_1397,plain,
join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_1396]) ).
cnf(refute_0_1398,plain,
( join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) != join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107))
| join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) != join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))))
| join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)))),bind(Y,$fot(join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)))),bind(Z,$fot(join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))))))]]) ).
cnf(refute_0_1399,plain,
( join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) != join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))))
| join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107))) )],[refute_0_1397,refute_0_1398]) ).
cnf(refute_0_1400,plain,
join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))),
inference(resolve,[$cnf( $equal(join(zero,meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))))) )],[refute_0_1393,refute_0_1399]) ).
cnf(refute_0_1401,plain,
( join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) != join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))))
| join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) != meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))
| join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)))),bind(Y,$fot(join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))))),bind(Z,$fot(meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))))]]) ).
cnf(refute_0_1402,plain,
( join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) != meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))
| join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))))) )],[refute_0_1400,refute_0_1401]) ).
cnf(refute_0_1403,plain,
join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) = meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))),
inference(resolve,[$cnf( $equal(join(zero,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))),meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) )],[refute_0_1388,refute_0_1402]) ).
cnf(refute_0_1404,plain,
join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)) = join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)))]]) ).
cnf(refute_0_1405,plain,
( join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) != meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))
| join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)) != join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107))
| join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)) = meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)))),bind(Y,$fot(join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)))),bind(Z,$fot(meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))))]]) ).
cnf(refute_0_1406,plain,
( join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)) != meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))
| join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)) = meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)),join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107))) )],[refute_0_1404,refute_0_1405]) ).
cnf(refute_0_1407,plain,
join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)) = meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(X_205,complement(join(complement(X_107),X_205))),X_107)),meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) )],[refute_0_1403,refute_0_1406]) ).
cnf(refute_0_1408,plain,
( X_107 != join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top))
| join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)) != meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))
| X_107 = meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) ),[0],$fot(join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)))]]) ).
cnf(refute_0_1409,plain,
( X_107 != join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top))
| X_107 = meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top)),meet(X_107,join(X_205,complement(join(complement(X_107),X_205))))) )],[refute_0_1407,refute_0_1408]) ).
cnf(refute_0_1410,plain,
X_107 = meet(X_107,join(X_205,complement(join(complement(X_107),X_205)))),
inference(resolve,[$cnf( $equal(X_107,join(meet(join(X_205,complement(join(complement(X_107),X_205))),X_107),complement(top))) )],[refute_0_1387,refute_0_1409]) ).
cnf(refute_0_1411,plain,
X_107 = meet(X_107,join(composition(complement(complement(X_107)),top),complement(join(complement(X_107),composition(complement(complement(X_107)),top))))),
inference(subst,[],[refute_0_1410:[bind(X_205,$fot(composition(complement(complement(X_107)),top)))]]) ).
cnf(refute_0_1412,plain,
converse(join(converse(A),composition(top,complement(converse(A))))) = join(A,converse(composition(top,complement(converse(A))))),
inference(subst,[],[refute_0_918:[bind(X_5,$fot(composition(top,complement(converse(A)))))]]) ).
cnf(refute_0_1413,plain,
join(X_41,join(complement(X_41),meet(X_41,composition(top,complement(X_41))))) = top,
inference(subst,[],[refute_0_585:[bind(X_43,$fot(meet(X_41,composition(top,complement(X_41)))))]]) ).
cnf(refute_0_1414,plain,
X_107 = join(meet(X_107,complement(B)),complement(join(complement(X_107),complement(B)))),
inference(subst,[],[refute_0_146:[bind(A,$fot(X_107)),bind(B,$fot(complement(B)))]]) ).
cnf(refute_0_1415,plain,
meet(X_107,B) = complement(join(complement(X_107),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_107))]]) ).
cnf(refute_0_1416,plain,
( meet(X_107,B) != complement(join(complement(X_107),complement(B)))
| complement(join(complement(X_107),complement(B))) = meet(X_107,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_107,B))),bind(Y,$fot(complement(join(complement(X_107),complement(B)))))]]) ).
cnf(refute_0_1417,plain,
complement(join(complement(X_107),complement(B))) = meet(X_107,B),
inference(resolve,[$cnf( $equal(meet(X_107,B),complement(join(complement(X_107),complement(B)))) )],[refute_0_1415,refute_0_1416]) ).
cnf(refute_0_1418,plain,
( X_107 != join(meet(X_107,complement(B)),complement(join(complement(X_107),complement(B))))
| complement(join(complement(X_107),complement(B))) != meet(X_107,B)
| X_107 = join(meet(X_107,complement(B)),meet(X_107,B)) ),
introduced(tautology,[equality,[$cnf( $equal(X_107,join(meet(X_107,complement(B)),complement(join(complement(X_107),complement(B))))) ),[1,1],$fot(meet(X_107,B))]]) ).
cnf(refute_0_1419,plain,
( X_107 != join(meet(X_107,complement(B)),complement(join(complement(X_107),complement(B))))
| X_107 = join(meet(X_107,complement(B)),meet(X_107,B)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_107),complement(B))),meet(X_107,B)) )],[refute_0_1417,refute_0_1418]) ).
cnf(refute_0_1420,plain,
X_107 = join(meet(X_107,complement(B)),meet(X_107,B)),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,complement(B)),complement(join(complement(X_107),complement(B))))) )],[refute_0_1414,refute_0_1419]) ).
cnf(refute_0_1421,plain,
join(meet(X_107,complement(B)),meet(X_107,B)) = join(meet(X_107,B),meet(X_107,complement(B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(X_107,B))),bind(B,$fot(meet(X_107,complement(B))))]]) ).
cnf(refute_0_1422,plain,
( X_107 != join(meet(X_107,complement(B)),meet(X_107,B))
| join(meet(X_107,complement(B)),meet(X_107,B)) != join(meet(X_107,B),meet(X_107,complement(B)))
| X_107 = join(meet(X_107,B),meet(X_107,complement(B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,join(meet(X_107,B),meet(X_107,complement(B)))) ),[0],$fot(join(meet(X_107,complement(B)),meet(X_107,B)))]]) ).
cnf(refute_0_1423,plain,
( X_107 != join(meet(X_107,complement(B)),meet(X_107,B))
| X_107 = join(meet(X_107,B),meet(X_107,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_107,complement(B)),meet(X_107,B)),join(meet(X_107,B),meet(X_107,complement(B)))) )],[refute_0_1421,refute_0_1422]) ).
cnf(refute_0_1424,plain,
X_107 = join(meet(X_107,B),meet(X_107,complement(B))),
inference(resolve,[$cnf( $equal(X_107,join(meet(X_107,complement(B)),meet(X_107,B))) )],[refute_0_1420,refute_0_1423]) ).
cnf(refute_0_1425,plain,
X_211 = join(meet(X_211,X_210),meet(X_211,complement(X_210))),
inference(subst,[],[refute_0_1424:[bind(B,$fot(X_210)),bind(X_107,$fot(X_211))]]) ).
cnf(refute_0_1426,plain,
meet(complement(X_210),X_211) = meet(X_211,complement(X_210)),
inference(subst,[],[refute_0_158:[bind(X_10,$fot(complement(X_210))),bind(X_11,$fot(X_211))]]) ).
cnf(refute_0_1427,plain,
( meet(complement(X_210),X_211) != meet(X_211,complement(X_210))
| meet(X_211,complement(X_210)) = meet(complement(X_210),X_211) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_210),X_211))),bind(Y,$fot(meet(X_211,complement(X_210))))]]) ).
cnf(refute_0_1428,plain,
meet(X_211,complement(X_210)) = meet(complement(X_210),X_211),
inference(resolve,[$cnf( $equal(meet(complement(X_210),X_211),meet(X_211,complement(X_210))) )],[refute_0_1426,refute_0_1427]) ).
cnf(refute_0_1429,plain,
( X_211 != join(meet(X_211,X_210),meet(X_211,complement(X_210)))
| meet(X_211,complement(X_210)) != meet(complement(X_210),X_211)
| X_211 = join(meet(X_211,X_210),meet(complement(X_210),X_211)) ),
introduced(tautology,[equality,[$cnf( $equal(X_211,join(meet(X_211,X_210),meet(X_211,complement(X_210)))) ),[1,1],$fot(meet(complement(X_210),X_211))]]) ).
cnf(refute_0_1430,plain,
( X_211 != join(meet(X_211,X_210),meet(X_211,complement(X_210)))
| X_211 = join(meet(X_211,X_210),meet(complement(X_210),X_211)) ),
inference(resolve,[$cnf( $equal(meet(X_211,complement(X_210)),meet(complement(X_210),X_211)) )],[refute_0_1428,refute_0_1429]) ).
cnf(refute_0_1431,plain,
X_211 = join(meet(X_211,X_210),meet(complement(X_210),X_211)),
inference(resolve,[$cnf( $equal(X_211,join(meet(X_211,X_210),meet(X_211,complement(X_210)))) )],[refute_0_1425,refute_0_1430]) ).
cnf(refute_0_1432,plain,
composition(top,complement(X_210)) = join(meet(composition(top,complement(X_210)),X_210),meet(complement(X_210),composition(top,complement(X_210)))),
inference(subst,[],[refute_0_1431:[bind(X_211,$fot(composition(top,complement(X_210))))]]) ).
cnf(refute_0_1433,plain,
X_149 = meet(X_149,join(X_149,composition(X_31,X_149))),
inference(subst,[],[refute_0_907:[bind(X_107,$fot(X_149)),bind(X_148,$fot(composition(X_31,X_149)))]]) ).
cnf(refute_0_1434,plain,
composition(join(X_31,one),X_149) = join(X_149,composition(X_31,X_149)),
inference(subst,[],[refute_0_54:[bind(X_33,$fot(X_149))]]) ).
cnf(refute_0_1435,plain,
( composition(join(X_31,one),X_149) != join(X_149,composition(X_31,X_149))
| join(X_149,composition(X_31,X_149)) = composition(join(X_31,one),X_149) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_31,one),X_149))),bind(Y,$fot(join(X_149,composition(X_31,X_149))))]]) ).
cnf(refute_0_1436,plain,
join(X_149,composition(X_31,X_149)) = composition(join(X_31,one),X_149),
inference(resolve,[$cnf( $equal(composition(join(X_31,one),X_149),join(X_149,composition(X_31,X_149))) )],[refute_0_1434,refute_0_1435]) ).
cnf(refute_0_1437,plain,
( X_149 != meet(X_149,join(X_149,composition(X_31,X_149)))
| join(X_149,composition(X_31,X_149)) != composition(join(X_31,one),X_149)
| X_149 = meet(X_149,composition(join(X_31,one),X_149)) ),
introduced(tautology,[equality,[$cnf( $equal(X_149,meet(X_149,join(X_149,composition(X_31,X_149)))) ),[1,1],$fot(composition(join(X_31,one),X_149))]]) ).
cnf(refute_0_1438,plain,
( X_149 != meet(X_149,join(X_149,composition(X_31,X_149)))
| X_149 = meet(X_149,composition(join(X_31,one),X_149)) ),
inference(resolve,[$cnf( $equal(join(X_149,composition(X_31,X_149)),composition(join(X_31,one),X_149)) )],[refute_0_1436,refute_0_1437]) ).
cnf(refute_0_1439,plain,
X_149 = meet(X_149,composition(join(X_31,one),X_149)),
inference(resolve,[$cnf( $equal(X_149,meet(X_149,join(X_149,composition(X_31,X_149)))) )],[refute_0_1433,refute_0_1438]) ).
cnf(refute_0_1440,plain,
converse(X_170) = meet(converse(X_170),composition(join(converse(X_171),one),converse(X_170))),
inference(subst,[],[refute_0_1439:[bind(X_149,$fot(converse(X_170))),bind(X_31,$fot(converse(X_171)))]]) ).
cnf(refute_0_1441,plain,
( composition(join(converse(X_171),one),converse(X_170)) != converse(composition(X_170,join(X_171,converse(one))))
| converse(X_170) != meet(converse(X_170),composition(join(converse(X_171),one),converse(X_170)))
| converse(X_170) = meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(X_170),meet(converse(X_170),composition(join(converse(X_171),one),converse(X_170)))) ),[1,1],$fot(converse(composition(X_170,join(X_171,converse(one)))))]]) ).
cnf(refute_0_1442,plain,
( converse(X_170) != meet(converse(X_170),composition(join(converse(X_171),one),converse(X_170)))
| converse(X_170) = meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(X_171),one),converse(X_170)),converse(composition(X_170,join(X_171,converse(one))))) )],[refute_0_1060,refute_0_1441]) ).
cnf(refute_0_1443,plain,
converse(X_170) = meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))),
inference(resolve,[$cnf( $equal(converse(X_170),meet(converse(X_170),composition(join(converse(X_171),one),converse(X_170)))) )],[refute_0_1440,refute_0_1442]) ).
cnf(refute_0_1444,plain,
meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))) = meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))),
introduced(tautology,[refl,[$fot(meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))))]]) ).
cnf(refute_0_1445,plain,
( converse(composition(X_170,join(X_171,converse(one)))) != converse(composition(X_170,join(X_171,one)))
| meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))) != meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one)))))
| meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))) = meet(converse(X_170),converse(composition(X_170,join(X_171,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))),meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one)))))) ),[1,1],$fot(converse(composition(X_170,join(X_171,one))))]]) ).
cnf(refute_0_1446,plain,
( converse(composition(X_170,join(X_171,converse(one)))) != converse(composition(X_170,join(X_171,one)))
| meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))) = meet(converse(X_170),converse(composition(X_170,join(X_171,one)))) ),
inference(resolve,[$cnf( $equal(meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))),meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one)))))) )],[refute_0_1444,refute_0_1445]) ).
cnf(refute_0_1447,plain,
meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))) = meet(converse(X_170),converse(composition(X_170,join(X_171,one)))),
inference(resolve,[$cnf( $equal(converse(composition(X_170,join(X_171,converse(one)))),converse(composition(X_170,join(X_171,one)))) )],[refute_0_1099,refute_0_1446]) ).
cnf(refute_0_1448,plain,
( converse(X_170) != meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one)))))
| meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))) != meet(converse(X_170),converse(composition(X_170,join(X_171,one))))
| converse(X_170) = meet(converse(X_170),converse(composition(X_170,join(X_171,one)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(X_170),meet(converse(X_170),converse(composition(X_170,join(X_171,one))))) ),[0],$fot(meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))))]]) ).
cnf(refute_0_1449,plain,
( converse(X_170) != meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one)))))
| converse(X_170) = meet(converse(X_170),converse(composition(X_170,join(X_171,one)))) ),
inference(resolve,[$cnf( $equal(meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one))))),meet(converse(X_170),converse(composition(X_170,join(X_171,one))))) )],[refute_0_1447,refute_0_1448]) ).
cnf(refute_0_1450,plain,
converse(X_170) = meet(converse(X_170),converse(composition(X_170,join(X_171,one)))),
inference(resolve,[$cnf( $equal(converse(X_170),meet(converse(X_170),converse(composition(X_170,join(X_171,converse(one)))))) )],[refute_0_1443,refute_0_1449]) ).
cnf(refute_0_1451,plain,
converse(converse(A)) = meet(converse(converse(A)),converse(composition(converse(A),join(X_173,one)))),
inference(subst,[],[refute_0_1450:[bind(X_170,$fot(converse(A))),bind(X_171,$fot(X_173))]]) ).
cnf(refute_0_1452,plain,
converse(composition(converse(A),join(X_173,one))) = composition(converse(join(X_173,one)),A),
inference(subst,[],[refute_0_19:[bind(X_15,$fot(join(X_173,one)))]]) ).
cnf(refute_0_1453,plain,
( converse(composition(converse(A),join(X_173,one))) != composition(converse(join(X_173,one)),A)
| converse(converse(A)) != meet(converse(converse(A)),converse(composition(converse(A),join(X_173,one))))
| converse(converse(A)) = meet(converse(converse(A)),composition(converse(join(X_173,one)),A)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(A)),meet(converse(converse(A)),converse(composition(converse(A),join(X_173,one))))) ),[1,1],$fot(composition(converse(join(X_173,one)),A))]]) ).
cnf(refute_0_1454,plain,
( converse(converse(A)) != meet(converse(converse(A)),converse(composition(converse(A),join(X_173,one))))
| converse(converse(A)) = meet(converse(converse(A)),composition(converse(join(X_173,one)),A)) ),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),join(X_173,one))),composition(converse(join(X_173,one)),A)) )],[refute_0_1452,refute_0_1453]) ).
cnf(refute_0_1455,plain,
converse(converse(A)) = meet(converse(converse(A)),composition(converse(join(X_173,one)),A)),
inference(resolve,[$cnf( $equal(converse(converse(A)),meet(converse(converse(A)),converse(composition(converse(A),join(X_173,one))))) )],[refute_0_1451,refute_0_1454]) ).
cnf(refute_0_1456,plain,
( converse(converse(A)) != A
| converse(converse(A)) != meet(converse(converse(A)),composition(converse(join(X_173,one)),A))
| A = meet(converse(converse(A)),composition(converse(join(X_173,one)),A)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(A)),meet(converse(converse(A)),composition(converse(join(X_173,one)),A))) ),[0],$fot(A)]]) ).
cnf(refute_0_1457,plain,
( converse(converse(A)) != meet(converse(converse(A)),composition(converse(join(X_173,one)),A))
| A = meet(converse(converse(A)),composition(converse(join(X_173,one)),A)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1456]) ).
cnf(refute_0_1458,plain,
meet(converse(converse(A)),composition(converse(join(X_173,one)),A)) = meet(converse(converse(A)),composition(converse(join(X_173,one)),A)),
introduced(tautology,[refl,[$fot(meet(converse(converse(A)),composition(converse(join(X_173,one)),A)))]]) ).
cnf(refute_0_1459,plain,
( converse(converse(A)) != A
| meet(converse(converse(A)),composition(converse(join(X_173,one)),A)) != meet(converse(converse(A)),composition(converse(join(X_173,one)),A))
| meet(converse(converse(A)),composition(converse(join(X_173,one)),A)) = meet(A,composition(converse(join(X_173,one)),A)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(converse(converse(A)),composition(converse(join(X_173,one)),A)),meet(converse(converse(A)),composition(converse(join(X_173,one)),A))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_1460,plain,
( converse(converse(A)) != A
| meet(converse(converse(A)),composition(converse(join(X_173,one)),A)) = meet(A,composition(converse(join(X_173,one)),A)) ),
inference(resolve,[$cnf( $equal(meet(converse(converse(A)),composition(converse(join(X_173,one)),A)),meet(converse(converse(A)),composition(converse(join(X_173,one)),A))) )],[refute_0_1458,refute_0_1459]) ).
cnf(refute_0_1461,plain,
meet(converse(converse(A)),composition(converse(join(X_173,one)),A)) = meet(A,composition(converse(join(X_173,one)),A)),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1460]) ).
cnf(refute_0_1462,plain,
( A != meet(converse(converse(A)),composition(converse(join(X_173,one)),A))
| meet(converse(converse(A)),composition(converse(join(X_173,one)),A)) != meet(A,composition(converse(join(X_173,one)),A))
| A = meet(A,composition(converse(join(X_173,one)),A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,meet(A,composition(converse(join(X_173,one)),A))) ),[0],$fot(meet(converse(converse(A)),composition(converse(join(X_173,one)),A)))]]) ).
