TSTP Solution File: REL018-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL018-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:43:32 EDT 2022
% Result : Unsatisfiable 1.07s 1.26s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 103
% Number of leaves : 231
% Syntax : Number of clauses : 984 ( 494 unt; 0 nHn; 614 RR)
% Number of literals : 1691 (1690 equ; 709 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 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 : 946 ( 39 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(maddux1_join_commutativity_1,axiom,
join(A,B) = join(B,A) ).
cnf(maddux2_join_associativity_2,axiom,
join(A,join(B,C)) = join(join(A,B),C) ).
cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(A,B) = complement(join(complement(A),complement(B))) ).
cnf(composition_identity_6,axiom,
composition(A,one) = A ).
cnf(composition_distributivity_7,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ).
cnf(converse_idempotence_8,axiom,
converse(converse(A)) = A ).
cnf(converse_additivity_9,axiom,
converse(join(A,B)) = join(converse(A),converse(B)) ).
cnf(converse_multiplicativity_10,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ).
cnf(def_top_12,axiom,
top = join(A,complement(A)) ).
cnf(def_zero_13,axiom,
zero = meet(A,complement(A)) ).
cnf(goals_14,negated_conjecture,
composition(sk1,top) = sk1 ).
cnf(goals_15,negated_conjecture,
composition(complement(sk1),top) != complement(sk1) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_4,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_3]) ).
cnf(refute_0_5,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_6,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$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_7,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( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_7]) ).
cnf(refute_0_9,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_10,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_11,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_10]) ).
cnf(refute_0_12,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_13,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_14,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_16]) ).
cnf(refute_0_18,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_17:[bind(X,$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_19,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_9,refute_0_19]) ).
cnf(refute_0_21,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$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_22,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_8,refute_0_22]) ).
cnf(refute_0_24,plain,
X_38 = join(meet(X_38,X_39),complement(join(complement(X_38),X_39))),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_38)),bind(B,$fot(X_39))]]) ).
cnf(refute_0_25,plain,
join(X_39,complement(X_38)) = join(complement(X_38),X_39),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_39)),bind(B,$fot(complement(X_38)))]]) ).
cnf(refute_0_26,plain,
( join(X_39,complement(X_38)) != join(complement(X_38),X_39)
| join(complement(X_38),X_39) = join(X_39,complement(X_38)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_39,complement(X_38)))),bind(Y,$fot(join(complement(X_38),X_39)))]]) ).
cnf(refute_0_27,plain,
join(complement(X_38),X_39) = join(X_39,complement(X_38)),
inference(resolve,[$cnf( $equal(join(X_39,complement(X_38)),join(complement(X_38),X_39)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( X_38 != join(meet(X_38,X_39),complement(join(complement(X_38),X_39)))
| join(complement(X_38),X_39) != join(X_39,complement(X_38))
| X_38 = join(meet(X_38,X_39),complement(join(X_39,complement(X_38)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_38,join(meet(X_38,X_39),complement(join(complement(X_38),X_39)))) ),[1,1,0],$fot(join(X_39,complement(X_38)))]]) ).
cnf(refute_0_29,plain,
( X_38 != join(meet(X_38,X_39),complement(join(complement(X_38),X_39)))
| X_38 = join(meet(X_38,X_39),complement(join(X_39,complement(X_38)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_38),X_39),join(X_39,complement(X_38))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
X_38 = join(meet(X_38,X_39),complement(join(X_39,complement(X_38)))),
inference(resolve,[$cnf( $equal(X_38,join(meet(X_38,X_39),complement(join(complement(X_38),X_39)))) )],[refute_0_24,refute_0_29]) ).
cnf(refute_0_31,plain,
complement(sk1) = join(meet(complement(sk1),composition(complement(sk1),top)),complement(join(composition(complement(sk1),top),complement(complement(sk1))))),
inference(subst,[],[refute_0_30:[bind(X_38,$fot(complement(sk1))),bind(X_39,$fot(composition(complement(sk1),top)))]]) ).
cnf(refute_0_32,plain,
meet(X_18,X_19) = complement(join(complement(X_18),complement(X_19))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_18)),bind(B,$fot(X_19))]]) ).
cnf(refute_0_33,plain,
join(complement(X_19),complement(X_18)) = join(complement(X_18),complement(X_19)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_19))),bind(B,$fot(complement(X_18)))]]) ).
cnf(refute_0_34,plain,
( join(complement(X_19),complement(X_18)) != join(complement(X_18),complement(X_19))
| join(complement(X_18),complement(X_19)) = join(complement(X_19),complement(X_18)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_19),complement(X_18)))),bind(Y,$fot(join(complement(X_18),complement(X_19))))]]) ).
cnf(refute_0_35,plain,
join(complement(X_18),complement(X_19)) = join(complement(X_19),complement(X_18)),
inference(resolve,[$cnf( $equal(join(complement(X_19),complement(X_18)),join(complement(X_18),complement(X_19))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( join(complement(X_18),complement(X_19)) != join(complement(X_19),complement(X_18))
| meet(X_18,X_19) != complement(join(complement(X_18),complement(X_19)))
| meet(X_18,X_19) = complement(join(complement(X_19),complement(X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_18,X_19),complement(join(complement(X_18),complement(X_19)))) ),[1,0],$fot(join(complement(X_19),complement(X_18)))]]) ).
cnf(refute_0_37,plain,
( meet(X_18,X_19) != complement(join(complement(X_18),complement(X_19)))
| meet(X_18,X_19) = complement(join(complement(X_19),complement(X_18))) ),
inference(resolve,[$cnf( $equal(join(complement(X_18),complement(X_19)),join(complement(X_19),complement(X_18))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
meet(X_18,X_19) = complement(join(complement(X_19),complement(X_18))),
inference(resolve,[$cnf( $equal(meet(X_18,X_19),complement(join(complement(X_18),complement(X_19)))) )],[refute_0_32,refute_0_37]) ).
cnf(refute_0_39,plain,
complement(join(complement(X_19),complement(X_18))) = meet(X_19,X_18),
inference(subst,[],[refute_0_11:[bind(A,$fot(X_19)),bind(B,$fot(X_18))]]) ).
cnf(refute_0_40,plain,
( complement(join(complement(X_19),complement(X_18))) != meet(X_19,X_18)
| meet(X_18,X_19) != complement(join(complement(X_19),complement(X_18)))
| meet(X_18,X_19) = meet(X_19,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_18,X_19),complement(join(complement(X_19),complement(X_18)))) ),[1],$fot(meet(X_19,X_18))]]) ).
cnf(refute_0_41,plain,
( meet(X_18,X_19) != complement(join(complement(X_19),complement(X_18)))
| meet(X_18,X_19) = meet(X_19,X_18) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_19),complement(X_18))),meet(X_19,X_18)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
meet(X_18,X_19) = meet(X_19,X_18),
inference(resolve,[$cnf( $equal(meet(X_18,X_19),complement(join(complement(X_19),complement(X_18)))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
meet(X_39,X_38) = meet(X_38,X_39),
inference(subst,[],[refute_0_42:[bind(X_18,$fot(X_39)),bind(X_19,$fot(X_38))]]) ).
cnf(refute_0_44,plain,
( meet(X_39,X_38) != meet(X_38,X_39)
| meet(X_38,X_39) = meet(X_39,X_38) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_39,X_38))),bind(Y,$fot(meet(X_38,X_39)))]]) ).
cnf(refute_0_45,plain,
meet(X_38,X_39) = meet(X_39,X_38),
inference(resolve,[$cnf( $equal(meet(X_39,X_38),meet(X_38,X_39)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( X_38 != join(meet(X_38,X_39),complement(join(complement(X_38),X_39)))
| meet(X_38,X_39) != meet(X_39,X_38)
| X_38 = join(meet(X_39,X_38),complement(join(complement(X_38),X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(X_38,join(meet(X_38,X_39),complement(join(complement(X_38),X_39)))) ),[1,0],$fot(meet(X_39,X_38))]]) ).
cnf(refute_0_47,plain,
( X_38 != join(meet(X_38,X_39),complement(join(complement(X_38),X_39)))
| X_38 = join(meet(X_39,X_38),complement(join(complement(X_38),X_39))) ),
inference(resolve,[$cnf( $equal(meet(X_38,X_39),meet(X_39,X_38)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
X_38 = join(meet(X_39,X_38),complement(join(complement(X_38),X_39))),
inference(resolve,[$cnf( $equal(X_38,join(meet(X_38,X_39),complement(join(complement(X_38),X_39)))) )],[refute_0_24,refute_0_47]) ).
cnf(refute_0_49,plain,
X_38 = join(meet(join(complement(complement(X_38)),X_107),X_38),complement(join(complement(X_38),join(complement(complement(X_38)),X_107)))),
inference(subst,[],[refute_0_48:[bind(X_39,$fot(join(complement(complement(X_38)),X_107)))]]) ).
cnf(refute_0_50,plain,
join(X_102,join(complement(X_102),X_104)) = join(join(X_102,complement(X_102)),X_104),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_102)),bind(B,$fot(complement(X_102))),bind(C,$fot(X_104))]]) ).
cnf(refute_0_51,plain,
top = join(X_102,complement(X_102)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_102))]]) ).
cnf(refute_0_52,plain,
( top != join(X_102,complement(X_102))
| join(X_102,complement(X_102)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(X_102,complement(X_102))))]]) ).
cnf(refute_0_53,plain,
join(X_102,complement(X_102)) = top,
inference(resolve,[$cnf( $equal(top,join(X_102,complement(X_102))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( join(X_102,complement(X_102)) != top
| join(X_102,join(complement(X_102),X_104)) != join(join(X_102,complement(X_102)),X_104)
| join(X_102,join(complement(X_102),X_104)) = join(top,X_104) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_102,join(complement(X_102),X_104)),join(join(X_102,complement(X_102)),X_104)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_55,plain,
( join(X_102,join(complement(X_102),X_104)) != join(join(X_102,complement(X_102)),X_104)
| join(X_102,join(complement(X_102),X_104)) = join(top,X_104) ),
inference(resolve,[$cnf( $equal(join(X_102,complement(X_102)),top) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
join(X_102,join(complement(X_102),X_104)) = join(top,X_104),
inference(resolve,[$cnf( $equal(join(X_102,join(complement(X_102),X_104)),join(join(X_102,complement(X_102)),X_104)) )],[refute_0_50,refute_0_55]) ).
cnf(refute_0_57,plain,
join(top,B) = join(B,top),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(top))]]) ).
cnf(refute_0_58,plain,
top = join(join(complement(X_18),complement(X_19)),complement(join(complement(X_18),complement(X_19)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(complement(X_18),complement(X_19))))]]) ).
cnf(refute_0_59,plain,
( meet(X_18,X_19) != complement(join(complement(X_18),complement(X_19)))
| complement(join(complement(X_18),complement(X_19))) = meet(X_18,X_19) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_18,X_19))),bind(Y,$fot(complement(join(complement(X_18),complement(X_19)))))]]) ).
cnf(refute_0_60,plain,
complement(join(complement(X_18),complement(X_19))) = meet(X_18,X_19),
inference(resolve,[$cnf( $equal(meet(X_18,X_19),complement(join(complement(X_18),complement(X_19)))) )],[refute_0_32,refute_0_59]) ).
cnf(refute_0_61,plain,
( complement(join(complement(X_18),complement(X_19))) != meet(X_18,X_19)
| top != join(join(complement(X_18),complement(X_19)),complement(join(complement(X_18),complement(X_19))))
| top = join(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_18),complement(X_19)),complement(join(complement(X_18),complement(X_19))))) ),[1,1],$fot(meet(X_18,X_19))]]) ).
cnf(refute_0_62,plain,
( top != join(join(complement(X_18),complement(X_19)),complement(join(complement(X_18),complement(X_19))))
| top = join(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_18),complement(X_19))),meet(X_18,X_19)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
top = join(join(complement(X_18),complement(X_19)),meet(X_18,X_19)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_18),complement(X_19)),complement(join(complement(X_18),complement(X_19))))) )],[refute_0_58,refute_0_62]) ).
cnf(refute_0_64,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_65,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_64]) ).
cnf(refute_0_66,plain,
join(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) = join(complement(X_18),join(complement(X_19),meet(X_18,X_19))),
inference(subst,[],[refute_0_65:[bind(A,$fot(complement(X_18))),bind(B,$fot(complement(X_19))),bind(C,$fot(meet(X_18,X_19)))]]) ).
cnf(refute_0_67,plain,
( join(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) != join(complement(X_18),join(complement(X_19),meet(X_18,X_19)))
| top != join(join(complement(X_18),complement(X_19)),meet(X_18,X_19))
| top = join(complement(X_18),join(complement(X_19),meet(X_18,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_18),complement(X_19)),meet(X_18,X_19))) ),[1],$fot(join(complement(X_18),join(complement(X_19),meet(X_18,X_19))))]]) ).
cnf(refute_0_68,plain,
( top != join(join(complement(X_18),complement(X_19)),meet(X_18,X_19))
| top = join(complement(X_18),join(complement(X_19),meet(X_18,X_19))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_18),complement(X_19)),meet(X_18,X_19)),join(complement(X_18),join(complement(X_19),meet(X_18,X_19)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
top = join(complement(X_18),join(complement(X_19),meet(X_18,X_19))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_18),complement(X_19)),meet(X_18,X_19))) )],[refute_0_63,refute_0_68]) ).
cnf(refute_0_70,plain,
top = join(complement(join(X_69,top)),join(complement(X_19),meet(join(X_69,top),X_19))),
inference(subst,[],[refute_0_69:[bind(X_18,$fot(join(X_69,top)))]]) ).
cnf(refute_0_71,plain,
zero = join(meet(zero,X_64),complement(join(X_64,complement(zero)))),
inference(subst,[],[refute_0_30:[bind(X_38,$fot(zero)),bind(X_39,$fot(X_64))]]) ).