cnf(refute_0_1463,plain,
( A != meet(converse(converse(A)),composition(converse(join(X_173,one)),A))
| A = meet(A,composition(converse(join(X_173,one)),A)) ),
inference(resolve,[$cnf( $equal(meet(converse(converse(A)),composition(converse(join(X_173,one)),A)),meet(A,composition(converse(join(X_173,one)),A))) )],[refute_0_1461,refute_0_1462]) ).
cnf(refute_0_1464,plain,
( converse(converse(A)) != meet(converse(converse(A)),composition(converse(join(X_173,one)),A))
| A = meet(A,composition(converse(join(X_173,one)),A)) ),
inference(resolve,[$cnf( $equal(A,meet(converse(converse(A)),composition(converse(join(X_173,one)),A))) )],[refute_0_1457,refute_0_1463]) ).
cnf(refute_0_1465,plain,
A = meet(A,composition(converse(join(X_173,one)),A)),
inference(resolve,[$cnf( $equal(converse(converse(A)),meet(converse(converse(A)),composition(converse(join(X_173,one)),A))) )],[refute_0_1455,refute_0_1464]) ).
cnf(refute_0_1466,plain,
A = meet(A,composition(converse(join(top,one)),A)),
inference(subst,[],[refute_0_1465:[bind(X_173,$fot(top))]]) ).
cnf(refute_0_1467,plain,
top = join(top,one),
inference(subst,[],[refute_0_579:[bind(X_41,$fot(one))]]) ).
cnf(refute_0_1468,plain,
( top != join(top,one)
| join(top,one) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,one)))]]) ).
cnf(refute_0_1469,plain,
join(top,one) = top,
inference(resolve,[$cnf( $equal(top,join(top,one)) )],[refute_0_1467,refute_0_1468]) ).
cnf(refute_0_1470,plain,
( A != meet(A,composition(converse(join(top,one)),A))
| join(top,one) != top
| A = meet(A,composition(converse(top),A)) ),
introduced(tautology,[equality,[$cnf( $equal(A,meet(A,composition(converse(join(top,one)),A))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_0_1471,plain,
( A != meet(A,composition(converse(join(top,one)),A))
| A = meet(A,composition(converse(top),A)) ),
inference(resolve,[$cnf( $equal(join(top,one),top) )],[refute_0_1469,refute_0_1470]) ).
cnf(refute_0_1472,plain,
A = meet(A,composition(converse(top),A)),
inference(resolve,[$cnf( $equal(A,meet(A,composition(converse(join(top,one)),A))) )],[refute_0_1466,refute_0_1471]) ).
cnf(refute_0_1473,plain,
composition(converse(top),A) = composition(converse(top),A),
introduced(tautology,[refl,[$fot(composition(converse(top),A))]]) ).
cnf(refute_0_1474,plain,
( composition(converse(top),A) != composition(converse(top),A)
| converse(top) != top
| composition(converse(top),A) = composition(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(top),A),composition(converse(top),A)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1475,plain,
( converse(top) != top
| composition(converse(top),A) = composition(top,A) ),
inference(resolve,[$cnf( $equal(composition(converse(top),A),composition(converse(top),A)) )],[refute_0_1473,refute_0_1474]) ).
cnf(refute_0_1476,plain,
composition(converse(top),A) = composition(top,A),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_953,refute_0_1475]) ).
cnf(refute_0_1477,plain,
meet(A,composition(converse(top),A)) = meet(A,composition(converse(top),A)),
introduced(tautology,[refl,[$fot(meet(A,composition(converse(top),A)))]]) ).
cnf(refute_0_1478,plain,
( composition(converse(top),A) != composition(top,A)
| meet(A,composition(converse(top),A)) != meet(A,composition(converse(top),A))
| meet(A,composition(converse(top),A)) = meet(A,composition(top,A)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,composition(converse(top),A)),meet(A,composition(converse(top),A))) ),[1,1],$fot(composition(top,A))]]) ).
cnf(refute_0_1479,plain,
( composition(converse(top),A) != composition(top,A)
| meet(A,composition(converse(top),A)) = meet(A,composition(top,A)) ),
inference(resolve,[$cnf( $equal(meet(A,composition(converse(top),A)),meet(A,composition(converse(top),A))) )],[refute_0_1477,refute_0_1478]) ).
cnf(refute_0_1480,plain,
meet(A,composition(converse(top),A)) = meet(A,composition(top,A)),
inference(resolve,[$cnf( $equal(composition(converse(top),A),composition(top,A)) )],[refute_0_1476,refute_0_1479]) ).
cnf(refute_0_1481,plain,
( A != meet(A,composition(converse(top),A))
| meet(A,composition(converse(top),A)) != meet(A,composition(top,A))
| A = meet(A,composition(top,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,meet(A,composition(top,A))) ),[0],$fot(meet(A,composition(converse(top),A)))]]) ).
cnf(refute_0_1482,plain,
( A != meet(A,composition(converse(top),A))
| A = meet(A,composition(top,A)) ),
inference(resolve,[$cnf( $equal(meet(A,composition(converse(top),A)),meet(A,composition(top,A))) )],[refute_0_1480,refute_0_1481]) ).
cnf(refute_0_1483,plain,
A = meet(A,composition(top,A)),
inference(resolve,[$cnf( $equal(A,meet(A,composition(converse(top),A))) )],[refute_0_1472,refute_0_1482]) ).
cnf(refute_0_1484,plain,
complement(X_210) = meet(complement(X_210),composition(top,complement(X_210))),
inference(subst,[],[refute_0_1483:[bind(A,$fot(complement(X_210)))]]) ).
cnf(refute_0_1485,plain,
( complement(X_210) != meet(complement(X_210),composition(top,complement(X_210)))
| meet(complement(X_210),composition(top,complement(X_210))) = complement(X_210) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_210))),bind(Y,$fot(meet(complement(X_210),composition(top,complement(X_210)))))]]) ).
cnf(refute_0_1486,plain,
meet(complement(X_210),composition(top,complement(X_210))) = complement(X_210),
inference(resolve,[$cnf( $equal(complement(X_210),meet(complement(X_210),composition(top,complement(X_210)))) )],[refute_0_1484,refute_0_1485]) ).
cnf(refute_0_1487,plain,
( composition(top,complement(X_210)) != join(meet(composition(top,complement(X_210)),X_210),meet(complement(X_210),composition(top,complement(X_210))))
| meet(complement(X_210),composition(top,complement(X_210))) != complement(X_210)
| composition(top,complement(X_210)) = join(meet(composition(top,complement(X_210)),X_210),complement(X_210)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(X_210)),join(meet(composition(top,complement(X_210)),X_210),meet(complement(X_210),composition(top,complement(X_210))))) ),[1,1],$fot(complement(X_210))]]) ).
cnf(refute_0_1488,plain,
( composition(top,complement(X_210)) != join(meet(composition(top,complement(X_210)),X_210),meet(complement(X_210),composition(top,complement(X_210))))
| composition(top,complement(X_210)) = join(meet(composition(top,complement(X_210)),X_210),complement(X_210)) ),
inference(resolve,[$cnf( $equal(meet(complement(X_210),composition(top,complement(X_210))),complement(X_210)) )],[refute_0_1486,refute_0_1487]) ).
cnf(refute_0_1489,plain,
composition(top,complement(X_210)) = join(meet(composition(top,complement(X_210)),X_210),complement(X_210)),
inference(resolve,[$cnf( $equal(composition(top,complement(X_210)),join(meet(composition(top,complement(X_210)),X_210),meet(complement(X_210),composition(top,complement(X_210))))) )],[refute_0_1432,refute_0_1488]) ).
cnf(refute_0_1490,plain,
meet(composition(top,complement(X_210)),X_210) = meet(X_210,composition(top,complement(X_210))),
inference(subst,[],[refute_0_882:[bind(X_10,$fot(X_210)),bind(X_11,$fot(composition(top,complement(X_210))))]]) ).
cnf(refute_0_1491,plain,
join(complement(X_210),meet(composition(top,complement(X_210)),X_210)) = join(complement(X_210),meet(composition(top,complement(X_210)),X_210)),
introduced(tautology,[refl,[$fot(join(complement(X_210),meet(composition(top,complement(X_210)),X_210)))]]) ).
cnf(refute_0_1492,plain,
( join(complement(X_210),meet(composition(top,complement(X_210)),X_210)) != join(complement(X_210),meet(composition(top,complement(X_210)),X_210))
| meet(composition(top,complement(X_210)),X_210) != meet(X_210,composition(top,complement(X_210)))
| join(complement(X_210),meet(composition(top,complement(X_210)),X_210)) = join(complement(X_210),meet(X_210,composition(top,complement(X_210)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_210),meet(composition(top,complement(X_210)),X_210)),join(complement(X_210),meet(composition(top,complement(X_210)),X_210))) ),[1,1],$fot(meet(X_210,composition(top,complement(X_210))))]]) ).
cnf(refute_0_1493,plain,
( meet(composition(top,complement(X_210)),X_210) != meet(X_210,composition(top,complement(X_210)))
| join(complement(X_210),meet(composition(top,complement(X_210)),X_210)) = join(complement(X_210),meet(X_210,composition(top,complement(X_210)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_210),meet(composition(top,complement(X_210)),X_210)),join(complement(X_210),meet(composition(top,complement(X_210)),X_210))) )],[refute_0_1491,refute_0_1492]) ).
cnf(refute_0_1494,plain,
join(complement(X_210),meet(composition(top,complement(X_210)),X_210)) = join(complement(X_210),meet(X_210,composition(top,complement(X_210)))),
inference(resolve,[$cnf( $equal(meet(composition(top,complement(X_210)),X_210),meet(X_210,composition(top,complement(X_210)))) )],[refute_0_1490,refute_0_1493]) ).
cnf(refute_0_1495,plain,
join(meet(composition(top,complement(X_210)),X_210),complement(X_210)) = join(complement(X_210),meet(composition(top,complement(X_210)),X_210)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_210))),bind(B,$fot(meet(composition(top,complement(X_210)),X_210)))]]) ).
cnf(refute_0_1496,plain,
( join(complement(X_210),meet(composition(top,complement(X_210)),X_210)) != join(complement(X_210),meet(X_210,composition(top,complement(X_210))))
| join(meet(composition(top,complement(X_210)),X_210),complement(X_210)) != join(complement(X_210),meet(composition(top,complement(X_210)),X_210))
| join(meet(composition(top,complement(X_210)),X_210),complement(X_210)) = join(complement(X_210),meet(X_210,composition(top,complement(X_210)))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(composition(top,complement(X_210)),X_210),complement(X_210)))),bind(Y,$fot(join(complement(X_210),meet(composition(top,complement(X_210)),X_210)))),bind(Z,$fot(join(complement(X_210),meet(X_210,composition(top,complement(X_210))))))]]) ).
cnf(refute_0_1497,plain,
( join(complement(X_210),meet(composition(top,complement(X_210)),X_210)) != join(complement(X_210),meet(X_210,composition(top,complement(X_210))))
| join(meet(composition(top,complement(X_210)),X_210),complement(X_210)) = join(complement(X_210),meet(X_210,composition(top,complement(X_210)))) ),
inference(resolve,[$cnf( $equal(join(meet(composition(top,complement(X_210)),X_210),complement(X_210)),join(complement(X_210),meet(composition(top,complement(X_210)),X_210))) )],[refute_0_1495,refute_0_1496]) ).
cnf(refute_0_1498,plain,
join(meet(composition(top,complement(X_210)),X_210),complement(X_210)) = join(complement(X_210),meet(X_210,composition(top,complement(X_210)))),
inference(resolve,[$cnf( $equal(join(complement(X_210),meet(composition(top,complement(X_210)),X_210)),join(complement(X_210),meet(X_210,composition(top,complement(X_210))))) )],[refute_0_1494,refute_0_1497]) ).
cnf(refute_0_1499,plain,
( composition(top,complement(X_210)) != join(meet(composition(top,complement(X_210)),X_210),complement(X_210))
| join(meet(composition(top,complement(X_210)),X_210),complement(X_210)) != join(complement(X_210),meet(X_210,composition(top,complement(X_210))))
| composition(top,complement(X_210)) = join(complement(X_210),meet(X_210,composition(top,complement(X_210)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(top,complement(X_210)),join(complement(X_210),meet(X_210,composition(top,complement(X_210))))) ),[0],$fot(join(meet(composition(top,complement(X_210)),X_210),complement(X_210)))]]) ).
cnf(refute_0_1500,plain,
( composition(top,complement(X_210)) != join(meet(composition(top,complement(X_210)),X_210),complement(X_210))
| composition(top,complement(X_210)) = join(complement(X_210),meet(X_210,composition(top,complement(X_210)))) ),
inference(resolve,[$cnf( $equal(join(meet(composition(top,complement(X_210)),X_210),complement(X_210)),join(complement(X_210),meet(X_210,composition(top,complement(X_210))))) )],[refute_0_1498,refute_0_1499]) ).
cnf(refute_0_1501,plain,
composition(top,complement(X_210)) = join(complement(X_210),meet(X_210,composition(top,complement(X_210)))),
inference(resolve,[$cnf( $equal(composition(top,complement(X_210)),join(meet(composition(top,complement(X_210)),X_210),complement(X_210))) )],[refute_0_1489,refute_0_1500]) ).
cnf(refute_0_1502,plain,
composition(top,complement(X_41)) = join(complement(X_41),meet(X_41,composition(top,complement(X_41)))),
inference(subst,[],[refute_0_1501:[bind(X_210,$fot(X_41))]]) ).
cnf(refute_0_1503,plain,
( composition(top,complement(X_41)) != join(complement(X_41),meet(X_41,composition(top,complement(X_41))))
| join(complement(X_41),meet(X_41,composition(top,complement(X_41)))) = composition(top,complement(X_41)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(top,complement(X_41)))),bind(Y,$fot(join(complement(X_41),meet(X_41,composition(top,complement(X_41))))))]]) ).
cnf(refute_0_1504,plain,
join(complement(X_41),meet(X_41,composition(top,complement(X_41)))) = composition(top,complement(X_41)),
inference(resolve,[$cnf( $equal(composition(top,complement(X_41)),join(complement(X_41),meet(X_41,composition(top,complement(X_41))))) )],[refute_0_1502,refute_0_1503]) ).
cnf(refute_0_1505,plain,
( join(X_41,join(complement(X_41),meet(X_41,composition(top,complement(X_41))))) != top
| join(complement(X_41),meet(X_41,composition(top,complement(X_41)))) != composition(top,complement(X_41))
| join(X_41,composition(top,complement(X_41))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,join(complement(X_41),meet(X_41,composition(top,complement(X_41))))),top) ),[0,1],$fot(composition(top,complement(X_41)))]]) ).
cnf(refute_0_1506,plain,
( join(X_41,join(complement(X_41),meet(X_41,composition(top,complement(X_41))))) != top
| join(X_41,composition(top,complement(X_41))) = top ),
inference(resolve,[$cnf( $equal(join(complement(X_41),meet(X_41,composition(top,complement(X_41)))),composition(top,complement(X_41))) )],[refute_0_1504,refute_0_1505]) ).
cnf(refute_0_1507,plain,
join(X_41,composition(top,complement(X_41))) = top,
inference(resolve,[$cnf( $equal(join(X_41,join(complement(X_41),meet(X_41,composition(top,complement(X_41))))),top) )],[refute_0_1413,refute_0_1506]) ).
cnf(refute_0_1508,plain,
join(converse(A),composition(top,complement(converse(A)))) = top,
inference(subst,[],[refute_0_1507:[bind(X_41,$fot(converse(A)))]]) ).
cnf(refute_0_1509,plain,
( converse(join(converse(A),composition(top,complement(converse(A))))) != join(A,converse(composition(top,complement(converse(A)))))
| join(converse(A),composition(top,complement(converse(A)))) != top
| converse(top) = join(A,converse(composition(top,complement(converse(A))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),composition(top,complement(converse(A))))),join(A,converse(composition(top,complement(converse(A)))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_1510,plain,
( converse(join(converse(A),composition(top,complement(converse(A))))) != join(A,converse(composition(top,complement(converse(A)))))
| converse(top) = join(A,converse(composition(top,complement(converse(A))))) ),
inference(resolve,[$cnf( $equal(join(converse(A),composition(top,complement(converse(A)))),top) )],[refute_0_1508,refute_0_1509]) ).
cnf(refute_0_1511,plain,
converse(top) = join(A,converse(composition(top,complement(converse(A))))),
inference(resolve,[$cnf( $equal(converse(join(converse(A),composition(top,complement(converse(A))))),join(A,converse(composition(top,complement(converse(A)))))) )],[refute_0_1412,refute_0_1510]) ).
cnf(refute_0_1512,plain,
( converse(top) != join(A,converse(composition(top,complement(converse(A)))))
| converse(top) != top
| top = join(A,converse(composition(top,complement(converse(A))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(A,converse(composition(top,complement(converse(A)))))) ),[0],$fot(top)]]) ).
cnf(refute_0_1513,plain,
( converse(top) != join(A,converse(composition(top,complement(converse(A)))))
| top = join(A,converse(composition(top,complement(converse(A))))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_953,refute_0_1512]) ).
cnf(refute_0_1514,plain,
composition(complement(A),converse(top)) = composition(complement(A),converse(top)),
introduced(tautology,[refl,[$fot(composition(complement(A),converse(top)))]]) ).
cnf(refute_0_1515,plain,
( composition(complement(A),converse(top)) != composition(complement(A),converse(top))
| converse(top) != top
| composition(complement(A),converse(top)) = composition(complement(A),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(A),converse(top)),composition(complement(A),converse(top))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1516,plain,
( converse(top) != top
| composition(complement(A),converse(top)) = composition(complement(A),top) ),
inference(resolve,[$cnf( $equal(composition(complement(A),converse(top)),composition(complement(A),converse(top))) )],[refute_0_1514,refute_0_1515]) ).
cnf(refute_0_1517,plain,
composition(complement(A),converse(top)) = composition(complement(A),top),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_953,refute_0_1516]) ).
cnf(refute_0_1518,plain,
converse(composition(X_14,converse(complement(X_198)))) = composition(complement(X_198),converse(X_14)),
inference(subst,[],[refute_0_642:[bind(A,$fot(complement(X_198)))]]) ).
cnf(refute_0_1519,plain,
converse(complement(X_198)) = complement(converse(X_198)),
inference(subst,[],[refute_0_1034:[bind(X_107,$fot(X_198))]]) ).
cnf(refute_0_1520,plain,
( converse(complement(X_198)) != complement(converse(X_198))
| converse(composition(X_14,converse(complement(X_198)))) != composition(complement(X_198),converse(X_14))
| converse(composition(X_14,complement(converse(X_198)))) = composition(complement(X_198),converse(X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_14,converse(complement(X_198)))),composition(complement(X_198),converse(X_14))) ),[0,0,1],$fot(complement(converse(X_198)))]]) ).