cnf(refute_0_72,plain,
meet(zero,B) = complement(join(complement(zero),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(zero))]]) ).
cnf(refute_0_73,plain,
X_38 = join(meet(X_38,top),complement(join(complement(X_38),top))),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_38)),bind(B,$fot(top))]]) ).
cnf(refute_0_74,plain,
meet(A,top) = complement(join(complement(A),complement(top))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(top))]]) ).
cnf(refute_0_75,plain,
zero = meet(join(complement(X_18),complement(X_19)),complement(join(complement(X_18),complement(X_19)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_18),complement(X_19))))]]) ).
cnf(refute_0_76,plain,
( complement(join(complement(X_18),complement(X_19))) != meet(X_18,X_19)
| zero != meet(join(complement(X_18),complement(X_19)),complement(join(complement(X_18),complement(X_19))))
| zero = meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_18),complement(X_19)),complement(join(complement(X_18),complement(X_19))))) ),[1,1],$fot(meet(X_18,X_19))]]) ).
cnf(refute_0_77,plain,
( zero != meet(join(complement(X_18),complement(X_19)),complement(join(complement(X_18),complement(X_19))))
| zero = meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_18),complement(X_19))),meet(X_18,X_19)) )],[refute_0_60,refute_0_76]) ).
cnf(refute_0_78,plain,
zero = meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_18),complement(X_19)),complement(join(complement(X_18),complement(X_19))))) )],[refute_0_75,refute_0_77]) ).
cnf(refute_0_79,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_80,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_79]) ).
cnf(refute_0_81,plain,
join(meet(X_18,X_19),complement(meet(X_18,X_19))) = top,
inference(subst,[],[refute_0_80:[bind(A,$fot(meet(X_18,X_19)))]]) ).
cnf(refute_0_82,plain,
complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))) = complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))))]]) ).
cnf(refute_0_83,plain,
( complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))) != complement(join(meet(X_18,X_19),complement(meet(X_18,X_19))))
| join(meet(X_18,X_19),complement(meet(X_18,X_19))) != top
| complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))),complement(join(meet(X_18,X_19),complement(meet(X_18,X_19))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_84,plain,
( join(meet(X_18,X_19),complement(meet(X_18,X_19))) != top
| complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))),complement(join(meet(X_18,X_19),complement(meet(X_18,X_19))))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_18,X_19),complement(meet(X_18,X_19))),top) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
meet(join(complement(X_18),complement(X_19)),B) = complement(join(complement(join(complement(X_18),complement(X_19))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_18),complement(X_19))))]]) ).
cnf(refute_0_87,plain,
( complement(join(complement(X_18),complement(X_19))) != meet(X_18,X_19)
| meet(join(complement(X_18),complement(X_19)),B) != complement(join(complement(join(complement(X_18),complement(X_19))),complement(B)))
| meet(join(complement(X_18),complement(X_19)),B) = complement(join(meet(X_18,X_19),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_18),complement(X_19)),B),complement(join(complement(join(complement(X_18),complement(X_19))),complement(B)))) ),[1,0,0],$fot(meet(X_18,X_19))]]) ).
cnf(refute_0_88,plain,
( meet(join(complement(X_18),complement(X_19)),B) != complement(join(complement(join(complement(X_18),complement(X_19))),complement(B)))
| meet(join(complement(X_18),complement(X_19)),B) = complement(join(meet(X_18,X_19),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_18),complement(X_19))),meet(X_18,X_19)) )],[refute_0_60,refute_0_87]) ).
cnf(refute_0_89,plain,
meet(join(complement(X_18),complement(X_19)),B) = complement(join(meet(X_18,X_19),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_18),complement(X_19)),B),complement(join(complement(join(complement(X_18),complement(X_19))),complement(B)))) )],[refute_0_86,refute_0_88]) ).
cnf(refute_0_90,plain,
meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) = complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))),
inference(subst,[],[refute_0_89:[bind(B,$fot(meet(X_18,X_19)))]]) ).
cnf(refute_0_91,plain,
( complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))) != complement(top)
| meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) != complement(join(meet(X_18,X_19),complement(meet(X_18,X_19))))
| meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) = complement(top) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)))),bind(Y,$fot(complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_92,plain,
( complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))) != complement(top)
| meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)),complement(join(meet(X_18,X_19),complement(meet(X_18,X_19))))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_18,X_19),complement(meet(X_18,X_19)))),complement(top)) )],[refute_0_85,refute_0_92]) ).
cnf(refute_0_94,plain,
( meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)) != complement(top)
| zero != meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_95,plain,
( zero != meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19)),complement(top)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_18),complement(X_19)),meet(X_18,X_19))) )],[refute_0_78,refute_0_95]) ).
cnf(refute_0_97,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_98,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( complement(top) != zero
| meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_100,plain,
( meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
meet(A,top) = complement(join(complement(A),zero)),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) )],[refute_0_74,refute_0_100]) ).
cnf(refute_0_102,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_103,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_104,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_103]) ).
cnf(refute_0_105,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_102,refute_0_104]) ).
cnf(refute_0_106,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) = meet(top,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,B))),bind(Y,$fot(complement(join(zero,complement(B)))))]]) ).
cnf(refute_0_107,plain,
complement(join(zero,complement(B))) = meet(top,B),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
complement(join(zero,complement(A))) = meet(top,A),
inference(subst,[],[refute_0_107:[bind(B,$fot(A))]]) ).
cnf(refute_0_109,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_110,plain,
complement(join(complement(A),zero)) = complement(join(complement(A),zero)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),zero)))]]) ).
cnf(refute_0_111,plain,
( complement(join(complement(A),zero)) != complement(join(complement(A),zero))
| join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) ),[1,0],$fot(join(zero,complement(A)))]]) ).
cnf(refute_0_112,plain,
( join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
complement(join(complement(A),zero)) = complement(join(zero,complement(A))),
inference(resolve,[$cnf( $equal(join(complement(A),zero),join(zero,complement(A))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
( complement(join(complement(A),zero)) != complement(join(zero,complement(A)))
| complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(complement(join(complement(A),zero)))),bind(Y,$fot(complement(join(zero,complement(A))))),bind(Z,$fot(meet(top,A)))]]) ).
cnf(refute_0_115,plain,
( complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(zero,complement(A)))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
complement(join(complement(A),zero)) = meet(top,A),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(A))),meet(top,A)) )],[refute_0_108,refute_0_115]) ).
cnf(refute_0_117,plain,
( complement(join(complement(A),zero)) != meet(top,A)
| meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) ),[1],$fot(meet(top,A))]]) ).
cnf(refute_0_118,plain,
( meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),meet(top,A)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
meet(A,top) = meet(top,A),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) )],[refute_0_101,refute_0_118]) ).
cnf(refute_0_120,plain,
meet(X_38,top) = meet(top,X_38),
inference(subst,[],[refute_0_119:[bind(A,$fot(X_38))]]) ).