cnf(refute_0_1521,plain,
( converse(composition(X_14,converse(complement(X_198)))) != composition(complement(X_198),converse(X_14))
| converse(composition(X_14,complement(converse(X_198)))) = composition(complement(X_198),converse(X_14)) ),
inference(resolve,[$cnf( $equal(converse(complement(X_198)),complement(converse(X_198))) )],[refute_0_1519,refute_0_1520]) ).
cnf(refute_0_1522,plain,
converse(composition(X_14,complement(converse(X_198)))) = composition(complement(X_198),converse(X_14)),
inference(resolve,[$cnf( $equal(converse(composition(X_14,converse(complement(X_198)))),composition(complement(X_198),converse(X_14))) )],[refute_0_1518,refute_0_1521]) ).
cnf(refute_0_1523,plain,
converse(composition(top,complement(converse(A)))) = composition(complement(A),converse(top)),
inference(subst,[],[refute_0_1522:[bind(X_14,$fot(top)),bind(X_198,$fot(A))]]) ).
cnf(refute_0_1524,plain,
( composition(complement(A),converse(top)) != composition(complement(A),top)
| converse(composition(top,complement(converse(A)))) != composition(complement(A),converse(top))
| converse(composition(top,complement(converse(A)))) = composition(complement(A),top) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(converse(composition(top,complement(converse(A)))))),bind(Y,$fot(composition(complement(A),converse(top)))),bind(Z,$fot(composition(complement(A),top)))]]) ).
cnf(refute_0_1525,plain,
( composition(complement(A),converse(top)) != composition(complement(A),top)
| converse(composition(top,complement(converse(A)))) = composition(complement(A),top) ),
inference(resolve,[$cnf( $equal(converse(composition(top,complement(converse(A)))),composition(complement(A),converse(top))) )],[refute_0_1523,refute_0_1524]) ).
cnf(refute_0_1526,plain,
converse(composition(top,complement(converse(A)))) = composition(complement(A),top),
inference(resolve,[$cnf( $equal(composition(complement(A),converse(top)),composition(complement(A),top)) )],[refute_0_1517,refute_0_1525]) ).
cnf(refute_0_1527,plain,
join(A,converse(composition(top,complement(converse(A))))) = join(A,converse(composition(top,complement(converse(A))))),
introduced(tautology,[refl,[$fot(join(A,converse(composition(top,complement(converse(A))))))]]) ).
cnf(refute_0_1528,plain,
( converse(composition(top,complement(converse(A)))) != composition(complement(A),top)
| join(A,converse(composition(top,complement(converse(A))))) != join(A,converse(composition(top,complement(converse(A)))))
| join(A,converse(composition(top,complement(converse(A))))) = join(A,composition(complement(A),top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,converse(composition(top,complement(converse(A))))),join(A,converse(composition(top,complement(converse(A)))))) ),[1,1],$fot(composition(complement(A),top))]]) ).
cnf(refute_0_1529,plain,
( converse(composition(top,complement(converse(A)))) != composition(complement(A),top)
| join(A,converse(composition(top,complement(converse(A))))) = join(A,composition(complement(A),top)) ),
inference(resolve,[$cnf( $equal(join(A,converse(composition(top,complement(converse(A))))),join(A,converse(composition(top,complement(converse(A)))))) )],[refute_0_1527,refute_0_1528]) ).
cnf(refute_0_1530,plain,
join(A,converse(composition(top,complement(converse(A))))) = join(A,composition(complement(A),top)),
inference(resolve,[$cnf( $equal(converse(composition(top,complement(converse(A)))),composition(complement(A),top)) )],[refute_0_1526,refute_0_1529]) ).
cnf(refute_0_1531,plain,
( join(A,converse(composition(top,complement(converse(A))))) != join(A,composition(complement(A),top))
| top != join(A,converse(composition(top,complement(converse(A)))))
| top = join(A,composition(complement(A),top)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(A,converse(composition(top,complement(converse(A)))))) ),[1],$fot(join(A,composition(complement(A),top)))]]) ).
cnf(refute_0_1532,plain,
( top != join(A,converse(composition(top,complement(converse(A)))))
| top = join(A,composition(complement(A),top)) ),
inference(resolve,[$cnf( $equal(join(A,converse(composition(top,complement(converse(A))))),join(A,composition(complement(A),top))) )],[refute_0_1530,refute_0_1531]) ).
cnf(refute_0_1533,plain,
( converse(top) != join(A,converse(composition(top,complement(converse(A)))))
| top = join(A,composition(complement(A),top)) ),
inference(resolve,[$cnf( $equal(top,join(A,converse(composition(top,complement(converse(A)))))) )],[refute_0_1513,refute_0_1532]) ).
cnf(refute_0_1534,plain,
top = join(A,composition(complement(A),top)),
inference(resolve,[$cnf( $equal(converse(top),join(A,converse(composition(top,complement(converse(A)))))) )],[refute_0_1511,refute_0_1533]) ).
cnf(refute_0_1535,plain,
top = join(complement(X_107),composition(complement(complement(X_107)),top)),
inference(subst,[],[refute_0_1534:[bind(A,$fot(complement(X_107)))]]) ).
cnf(refute_0_1536,plain,
( top != join(complement(X_107),composition(complement(complement(X_107)),top))
| join(complement(X_107),composition(complement(complement(X_107)),top)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_107),composition(complement(complement(X_107)),top))))]]) ).
cnf(refute_0_1537,plain,
join(complement(X_107),composition(complement(complement(X_107)),top)) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_107),composition(complement(complement(X_107)),top))) )],[refute_0_1535,refute_0_1536]) ).
cnf(refute_0_1538,plain,
( X_107 != meet(X_107,join(composition(complement(complement(X_107)),top),complement(join(complement(X_107),composition(complement(complement(X_107)),top)))))
| join(complement(X_107),composition(complement(complement(X_107)),top)) != top
| X_107 = meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_107,meet(X_107,join(composition(complement(complement(X_107)),top),complement(join(complement(X_107),composition(complement(complement(X_107)),top)))))) ),[1,1,1,0],$fot(top)]]) ).
cnf(refute_0_1539,plain,
( X_107 != meet(X_107,join(composition(complement(complement(X_107)),top),complement(join(complement(X_107),composition(complement(complement(X_107)),top)))))
| X_107 = meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))) ),
inference(resolve,[$cnf( $equal(join(complement(X_107),composition(complement(complement(X_107)),top)),top) )],[refute_0_1537,refute_0_1538]) ).
cnf(refute_0_1540,plain,
X_107 = meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))),
inference(resolve,[$cnf( $equal(X_107,meet(X_107,join(composition(complement(complement(X_107)),top),complement(join(complement(X_107),composition(complement(complement(X_107)),top)))))) )],[refute_0_1411,refute_0_1539]) ).
cnf(refute_0_1541,plain,
join(zero,composition(X_107,top)) = composition(X_107,top),
inference(subst,[],[refute_0_871:[bind(X_107,$fot(composition(X_107,top)))]]) ).
cnf(refute_0_1542,plain,
composition(complement(complement(X_107)),top) = composition(complement(complement(X_107)),top),
introduced(tautology,[refl,[$fot(composition(complement(complement(X_107)),top))]]) ).
cnf(refute_0_1543,plain,
( complement(complement(X_107)) != X_107
| composition(complement(complement(X_107)),top) != composition(complement(complement(X_107)),top)
| composition(complement(complement(X_107)),top) = composition(X_107,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(complement(X_107)),top),composition(complement(complement(X_107)),top)) ),[1,0],$fot(X_107)]]) ).
cnf(refute_0_1544,plain,
( complement(complement(X_107)) != X_107
| composition(complement(complement(X_107)),top) = composition(X_107,top) ),
inference(resolve,[$cnf( $equal(composition(complement(complement(X_107)),top),composition(complement(complement(X_107)),top)) )],[refute_0_1542,refute_0_1543]) ).
cnf(refute_0_1545,plain,
composition(complement(complement(X_107)),top) = composition(X_107,top),
inference(resolve,[$cnf( $equal(complement(complement(X_107)),X_107) )],[refute_0_848,refute_0_1544]) ).
cnf(refute_0_1546,plain,
join(zero,composition(complement(complement(X_107)),top)) = join(zero,composition(complement(complement(X_107)),top)),
introduced(tautology,[refl,[$fot(join(zero,composition(complement(complement(X_107)),top)))]]) ).
cnf(refute_0_1547,plain,
( composition(complement(complement(X_107)),top) != composition(X_107,top)
| join(zero,composition(complement(complement(X_107)),top)) != join(zero,composition(complement(complement(X_107)),top))
| join(zero,composition(complement(complement(X_107)),top)) = join(zero,composition(X_107,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(complement(complement(X_107)),top)),join(zero,composition(complement(complement(X_107)),top))) ),[1,1],$fot(composition(X_107,top))]]) ).
cnf(refute_0_1548,plain,
( composition(complement(complement(X_107)),top) != composition(X_107,top)
| join(zero,composition(complement(complement(X_107)),top)) = join(zero,composition(X_107,top)) ),
inference(resolve,[$cnf( $equal(join(zero,composition(complement(complement(X_107)),top)),join(zero,composition(complement(complement(X_107)),top))) )],[refute_0_1546,refute_0_1547]) ).
cnf(refute_0_1549,plain,
join(zero,composition(complement(complement(X_107)),top)) = join(zero,composition(X_107,top)),
inference(resolve,[$cnf( $equal(composition(complement(complement(X_107)),top),composition(X_107,top)) )],[refute_0_1545,refute_0_1548]) ).
cnf(refute_0_1550,plain,
join(complement(top),composition(complement(complement(X_107)),top)) = join(complement(top),composition(complement(complement(X_107)),top)),
introduced(tautology,[refl,[$fot(join(complement(top),composition(complement(complement(X_107)),top)))]]) ).
cnf(refute_0_1551,plain,
( complement(top) != zero
| join(complement(top),composition(complement(complement(X_107)),top)) != join(complement(top),composition(complement(complement(X_107)),top))
| join(complement(top),composition(complement(complement(X_107)),top)) = join(zero,composition(complement(complement(X_107)),top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(complement(complement(X_107)),top)),join(complement(top),composition(complement(complement(X_107)),top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1552,plain,
( complement(top) != zero
| join(complement(top),composition(complement(complement(X_107)),top)) = join(zero,composition(complement(complement(X_107)),top)) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(complement(complement(X_107)),top)),join(complement(top),composition(complement(complement(X_107)),top))) )],[refute_0_1550,refute_0_1551]) ).
cnf(refute_0_1553,plain,
join(complement(top),composition(complement(complement(X_107)),top)) = join(zero,composition(complement(complement(X_107)),top)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_1552]) ).
cnf(refute_0_1554,plain,
( join(complement(top),composition(complement(complement(X_107)),top)) != join(zero,composition(complement(complement(X_107)),top))
| join(zero,composition(complement(complement(X_107)),top)) != join(zero,composition(X_107,top))
| join(complement(top),composition(complement(complement(X_107)),top)) = join(zero,composition(X_107,top)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(top),composition(complement(complement(X_107)),top)))),bind(Y,$fot(join(zero,composition(complement(complement(X_107)),top)))),bind(Z,$fot(join(zero,composition(X_107,top))))]]) ).
cnf(refute_0_1555,plain,
( join(zero,composition(complement(complement(X_107)),top)) != join(zero,composition(X_107,top))
| join(complement(top),composition(complement(complement(X_107)),top)) = join(zero,composition(X_107,top)) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(complement(complement(X_107)),top)),join(zero,composition(complement(complement(X_107)),top))) )],[refute_0_1553,refute_0_1554]) ).
cnf(refute_0_1556,plain,
join(complement(top),composition(complement(complement(X_107)),top)) = join(zero,composition(X_107,top)),
inference(resolve,[$cnf( $equal(join(zero,composition(complement(complement(X_107)),top)),join(zero,composition(X_107,top))) )],[refute_0_1549,refute_0_1555]) ).
cnf(refute_0_1557,plain,
( join(complement(top),composition(complement(complement(X_107)),top)) != join(zero,composition(X_107,top))
| join(zero,composition(X_107,top)) != composition(X_107,top)
| join(complement(top),composition(complement(complement(X_107)),top)) = composition(X_107,top) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(top),composition(complement(complement(X_107)),top)))),bind(Y,$fot(join(zero,composition(X_107,top)))),bind(Z,$fot(composition(X_107,top)))]]) ).
cnf(refute_0_1558,plain,
( join(zero,composition(X_107,top)) != composition(X_107,top)
| join(complement(top),composition(complement(complement(X_107)),top)) = composition(X_107,top) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(complement(complement(X_107)),top)),join(zero,composition(X_107,top))) )],[refute_0_1556,refute_0_1557]) ).
cnf(refute_0_1559,plain,
join(complement(top),composition(complement(complement(X_107)),top)) = composition(X_107,top),
inference(resolve,[$cnf( $equal(join(zero,composition(X_107,top)),composition(X_107,top)) )],[refute_0_1541,refute_0_1558]) ).
cnf(refute_0_1560,plain,
join(composition(complement(complement(X_107)),top),complement(top)) = join(complement(top),composition(complement(complement(X_107)),top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(composition(complement(complement(X_107)),top)))]]) ).
cnf(refute_0_1561,plain,
( join(complement(top),composition(complement(complement(X_107)),top)) != composition(X_107,top)
| join(composition(complement(complement(X_107)),top),complement(top)) != join(complement(top),composition(complement(complement(X_107)),top))
| join(composition(complement(complement(X_107)),top),complement(top)) = composition(X_107,top) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(composition(complement(complement(X_107)),top),complement(top)))),bind(Y,$fot(join(complement(top),composition(complement(complement(X_107)),top)))),bind(Z,$fot(composition(X_107,top)))]]) ).
cnf(refute_0_1562,plain,
( join(complement(top),composition(complement(complement(X_107)),top)) != composition(X_107,top)
| join(composition(complement(complement(X_107)),top),complement(top)) = composition(X_107,top) ),
inference(resolve,[$cnf( $equal(join(composition(complement(complement(X_107)),top),complement(top)),join(complement(top),composition(complement(complement(X_107)),top))) )],[refute_0_1560,refute_0_1561]) ).
cnf(refute_0_1563,plain,
join(composition(complement(complement(X_107)),top),complement(top)) = composition(X_107,top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(complement(complement(X_107)),top)),composition(X_107,top)) )],[refute_0_1559,refute_0_1562]) ).
cnf(refute_0_1564,plain,
meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))) = meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))),
introduced(tautology,[refl,[$fot(meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))))]]) ).
cnf(refute_0_1565,plain,
( join(composition(complement(complement(X_107)),top),complement(top)) != composition(X_107,top)
| meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))) != meet(X_107,join(composition(complement(complement(X_107)),top),complement(top)))
| meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))) = meet(X_107,composition(X_107,top)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))),meet(X_107,join(composition(complement(complement(X_107)),top),complement(top)))) ),[1,1],$fot(composition(X_107,top))]]) ).
cnf(refute_0_1566,plain,
( join(composition(complement(complement(X_107)),top),complement(top)) != composition(X_107,top)
| meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))) = meet(X_107,composition(X_107,top)) ),
inference(resolve,[$cnf( $equal(meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))),meet(X_107,join(composition(complement(complement(X_107)),top),complement(top)))) )],[refute_0_1564,refute_0_1565]) ).
cnf(refute_0_1567,plain,
meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))) = meet(X_107,composition(X_107,top)),
inference(resolve,[$cnf( $equal(join(composition(complement(complement(X_107)),top),complement(top)),composition(X_107,top)) )],[refute_0_1563,refute_0_1566]) ).
cnf(refute_0_1568,plain,
( X_107 != meet(X_107,join(composition(complement(complement(X_107)),top),complement(top)))
| meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))) != meet(X_107,composition(X_107,top))
| X_107 = meet(X_107,composition(X_107,top)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_107,meet(X_107,composition(X_107,top))) ),[0],$fot(meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))))]]) ).
cnf(refute_0_1569,plain,
( X_107 != meet(X_107,join(composition(complement(complement(X_107)),top),complement(top)))
| X_107 = meet(X_107,composition(X_107,top)) ),
inference(resolve,[$cnf( $equal(meet(X_107,join(composition(complement(complement(X_107)),top),complement(top))),meet(X_107,composition(X_107,top))) )],[refute_0_1567,refute_0_1568]) ).
cnf(refute_0_1570,plain,
X_107 = meet(X_107,composition(X_107,top)),
inference(resolve,[$cnf( $equal(X_107,meet(X_107,join(composition(complement(complement(X_107)),top),complement(top)))) )],[refute_0_1540,refute_0_1569]) ).
cnf(refute_0_1571,plain,
complement(X_444) = meet(complement(X_444),composition(complement(X_444),top)),
inference(subst,[],[refute_0_1570:[bind(X_107,$fot(complement(X_444)))]]) ).
cnf(refute_0_1572,plain,
( complement(X_444) != meet(complement(X_444),composition(complement(X_444),top))
| meet(complement(X_444),composition(complement(X_444),top)) = complement(X_444) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_444))),bind(Y,$fot(meet(complement(X_444),composition(complement(X_444),top))))]]) ).
cnf(refute_0_1573,plain,
meet(complement(X_444),composition(complement(X_444),top)) = complement(X_444),
inference(resolve,[$cnf( $equal(complement(X_444),meet(complement(X_444),composition(complement(X_444),top))) )],[refute_0_1571,refute_0_1572]) ).
cnf(refute_0_1574,plain,
( join(X_444,complement(composition(complement(X_444),top))) != complement(meet(complement(X_444),composition(complement(X_444),top)))
| meet(complement(X_444),composition(complement(X_444),top)) != complement(X_444)
| join(X_444,complement(composition(complement(X_444),top))) = complement(complement(X_444)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_444,complement(composition(complement(X_444),top))),complement(meet(complement(X_444),composition(complement(X_444),top)))) ),[1,0],$fot(complement(X_444))]]) ).
cnf(refute_0_1575,plain,
( join(X_444,complement(composition(complement(X_444),top))) != complement(meet(complement(X_444),composition(complement(X_444),top)))
| join(X_444,complement(composition(complement(X_444),top))) = complement(complement(X_444)) ),
inference(resolve,[$cnf( $equal(meet(complement(X_444),composition(complement(X_444),top)),complement(X_444)) )],[refute_0_1573,refute_0_1574]) ).
cnf(refute_0_1576,plain,
join(X_444,complement(composition(complement(X_444),top))) = complement(complement(X_444)),
inference(resolve,[$cnf( $equal(join(X_444,complement(composition(complement(X_444),top))),complement(meet(complement(X_444),composition(complement(X_444),top)))) )],[refute_0_1373,refute_0_1575]) ).
cnf(refute_0_1577,plain,
( complement(complement(X_444)) != X_444
| join(X_444,complement(composition(complement(X_444),top))) != complement(complement(X_444))
| join(X_444,complement(composition(complement(X_444),top))) = X_444 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_444,complement(composition(complement(X_444),top))),complement(complement(X_444))) ),[1],$fot(X_444)]]) ).