cnf(refute_0_121,plain,
( X_38 != join(meet(X_38,top),complement(join(complement(X_38),top)))
| meet(X_38,top) != meet(top,X_38)
| X_38 = join(meet(top,X_38),complement(join(complement(X_38),top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_38,join(meet(X_38,top),complement(join(complement(X_38),top)))) ),[1,0],$fot(meet(top,X_38))]]) ).
cnf(refute_0_122,plain,
( X_38 != join(meet(X_38,top),complement(join(complement(X_38),top)))
| X_38 = join(meet(top,X_38),complement(join(complement(X_38),top))) ),
inference(resolve,[$cnf( $equal(meet(X_38,top),meet(top,X_38)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
X_38 = join(meet(top,X_38),complement(join(complement(X_38),top))),
inference(resolve,[$cnf( $equal(X_38,join(meet(X_38,top),complement(join(complement(X_38),top)))) )],[refute_0_73,refute_0_122]) ).
cnf(refute_0_124,plain,
join(meet(top,X_38),zero) = join(zero,meet(top,X_38)),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(meet(top,X_38)))]]) ).
cnf(refute_0_125,plain,
top = join(complement(X_32),join(complement(X_32),meet(X_32,X_32))),
inference(subst,[],[refute_0_69:[bind(X_18,$fot(X_32)),bind(X_19,$fot(X_32))]]) ).
cnf(refute_0_126,plain,
meet(X_19,X_19) = complement(join(complement(X_19),complement(X_19))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_19)),bind(B,$fot(X_19))]]) ).
cnf(refute_0_127,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_128,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
introduced(tautology,[equality,[$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_129,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( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_129]) ).
cnf(refute_0_131,plain,
join(complement(X_15),composition(converse(one),complement(composition(one,X_15)))) = complement(X_15),
inference(subst,[],[refute_0_130:[bind(A,$fot(one)),bind(B,$fot(X_15))]]) ).
cnf(refute_0_132,plain,
converse(composition(converse(A),X_5)) = composition(converse(X_5),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_5))]]) ).
cnf(refute_0_133,plain,
( converse(composition(converse(A),X_5)) != composition(converse(X_5),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_5)) = composition(converse(X_5),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_5)),composition(converse(X_5),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_134,plain,
( converse(composition(converse(A),X_5)) != composition(converse(X_5),converse(converse(A)))
| converse(composition(converse(A),X_5)) = composition(converse(X_5),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_133]) ).
cnf(refute_0_135,plain,
converse(composition(converse(A),X_5)) = composition(converse(X_5),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_5)),composition(converse(X_5),converse(converse(A)))) )],[refute_0_132,refute_0_134]) ).
cnf(refute_0_136,plain,
converse(composition(converse(X_8),one)) = composition(converse(one),X_8),
inference(subst,[],[refute_0_135:[bind(A,$fot(X_8)),bind(X_5,$fot(one))]]) ).
cnf(refute_0_137,plain,
composition(converse(X_8),one) = converse(X_8),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_8)))]]) ).
cnf(refute_0_138,plain,
( composition(converse(X_8),one) != converse(X_8)
| converse(composition(converse(X_8),one)) != composition(converse(one),X_8)
| converse(converse(X_8)) = composition(converse(one),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_8),one)),composition(converse(one),X_8)) ),[0,0],$fot(converse(X_8))]]) ).
cnf(refute_0_139,plain,
( converse(composition(converse(X_8),one)) != composition(converse(one),X_8)
| converse(converse(X_8)) = composition(converse(one),X_8) ),
inference(resolve,[$cnf( $equal(composition(converse(X_8),one),converse(X_8)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
converse(converse(X_8)) = composition(converse(one),X_8),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_8),one)),composition(converse(one),X_8)) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
converse(converse(X_8)) = X_8,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_8))]]) ).
cnf(refute_0_142,plain,
( converse(converse(X_8)) != X_8
| converse(converse(X_8)) != composition(converse(one),X_8)
| X_8 = composition(converse(one),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_8)),composition(converse(one),X_8)) ),[0],$fot(X_8)]]) ).
cnf(refute_0_143,plain,
( converse(converse(X_8)) != composition(converse(one),X_8)
| X_8 = composition(converse(one),X_8) ),
inference(resolve,[$cnf( $equal(converse(converse(X_8)),X_8) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
X_8 = composition(converse(one),X_8),
inference(resolve,[$cnf( $equal(converse(converse(X_8)),composition(converse(one),X_8)) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_146,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_144:[bind(X_8,$fot(one))]]) ).
cnf(refute_0_147,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_148,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_150,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_145,refute_0_150]) ).
cnf(refute_0_152,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_153,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
composition(converse(one),X_8) = composition(converse(one),X_8),
introduced(tautology,[refl,[$fot(composition(converse(one),X_8))]]) ).
cnf(refute_0_155,plain,
( composition(converse(one),X_8) != composition(converse(one),X_8)
| converse(one) != one
| composition(converse(one),X_8) = composition(one,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_8),composition(converse(one),X_8)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_156,plain,
( converse(one) != one
| composition(converse(one),X_8) = composition(one,X_8) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_8),composition(converse(one),X_8)) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
composition(converse(one),X_8) = composition(one,X_8),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
( X_8 != composition(converse(one),X_8)
| composition(converse(one),X_8) != composition(one,X_8)
| X_8 = composition(one,X_8) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_8,composition(one,X_8)) ),[0],$fot(composition(converse(one),X_8))]]) ).
cnf(refute_0_159,plain,
( X_8 != composition(converse(one),X_8)
| X_8 = composition(one,X_8) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_8),composition(one,X_8)) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
X_8 = composition(one,X_8),
inference(resolve,[$cnf( $equal(X_8,composition(converse(one),X_8)) )],[refute_0_144,refute_0_159]) ).
cnf(refute_0_161,plain,
X_15 = composition(one,X_15),
inference(subst,[],[refute_0_160:[bind(X_8,$fot(X_15))]]) ).
cnf(refute_0_162,plain,
( X_15 != composition(one,X_15)
| composition(one,X_15) = X_15 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_15)),bind(Y,$fot(composition(one,X_15)))]]) ).
cnf(refute_0_163,plain,
composition(one,X_15) = X_15,
inference(resolve,[$cnf( $equal(X_15,composition(one,X_15)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
( composition(one,X_15) != X_15
| join(complement(X_15),composition(converse(one),complement(composition(one,X_15)))) != complement(X_15)
| join(complement(X_15),composition(converse(one),complement(X_15))) = complement(X_15) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_15),composition(converse(one),complement(composition(one,X_15)))),complement(X_15)) ),[0,1,1,0],$fot(X_15)]]) ).
cnf(refute_0_165,plain,
( join(complement(X_15),composition(converse(one),complement(composition(one,X_15)))) != complement(X_15)
| join(complement(X_15),composition(converse(one),complement(X_15))) = complement(X_15) ),
inference(resolve,[$cnf( $equal(composition(one,X_15),X_15) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
join(complement(X_15),composition(converse(one),complement(X_15))) = complement(X_15),
inference(resolve,[$cnf( $equal(join(complement(X_15),composition(converse(one),complement(composition(one,X_15)))),complement(X_15)) )],[refute_0_131,refute_0_165]) ).