cnf(refute_0_1578,plain,
( join(X_444,complement(composition(complement(X_444),top))) != complement(complement(X_444))
| join(X_444,complement(composition(complement(X_444),top))) = X_444 ),
inference(resolve,[$cnf( $equal(complement(complement(X_444)),X_444) )],[refute_0_1312,refute_0_1577]) ).
cnf(refute_0_1579,plain,
join(X_444,complement(composition(complement(X_444),top))) = X_444,
inference(resolve,[$cnf( $equal(join(X_444,complement(composition(complement(X_444),top))),complement(complement(X_444))) )],[refute_0_1576,refute_0_1578]) ).
cnf(refute_0_1580,plain,
join(join(complement(X_447),X_448),complement(composition(complement(join(complement(X_447),X_448)),top))) = join(complement(X_447),X_448),
inference(subst,[],[refute_0_1579:[bind(X_444,$fot(join(complement(X_447),X_448)))]]) ).
cnf(refute_0_1581,plain,
join(complement(X_299),X_300) = join(X_300,complement(X_299)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_299))),bind(B,$fot(X_300))]]) ).
cnf(refute_0_1582,plain,
( join(complement(X_299),X_300) != join(X_300,complement(X_299))
| join(X_300,complement(X_299)) = join(complement(X_299),X_300) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_299),X_300))),bind(Y,$fot(join(X_300,complement(X_299))))]]) ).
cnf(refute_0_1583,plain,
join(X_300,complement(X_299)) = join(complement(X_299),X_300),
inference(resolve,[$cnf( $equal(join(complement(X_299),X_300),join(X_300,complement(X_299))) )],[refute_0_1581,refute_0_1582]) ).
cnf(refute_0_1584,plain,
( join(X_300,complement(X_299)) != join(complement(X_299),X_300)
| meet(complement(X_300),X_299) != complement(join(X_300,complement(X_299)))
| meet(complement(X_300),X_299) = complement(join(complement(X_299),X_300)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_300),X_299),complement(join(X_300,complement(X_299)))) ),[1,0],$fot(join(complement(X_299),X_300))]]) ).
cnf(refute_0_1585,plain,
( meet(complement(X_300),X_299) != complement(join(X_300,complement(X_299)))
| meet(complement(X_300),X_299) = complement(join(complement(X_299),X_300)) ),
inference(resolve,[$cnf( $equal(join(X_300,complement(X_299)),join(complement(X_299),X_300)) )],[refute_0_1583,refute_0_1584]) ).
cnf(refute_0_1586,plain,
meet(complement(X_300),X_299) = complement(join(complement(X_299),X_300)),
inference(resolve,[$cnf( $equal(meet(complement(X_300),X_299),complement(join(X_300,complement(X_299)))) )],[refute_0_1283,refute_0_1585]) ).
cnf(refute_0_1587,plain,
meet(complement(X_448),X_447) = complement(join(complement(X_447),X_448)),
inference(subst,[],[refute_0_1586:[bind(X_299,$fot(X_447)),bind(X_300,$fot(X_448))]]) ).
cnf(refute_0_1588,plain,
( meet(complement(X_448),X_447) != complement(join(complement(X_447),X_448))
| complement(join(complement(X_447),X_448)) = meet(complement(X_448),X_447) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_448),X_447))),bind(Y,$fot(complement(join(complement(X_447),X_448))))]]) ).
cnf(refute_0_1589,plain,
complement(join(complement(X_447),X_448)) = meet(complement(X_448),X_447),
inference(resolve,[$cnf( $equal(meet(complement(X_448),X_447),complement(join(complement(X_447),X_448))) )],[refute_0_1587,refute_0_1588]) ).
cnf(refute_0_1590,plain,
( complement(join(complement(X_447),X_448)) != meet(complement(X_448),X_447)
| join(join(complement(X_447),X_448),complement(composition(complement(join(complement(X_447),X_448)),top))) != join(complement(X_447),X_448)
| join(join(complement(X_447),X_448),complement(composition(meet(complement(X_448),X_447),top))) = join(complement(X_447),X_448) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_447),X_448),complement(composition(complement(join(complement(X_447),X_448)),top))),join(complement(X_447),X_448)) ),[0,1,0,0],$fot(meet(complement(X_448),X_447))]]) ).
cnf(refute_0_1591,plain,
( join(join(complement(X_447),X_448),complement(composition(complement(join(complement(X_447),X_448)),top))) != join(complement(X_447),X_448)
| join(join(complement(X_447),X_448),complement(composition(meet(complement(X_448),X_447),top))) = join(complement(X_447),X_448) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_447),X_448)),meet(complement(X_448),X_447)) )],[refute_0_1589,refute_0_1590]) ).
cnf(refute_0_1592,plain,
join(join(complement(X_447),X_448),complement(composition(meet(complement(X_448),X_447),top))) = join(complement(X_447),X_448),
inference(resolve,[$cnf( $equal(join(join(complement(X_447),X_448),complement(composition(complement(join(complement(X_447),X_448)),top))),join(complement(X_447),X_448)) )],[refute_0_1580,refute_0_1591]) ).
cnf(refute_0_1593,plain,
join(join(complement(X_447),X_448),complement(composition(meet(complement(X_448),X_447),top))) = join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))),
inference(subst,[],[refute_0_181:[bind(A,$fot(complement(X_447))),bind(B,$fot(X_448)),bind(C,$fot(complement(composition(meet(complement(X_448),X_447),top))))]]) ).
cnf(refute_0_1594,plain,
( join(join(complement(X_447),X_448),complement(composition(meet(complement(X_448),X_447),top))) != join(complement(X_447),X_448)
| join(join(complement(X_447),X_448),complement(composition(meet(complement(X_448),X_447),top))) != join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top))))
| join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))) = join(complement(X_447),X_448) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_447),X_448),complement(composition(meet(complement(X_448),X_447),top))),join(complement(X_447),X_448)) ),[0],$fot(join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))))]]) ).
cnf(refute_0_1595,plain,
( join(join(complement(X_447),X_448),complement(composition(meet(complement(X_448),X_447),top))) != join(complement(X_447),X_448)
| join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))) = join(complement(X_447),X_448) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_447),X_448),complement(composition(meet(complement(X_448),X_447),top))),join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top))))) )],[refute_0_1593,refute_0_1594]) ).
cnf(refute_0_1596,plain,
join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))) = join(complement(X_447),X_448),
inference(resolve,[$cnf( $equal(join(join(complement(X_447),X_448),complement(composition(meet(complement(X_448),X_447),top))),join(complement(X_447),X_448)) )],[refute_0_1592,refute_0_1595]) ).
cnf(refute_0_1597,plain,
join(join(X_298,complement(X_296)),complement(composition(complement(join(X_298,complement(X_296))),top))) = join(X_298,complement(X_296)),
inference(subst,[],[refute_0_1579:[bind(X_444,$fot(join(X_298,complement(X_296))))]]) ).
cnf(refute_0_1598,plain,
( complement(join(X_298,complement(X_296))) != meet(complement(X_298),X_296)
| join(join(X_298,complement(X_296)),complement(composition(complement(join(X_298,complement(X_296))),top))) != join(X_298,complement(X_296))
| join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))) = join(X_298,complement(X_296)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(composition(complement(join(X_298,complement(X_296))),top))),join(X_298,complement(X_296))) ),[0,1,0,0],$fot(meet(complement(X_298),X_296))]]) ).
cnf(refute_0_1599,plain,
( join(join(X_298,complement(X_296)),complement(composition(complement(join(X_298,complement(X_296))),top))) != join(X_298,complement(X_296))
| join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))) = join(X_298,complement(X_296)) ),
inference(resolve,[$cnf( $equal(complement(join(X_298,complement(X_296))),meet(complement(X_298),X_296)) )],[refute_0_1304,refute_0_1598]) ).
cnf(refute_0_1600,plain,
join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))) = join(X_298,complement(X_296)),
inference(resolve,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(composition(complement(join(X_298,complement(X_296))),top))),join(X_298,complement(X_296))) )],[refute_0_1597,refute_0_1599]) ).
cnf(refute_0_1601,plain,
join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top))) = complement(meet(X_296,composition(meet(complement(X_298),X_296),top))),
inference(subst,[],[refute_0_1241:[bind(A,$fot(X_296)),bind(B,$fot(composition(meet(complement(X_298),X_296),top)))]]) ).
cnf(refute_0_1602,plain,
join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))) = join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))),
introduced(tautology,[refl,[$fot(join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))))]]) ).
cnf(refute_0_1603,plain,
( join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))) != join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top))))
| join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top))) != complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))
| join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))) = join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))),join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top))))) ),[1,1],$fot(complement(meet(X_296,composition(meet(complement(X_298),X_296),top))))]]) ).
cnf(refute_0_1604,plain,
( join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top))) != complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))
| join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))) = join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))) ),
inference(resolve,[$cnf( $equal(join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))),join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top))))) )],[refute_0_1602,refute_0_1603]) ).
cnf(refute_0_1605,plain,
join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))) = join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))),
inference(resolve,[$cnf( $equal(join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top))),complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))) )],[refute_0_1601,refute_0_1604]) ).
cnf(refute_0_1606,plain,
join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))) = join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))),
inference(subst,[],[refute_0_181:[bind(A,$fot(X_298)),bind(B,$fot(complement(X_296))),bind(C,$fot(complement(composition(meet(complement(X_298),X_296),top))))]]) ).
cnf(refute_0_1607,plain,
( join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))) != join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top))))
| join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))) != join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top))))
| join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))) = join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))))),bind(Y,$fot(join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))))),bind(Z,$fot(join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top))))))]]) ).
cnf(refute_0_1608,plain,
( join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))) != join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top))))
| join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))) = join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))) ),
inference(resolve,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))),join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top))))) )],[refute_0_1606,refute_0_1607]) ).
cnf(refute_0_1609,plain,
join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))) = join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))),
inference(resolve,[$cnf( $equal(join(X_298,join(complement(X_296),complement(composition(meet(complement(X_298),X_296),top)))),join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top))))) )],[refute_0_1605,refute_0_1608]) ).
cnf(refute_0_1610,plain,
( join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))) != join(X_298,complement(X_296))
| join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))) != join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top))))
| join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))) = join(X_298,complement(X_296)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))),join(X_298,complement(X_296))) ),[0],$fot(join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))))]]) ).
cnf(refute_0_1611,plain,
( join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))) != join(X_298,complement(X_296))
| join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))) = join(X_298,complement(X_296)) ),
inference(resolve,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))),join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top))))) )],[refute_0_1609,refute_0_1610]) ).
cnf(refute_0_1612,plain,
join(X_298,complement(meet(X_296,composition(meet(complement(X_298),X_296),top)))) = join(X_298,complement(X_296)),
inference(resolve,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(composition(meet(complement(X_298),X_296),top))),join(X_298,complement(X_296))) )],[refute_0_1600,refute_0_1611]) ).
cnf(refute_0_1613,plain,
join(X_448,complement(meet(X_447,composition(meet(complement(X_448),X_447),top)))) = join(X_448,complement(X_447)),
inference(subst,[],[refute_0_1612:[bind(X_296,$fot(X_447)),bind(X_298,$fot(X_448))]]) ).
cnf(refute_0_1614,plain,
join(join(complement(X_447),X_448),complement(X_299)) = complement(meet(complement(join(complement(X_447),X_448)),X_299)),
inference(subst,[],[refute_0_1288:[bind(X_300,$fot(join(complement(X_447),X_448)))]]) ).
cnf(refute_0_1615,plain,
( complement(join(complement(X_447),X_448)) != meet(complement(X_448),X_447)
| join(join(complement(X_447),X_448),complement(X_299)) != complement(meet(complement(join(complement(X_447),X_448)),X_299))
| join(join(complement(X_447),X_448),complement(X_299)) = complement(meet(meet(complement(X_448),X_447),X_299)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_447),X_448),complement(X_299)),complement(meet(complement(join(complement(X_447),X_448)),X_299))) ),[1,0,0],$fot(meet(complement(X_448),X_447))]]) ).
cnf(refute_0_1616,plain,
( join(join(complement(X_447),X_448),complement(X_299)) != complement(meet(complement(join(complement(X_447),X_448)),X_299))
| join(join(complement(X_447),X_448),complement(X_299)) = complement(meet(meet(complement(X_448),X_447),X_299)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_447),X_448)),meet(complement(X_448),X_447)) )],[refute_0_1589,refute_0_1615]) ).
cnf(refute_0_1617,plain,
join(join(complement(X_447),X_448),complement(X_299)) = complement(meet(meet(complement(X_448),X_447),X_299)),
inference(resolve,[$cnf( $equal(join(join(complement(X_447),X_448),complement(X_299)),complement(meet(complement(join(complement(X_447),X_448)),X_299))) )],[refute_0_1614,refute_0_1616]) ).
cnf(refute_0_1618,plain,
join(join(complement(X_447),X_448),complement(X_299)) = join(complement(X_447),join(X_448,complement(X_299))),
inference(subst,[],[refute_0_181:[bind(A,$fot(complement(X_447))),bind(B,$fot(X_448)),bind(C,$fot(complement(X_299)))]]) ).
cnf(refute_0_1619,plain,
( join(join(complement(X_447),X_448),complement(X_299)) != complement(meet(meet(complement(X_448),X_447),X_299))
| join(join(complement(X_447),X_448),complement(X_299)) != join(complement(X_447),join(X_448,complement(X_299)))
| join(complement(X_447),join(X_448,complement(X_299))) = complement(meet(meet(complement(X_448),X_447),X_299)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_447),X_448),complement(X_299)),complement(meet(meet(complement(X_448),X_447),X_299))) ),[0],$fot(join(complement(X_447),join(X_448,complement(X_299))))]]) ).
cnf(refute_0_1620,plain,
( join(join(complement(X_447),X_448),complement(X_299)) != complement(meet(meet(complement(X_448),X_447),X_299))
| join(complement(X_447),join(X_448,complement(X_299))) = complement(meet(meet(complement(X_448),X_447),X_299)) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_447),X_448),complement(X_299)),join(complement(X_447),join(X_448,complement(X_299)))) )],[refute_0_1618,refute_0_1619]) ).
cnf(refute_0_1621,plain,
join(join(X_298,complement(X_296)),complement(X_443)) = complement(meet(complement(join(X_298,complement(X_296))),X_443)),
inference(subst,[],[refute_0_1288:[bind(X_299,$fot(X_443)),bind(X_300,$fot(join(X_298,complement(X_296))))]]) ).
cnf(refute_0_1622,plain,
( complement(join(X_298,complement(X_296))) != meet(complement(X_298),X_296)
| join(join(X_298,complement(X_296)),complement(X_443)) != complement(meet(complement(join(X_298,complement(X_296))),X_443))
| join(join(X_298,complement(X_296)),complement(X_443)) = complement(meet(meet(complement(X_298),X_296),X_443)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(X_443)),complement(meet(complement(join(X_298,complement(X_296))),X_443))) ),[1,0,0],$fot(meet(complement(X_298),X_296))]]) ).
cnf(refute_0_1623,plain,
( join(join(X_298,complement(X_296)),complement(X_443)) != complement(meet(complement(join(X_298,complement(X_296))),X_443))
| join(join(X_298,complement(X_296)),complement(X_443)) = complement(meet(meet(complement(X_298),X_296),X_443)) ),
inference(resolve,[$cnf( $equal(complement(join(X_298,complement(X_296))),meet(complement(X_298),X_296)) )],[refute_0_1304,refute_0_1622]) ).
cnf(refute_0_1624,plain,
join(join(X_298,complement(X_296)),complement(X_443)) = complement(meet(meet(complement(X_298),X_296),X_443)),
inference(resolve,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(X_443)),complement(meet(complement(join(X_298,complement(X_296))),X_443))) )],[refute_0_1621,refute_0_1623]) ).
cnf(refute_0_1625,plain,
join(complement(X_296),complement(X_443)) = complement(meet(X_296,X_443)),
inference(subst,[],[refute_0_1241:[bind(A,$fot(X_296)),bind(B,$fot(X_443))]]) ).
cnf(refute_0_1626,plain,
join(X_298,join(complement(X_296),complement(X_443))) = join(X_298,join(complement(X_296),complement(X_443))),
introduced(tautology,[refl,[$fot(join(X_298,join(complement(X_296),complement(X_443))))]]) ).
cnf(refute_0_1627,plain,
( join(X_298,join(complement(X_296),complement(X_443))) != join(X_298,join(complement(X_296),complement(X_443)))
| join(complement(X_296),complement(X_443)) != complement(meet(X_296,X_443))
| join(X_298,join(complement(X_296),complement(X_443))) = join(X_298,complement(meet(X_296,X_443))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_298,join(complement(X_296),complement(X_443))),join(X_298,join(complement(X_296),complement(X_443)))) ),[1,1],$fot(complement(meet(X_296,X_443)))]]) ).
cnf(refute_0_1628,plain,
( join(complement(X_296),complement(X_443)) != complement(meet(X_296,X_443))
| join(X_298,join(complement(X_296),complement(X_443))) = join(X_298,complement(meet(X_296,X_443))) ),
inference(resolve,[$cnf( $equal(join(X_298,join(complement(X_296),complement(X_443))),join(X_298,join(complement(X_296),complement(X_443)))) )],[refute_0_1626,refute_0_1627]) ).
cnf(refute_0_1629,plain,
join(X_298,join(complement(X_296),complement(X_443))) = join(X_298,complement(meet(X_296,X_443))),
inference(resolve,[$cnf( $equal(join(complement(X_296),complement(X_443)),complement(meet(X_296,X_443))) )],[refute_0_1625,refute_0_1628]) ).
cnf(refute_0_1630,plain,
join(join(X_298,complement(X_296)),complement(X_443)) = join(X_298,join(complement(X_296),complement(X_443))),
inference(subst,[],[refute_0_181:[bind(A,$fot(X_298)),bind(B,$fot(complement(X_296))),bind(C,$fot(complement(X_443)))]]) ).
cnf(refute_0_1631,plain,
( join(X_298,join(complement(X_296),complement(X_443))) != join(X_298,complement(meet(X_296,X_443)))
| join(join(X_298,complement(X_296)),complement(X_443)) != join(X_298,join(complement(X_296),complement(X_443)))
| join(join(X_298,complement(X_296)),complement(X_443)) = join(X_298,complement(meet(X_296,X_443))) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(join(X_298,complement(X_296)),complement(X_443)))),bind(Y,$fot(join(X_298,join(complement(X_296),complement(X_443))))),bind(Z,$fot(join(X_298,complement(meet(X_296,X_443)))))]]) ).
cnf(refute_0_1632,plain,
( join(X_298,join(complement(X_296),complement(X_443))) != join(X_298,complement(meet(X_296,X_443)))
| join(join(X_298,complement(X_296)),complement(X_443)) = join(X_298,complement(meet(X_296,X_443))) ),
inference(resolve,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(X_443)),join(X_298,join(complement(X_296),complement(X_443)))) )],[refute_0_1630,refute_0_1631]) ).
cnf(refute_0_1633,plain,
join(join(X_298,complement(X_296)),complement(X_443)) = join(X_298,complement(meet(X_296,X_443))),
inference(resolve,[$cnf( $equal(join(X_298,join(complement(X_296),complement(X_443))),join(X_298,complement(meet(X_296,X_443)))) )],[refute_0_1629,refute_0_1632]) ).
cnf(refute_0_1634,plain,
( join(join(X_298,complement(X_296)),complement(X_443)) != complement(meet(meet(complement(X_298),X_296),X_443))
| join(join(X_298,complement(X_296)),complement(X_443)) != join(X_298,complement(meet(X_296,X_443)))
| join(X_298,complement(meet(X_296,X_443))) = complement(meet(meet(complement(X_298),X_296),X_443)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(X_443)),complement(meet(meet(complement(X_298),X_296),X_443))) ),[0],$fot(join(X_298,complement(meet(X_296,X_443))))]]) ).
cnf(refute_0_1635,plain,
( join(join(X_298,complement(X_296)),complement(X_443)) != complement(meet(meet(complement(X_298),X_296),X_443))
| join(X_298,complement(meet(X_296,X_443))) = complement(meet(meet(complement(X_298),X_296),X_443)) ),
inference(resolve,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(X_443)),join(X_298,complement(meet(X_296,X_443)))) )],[refute_0_1633,refute_0_1634]) ).
cnf(refute_0_1636,plain,
join(X_298,complement(meet(X_296,X_443))) = complement(meet(meet(complement(X_298),X_296),X_443)),
inference(resolve,[$cnf( $equal(join(join(X_298,complement(X_296)),complement(X_443)),complement(meet(meet(complement(X_298),X_296),X_443))) )],[refute_0_1624,refute_0_1635]) ).
cnf(refute_0_1637,plain,
( join(X_298,complement(meet(X_296,X_443))) != complement(meet(meet(complement(X_298),X_296),X_443))
| complement(meet(meet(complement(X_298),X_296),X_443)) = join(X_298,complement(meet(X_296,X_443))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_298,complement(meet(X_296,X_443))))),bind(Y,$fot(complement(meet(meet(complement(X_298),X_296),X_443))))]]) ).
cnf(refute_0_1638,plain,
complement(meet(meet(complement(X_298),X_296),X_443)) = join(X_298,complement(meet(X_296,X_443))),
inference(resolve,[$cnf( $equal(join(X_298,complement(meet(X_296,X_443))),complement(meet(meet(complement(X_298),X_296),X_443))) )],[refute_0_1636,refute_0_1637]) ).
cnf(refute_0_1639,plain,
complement(meet(meet(complement(X_448),X_447),X_299)) = join(X_448,complement(meet(X_447,X_299))),
inference(subst,[],[refute_0_1638:[bind(X_296,$fot(X_447)),bind(X_298,$fot(X_448)),bind(X_443,$fot(X_299))]]) ).
cnf(refute_0_1640,plain,
( complement(meet(meet(complement(X_448),X_447),X_299)) != join(X_448,complement(meet(X_447,X_299)))
| join(complement(X_447),join(X_448,complement(X_299))) != complement(meet(meet(complement(X_448),X_447),X_299))
| join(complement(X_447),join(X_448,complement(X_299))) = join(X_448,complement(meet(X_447,X_299))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_447),join(X_448,complement(X_299))),complement(meet(meet(complement(X_448),X_447),X_299))) ),[1],$fot(join(X_448,complement(meet(X_447,X_299))))]]) ).
cnf(refute_0_1641,plain,
( join(complement(X_447),join(X_448,complement(X_299))) != complement(meet(meet(complement(X_448),X_447),X_299))
| join(complement(X_447),join(X_448,complement(X_299))) = join(X_448,complement(meet(X_447,X_299))) ),
inference(resolve,[$cnf( $equal(complement(meet(meet(complement(X_448),X_447),X_299)),join(X_448,complement(meet(X_447,X_299)))) )],[refute_0_1639,refute_0_1640]) ).
cnf(refute_0_1642,plain,
( join(join(complement(X_447),X_448),complement(X_299)) != complement(meet(meet(complement(X_448),X_447),X_299))
| join(complement(X_447),join(X_448,complement(X_299))) = join(X_448,complement(meet(X_447,X_299))) ),
inference(resolve,[$cnf( $equal(join(complement(X_447),join(X_448,complement(X_299))),complement(meet(meet(complement(X_448),X_447),X_299))) )],[refute_0_1620,refute_0_1641]) ).
cnf(refute_0_1643,plain,
join(complement(X_447),join(X_448,complement(X_299))) = join(X_448,complement(meet(X_447,X_299))),
inference(resolve,[$cnf( $equal(join(join(complement(X_447),X_448),complement(X_299)),complement(meet(meet(complement(X_448),X_447),X_299))) )],[refute_0_1617,refute_0_1642]) ).
cnf(refute_0_1644,plain,
join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))) = join(X_448,complement(meet(X_447,composition(meet(complement(X_448),X_447),top)))),
inference(subst,[],[refute_0_1643:[bind(X_299,$fot(composition(meet(complement(X_448),X_447),top)))]]) ).
cnf(refute_0_1645,plain,
( join(X_448,complement(meet(X_447,composition(meet(complement(X_448),X_447),top)))) != join(X_448,complement(X_447))
| join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))) != join(X_448,complement(meet(X_447,composition(meet(complement(X_448),X_447),top))))
| join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))) = join(X_448,complement(X_447)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))))),bind(Y,$fot(join(X_448,complement(meet(X_447,composition(meet(complement(X_448),X_447),top)))))),bind(Z,$fot(join(X_448,complement(X_447))))]]) ).
cnf(refute_0_1646,plain,
( join(X_448,complement(meet(X_447,composition(meet(complement(X_448),X_447),top)))) != join(X_448,complement(X_447))
| join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))) = join(X_448,complement(X_447)) ),
inference(resolve,[$cnf( $equal(join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))),join(X_448,complement(meet(X_447,composition(meet(complement(X_448),X_447),top))))) )],[refute_0_1644,refute_0_1645]) ).
cnf(refute_0_1647,plain,
join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))) = join(X_448,complement(X_447)),
inference(resolve,[$cnf( $equal(join(X_448,complement(meet(X_447,composition(meet(complement(X_448),X_447),top)))),join(X_448,complement(X_447))) )],[refute_0_1613,refute_0_1646]) ).
cnf(refute_0_1648,plain,
( join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))) != join(X_448,complement(X_447))
| join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))) != join(complement(X_447),X_448)
| join(X_448,complement(X_447)) = join(complement(X_447),X_448) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))),join(complement(X_447),X_448)) ),[0],$fot(join(X_448,complement(X_447)))]]) ).
cnf(refute_0_1649,plain,
( join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))) != join(complement(X_447),X_448)
| join(X_448,complement(X_447)) = join(complement(X_447),X_448) ),
inference(resolve,[$cnf( $equal(join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))),join(X_448,complement(X_447))) )],[refute_0_1647,refute_0_1648]) ).
cnf(refute_0_1650,plain,
join(X_448,complement(X_447)) = join(complement(X_447),X_448),
inference(resolve,[$cnf( $equal(join(complement(X_447),join(X_448,complement(composition(meet(complement(X_448),X_447),top)))),join(complement(X_447),X_448)) )],[refute_0_1596,refute_0_1649]) ).
cnf(refute_0_1651,plain,
join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) = join(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583)))),
inference(subst,[],[refute_0_1650:[bind(X_447,$fot(X_583)),bind(X_448,$fot(join(X_107,meet(complement(X_107),complement(X_583)))))]]) ).
cnf(refute_0_1652,plain,
( join(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583)))) != join(X_107,complement(X_583))
| join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) != join(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583))))
| join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) = join(X_107,complement(X_583)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)))),bind(Y,$fot(join(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583)))))),bind(Z,$fot(join(X_107,complement(X_583))))]]) ).
cnf(refute_0_1653,plain,
( join(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583)))) != join(X_107,complement(X_583))
| join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) = join(X_107,complement(X_583)) ),
inference(resolve,[$cnf( $equal(join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)),join(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583))))) )],[refute_0_1651,refute_0_1652]) ).
cnf(refute_0_1654,plain,
join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) = join(X_107,complement(X_583)),
inference(resolve,[$cnf( $equal(join(complement(X_583),join(X_107,meet(complement(X_107),complement(X_583)))),join(X_107,complement(X_583))) )],[refute_0_1372,refute_0_1653]) ).
cnf(refute_0_1655,plain,
( join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) != join(X_107,complement(X_583))
| join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) != join(X_107,meet(complement(X_107),complement(X_583)))
| join(X_107,complement(X_583)) = join(X_107,meet(complement(X_107),complement(X_583))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)),join(X_107,meet(complement(X_107),complement(X_583)))) ),[0],$fot(join(X_107,complement(X_583)))]]) ).
cnf(refute_0_1656,plain,
( join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) != join(X_107,meet(complement(X_107),complement(X_583)))
| join(X_107,complement(X_583)) = join(X_107,meet(complement(X_107),complement(X_583))) ),
inference(resolve,[$cnf( $equal(join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)),join(X_107,complement(X_583))) )],[refute_0_1654,refute_0_1655]) ).
cnf(refute_0_1657,plain,
meet(complement(X_107),complement(X_583)) = complement(join(X_107,X_583)),
inference(subst,[],[refute_0_1273:[bind(X_107,$fot(X_583)),bind(X_300,$fot(X_107))]]) ).
cnf(refute_0_1658,plain,
join(X_107,meet(complement(X_107),complement(X_583))) = join(X_107,meet(complement(X_107),complement(X_583))),
introduced(tautology,[refl,[$fot(join(X_107,meet(complement(X_107),complement(X_583))))]]) ).
cnf(refute_0_1659,plain,
( join(X_107,meet(complement(X_107),complement(X_583))) != join(X_107,meet(complement(X_107),complement(X_583)))
| meet(complement(X_107),complement(X_583)) != complement(join(X_107,X_583))
| join(X_107,meet(complement(X_107),complement(X_583))) = join(X_107,complement(join(X_107,X_583))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_107,meet(complement(X_107),complement(X_583))),join(X_107,meet(complement(X_107),complement(X_583)))) ),[1,1],$fot(complement(join(X_107,X_583)))]]) ).
cnf(refute_0_1660,plain,
( meet(complement(X_107),complement(X_583)) != complement(join(X_107,X_583))
| join(X_107,meet(complement(X_107),complement(X_583))) = join(X_107,complement(join(X_107,X_583))) ),
inference(resolve,[$cnf( $equal(join(X_107,meet(complement(X_107),complement(X_583))),join(X_107,meet(complement(X_107),complement(X_583)))) )],[refute_0_1658,refute_0_1659]) ).
cnf(refute_0_1661,plain,
join(X_107,meet(complement(X_107),complement(X_583))) = join(X_107,complement(join(X_107,X_583))),
inference(resolve,[$cnf( $equal(meet(complement(X_107),complement(X_583)),complement(join(X_107,X_583))) )],[refute_0_1657,refute_0_1660]) ).
cnf(refute_0_1662,plain,
( join(X_107,complement(X_583)) != join(X_107,meet(complement(X_107),complement(X_583)))
| join(X_107,meet(complement(X_107),complement(X_583))) != join(X_107,complement(join(X_107,X_583)))
| join(X_107,complement(X_583)) = join(X_107,complement(join(X_107,X_583))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_107,complement(X_583)),join(X_107,complement(join(X_107,X_583)))) ),[0],$fot(join(X_107,meet(complement(X_107),complement(X_583))))]]) ).
cnf(refute_0_1663,plain,
( join(X_107,complement(X_583)) != join(X_107,meet(complement(X_107),complement(X_583)))
| join(X_107,complement(X_583)) = join(X_107,complement(join(X_107,X_583))) ),
inference(resolve,[$cnf( $equal(join(X_107,meet(complement(X_107),complement(X_583))),join(X_107,complement(join(X_107,X_583)))) )],[refute_0_1661,refute_0_1662]) ).
cnf(refute_0_1664,plain,
( join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)) != join(X_107,meet(complement(X_107),complement(X_583)))
| join(X_107,complement(X_583)) = join(X_107,complement(join(X_107,X_583))) ),
inference(resolve,[$cnf( $equal(join(X_107,complement(X_583)),join(X_107,meet(complement(X_107),complement(X_583)))) )],[refute_0_1656,refute_0_1663]) ).
cnf(refute_0_1665,plain,
join(X_107,complement(X_583)) = join(X_107,complement(join(X_107,X_583))),
inference(resolve,[$cnf( $equal(join(join(X_107,meet(complement(X_107),complement(X_583))),complement(X_583)),join(X_107,meet(complement(X_107),complement(X_583)))) )],[refute_0_1366,refute_0_1664]) ).
cnf(refute_0_1666,plain,
( join(X_107,complement(X_583)) != join(X_107,complement(join(X_107,X_583)))
| join(X_107,complement(join(X_107,X_583))) = join(X_107,complement(X_583)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_107,complement(X_583)))),bind(Y,$fot(join(X_107,complement(join(X_107,X_583)))))]]) ).
cnf(refute_0_1667,plain,
join(X_107,complement(join(X_107,X_583))) = join(X_107,complement(X_583)),
inference(resolve,[$cnf( $equal(join(X_107,complement(X_583)),join(X_107,complement(join(X_107,X_583)))) )],[refute_0_1665,refute_0_1666]) ).
cnf(refute_0_1668,plain,
join(one,complement(join(one,composition(complement(converse(X_125)),X_125)))) = join(one,complement(composition(complement(converse(X_125)),X_125))),
inference(subst,[],[refute_0_1667:[bind(X_107,$fot(one)),bind(X_583,$fot(composition(complement(converse(X_125)),X_125)))]]) ).
cnf(refute_0_1669,plain,
( complement(composition(complement(converse(X_125)),X_125)) != join(one,complement(join(one,composition(complement(converse(X_125)),X_125))))
| join(one,complement(join(one,composition(complement(converse(X_125)),X_125)))) != join(one,complement(composition(complement(converse(X_125)),X_125)))
| complement(composition(complement(converse(X_125)),X_125)) = join(one,complement(composition(complement(converse(X_125)),X_125))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(complement(converse(X_125)),X_125)),join(one,complement(composition(complement(converse(X_125)),X_125)))) ),[0],$fot(join(one,complement(join(one,composition(complement(converse(X_125)),X_125)))))]]) ).
cnf(refute_0_1670,plain,
( complement(composition(complement(converse(X_125)),X_125)) != join(one,complement(join(one,composition(complement(converse(X_125)),X_125))))
| complement(composition(complement(converse(X_125)),X_125)) = join(one,complement(composition(complement(converse(X_125)),X_125))) ),
inference(resolve,[$cnf( $equal(join(one,complement(join(one,composition(complement(converse(X_125)),X_125)))),join(one,complement(composition(complement(converse(X_125)),X_125)))) )],[refute_0_1668,refute_0_1669]) ).
cnf(refute_0_1671,plain,
complement(composition(complement(converse(X_125)),X_125)) = join(one,complement(composition(complement(converse(X_125)),X_125))),
inference(resolve,[$cnf( $equal(complement(composition(complement(converse(X_125)),X_125)),join(one,complement(join(one,composition(complement(converse(X_125)),X_125))))) )],[refute_0_1281,refute_0_1670]) ).
cnf(refute_0_1672,plain,
( complement(composition(complement(converse(X_125)),X_125)) != join(one,complement(composition(complement(converse(X_125)),X_125)))
| join(one,complement(composition(complement(converse(X_125)),X_125))) = complement(composition(complement(converse(X_125)),X_125)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(composition(complement(converse(X_125)),X_125)))),bind(Y,$fot(join(one,complement(composition(complement(converse(X_125)),X_125)))))]]) ).
cnf(refute_0_1673,plain,
join(one,complement(composition(complement(converse(X_125)),X_125))) = complement(composition(complement(converse(X_125)),X_125)),
inference(resolve,[$cnf( $equal(complement(composition(complement(converse(X_125)),X_125)),join(one,complement(composition(complement(converse(X_125)),X_125)))) )],[refute_0_1671,refute_0_1672]) ).
cnf(refute_0_1674,plain,
join(one,complement(composition(complement(converse(X_79)),X_79))) = complement(composition(complement(converse(X_79)),X_79)),
inference(subst,[],[refute_0_1673:[bind(X_125,$fot(X_79))]]) ).
cnf(refute_0_1675,plain,
composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) = composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))),
introduced(tautology,[refl,[$fot(composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))))]]) ).
cnf(refute_0_1676,plain,
( composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) != composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79))))
| join(one,complement(composition(complement(converse(X_79)),X_79))) != complement(composition(complement(converse(X_79)),X_79))
| composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) = composition(complement(X_79),complement(composition(complement(converse(X_79)),X_79))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))),composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79))))) ),[1,1],$fot(complement(composition(complement(converse(X_79)),X_79)))]]) ).
cnf(refute_0_1677,plain,
( join(one,complement(composition(complement(converse(X_79)),X_79))) != complement(composition(complement(converse(X_79)),X_79))
| composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) = composition(complement(X_79),complement(composition(complement(converse(X_79)),X_79))) ),
inference(resolve,[$cnf( $equal(composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))),composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79))))) )],[refute_0_1675,refute_0_1676]) ).
cnf(refute_0_1678,plain,
composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) = composition(complement(X_79),complement(composition(complement(converse(X_79)),X_79))),
inference(resolve,[$cnf( $equal(join(one,complement(composition(complement(converse(X_79)),X_79))),complement(composition(complement(converse(X_79)),X_79))) )],[refute_0_1674,refute_0_1677]) ).
cnf(refute_0_1679,plain,
( composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) != complement(X_79)
| composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) != composition(complement(X_79),complement(composition(complement(converse(X_79)),X_79)))
| composition(complement(X_79),complement(composition(complement(converse(X_79)),X_79))) = complement(X_79) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))),complement(X_79)) ),[0],$fot(composition(complement(X_79),complement(composition(complement(converse(X_79)),X_79))))]]) ).
cnf(refute_0_1680,plain,
( composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))) != complement(X_79)
| composition(complement(X_79),complement(composition(complement(converse(X_79)),X_79))) = complement(X_79) ),
inference(resolve,[$cnf( $equal(composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))),composition(complement(X_79),complement(composition(complement(converse(X_79)),X_79)))) )],[refute_0_1678,refute_0_1679]) ).
cnf(refute_0_1681,plain,
composition(complement(X_79),complement(composition(complement(converse(X_79)),X_79))) = complement(X_79),
inference(resolve,[$cnf( $equal(composition(complement(X_79),join(one,complement(composition(complement(converse(X_79)),X_79)))),complement(X_79)) )],[refute_0_1118,refute_0_1680]) ).
cnf(refute_0_1682,plain,
composition(complement(composition(B,top)),complement(composition(complement(converse(composition(B,top))),composition(B,top)))) = complement(composition(B,top)),
inference(subst,[],[refute_0_1681:[bind(X_79,$fot(composition(B,top)))]]) ).
cnf(refute_0_1683,plain,
composition(converse(complement(composition(B,top))),composition(B,C)) = composition(composition(converse(complement(composition(B,top))),B),C),
inference(subst,[],[composition_associativity_5:[bind(A,$fot(converse(complement(composition(B,top)))))]]) ).