cnf(refute_0_167,plain,
( X_8 != composition(one,X_8)
| composition(one,X_8) = X_8 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_8)),bind(Y,$fot(composition(one,X_8)))]]) ).
cnf(refute_0_168,plain,
composition(one,X_8) = X_8,
inference(resolve,[$cnf( $equal(X_8,composition(one,X_8)) )],[refute_0_160,refute_0_167]) ).
cnf(refute_0_169,plain,
composition(one,complement(X_15)) = complement(X_15),
inference(subst,[],[refute_0_168:[bind(X_8,$fot(complement(X_15)))]]) ).
cnf(refute_0_170,plain,
composition(converse(one),complement(X_15)) = composition(converse(one),complement(X_15)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(X_15)))]]) ).
cnf(refute_0_171,plain,
( composition(converse(one),complement(X_15)) != composition(converse(one),complement(X_15))
| converse(one) != one
| composition(converse(one),complement(X_15)) = composition(one,complement(X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(X_15)),composition(converse(one),complement(X_15))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_172,plain,
( converse(one) != one
| composition(converse(one),complement(X_15)) = composition(one,complement(X_15)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_15)),composition(converse(one),complement(X_15))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
composition(converse(one),complement(X_15)) = composition(one,complement(X_15)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_153,refute_0_172]) ).
cnf(refute_0_174,plain,
( composition(converse(one),complement(X_15)) != composition(one,complement(X_15))
| composition(one,complement(X_15)) != complement(X_15)
| composition(converse(one),complement(X_15)) = complement(X_15) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(composition(converse(one),complement(X_15)))),bind(Y,$fot(composition(one,complement(X_15)))),bind(Z,$fot(complement(X_15)))]]) ).
cnf(refute_0_175,plain,
( composition(one,complement(X_15)) != complement(X_15)
| composition(converse(one),complement(X_15)) = complement(X_15) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_15)),composition(one,complement(X_15))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
composition(converse(one),complement(X_15)) = complement(X_15),
inference(resolve,[$cnf( $equal(composition(one,complement(X_15)),complement(X_15)) )],[refute_0_169,refute_0_175]) ).
cnf(refute_0_177,plain,
join(complement(X_15),composition(converse(one),complement(X_15))) = join(complement(X_15),composition(converse(one),complement(X_15))),
introduced(tautology,[refl,[$fot(join(complement(X_15),composition(converse(one),complement(X_15))))]]) ).
cnf(refute_0_178,plain,
( composition(converse(one),complement(X_15)) != complement(X_15)
| join(complement(X_15),composition(converse(one),complement(X_15))) != join(complement(X_15),composition(converse(one),complement(X_15)))
| join(complement(X_15),composition(converse(one),complement(X_15))) = join(complement(X_15),complement(X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_15),composition(converse(one),complement(X_15))),join(complement(X_15),composition(converse(one),complement(X_15)))) ),[1,1],$fot(complement(X_15))]]) ).
cnf(refute_0_179,plain,
( composition(converse(one),complement(X_15)) != complement(X_15)
| join(complement(X_15),composition(converse(one),complement(X_15))) = join(complement(X_15),complement(X_15)) ),
inference(resolve,[$cnf( $equal(join(complement(X_15),composition(converse(one),complement(X_15))),join(complement(X_15),composition(converse(one),complement(X_15)))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
join(complement(X_15),composition(converse(one),complement(X_15))) = join(complement(X_15),complement(X_15)),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_15)),complement(X_15)) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
( join(complement(X_15),composition(converse(one),complement(X_15))) != complement(X_15)
| join(complement(X_15),composition(converse(one),complement(X_15))) != join(complement(X_15),complement(X_15))
| join(complement(X_15),complement(X_15)) = complement(X_15) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_15),composition(converse(one),complement(X_15))),complement(X_15)) ),[0],$fot(join(complement(X_15),complement(X_15)))]]) ).
cnf(refute_0_182,plain,
( join(complement(X_15),composition(converse(one),complement(X_15))) != complement(X_15)
| join(complement(X_15),complement(X_15)) = complement(X_15) ),
inference(resolve,[$cnf( $equal(join(complement(X_15),composition(converse(one),complement(X_15))),join(complement(X_15),complement(X_15))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
join(complement(X_15),complement(X_15)) = complement(X_15),
inference(resolve,[$cnf( $equal(join(complement(X_15),composition(converse(one),complement(X_15))),complement(X_15)) )],[refute_0_166,refute_0_182]) ).
cnf(refute_0_184,plain,
join(complement(X_19),complement(X_19)) = complement(X_19),
inference(subst,[],[refute_0_183:[bind(X_15,$fot(X_19))]]) ).
cnf(refute_0_185,plain,
( join(complement(X_19),complement(X_19)) != complement(X_19)
| meet(X_19,X_19) != complement(join(complement(X_19),complement(X_19)))
| meet(X_19,X_19) = complement(complement(X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_19,X_19),complement(join(complement(X_19),complement(X_19)))) ),[1,0],$fot(complement(X_19))]]) ).
cnf(refute_0_186,plain,
( meet(X_19,X_19) != complement(join(complement(X_19),complement(X_19)))
| meet(X_19,X_19) = complement(complement(X_19)) ),
inference(resolve,[$cnf( $equal(join(complement(X_19),complement(X_19)),complement(X_19)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
meet(X_19,X_19) = complement(complement(X_19)),
inference(resolve,[$cnf( $equal(meet(X_19,X_19),complement(join(complement(X_19),complement(X_19)))) )],[refute_0_126,refute_0_186]) ).
cnf(refute_0_188,plain,
meet(X_32,X_32) = complement(complement(X_32)),
inference(subst,[],[refute_0_187:[bind(X_19,$fot(X_32))]]) ).
cnf(refute_0_189,plain,
( meet(X_32,X_32) != complement(complement(X_32))
| top != join(complement(X_32),join(complement(X_32),meet(X_32,X_32)))
| top = join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_32),join(complement(X_32),meet(X_32,X_32)))) ),[1,1,1],$fot(complement(complement(X_32)))]]) ).
cnf(refute_0_190,plain,
( top != join(complement(X_32),join(complement(X_32),meet(X_32,X_32)))
| top = join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) ),
inference(resolve,[$cnf( $equal(meet(X_32,X_32),complement(complement(X_32))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
top = join(complement(X_32),join(complement(X_32),complement(complement(X_32)))),
inference(resolve,[$cnf( $equal(top,join(complement(X_32),join(complement(X_32),meet(X_32,X_32)))) )],[refute_0_125,refute_0_190]) ).
cnf(refute_0_192,plain,
join(complement(X_32),top) = join(top,complement(X_32)),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(complement(X_32)))]]) ).
cnf(refute_0_193,plain,
join(complement(X_32),complement(complement(X_32))) = top,
inference(subst,[],[refute_0_80:[bind(A,$fot(complement(X_32)))]]) ).