cnf(refute_0_1684,plain,
converse(composition(converse(X_126),complement(composition(X_126,top)))) = composition(converse(complement(composition(X_126,top))),converse(converse(X_126))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(X_126))),bind(B,$fot(complement(composition(X_126,top))))]]) ).
cnf(refute_0_1685,plain,
join(complement(top),composition(converse(X_78),complement(composition(X_78,top)))) = complement(top),
inference(subst,[],[refute_0_8:[bind(A,$fot(X_78)),bind(B,$fot(top))]]) ).
cnf(refute_0_1686,plain,
( complement(top) != zero
| join(complement(top),composition(converse(X_78),complement(composition(X_78,top)))) != complement(top)
| join(zero,composition(converse(X_78),complement(composition(X_78,top)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(X_78),complement(composition(X_78,top)))),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_1687,plain,
( join(complement(top),composition(converse(X_78),complement(composition(X_78,top)))) != complement(top)
| join(zero,composition(converse(X_78),complement(composition(X_78,top)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_1686]) ).
cnf(refute_0_1688,plain,
join(zero,composition(converse(X_78),complement(composition(X_78,top)))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(X_78),complement(composition(X_78,top)))),complement(top)) )],[refute_0_1685,refute_0_1687]) ).
cnf(refute_0_1689,plain,
( complement(top) != zero
| join(zero,composition(converse(X_78),complement(composition(X_78,top)))) != complement(top)
| join(zero,composition(converse(X_78),complement(composition(X_78,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(X_78),complement(composition(X_78,top)))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_1690,plain,
( join(zero,composition(converse(X_78),complement(composition(X_78,top)))) != complement(top)
| join(zero,composition(converse(X_78),complement(composition(X_78,top)))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_1689]) ).
cnf(refute_0_1691,plain,
join(zero,composition(converse(X_78),complement(composition(X_78,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_78),complement(composition(X_78,top)))),complement(top)) )],[refute_0_1688,refute_0_1690]) ).
cnf(refute_0_1692,plain,
join(zero,composition(converse(X_78),complement(composition(X_78,top)))) = composition(converse(X_78),complement(composition(X_78,top))),
inference(subst,[],[refute_0_871:[bind(X_107,$fot(composition(converse(X_78),complement(composition(X_78,top)))))]]) ).
cnf(refute_0_1693,plain,
( join(zero,composition(converse(X_78),complement(composition(X_78,top)))) != composition(converse(X_78),complement(composition(X_78,top)))
| join(zero,composition(converse(X_78),complement(composition(X_78,top)))) != zero
| composition(converse(X_78),complement(composition(X_78,top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(X_78),complement(composition(X_78,top)))),zero) ),[0],$fot(composition(converse(X_78),complement(composition(X_78,top))))]]) ).
cnf(refute_0_1694,plain,
( join(zero,composition(converse(X_78),complement(composition(X_78,top)))) != zero
| composition(converse(X_78),complement(composition(X_78,top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_78),complement(composition(X_78,top)))),composition(converse(X_78),complement(composition(X_78,top)))) )],[refute_0_1692,refute_0_1693]) ).
cnf(refute_0_1695,plain,
composition(converse(X_78),complement(composition(X_78,top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_78),complement(composition(X_78,top)))),zero) )],[refute_0_1691,refute_0_1694]) ).
cnf(refute_0_1696,plain,
composition(converse(X_126),complement(composition(X_126,top))) = zero,
inference(subst,[],[refute_0_1695:[bind(X_78,$fot(X_126))]]) ).
cnf(refute_0_1697,plain,
( composition(converse(X_126),complement(composition(X_126,top))) != zero
| converse(composition(converse(X_126),complement(composition(X_126,top)))) != composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))
| converse(zero) = composition(converse(complement(composition(X_126,top))),converse(converse(X_126))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_126),complement(composition(X_126,top)))),composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_1698,plain,
( converse(composition(converse(X_126),complement(composition(X_126,top)))) != composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))
| converse(zero) = composition(converse(complement(composition(X_126,top))),converse(converse(X_126))) ),
inference(resolve,[$cnf( $equal(composition(converse(X_126),complement(composition(X_126,top))),zero) )],[refute_0_1696,refute_0_1697]) ).
cnf(refute_0_1699,plain,
converse(zero) = composition(converse(complement(composition(X_126,top))),converse(converse(X_126))),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_126),complement(composition(X_126,top)))),composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))) )],[refute_0_1684,refute_0_1698]) ).
cnf(refute_0_1700,plain,
zero = meet(converse(zero),complement(converse(zero))),
inference(subst,[],[def_zero_13:[bind(A,$fot(converse(zero)))]]) ).
cnf(refute_0_1701,plain,
converse(converse(complement(converse(zero)))) = complement(converse(zero)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_1702,plain,
top = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_956:[bind(X_66,$fot(zero))]]) ).
cnf(refute_0_1703,plain,
converse(complement(converse(zero))) = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_869:[bind(X_107,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_1704,plain,
( converse(complement(converse(zero))) != join(zero,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) = converse(complement(converse(zero))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(complement(converse(zero))))),bind(Y,$fot(join(zero,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_1705,plain,
join(zero,converse(complement(converse(zero)))) = converse(complement(converse(zero))),
inference(resolve,[$cnf( $equal(converse(complement(converse(zero))),join(zero,converse(complement(converse(zero))))) )],[refute_0_1703,refute_0_1704]) ).
cnf(refute_0_1706,plain,
( join(zero,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| top != join(zero,converse(complement(converse(zero))))
| top = converse(complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,converse(complement(converse(zero))))) ),[1],$fot(converse(complement(converse(zero))))]]) ).
cnf(refute_0_1707,plain,
( top != join(zero,converse(complement(converse(zero))))
| top = converse(complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,converse(complement(converse(zero)))),converse(complement(converse(zero)))) )],[refute_0_1705,refute_0_1706]) ).
cnf(refute_0_1708,plain,
top = converse(complement(converse(zero))),
inference(resolve,[$cnf( $equal(top,join(zero,converse(complement(converse(zero))))) )],[refute_0_1702,refute_0_1707]) ).
cnf(refute_0_1709,plain,
( top != converse(complement(converse(zero)))
| converse(complement(converse(zero))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_1710,plain,
converse(complement(converse(zero))) = top,
inference(resolve,[$cnf( $equal(top,converse(complement(converse(zero)))) )],[refute_0_1708,refute_0_1709]) ).
cnf(refute_0_1711,plain,
( converse(complement(converse(zero))) != top
| converse(converse(complement(converse(zero)))) != complement(converse(zero))
| converse(top) = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(complement(converse(zero)))),complement(converse(zero))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_1712,plain,
( converse(converse(complement(converse(zero)))) != complement(converse(zero))
| converse(top) = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(zero))),top) )],[refute_0_1710,refute_0_1711]) ).
cnf(refute_0_1713,plain,
converse(top) = complement(converse(zero)),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(zero)))),complement(converse(zero))) )],[refute_0_1701,refute_0_1712]) ).
cnf(refute_0_1714,plain,
( converse(top) != complement(converse(zero))
| converse(top) != top
| top = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),complement(converse(zero))) ),[0],$fot(top)]]) ).
cnf(refute_0_1715,plain,
( converse(top) != complement(converse(zero))
| top = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_953,refute_0_1714]) ).
cnf(refute_0_1716,plain,
top = complement(converse(zero)),
inference(resolve,[$cnf( $equal(converse(top),complement(converse(zero))) )],[refute_0_1713,refute_0_1715]) ).
cnf(refute_0_1717,plain,
( top != complement(converse(zero))
| complement(converse(zero)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_1718,plain,
complement(converse(zero)) = top,
inference(resolve,[$cnf( $equal(top,complement(converse(zero))) )],[refute_0_1716,refute_0_1717]) ).
cnf(refute_0_1719,plain,
( complement(converse(zero)) != top
| zero != meet(converse(zero),complement(converse(zero)))
| zero = meet(converse(zero),top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(converse(zero),complement(converse(zero)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1720,plain,
( zero != meet(converse(zero),complement(converse(zero)))
| zero = meet(converse(zero),top) ),
inference(resolve,[$cnf( $equal(complement(converse(zero)),top) )],[refute_0_1718,refute_0_1719]) ).
cnf(refute_0_1721,plain,
zero = meet(converse(zero),top),
inference(resolve,[$cnf( $equal(zero,meet(converse(zero),complement(converse(zero)))) )],[refute_0_1700,refute_0_1720]) ).
cnf(refute_0_1722,plain,
converse(zero) = join(meet(converse(zero),B),complement(join(complement(converse(zero)),B))),
inference(subst,[],[refute_0_146:[bind(A,$fot(converse(zero)))]]) ).
cnf(refute_0_1723,plain,
( complement(converse(zero)) != top
| converse(zero) != join(meet(converse(zero),B),complement(join(complement(converse(zero)),B)))
| converse(zero) = join(meet(converse(zero),B),complement(join(top,B))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(zero),join(meet(converse(zero),B),complement(join(complement(converse(zero)),B)))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_0_1724,plain,
( converse(zero) != join(meet(converse(zero),B),complement(join(complement(converse(zero)),B)))
| converse(zero) = join(meet(converse(zero),B),complement(join(top,B))) ),
inference(resolve,[$cnf( $equal(complement(converse(zero)),top) )],[refute_0_1718,refute_0_1723]) ).
cnf(refute_0_1725,plain,
converse(zero) = join(meet(converse(zero),B),complement(join(top,B))),
inference(resolve,[$cnf( $equal(converse(zero),join(meet(converse(zero),B),complement(join(complement(converse(zero)),B)))) )],[refute_0_1722,refute_0_1724]) ).
cnf(refute_0_1726,plain,
join(zero,meet(converse(zero),B)) = meet(converse(zero),B),
inference(subst,[],[refute_0_871:[bind(X_107,$fot(meet(converse(zero),B)))]]) ).
cnf(refute_0_1727,plain,
join(top,B) = top,
inference(subst,[],[refute_0_581:[bind(X_41,$fot(B))]]) ).
cnf(refute_0_1728,plain,
complement(join(top,B)) = complement(join(top,B)),
introduced(tautology,[refl,[$fot(complement(join(top,B)))]]) ).
cnf(refute_0_1729,plain,
( complement(join(top,B)) != complement(join(top,B))
| join(top,B) != top
| complement(join(top,B)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(top,B)),complement(join(top,B))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1730,plain,
( join(top,B) != top
| complement(join(top,B)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(top,B)),complement(join(top,B))) )],[refute_0_1728,refute_0_1729]) ).
cnf(refute_0_1731,plain,
complement(join(top,B)) = complement(top),
inference(resolve,[$cnf( $equal(join(top,B),top) )],[refute_0_1727,refute_0_1730]) ).
cnf(refute_0_1732,plain,
( complement(join(top,B)) != complement(top)
| complement(top) != zero
| complement(join(top,B)) = zero ),
inference(subst,[],[refute_0_82:[bind(X,$fot(complement(join(top,B)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1733,plain,
( complement(top) != zero
| complement(join(top,B)) = zero ),
inference(resolve,[$cnf( $equal(complement(join(top,B)),complement(top)) )],[refute_0_1731,refute_0_1732]) ).
cnf(refute_0_1734,plain,
complement(join(top,B)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_210,refute_0_1733]) ).
cnf(refute_0_1735,plain,
join(complement(join(top,B)),meet(converse(zero),B)) = join(complement(join(top,B)),meet(converse(zero),B)),
introduced(tautology,[refl,[$fot(join(complement(join(top,B)),meet(converse(zero),B)))]]) ).
cnf(refute_0_1736,plain,
( complement(join(top,B)) != zero
| join(complement(join(top,B)),meet(converse(zero),B)) != join(complement(join(top,B)),meet(converse(zero),B))
| join(complement(join(top,B)),meet(converse(zero),B)) = join(zero,meet(converse(zero),B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(top,B)),meet(converse(zero),B)),join(complement(join(top,B)),meet(converse(zero),B))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1737,plain,
( complement(join(top,B)) != zero
| join(complement(join(top,B)),meet(converse(zero),B)) = join(zero,meet(converse(zero),B)) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(converse(zero),B)),join(complement(join(top,B)),meet(converse(zero),B))) )],[refute_0_1735,refute_0_1736]) ).
cnf(refute_0_1738,plain,
join(complement(join(top,B)),meet(converse(zero),B)) = join(zero,meet(converse(zero),B)),
inference(resolve,[$cnf( $equal(complement(join(top,B)),zero) )],[refute_0_1734,refute_0_1737]) ).
cnf(refute_0_1739,plain,
( join(complement(join(top,B)),meet(converse(zero),B)) != join(zero,meet(converse(zero),B))
| join(zero,meet(converse(zero),B)) != meet(converse(zero),B)
| join(complement(join(top,B)),meet(converse(zero),B)) = meet(converse(zero),B) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(join(top,B)),meet(converse(zero),B)))),bind(Y,$fot(join(zero,meet(converse(zero),B)))),bind(Z,$fot(meet(converse(zero),B)))]]) ).
cnf(refute_0_1740,plain,
( join(zero,meet(converse(zero),B)) != meet(converse(zero),B)
| join(complement(join(top,B)),meet(converse(zero),B)) = meet(converse(zero),B) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(converse(zero),B)),join(zero,meet(converse(zero),B))) )],[refute_0_1738,refute_0_1739]) ).
cnf(refute_0_1741,plain,
join(complement(join(top,B)),meet(converse(zero),B)) = meet(converse(zero),B),
inference(resolve,[$cnf( $equal(join(zero,meet(converse(zero),B)),meet(converse(zero),B)) )],[refute_0_1726,refute_0_1740]) ).
cnf(refute_0_1742,plain,
join(meet(converse(zero),B),complement(join(top,B))) = join(complement(join(top,B)),meet(converse(zero),B)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(top,B)))),bind(B,$fot(meet(converse(zero),B)))]]) ).
cnf(refute_0_1743,plain,
( join(complement(join(top,B)),meet(converse(zero),B)) != meet(converse(zero),B)
| join(meet(converse(zero),B),complement(join(top,B))) != join(complement(join(top,B)),meet(converse(zero),B))
| join(meet(converse(zero),B),complement(join(top,B))) = meet(converse(zero),B) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(meet(converse(zero),B),complement(join(top,B))))),bind(Y,$fot(join(complement(join(top,B)),meet(converse(zero),B)))),bind(Z,$fot(meet(converse(zero),B)))]]) ).
cnf(refute_0_1744,plain,
( join(complement(join(top,B)),meet(converse(zero),B)) != meet(converse(zero),B)
| join(meet(converse(zero),B),complement(join(top,B))) = meet(converse(zero),B) ),
inference(resolve,[$cnf( $equal(join(meet(converse(zero),B),complement(join(top,B))),join(complement(join(top,B)),meet(converse(zero),B))) )],[refute_0_1742,refute_0_1743]) ).
cnf(refute_0_1745,plain,
join(meet(converse(zero),B),complement(join(top,B))) = meet(converse(zero),B),
inference(resolve,[$cnf( $equal(join(complement(join(top,B)),meet(converse(zero),B)),meet(converse(zero),B)) )],[refute_0_1741,refute_0_1744]) ).
cnf(refute_0_1746,plain,
( converse(zero) != join(meet(converse(zero),B),complement(join(top,B)))
| join(meet(converse(zero),B),complement(join(top,B))) != meet(converse(zero),B)
| converse(zero) = meet(converse(zero),B) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(zero),meet(converse(zero),B)) ),[0],$fot(join(meet(converse(zero),B),complement(join(top,B))))]]) ).
cnf(refute_0_1747,plain,
( converse(zero) != join(meet(converse(zero),B),complement(join(top,B)))
| converse(zero) = meet(converse(zero),B) ),
inference(resolve,[$cnf( $equal(join(meet(converse(zero),B),complement(join(top,B))),meet(converse(zero),B)) )],[refute_0_1745,refute_0_1746]) ).
cnf(refute_0_1748,plain,
converse(zero) = meet(converse(zero),B),
inference(resolve,[$cnf( $equal(converse(zero),join(meet(converse(zero),B),complement(join(top,B)))) )],[refute_0_1725,refute_0_1747]) ).
cnf(refute_0_1749,plain,
( converse(zero) != meet(converse(zero),B)
| meet(converse(zero),B) = converse(zero) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(zero))),bind(Y,$fot(meet(converse(zero),B)))]]) ).
cnf(refute_0_1750,plain,
meet(converse(zero),B) = converse(zero),
inference(resolve,[$cnf( $equal(converse(zero),meet(converse(zero),B)) )],[refute_0_1748,refute_0_1749]) ).
cnf(refute_0_1751,plain,
meet(converse(zero),top) = converse(zero),
inference(subst,[],[refute_0_1750:[bind(B,$fot(top))]]) ).
cnf(refute_0_1752,plain,
( meet(converse(zero),top) != converse(zero)
| zero != meet(converse(zero),top)
| zero = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(converse(zero),top)) ),[1],$fot(converse(zero))]]) ).
cnf(refute_0_1753,plain,
( zero != meet(converse(zero),top)
| zero = converse(zero) ),
inference(resolve,[$cnf( $equal(meet(converse(zero),top),converse(zero)) )],[refute_0_1751,refute_0_1752]) ).
cnf(refute_0_1754,plain,
zero = converse(zero),
inference(resolve,[$cnf( $equal(zero,meet(converse(zero),top)) )],[refute_0_1721,refute_0_1753]) ).
cnf(refute_0_1755,plain,
( zero != converse(zero)
| converse(zero) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(converse(zero)))]]) ).
cnf(refute_0_1756,plain,
converse(zero) = zero,
inference(resolve,[$cnf( $equal(zero,converse(zero)) )],[refute_0_1754,refute_0_1755]) ).
cnf(refute_0_1757,plain,
( converse(zero) != composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))
| converse(zero) != zero
| zero = composition(converse(complement(composition(X_126,top))),converse(converse(X_126))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(zero),composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))) ),[0],$fot(zero)]]) ).
cnf(refute_0_1758,plain,
( converse(zero) != composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))
| zero = composition(converse(complement(composition(X_126,top))),converse(converse(X_126))) ),
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_1756,refute_0_1757]) ).
cnf(refute_0_1759,plain,
converse(composition(converse(X_126),complement(composition(X_126,top)))) = composition(converse(complement(composition(X_126,top))),X_126),
inference(subst,[],[refute_0_19:[bind(A,$fot(X_126)),bind(X_15,$fot(complement(composition(X_126,top))))]]) ).
cnf(refute_0_1760,plain,
composition(converse(complement(composition(X_126,top))),converse(converse(X_126))) = converse(composition(converse(X_126),complement(composition(X_126,top)))),
inference(subst,[],[refute_0_57:[bind(A,$fot(converse(X_126))),bind(B,$fot(complement(composition(X_126,top))))]]) ).
cnf(refute_0_1761,plain,
( composition(converse(complement(composition(X_126,top))),converse(converse(X_126))) != converse(composition(converse(X_126),complement(composition(X_126,top))))
| converse(composition(converse(X_126),complement(composition(X_126,top)))) != composition(converse(complement(composition(X_126,top))),X_126)
| composition(converse(complement(composition(X_126,top))),converse(converse(X_126))) = composition(converse(complement(composition(X_126,top))),X_126) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(composition(converse(complement(composition(X_126,top))),converse(converse(X_126))))),bind(Y,$fot(converse(composition(converse(X_126),complement(composition(X_126,top)))))),bind(Z,$fot(composition(converse(complement(composition(X_126,top))),X_126)))]]) ).
cnf(refute_0_1762,plain,
( converse(composition(converse(X_126),complement(composition(X_126,top)))) != composition(converse(complement(composition(X_126,top))),X_126)
| composition(converse(complement(composition(X_126,top))),converse(converse(X_126))) = composition(converse(complement(composition(X_126,top))),X_126) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(X_126,top))),converse(converse(X_126))),converse(composition(converse(X_126),complement(composition(X_126,top))))) )],[refute_0_1760,refute_0_1761]) ).
cnf(refute_0_1763,plain,
composition(converse(complement(composition(X_126,top))),converse(converse(X_126))) = composition(converse(complement(composition(X_126,top))),X_126),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_126),complement(composition(X_126,top)))),composition(converse(complement(composition(X_126,top))),X_126)) )],[refute_0_1759,refute_0_1762]) ).
cnf(refute_0_1764,plain,
( composition(converse(complement(composition(X_126,top))),converse(converse(X_126))) != composition(converse(complement(composition(X_126,top))),X_126)
| zero != composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))
| zero = composition(converse(complement(composition(X_126,top))),X_126) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))) ),[1],$fot(composition(converse(complement(composition(X_126,top))),X_126))]]) ).
cnf(refute_0_1765,plain,
( zero != composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))
| zero = composition(converse(complement(composition(X_126,top))),X_126) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(X_126,top))),converse(converse(X_126))),composition(converse(complement(composition(X_126,top))),X_126)) )],[refute_0_1763,refute_0_1764]) ).
cnf(refute_0_1766,plain,
( converse(zero) != composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))
| zero = composition(converse(complement(composition(X_126,top))),X_126) ),
inference(resolve,[$cnf( $equal(zero,composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))) )],[refute_0_1758,refute_0_1765]) ).
cnf(refute_0_1767,plain,
zero = composition(converse(complement(composition(X_126,top))),X_126),
inference(resolve,[$cnf( $equal(converse(zero),composition(converse(complement(composition(X_126,top))),converse(converse(X_126)))) )],[refute_0_1699,refute_0_1766]) ).
cnf(refute_0_1768,plain,
zero = composition(converse(complement(composition(B,top))),B),
inference(subst,[],[refute_0_1767:[bind(X_126,$fot(B))]]) ).
cnf(refute_0_1769,plain,
( zero != composition(converse(complement(composition(B,top))),B)
| composition(converse(complement(composition(B,top))),B) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(composition(converse(complement(composition(B,top))),B)))]]) ).
cnf(refute_0_1770,plain,
composition(converse(complement(composition(B,top))),B) = zero,
inference(resolve,[$cnf( $equal(zero,composition(converse(complement(composition(B,top))),B)) )],[refute_0_1768,refute_0_1769]) ).
cnf(refute_0_1771,plain,
( composition(converse(complement(composition(B,top))),B) != zero
| composition(converse(complement(composition(B,top))),composition(B,C)) != composition(composition(converse(complement(composition(B,top))),B),C)
| composition(converse(complement(composition(B,top))),composition(B,C)) = composition(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(composition(B,top))),composition(B,C)),composition(composition(converse(complement(composition(B,top))),B),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1772,plain,
( composition(converse(complement(composition(B,top))),composition(B,C)) != composition(composition(converse(complement(composition(B,top))),B),C)
| composition(converse(complement(composition(B,top))),composition(B,C)) = composition(zero,C) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(B,top))),B),zero) )],[refute_0_1770,refute_0_1771]) ).
cnf(refute_0_1773,plain,
composition(converse(complement(composition(B,top))),composition(B,C)) = composition(zero,C),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(B,top))),composition(B,C)),composition(composition(converse(complement(composition(B,top))),B),C)) )],[refute_0_1683,refute_0_1772]) ).
cnf(refute_0_1774,plain,
converse(composition(converse(A),zero)) = composition(converse(zero),A),
inference(subst,[],[refute_0_19:[bind(X_15,$fot(zero))]]) ).
cnf(refute_0_1775,plain,
composition(join(top,B),complement(composition(top,top))) = join(composition(top,complement(composition(top,top))),composition(B,complement(composition(top,top)))),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(top)),bind(C,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_1776,plain,
join(zero,composition(converse(top),complement(composition(top,top)))) = zero,
inference(subst,[],[refute_0_1691:[bind(X_78,$fot(top))]]) ).
cnf(refute_0_1777,plain,
( converse(top) != top
| join(zero,composition(converse(top),complement(composition(top,top)))) != zero
| join(zero,composition(top,complement(composition(top,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(top),complement(composition(top,top)))),zero) ),[0,1,0],$fot(top)]]) ).
cnf(refute_0_1778,plain,
( join(zero,composition(converse(top),complement(composition(top,top)))) != zero
| join(zero,composition(top,complement(composition(top,top)))) = zero ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_953,refute_0_1777]) ).
cnf(refute_0_1779,plain,
join(zero,composition(top,complement(composition(top,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(top),complement(composition(top,top)))),zero) )],[refute_0_1776,refute_0_1778]) ).
cnf(refute_0_1780,plain,
join(zero,composition(top,complement(composition(top,top)))) = composition(top,complement(composition(top,top))),
inference(subst,[],[refute_0_871:[bind(X_107,$fot(composition(top,complement(composition(top,top)))))]]) ).
cnf(refute_0_1781,plain,
( join(zero,composition(top,complement(composition(top,top)))) != composition(top,complement(composition(top,top)))
| join(zero,composition(top,complement(composition(top,top)))) != zero
| composition(top,complement(composition(top,top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),zero) ),[0],$fot(composition(top,complement(composition(top,top))))]]) ).
cnf(refute_0_1782,plain,
( join(zero,composition(top,complement(composition(top,top)))) != zero
| composition(top,complement(composition(top,top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),composition(top,complement(composition(top,top)))) )],[refute_0_1780,refute_0_1781]) ).
cnf(refute_0_1783,plain,
composition(top,complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),zero) )],[refute_0_1779,refute_0_1782]) ).
cnf(refute_0_1784,plain,
( composition(join(top,B),complement(composition(top,top))) != join(composition(top,complement(composition(top,top))),composition(B,complement(composition(top,top))))
| composition(top,complement(composition(top,top))) != zero
| composition(join(top,B),complement(composition(top,top))) = join(zero,composition(B,complement(composition(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),join(composition(top,complement(composition(top,top))),composition(B,complement(composition(top,top))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1785,plain,
( composition(join(top,B),complement(composition(top,top))) != join(composition(top,complement(composition(top,top))),composition(B,complement(composition(top,top))))
| composition(join(top,B),complement(composition(top,top))) = join(zero,composition(B,complement(composition(top,top)))) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_1783,refute_0_1784]) ).
cnf(refute_0_1786,plain,
composition(join(top,B),complement(composition(top,top))) = join(zero,composition(B,complement(composition(top,top)))),
inference(resolve,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),join(composition(top,complement(composition(top,top))),composition(B,complement(composition(top,top))))) )],[refute_0_1775,refute_0_1785]) ).
cnf(refute_0_1787,plain,
composition(join(top,one),complement(composition(top,top))) = join(complement(composition(top,top)),composition(top,complement(composition(top,top)))),
inference(subst,[],[refute_0_54:[bind(X_31,$fot(top)),bind(X_33,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_1788,plain,
( composition(join(top,one),complement(composition(top,top))) != join(complement(composition(top,top)),composition(top,complement(composition(top,top))))
| composition(top,complement(composition(top,top))) != zero
| composition(join(top,one),complement(composition(top,top))) = join(complement(composition(top,top)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,one),complement(composition(top,top))),join(complement(composition(top,top)),composition(top,complement(composition(top,top))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_1789,plain,
( composition(join(top,one),complement(composition(top,top))) != join(complement(composition(top,top)),composition(top,complement(composition(top,top))))
| composition(join(top,one),complement(composition(top,top))) = join(complement(composition(top,top)),zero) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_1783,refute_0_1788]) ).
cnf(refute_0_1790,plain,
composition(join(top,one),complement(composition(top,top))) = join(complement(composition(top,top)),zero),
inference(resolve,[$cnf( $equal(composition(join(top,one),complement(composition(top,top))),join(complement(composition(top,top)),composition(top,complement(composition(top,top))))) )],[refute_0_1787,refute_0_1789]) ).
cnf(refute_0_1791,plain,
join(one,top) = top,
inference(subst,[],[refute_0_451:[bind(X_51,$fot(one))]]) ).
cnf(refute_0_1792,plain,
composition(join(one,top),complement(composition(top,top))) = composition(join(one,top),complement(composition(top,top))),
introduced(tautology,[refl,[$fot(composition(join(one,top),complement(composition(top,top))))]]) ).
cnf(refute_0_1793,plain,
( composition(join(one,top),complement(composition(top,top))) != composition(join(one,top),complement(composition(top,top)))
| join(one,top) != top
| composition(join(one,top),complement(composition(top,top))) = composition(top,complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,top),complement(composition(top,top))),composition(join(one,top),complement(composition(top,top)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1794,plain,
( join(one,top) != top
| composition(join(one,top),complement(composition(top,top))) = composition(top,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(composition(join(one,top),complement(composition(top,top))),composition(join(one,top),complement(composition(top,top)))) )],[refute_0_1792,refute_0_1793]) ).
cnf(refute_0_1795,plain,
composition(join(one,top),complement(composition(top,top))) = composition(top,complement(composition(top,top))),
inference(resolve,[$cnf( $equal(join(one,top),top) )],[refute_0_1791,refute_0_1794]) ).
cnf(refute_0_1796,plain,
( composition(join(one,top),complement(composition(top,top))) != composition(top,complement(composition(top,top)))
| composition(top,complement(composition(top,top))) != zero
| composition(join(one,top),complement(composition(top,top))) = zero ),
inference(subst,[],[refute_0_82:[bind(X,$fot(composition(join(one,top),complement(composition(top,top))))),bind(Y,$fot(composition(top,complement(composition(top,top))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1797,plain,
( composition(top,complement(composition(top,top))) != zero
| composition(join(one,top),complement(composition(top,top))) = zero ),
inference(resolve,[$cnf( $equal(composition(join(one,top),complement(composition(top,top))),composition(top,complement(composition(top,top)))) )],[refute_0_1795,refute_0_1796]) ).
cnf(refute_0_1798,plain,
composition(join(one,top),complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_1783,refute_0_1797]) ).
cnf(refute_0_1799,plain,
composition(join(top,one),complement(composition(top,top))) = composition(join(one,top),complement(composition(top,top))),
inference(subst,[],[refute_0_100:[bind(X_34,$fot(top)),bind(X_35,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_1800,plain,
( composition(join(one,top),complement(composition(top,top))) != zero
| composition(join(top,one),complement(composition(top,top))) != composition(join(one,top),complement(composition(top,top)))
| composition(join(top,one),complement(composition(top,top))) = zero ),
inference(subst,[],[refute_0_82:[bind(X,$fot(composition(join(top,one),complement(composition(top,top))))),bind(Y,$fot(composition(join(one,top),complement(composition(top,top))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1801,plain,
( composition(join(one,top),complement(composition(top,top))) != zero
| composition(join(top,one),complement(composition(top,top))) = zero ),
inference(resolve,[$cnf( $equal(composition(join(top,one),complement(composition(top,top))),composition(join(one,top),complement(composition(top,top)))) )],[refute_0_1799,refute_0_1800]) ).
cnf(refute_0_1802,plain,
composition(join(top,one),complement(composition(top,top))) = zero,
inference(resolve,[$cnf( $equal(composition(join(one,top),complement(composition(top,top))),zero) )],[refute_0_1798,refute_0_1801]) ).
cnf(refute_0_1803,plain,
( composition(join(top,one),complement(composition(top,top))) != join(complement(composition(top,top)),zero)
| composition(join(top,one),complement(composition(top,top))) != zero
| zero = join(complement(composition(top,top)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,one),complement(composition(top,top))),join(complement(composition(top,top)),zero)) ),[0],$fot(zero)]]) ).
cnf(refute_0_1804,plain,
( composition(join(top,one),complement(composition(top,top))) != join(complement(composition(top,top)),zero)
| zero = join(complement(composition(top,top)),zero) ),
inference(resolve,[$cnf( $equal(composition(join(top,one),complement(composition(top,top))),zero) )],[refute_0_1802,refute_0_1803]) ).
cnf(refute_0_1805,plain,
join(zero,complement(composition(top,top))) = complement(composition(top,top)),
inference(subst,[],[refute_0_871:[bind(X_107,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_1806,plain,
join(complement(composition(top,top)),zero) = join(zero,complement(composition(top,top))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_1807,plain,
( join(complement(composition(top,top)),zero) != join(zero,complement(composition(top,top)))
| join(zero,complement(composition(top,top))) != complement(composition(top,top))
| join(complement(composition(top,top)),zero) = complement(composition(top,top)) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(complement(composition(top,top)),zero))),bind(Y,$fot(join(zero,complement(composition(top,top))))),bind(Z,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_1808,plain,
( join(zero,complement(composition(top,top))) != complement(composition(top,top))
| join(complement(composition(top,top)),zero) = complement(composition(top,top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,top)),zero),join(zero,complement(composition(top,top)))) )],[refute_0_1806,refute_0_1807]) ).
cnf(refute_0_1809,plain,
join(complement(composition(top,top)),zero) = complement(composition(top,top)),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(top,top))),complement(composition(top,top))) )],[refute_0_1805,refute_0_1808]) ).
cnf(refute_0_1810,plain,
( join(complement(composition(top,top)),zero) != complement(composition(top,top))
| zero != join(complement(composition(top,top)),zero)
| zero = complement(composition(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(complement(composition(top,top)),zero)) ),[1],$fot(complement(composition(top,top)))]]) ).
cnf(refute_0_1811,plain,
( zero != join(complement(composition(top,top)),zero)
| zero = complement(composition(top,top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,top)),zero),complement(composition(top,top))) )],[refute_0_1809,refute_0_1810]) ).
cnf(refute_0_1812,plain,
( composition(join(top,one),complement(composition(top,top))) != join(complement(composition(top,top)),zero)
| zero = complement(composition(top,top)) ),
inference(resolve,[$cnf( $equal(zero,join(complement(composition(top,top)),zero)) )],[refute_0_1804,refute_0_1811]) ).
cnf(refute_0_1813,plain,
zero = complement(composition(top,top)),
inference(resolve,[$cnf( $equal(composition(join(top,one),complement(composition(top,top))),join(complement(composition(top,top)),zero)) )],[refute_0_1790,refute_0_1812]) ).
cnf(refute_0_1814,plain,
( zero != complement(composition(top,top))
| complement(composition(top,top)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(composition(top,top))))]]) ).
cnf(refute_0_1815,plain,
complement(composition(top,top)) = zero,
inference(resolve,[$cnf( $equal(zero,complement(composition(top,top))) )],[refute_0_1813,refute_0_1814]) ).
cnf(refute_0_1816,plain,
composition(top,complement(composition(top,top))) = composition(top,complement(composition(top,top))),
introduced(tautology,[refl,[$fot(composition(top,complement(composition(top,top))))]]) ).
cnf(refute_0_1817,plain,
( complement(composition(top,top)) != zero
| composition(top,complement(composition(top,top))) != composition(top,complement(composition(top,top)))
| composition(top,complement(composition(top,top))) = composition(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(composition(top,top))),composition(top,complement(composition(top,top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_1818,plain,
( complement(composition(top,top)) != zero
| composition(top,complement(composition(top,top))) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),composition(top,complement(composition(top,top)))) )],[refute_0_1816,refute_0_1817]) ).
cnf(refute_0_1819,plain,
composition(top,complement(composition(top,top))) = composition(top,zero),
inference(resolve,[$cnf( $equal(complement(composition(top,top)),zero) )],[refute_0_1815,refute_0_1818]) ).
cnf(refute_0_1820,plain,
composition(join(top,B),complement(composition(top,top))) = composition(join(top,B),complement(composition(top,top))),
introduced(tautology,[refl,[$fot(composition(join(top,B),complement(composition(top,top))))]]) ).
cnf(refute_0_1821,plain,
( composition(join(top,B),complement(composition(top,top))) != composition(join(top,B),complement(composition(top,top)))
| join(top,B) != top
| composition(join(top,B),complement(composition(top,top))) = composition(top,complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),composition(join(top,B),complement(composition(top,top)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1822,plain,
( join(top,B) != top
| composition(join(top,B),complement(composition(top,top))) = composition(top,complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),composition(join(top,B),complement(composition(top,top)))) )],[refute_0_1820,refute_0_1821]) ).
cnf(refute_0_1823,plain,
composition(join(top,B),complement(composition(top,top))) = composition(top,complement(composition(top,top))),
inference(resolve,[$cnf( $equal(join(top,B),top) )],[refute_0_1727,refute_0_1822]) ).
cnf(refute_0_1824,plain,
( composition(join(top,B),complement(composition(top,top))) != composition(top,complement(composition(top,top)))
| composition(top,complement(composition(top,top))) != composition(top,zero)
| composition(join(top,B),complement(composition(top,top))) = composition(top,zero) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(composition(join(top,B),complement(composition(top,top))))),bind(Y,$fot(composition(top,complement(composition(top,top))))),bind(Z,$fot(composition(top,zero)))]]) ).
cnf(refute_0_1825,plain,
( composition(top,complement(composition(top,top))) != composition(top,zero)
| composition(join(top,B),complement(composition(top,top))) = composition(top,zero) ),
inference(resolve,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),composition(top,complement(composition(top,top)))) )],[refute_0_1823,refute_0_1824]) ).
cnf(refute_0_1826,plain,
composition(join(top,B),complement(composition(top,top))) = composition(top,zero),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),composition(top,zero)) )],[refute_0_1819,refute_0_1825]) ).
cnf(refute_0_1827,plain,
( composition(join(top,B),complement(composition(top,top))) != composition(top,zero)
| composition(join(top,B),complement(composition(top,top))) != join(zero,composition(B,complement(composition(top,top))))
| composition(top,zero) = join(zero,composition(B,complement(composition(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),join(zero,composition(B,complement(composition(top,top))))) ),[0],$fot(composition(top,zero))]]) ).
cnf(refute_0_1828,plain,
( composition(join(top,B),complement(composition(top,top))) != join(zero,composition(B,complement(composition(top,top))))
| composition(top,zero) = join(zero,composition(B,complement(composition(top,top)))) ),
inference(resolve,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),composition(top,zero)) )],[refute_0_1826,refute_0_1827]) ).