cnf(refute_0_194,plain,
join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) = join(complement(X_32),join(complement(X_32),complement(complement(X_32)))),
introduced(tautology,[refl,[$fot(join(complement(X_32),join(complement(X_32),complement(complement(X_32)))))]]) ).
cnf(refute_0_195,plain,
( join(complement(X_32),complement(complement(X_32))) != top
| join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) != join(complement(X_32),join(complement(X_32),complement(complement(X_32))))
| join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) = join(complement(X_32),top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_32),join(complement(X_32),complement(complement(X_32)))),join(complement(X_32),join(complement(X_32),complement(complement(X_32))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_196,plain,
( join(complement(X_32),complement(complement(X_32))) != top
| join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) = join(complement(X_32),top) ),
inference(resolve,[$cnf( $equal(join(complement(X_32),join(complement(X_32),complement(complement(X_32)))),join(complement(X_32),join(complement(X_32),complement(complement(X_32))))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) = join(complement(X_32),top),
inference(resolve,[$cnf( $equal(join(complement(X_32),complement(complement(X_32))),top) )],[refute_0_193,refute_0_196]) ).
cnf(refute_0_198,plain,
( join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) != join(complement(X_32),top)
| join(complement(X_32),top) != join(top,complement(X_32))
| join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) = join(top,complement(X_32)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(X_32),join(complement(X_32),complement(complement(X_32)))))),bind(Y,$fot(join(complement(X_32),top))),bind(Z,$fot(join(top,complement(X_32))))]]) ).
cnf(refute_0_199,plain,
( join(complement(X_32),top) != join(top,complement(X_32))
| join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) = join(top,complement(X_32)) ),
inference(resolve,[$cnf( $equal(join(complement(X_32),join(complement(X_32),complement(complement(X_32)))),join(complement(X_32),top)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) = join(top,complement(X_32)),
inference(resolve,[$cnf( $equal(join(complement(X_32),top),join(top,complement(X_32))) )],[refute_0_192,refute_0_199]) ).
cnf(refute_0_201,plain,
( join(complement(X_32),join(complement(X_32),complement(complement(X_32)))) != join(top,complement(X_32))
| top != join(complement(X_32),join(complement(X_32),complement(complement(X_32))))
| top = join(top,complement(X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_32),join(complement(X_32),complement(complement(X_32))))) ),[1],$fot(join(top,complement(X_32)))]]) ).
cnf(refute_0_202,plain,
( top != join(complement(X_32),join(complement(X_32),complement(complement(X_32))))
| top = join(top,complement(X_32)) ),
inference(resolve,[$cnf( $equal(join(complement(X_32),join(complement(X_32),complement(complement(X_32)))),join(top,complement(X_32))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
top = join(top,complement(X_32)),
inference(resolve,[$cnf( $equal(top,join(complement(X_32),join(complement(X_32),complement(complement(X_32))))) )],[refute_0_191,refute_0_202]) ).
cnf(refute_0_204,plain,
( top != join(top,complement(X_32))
| join(top,complement(X_32)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(X_32))))]]) ).
cnf(refute_0_205,plain,
join(top,complement(X_32)) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(X_32))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
join(top,complement(X_38)) = top,
inference(subst,[],[refute_0_205:[bind(X_32,$fot(X_38))]]) ).
cnf(refute_0_207,plain,
join(complement(X_38),top) = join(top,complement(X_38)),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(complement(X_38)))]]) ).
cnf(refute_0_208,plain,
( join(complement(X_38),top) != join(top,complement(X_38))
| join(top,complement(X_38)) != top
| join(complement(X_38),top) = top ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(X_38),top))),bind(Y,$fot(join(top,complement(X_38)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_209,plain,
( join(top,complement(X_38)) != top
| join(complement(X_38),top) = top ),
inference(resolve,[$cnf( $equal(join(complement(X_38),top),join(top,complement(X_38))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
join(complement(X_38),top) = top,
inference(resolve,[$cnf( $equal(join(top,complement(X_38)),top) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
complement(join(complement(X_38),top)) = complement(join(complement(X_38),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(X_38),top)))]]) ).
cnf(refute_0_212,plain,
( complement(join(complement(X_38),top)) != complement(join(complement(X_38),top))
| join(complement(X_38),top) != top
| complement(join(complement(X_38),top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X_38),top)),complement(join(complement(X_38),top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_213,plain,
( join(complement(X_38),top) != top
| complement(join(complement(X_38),top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_38),top)),complement(join(complement(X_38),top))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
complement(join(complement(X_38),top)) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(X_38),top),top) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
( complement(join(complement(X_38),top)) != complement(top)
| complement(top) != zero
| complement(join(complement(X_38),top)) = zero ),
inference(subst,[],[refute_0_17:[bind(X,$fot(complement(join(complement(X_38),top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_216,plain,
( complement(top) != zero
| complement(join(complement(X_38),top)) = zero ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_38),top)),complement(top)) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
complement(join(complement(X_38),top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_216]) ).
cnf(refute_0_218,plain,
join(meet(top,X_38),complement(join(complement(X_38),top))) = join(meet(top,X_38),complement(join(complement(X_38),top))),
introduced(tautology,[refl,[$fot(join(meet(top,X_38),complement(join(complement(X_38),top))))]]) ).
cnf(refute_0_219,plain,
( complement(join(complement(X_38),top)) != zero
| join(meet(top,X_38),complement(join(complement(X_38),top))) != join(meet(top,X_38),complement(join(complement(X_38),top)))
| join(meet(top,X_38),complement(join(complement(X_38),top))) = join(meet(top,X_38),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_38),complement(join(complement(X_38),top))),join(meet(top,X_38),complement(join(complement(X_38),top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_220,plain,
( complement(join(complement(X_38),top)) != zero
| join(meet(top,X_38),complement(join(complement(X_38),top))) = join(meet(top,X_38),zero) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_38),complement(join(complement(X_38),top))),join(meet(top,X_38),complement(join(complement(X_38),top)))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
join(meet(top,X_38),complement(join(complement(X_38),top))) = join(meet(top,X_38),zero),
inference(resolve,[$cnf( $equal(complement(join(complement(X_38),top)),zero) )],[refute_0_217,refute_0_220]) ).
cnf(refute_0_222,plain,
( join(meet(top,X_38),complement(join(complement(X_38),top))) != join(meet(top,X_38),zero)
| join(meet(top,X_38),zero) != join(zero,meet(top,X_38))
| join(meet(top,X_38),complement(join(complement(X_38),top))) = join(zero,meet(top,X_38)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(top,X_38),complement(join(complement(X_38),top))))),bind(Y,$fot(join(meet(top,X_38),zero))),bind(Z,$fot(join(zero,meet(top,X_38))))]]) ).
cnf(refute_0_223,plain,
( join(meet(top,X_38),zero) != join(zero,meet(top,X_38))
| join(meet(top,X_38),complement(join(complement(X_38),top))) = join(zero,meet(top,X_38)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_38),complement(join(complement(X_38),top))),join(meet(top,X_38),zero)) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
join(meet(top,X_38),complement(join(complement(X_38),top))) = join(zero,meet(top,X_38)),
inference(resolve,[$cnf( $equal(join(meet(top,X_38),zero),join(zero,meet(top,X_38))) )],[refute_0_124,refute_0_223]) ).
cnf(refute_0_225,plain,
( X_38 != join(meet(top,X_38),complement(join(complement(X_38),top)))
| join(meet(top,X_38),complement(join(complement(X_38),top))) != join(zero,meet(top,X_38))
| X_38 = join(zero,meet(top,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_38,join(zero,meet(top,X_38))) ),[0],$fot(join(meet(top,X_38),complement(join(complement(X_38),top))))]]) ).
cnf(refute_0_226,plain,
( X_38 != join(meet(top,X_38),complement(join(complement(X_38),top)))
| X_38 = join(zero,meet(top,X_38)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_38),complement(join(complement(X_38),top))),join(zero,meet(top,X_38))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
X_38 = join(zero,meet(top,X_38)),
inference(resolve,[$cnf( $equal(X_38,join(meet(top,X_38),complement(join(complement(X_38),top)))) )],[refute_0_123,refute_0_226]) ).
cnf(refute_0_228,plain,
complement(complement(top)) = join(zero,meet(top,complement(complement(top)))),
inference(subst,[],[refute_0_227:[bind(X_38,$fot(complement(complement(top))))]]) ).
cnf(refute_0_229,plain,
X_38 = join(meet(X_38,complement(complement(X_38))),complement(join(complement(X_38),complement(complement(X_38))))),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_38)),bind(B,$fot(complement(complement(X_38))))]]) ).
cnf(refute_0_230,plain,
top = join(complement(X_38),complement(complement(X_38))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_38)))]]) ).
cnf(refute_0_231,plain,
( top != join(complement(X_38),complement(complement(X_38)))
| join(complement(X_38),complement(complement(X_38))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_38),complement(complement(X_38)))))]]) ).
cnf(refute_0_232,plain,
join(complement(X_38),complement(complement(X_38))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_38),complement(complement(X_38)))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
( X_38 != join(meet(X_38,complement(complement(X_38))),complement(join(complement(X_38),complement(complement(X_38)))))
| join(complement(X_38),complement(complement(X_38))) != top
| X_38 = join(meet(X_38,complement(complement(X_38))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_38,join(meet(X_38,complement(complement(X_38))),complement(join(complement(X_38),complement(complement(X_38)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_234,plain,
( X_38 != join(meet(X_38,complement(complement(X_38))),complement(join(complement(X_38),complement(complement(X_38)))))
| X_38 = join(meet(X_38,complement(complement(X_38))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_38),complement(complement(X_38))),top) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
X_38 = join(meet(X_38,complement(complement(X_38))),complement(top)),
inference(resolve,[$cnf( $equal(X_38,join(meet(X_38,complement(complement(X_38))),complement(join(complement(X_38),complement(complement(X_38)))))) )],[refute_0_229,refute_0_234]) ).
cnf(refute_0_236,plain,
join(complement(top),meet(X_38,complement(complement(X_38)))) = join(complement(top),meet(X_38,complement(complement(X_38)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_38,complement(complement(X_38)))))]]) ).
cnf(refute_0_237,plain,
( complement(top) != zero
| join(complement(top),meet(X_38,complement(complement(X_38)))) != join(complement(top),meet(X_38,complement(complement(X_38))))
| join(complement(top),meet(X_38,complement(complement(X_38)))) = join(zero,meet(X_38,complement(complement(X_38)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_38,complement(complement(X_38)))),join(complement(top),meet(X_38,complement(complement(X_38))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_238,plain,
( complement(top) != zero
| join(complement(top),meet(X_38,complement(complement(X_38)))) = join(zero,meet(X_38,complement(complement(X_38)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_38,complement(complement(X_38)))),join(complement(top),meet(X_38,complement(complement(X_38))))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
join(complement(top),meet(X_38,complement(complement(X_38)))) = join(zero,meet(X_38,complement(complement(X_38)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_238]) ).
cnf(refute_0_240,plain,
join(meet(X_38,complement(complement(X_38))),complement(top)) = join(complement(top),meet(X_38,complement(complement(X_38)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_38,complement(complement(X_38)))))]]) ).
cnf(refute_0_241,plain,
( join(complement(top),meet(X_38,complement(complement(X_38)))) != join(zero,meet(X_38,complement(complement(X_38))))
| join(meet(X_38,complement(complement(X_38))),complement(top)) != join(complement(top),meet(X_38,complement(complement(X_38))))
| join(meet(X_38,complement(complement(X_38))),complement(top)) = join(zero,meet(X_38,complement(complement(X_38)))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(X_38,complement(complement(X_38))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_38,complement(complement(X_38)))))),bind(Z,$fot(join(zero,meet(X_38,complement(complement(X_38))))))]]) ).
cnf(refute_0_242,plain,
( join(complement(top),meet(X_38,complement(complement(X_38)))) != join(zero,meet(X_38,complement(complement(X_38))))
| join(meet(X_38,complement(complement(X_38))),complement(top)) = join(zero,meet(X_38,complement(complement(X_38)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_38,complement(complement(X_38))),complement(top)),join(complement(top),meet(X_38,complement(complement(X_38))))) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
join(meet(X_38,complement(complement(X_38))),complement(top)) = join(zero,meet(X_38,complement(complement(X_38)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_38,complement(complement(X_38)))),join(zero,meet(X_38,complement(complement(X_38))))) )],[refute_0_239,refute_0_242]) ).
cnf(refute_0_244,plain,
( X_38 != join(meet(X_38,complement(complement(X_38))),complement(top))
| join(meet(X_38,complement(complement(X_38))),complement(top)) != join(zero,meet(X_38,complement(complement(X_38))))
| X_38 = join(zero,meet(X_38,complement(complement(X_38)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_38,join(zero,meet(X_38,complement(complement(X_38))))) ),[0],$fot(join(meet(X_38,complement(complement(X_38))),complement(top)))]]) ).
cnf(refute_0_245,plain,
( X_38 != join(meet(X_38,complement(complement(X_38))),complement(top))
| X_38 = join(zero,meet(X_38,complement(complement(X_38)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_38,complement(complement(X_38))),complement(top)),join(zero,meet(X_38,complement(complement(X_38))))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
X_38 = join(zero,meet(X_38,complement(complement(X_38)))),
inference(resolve,[$cnf( $equal(X_38,join(meet(X_38,complement(complement(X_38))),complement(top))) )],[refute_0_235,refute_0_245]) ).
cnf(refute_0_247,plain,
top = join(zero,meet(top,complement(complement(top)))),
inference(subst,[],[refute_0_246:[bind(X_38,$fot(top))]]) ).
cnf(refute_0_248,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_249,plain,
join(zero,meet(top,complement(complement(top)))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
( complement(complement(top)) != join(zero,meet(top,complement(complement(top))))
| join(zero,meet(top,complement(complement(top)))) != top
| complement(complement(top)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(complement(top)),top) ),[0],$fot(join(zero,meet(top,complement(complement(top)))))]]) ).