cnf(refute_0_1829,plain,
composition(B,complement(composition(top,top))) = composition(B,complement(composition(top,top))),
introduced(tautology,[refl,[$fot(composition(B,complement(composition(top,top))))]]) ).
cnf(refute_0_1830,plain,
( complement(composition(top,top)) != zero
| composition(B,complement(composition(top,top))) != composition(B,complement(composition(top,top)))
| composition(B,complement(composition(top,top))) = composition(B,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(B,complement(composition(top,top))),composition(B,complement(composition(top,top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_1831,plain,
( complement(composition(top,top)) != zero
| composition(B,complement(composition(top,top))) = composition(B,zero) ),
inference(resolve,[$cnf( $equal(composition(B,complement(composition(top,top))),composition(B,complement(composition(top,top)))) )],[refute_0_1829,refute_0_1830]) ).
cnf(refute_0_1832,plain,
composition(B,complement(composition(top,top))) = composition(B,zero),
inference(resolve,[$cnf( $equal(complement(composition(top,top)),zero) )],[refute_0_1815,refute_0_1831]) ).
cnf(refute_0_1833,plain,
join(zero,composition(B,complement(composition(top,top)))) = composition(B,complement(composition(top,top))),
inference(subst,[],[refute_0_871:[bind(X_107,$fot(composition(B,complement(composition(top,top)))))]]) ).
cnf(refute_0_1834,plain,
( composition(B,complement(composition(top,top))) != composition(B,zero)
| join(zero,composition(B,complement(composition(top,top)))) != composition(B,complement(composition(top,top)))
| join(zero,composition(B,complement(composition(top,top)))) = composition(B,zero) ),
inference(subst,[],[refute_0_82:[bind(X,$fot(join(zero,composition(B,complement(composition(top,top)))))),bind(Y,$fot(composition(B,complement(composition(top,top))))),bind(Z,$fot(composition(B,zero)))]]) ).
cnf(refute_0_1835,plain,
( composition(B,complement(composition(top,top))) != composition(B,zero)
| join(zero,composition(B,complement(composition(top,top)))) = composition(B,zero) ),
inference(resolve,[$cnf( $equal(join(zero,composition(B,complement(composition(top,top)))),composition(B,complement(composition(top,top)))) )],[refute_0_1833,refute_0_1834]) ).
cnf(refute_0_1836,plain,
join(zero,composition(B,complement(composition(top,top)))) = composition(B,zero),
inference(resolve,[$cnf( $equal(composition(B,complement(composition(top,top))),composition(B,zero)) )],[refute_0_1832,refute_0_1835]) ).
cnf(refute_0_1837,plain,
( composition(top,zero) != join(zero,composition(B,complement(composition(top,top))))
| join(zero,composition(B,complement(composition(top,top)))) != composition(B,zero)
| composition(top,zero) = composition(B,zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(top,zero),composition(B,zero)) ),[0],$fot(join(zero,composition(B,complement(composition(top,top)))))]]) ).
cnf(refute_0_1838,plain,
( composition(top,zero) != join(zero,composition(B,complement(composition(top,top))))
| composition(top,zero) = composition(B,zero) ),
inference(resolve,[$cnf( $equal(join(zero,composition(B,complement(composition(top,top)))),composition(B,zero)) )],[refute_0_1836,refute_0_1837]) ).
cnf(refute_0_1839,plain,
( composition(join(top,B),complement(composition(top,top))) != join(zero,composition(B,complement(composition(top,top))))
| composition(top,zero) = composition(B,zero) ),
inference(resolve,[$cnf( $equal(composition(top,zero),join(zero,composition(B,complement(composition(top,top))))) )],[refute_0_1828,refute_0_1838]) ).
cnf(refute_0_1840,plain,
composition(top,zero) = composition(B,zero),
inference(resolve,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),join(zero,composition(B,complement(composition(top,top))))) )],[refute_0_1786,refute_0_1839]) ).
cnf(refute_0_1841,plain,
( composition(top,complement(composition(top,top))) != composition(top,zero)
| composition(top,complement(composition(top,top))) != zero
| composition(top,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) ),[0],$fot(composition(top,zero))]]) ).
cnf(refute_0_1842,plain,
( composition(top,complement(composition(top,top))) != zero
| composition(top,zero) = zero ),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),composition(top,zero)) )],[refute_0_1819,refute_0_1841]) ).
cnf(refute_0_1843,plain,
composition(top,zero) = zero,
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_1783,refute_0_1842]) ).
cnf(refute_0_1844,plain,
( composition(top,zero) != composition(B,zero)
| composition(top,zero) != zero
| zero = composition(B,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,zero),composition(B,zero)) ),[0],$fot(zero)]]) ).
cnf(refute_0_1845,plain,
( composition(top,zero) != composition(B,zero)
| zero = composition(B,zero) ),
inference(resolve,[$cnf( $equal(composition(top,zero),zero) )],[refute_0_1843,refute_0_1844]) ).
cnf(refute_0_1846,plain,
zero = composition(B,zero),
inference(resolve,[$cnf( $equal(composition(top,zero),composition(B,zero)) )],[refute_0_1840,refute_0_1845]) ).
cnf(refute_0_1847,plain,
zero = composition(converse(A),zero),
inference(subst,[],[refute_0_1846:[bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_1848,plain,
( zero != composition(converse(A),zero)
| composition(converse(A),zero) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(composition(converse(A),zero)))]]) ).
cnf(refute_0_1849,plain,
composition(converse(A),zero) = zero,
inference(resolve,[$cnf( $equal(zero,composition(converse(A),zero)) )],[refute_0_1847,refute_0_1848]) ).
cnf(refute_0_1850,plain,
( composition(converse(A),zero) != zero
| converse(composition(converse(A),zero)) != composition(converse(zero),A)
| converse(zero) = composition(converse(zero),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),zero)),composition(converse(zero),A)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_1851,plain,
( converse(composition(converse(A),zero)) != composition(converse(zero),A)
| converse(zero) = composition(converse(zero),A) ),
inference(resolve,[$cnf( $equal(composition(converse(A),zero),zero) )],[refute_0_1849,refute_0_1850]) ).
cnf(refute_0_1852,plain,
converse(zero) = composition(converse(zero),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),zero)),composition(converse(zero),A)) )],[refute_0_1774,refute_0_1851]) ).
cnf(refute_0_1853,plain,
( converse(zero) != composition(converse(zero),A)
| converse(zero) != zero
| zero = composition(converse(zero),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(zero),composition(converse(zero),A)) ),[0],$fot(zero)]]) ).
cnf(refute_0_1854,plain,
( converse(zero) != composition(converse(zero),A)
| zero = composition(converse(zero),A) ),
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_1756,refute_0_1853]) ).
cnf(refute_0_1855,plain,
composition(converse(zero),A) = composition(converse(zero),A),
introduced(tautology,[refl,[$fot(composition(converse(zero),A))]]) ).
cnf(refute_0_1856,plain,
( composition(converse(zero),A) != composition(converse(zero),A)
| converse(zero) != zero
| composition(converse(zero),A) = composition(zero,A) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(zero),A),composition(converse(zero),A)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1857,plain,
( converse(zero) != zero
| composition(converse(zero),A) = composition(zero,A) ),
inference(resolve,[$cnf( $equal(composition(converse(zero),A),composition(converse(zero),A)) )],[refute_0_1855,refute_0_1856]) ).
cnf(refute_0_1858,plain,
composition(converse(zero),A) = composition(zero,A),
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_1756,refute_0_1857]) ).
cnf(refute_0_1859,plain,
( composition(converse(zero),A) != composition(zero,A)
| zero != composition(converse(zero),A)
| zero = composition(zero,A) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(zero),A)) ),[1],$fot(composition(zero,A))]]) ).
cnf(refute_0_1860,plain,
( zero != composition(converse(zero),A)
| zero = composition(zero,A) ),
inference(resolve,[$cnf( $equal(composition(converse(zero),A),composition(zero,A)) )],[refute_0_1858,refute_0_1859]) ).
cnf(refute_0_1861,plain,
( converse(zero) != composition(converse(zero),A)
| zero = composition(zero,A) ),
inference(resolve,[$cnf( $equal(zero,composition(converse(zero),A)) )],[refute_0_1854,refute_0_1860]) ).
cnf(refute_0_1862,plain,
zero = composition(zero,A),
inference(resolve,[$cnf( $equal(converse(zero),composition(converse(zero),A)) )],[refute_0_1852,refute_0_1861]) ).
cnf(refute_0_1863,plain,
( zero != composition(zero,A)
| composition(zero,A) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(composition(zero,A)))]]) ).
cnf(refute_0_1864,plain,
composition(zero,A) = zero,
inference(resolve,[$cnf( $equal(zero,composition(zero,A)) )],[refute_0_1862,refute_0_1863]) ).
cnf(refute_0_1865,plain,
composition(zero,C) = zero,
inference(subst,[],[refute_0_1864:[bind(A,$fot(C))]]) ).
cnf(refute_0_1866,plain,
( composition(converse(complement(composition(B,top))),composition(B,C)) != composition(zero,C)
| composition(zero,C) != zero
| composition(converse(complement(composition(B,top))),composition(B,C)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(converse(complement(composition(B,top))),composition(B,C)),zero) ),[0],$fot(composition(zero,C))]]) ).
cnf(refute_0_1867,plain,
( composition(converse(complement(composition(B,top))),composition(B,C)) != composition(zero,C)
| composition(converse(complement(composition(B,top))),composition(B,C)) = zero ),
inference(resolve,[$cnf( $equal(composition(zero,C),zero) )],[refute_0_1865,refute_0_1866]) ).
cnf(refute_0_1868,plain,
composition(converse(complement(composition(B,top))),composition(B,C)) = zero,
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(B,top))),composition(B,C)),composition(zero,C)) )],[refute_0_1773,refute_0_1867]) ).
cnf(refute_0_1869,plain,
converse(complement(composition(B,top))) = complement(converse(composition(B,top))),
inference(subst,[],[refute_0_1034:[bind(X_107,$fot(composition(B,top)))]]) ).
cnf(refute_0_1870,plain,
composition(converse(complement(composition(B,top))),composition(B,C)) = composition(converse(complement(composition(B,top))),composition(B,C)),
introduced(tautology,[refl,[$fot(composition(converse(complement(composition(B,top))),composition(B,C)))]]) ).
cnf(refute_0_1871,plain,
( composition(converse(complement(composition(B,top))),composition(B,C)) != composition(converse(complement(composition(B,top))),composition(B,C))
| converse(complement(composition(B,top))) != complement(converse(composition(B,top)))
| composition(converse(complement(composition(B,top))),composition(B,C)) = composition(complement(converse(composition(B,top))),composition(B,C)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(composition(B,top))),composition(B,C)),composition(converse(complement(composition(B,top))),composition(B,C))) ),[1,0],$fot(complement(converse(composition(B,top))))]]) ).
cnf(refute_0_1872,plain,
( converse(complement(composition(B,top))) != complement(converse(composition(B,top)))
| composition(converse(complement(composition(B,top))),composition(B,C)) = composition(complement(converse(composition(B,top))),composition(B,C)) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(B,top))),composition(B,C)),composition(converse(complement(composition(B,top))),composition(B,C))) )],[refute_0_1870,refute_0_1871]) ).
cnf(refute_0_1873,plain,
composition(converse(complement(composition(B,top))),composition(B,C)) = composition(complement(converse(composition(B,top))),composition(B,C)),
inference(resolve,[$cnf( $equal(converse(complement(composition(B,top))),complement(converse(composition(B,top)))) )],[refute_0_1869,refute_0_1872]) ).
cnf(refute_0_1874,plain,
( composition(converse(complement(composition(B,top))),composition(B,C)) != composition(complement(converse(composition(B,top))),composition(B,C))
| composition(converse(complement(composition(B,top))),composition(B,C)) != zero
| composition(complement(converse(composition(B,top))),composition(B,C)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(composition(B,top))),composition(B,C)),zero) ),[0],$fot(composition(complement(converse(composition(B,top))),composition(B,C)))]]) ).
cnf(refute_0_1875,plain,
( composition(converse(complement(composition(B,top))),composition(B,C)) != zero
| composition(complement(converse(composition(B,top))),composition(B,C)) = zero ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(B,top))),composition(B,C)),composition(complement(converse(composition(B,top))),composition(B,C))) )],[refute_0_1873,refute_0_1874]) ).
cnf(refute_0_1876,plain,
composition(complement(converse(composition(B,top))),composition(B,C)) = zero,
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(B,top))),composition(B,C)),zero) )],[refute_0_1868,refute_0_1875]) ).
cnf(refute_0_1877,plain,
composition(complement(converse(composition(B,top))),composition(B,top)) = zero,
inference(subst,[],[refute_0_1876:[bind(C,$fot(top))]]) ).
cnf(refute_0_1878,plain,
( composition(complement(composition(B,top)),complement(composition(complement(converse(composition(B,top))),composition(B,top)))) != complement(composition(B,top))
| composition(complement(converse(composition(B,top))),composition(B,top)) != zero
| composition(complement(composition(B,top)),complement(zero)) = complement(composition(B,top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(B,top)),complement(composition(complement(converse(composition(B,top))),composition(B,top)))),complement(composition(B,top))) ),[0,1,0],$fot(zero)]]) ).
cnf(refute_0_1879,plain,
( composition(complement(composition(B,top)),complement(composition(complement(converse(composition(B,top))),composition(B,top)))) != complement(composition(B,top))
| composition(complement(composition(B,top)),complement(zero)) = complement(composition(B,top)) ),
inference(resolve,[$cnf( $equal(composition(complement(converse(composition(B,top))),composition(B,top)),zero) )],[refute_0_1877,refute_0_1878]) ).
cnf(refute_0_1880,plain,
composition(complement(composition(B,top)),complement(zero)) = complement(composition(B,top)),
inference(resolve,[$cnf( $equal(composition(complement(composition(B,top)),complement(composition(complement(converse(composition(B,top))),composition(B,top)))),complement(composition(B,top))) )],[refute_0_1682,refute_0_1879]) ).
cnf(refute_0_1881,plain,
complement(complement(top)) = join(zero,meet(top,complement(complement(top)))),
inference(subst,[],[refute_0_783:[bind(X_107,$fot(complement(complement(top))))]]) ).
cnf(refute_0_1882,plain,
top = join(zero,meet(top,complement(complement(top)))),
inference(subst,[],[refute_0_607:[bind(X_107,$fot(top))]]) ).
cnf(refute_0_1883,plain,
( top != join(zero,meet(top,complement(complement(top))))
| join(zero,meet(top,complement(complement(top)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(zero,meet(top,complement(complement(top))))))]]) ).
cnf(refute_0_1884,plain,
join(zero,meet(top,complement(complement(top)))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) )],[refute_0_1882,refute_0_1883]) ).
cnf(refute_0_1885,plain,
( complement(complement(top)) != join(zero,meet(top,complement(complement(top))))
| join(zero,meet(top,complement(complement(top)))) != top
| complement(complement(top)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(complement(top)),top) ),[0],$fot(join(zero,meet(top,complement(complement(top)))))]]) ).
cnf(refute_0_1886,plain,
( complement(complement(top)) != join(zero,meet(top,complement(complement(top))))
| complement(complement(top)) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(complement(top)))),top) )],[refute_0_1884,refute_0_1885]) ).
cnf(refute_0_1887,plain,
complement(complement(top)) = top,
inference(resolve,[$cnf( $equal(complement(complement(top)),join(zero,meet(top,complement(complement(top))))) )],[refute_0_1881,refute_0_1886]) ).
cnf(refute_0_1888,plain,
( complement(complement(top)) != complement(zero)
| complement(complement(top)) != top
| complement(zero) = top ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),top) ),[0],$fot(complement(zero))]]) ).
cnf(refute_0_1889,plain,
( complement(complement(top)) != top
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_519,refute_0_1888]) ).
cnf(refute_0_1890,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(complement(complement(top)),top) )],[refute_0_1887,refute_0_1889]) ).
cnf(refute_0_1891,plain,
composition(complement(composition(B,top)),complement(zero)) = composition(complement(composition(B,top)),complement(zero)),
introduced(tautology,[refl,[$fot(composition(complement(composition(B,top)),complement(zero)))]]) ).
cnf(refute_0_1892,plain,
( complement(zero) != top
| composition(complement(composition(B,top)),complement(zero)) != composition(complement(composition(B,top)),complement(zero))
| composition(complement(composition(B,top)),complement(zero)) = composition(complement(composition(B,top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(B,top)),complement(zero)),composition(complement(composition(B,top)),complement(zero))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1893,plain,
( complement(zero) != top
| composition(complement(composition(B,top)),complement(zero)) = composition(complement(composition(B,top)),top) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(B,top)),complement(zero)),composition(complement(composition(B,top)),complement(zero))) )],[refute_0_1891,refute_0_1892]) ).
cnf(refute_0_1894,plain,
composition(complement(composition(B,top)),complement(zero)) = composition(complement(composition(B,top)),top),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_1890,refute_0_1893]) ).
cnf(refute_0_1895,plain,
( composition(complement(composition(B,top)),complement(zero)) != complement(composition(B,top))
| composition(complement(composition(B,top)),complement(zero)) != composition(complement(composition(B,top)),top)
| composition(complement(composition(B,top)),top) = complement(composition(B,top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(B,top)),complement(zero)),complement(composition(B,top))) ),[0],$fot(composition(complement(composition(B,top)),top))]]) ).
cnf(refute_0_1896,plain,
( composition(complement(composition(B,top)),complement(zero)) != complement(composition(B,top))
| composition(complement(composition(B,top)),top) = complement(composition(B,top)) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(B,top)),complement(zero)),composition(complement(composition(B,top)),top)) )],[refute_0_1894,refute_0_1895]) ).
cnf(refute_0_1897,plain,
composition(complement(composition(B,top)),top) = complement(composition(B,top)),
inference(resolve,[$cnf( $equal(composition(complement(composition(B,top)),complement(zero)),complement(composition(B,top))) )],[refute_0_1880,refute_0_1896]) ).
cnf(refute_0_1898,plain,
composition(complement(composition(sk1,top)),top) = complement(composition(sk1,top)),
inference(subst,[],[refute_0_1897:[bind(B,$fot(sk1))]]) ).
cnf(refute_0_1899,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| complement(composition(sk1,top)) = composition(complement(composition(sk1,top)),top) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) ),[1],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_1900,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| complement(composition(sk1,top)) = composition(complement(composition(sk1,top)),top) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) )],[refute_0_1898,refute_0_1899]) ).
cnf(refute_0_1901,plain,
complement(composition(sk1,top)) != complement(composition(sk1,top)),
inference(resolve,[$cnf( $equal(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) )],[refute_0_1900,goals_17]) ).
cnf(refute_0_1902,plain,
complement(composition(sk1,top)) = complement(composition(sk1,top)),
introduced(tautology,[refl,[$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_1903,plain,
$false,
inference(resolve,[$cnf( $equal(complement(composition(sk1,top)),complement(composition(sk1,top))) )],[refute_0_1902,refute_0_1901]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL050-3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 09:43:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 44.66/44.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.66/44.82
% 44.66/44.82 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 44.81/44.99
%------------------------------------------------------------------------------