cnf(refute_0_251,plain,
( complement(complement(top)) != join(zero,meet(top,complement(complement(top))))
| complement(complement(top)) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(complement(top)))),top) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
complement(complement(top)) = top,
inference(resolve,[$cnf( $equal(complement(complement(top)),join(zero,meet(top,complement(complement(top))))) )],[refute_0_228,refute_0_251]) ).
cnf(refute_0_253,plain,
complement(complement(top)) = complement(complement(top)),
introduced(tautology,[refl,[$fot(complement(complement(top)))]]) ).
cnf(refute_0_254,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_255,plain,
( complement(top) != zero
| complement(complement(top)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(complement(top))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
complement(complement(top)) = complement(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_255]) ).
cnf(refute_0_257,plain,
( complement(complement(top)) != complement(zero)
| complement(complement(top)) != top
| complement(zero) = top ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),top) ),[0],$fot(complement(zero))]]) ).
cnf(refute_0_258,plain,
( complement(complement(top)) != top
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(complement(complement(top)),top) )],[refute_0_252,refute_0_258]) ).
cnf(refute_0_260,plain,
( complement(zero) != top
| meet(zero,B) != complement(join(complement(zero),complement(B)))
| meet(zero,B) = complement(join(top,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,B),complement(join(complement(zero),complement(B)))) ),[1,0,0],$fot(top)]]) ).
cnf(refute_0_261,plain,
( meet(zero,B) != complement(join(complement(zero),complement(B)))
| meet(zero,B) = complement(join(top,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
meet(zero,B) = complement(join(top,complement(B))),
inference(resolve,[$cnf( $equal(meet(zero,B),complement(join(complement(zero),complement(B)))) )],[refute_0_72,refute_0_261]) ).
cnf(refute_0_263,plain,
join(top,complement(B)) = top,
inference(subst,[],[refute_0_205:[bind(X_32,$fot(B))]]) ).
cnf(refute_0_264,plain,
complement(join(top,complement(B))) = complement(join(top,complement(B))),
introduced(tautology,[refl,[$fot(complement(join(top,complement(B))))]]) ).
cnf(refute_0_265,plain,
( complement(join(top,complement(B))) != complement(join(top,complement(B)))
| join(top,complement(B)) != top
| complement(join(top,complement(B))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(top,complement(B))),complement(join(top,complement(B)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_266,plain,
( join(top,complement(B)) != top
| complement(join(top,complement(B))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(B))),complement(join(top,complement(B)))) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
complement(join(top,complement(B))) = complement(top),
inference(resolve,[$cnf( $equal(join(top,complement(B)),top) )],[refute_0_263,refute_0_266]) ).
cnf(refute_0_268,plain,
( complement(join(top,complement(B))) != complement(top)
| complement(top) != zero
| complement(join(top,complement(B))) = zero ),
inference(subst,[],[refute_0_17:[bind(X,$fot(complement(join(top,complement(B))))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_269,plain,
( complement(top) != zero
| complement(join(top,complement(B))) = zero ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(B))),complement(top)) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
complement(join(top,complement(B))) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_269]) ).
cnf(refute_0_271,plain,
( complement(join(top,complement(B))) != zero
| meet(zero,B) != complement(join(top,complement(B)))
| meet(zero,B) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,B),complement(join(top,complement(B)))) ),[1],$fot(zero)]]) ).
cnf(refute_0_272,plain,
( meet(zero,B) != complement(join(top,complement(B)))
| meet(zero,B) = zero ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(B))),zero) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
meet(zero,B) = zero,
inference(resolve,[$cnf( $equal(meet(zero,B),complement(join(top,complement(B)))) )],[refute_0_262,refute_0_272]) ).
cnf(refute_0_274,plain,
meet(zero,X_64) = zero,
inference(subst,[],[refute_0_273:[bind(B,$fot(X_64))]]) ).
cnf(refute_0_275,plain,
( meet(zero,X_64) != zero
| zero != join(meet(zero,X_64),complement(join(X_64,complement(zero))))
| zero = join(zero,complement(join(X_64,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(meet(zero,X_64),complement(join(X_64,complement(zero))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_276,plain,
( zero != join(meet(zero,X_64),complement(join(X_64,complement(zero))))
| zero = join(zero,complement(join(X_64,complement(zero)))) ),
inference(resolve,[$cnf( $equal(meet(zero,X_64),zero) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
zero = join(zero,complement(join(X_64,complement(zero)))),
inference(resolve,[$cnf( $equal(zero,join(meet(zero,X_64),complement(join(X_64,complement(zero))))) )],[refute_0_71,refute_0_276]) ).
cnf(refute_0_278,plain,
join(X_64,complement(zero)) = join(X_64,complement(zero)),
introduced(tautology,[refl,[$fot(join(X_64,complement(zero)))]]) ).
cnf(refute_0_279,plain,
( complement(zero) != top
| join(X_64,complement(zero)) != join(X_64,complement(zero))
| join(X_64,complement(zero)) = join(X_64,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_64,complement(zero)),join(X_64,complement(zero))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_280,plain,
( complement(zero) != top
| join(X_64,complement(zero)) = join(X_64,top) ),
inference(resolve,[$cnf( $equal(join(X_64,complement(zero)),join(X_64,complement(zero))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
join(X_64,complement(zero)) = join(X_64,top),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_259,refute_0_280]) ).
cnf(refute_0_282,plain,
complement(join(X_64,complement(zero))) = complement(join(X_64,complement(zero))),
introduced(tautology,[refl,[$fot(complement(join(X_64,complement(zero))))]]) ).
cnf(refute_0_283,plain,
( complement(join(X_64,complement(zero))) != complement(join(X_64,complement(zero)))
| join(X_64,complement(zero)) != join(X_64,top)
| complement(join(X_64,complement(zero))) = complement(join(X_64,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(X_64,complement(zero))),complement(join(X_64,complement(zero)))) ),[1,0],$fot(join(X_64,top))]]) ).
cnf(refute_0_284,plain,
( join(X_64,complement(zero)) != join(X_64,top)
| complement(join(X_64,complement(zero))) = complement(join(X_64,top)) ),
inference(resolve,[$cnf( $equal(complement(join(X_64,complement(zero))),complement(join(X_64,complement(zero)))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
complement(join(X_64,complement(zero))) = complement(join(X_64,top)),
inference(resolve,[$cnf( $equal(join(X_64,complement(zero)),join(X_64,top)) )],[refute_0_281,refute_0_284]) ).
cnf(refute_0_286,plain,
complement(X_38) = join(meet(complement(X_38),zero),complement(join(zero,complement(complement(X_38))))),
inference(subst,[],[refute_0_30:[bind(X_38,$fot(complement(X_38))),bind(X_39,$fot(zero))]]) ).
cnf(refute_0_287,plain,
X_38 = join(meet(X_38,complement(X_38)),complement(join(complement(X_38),complement(X_38)))),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_38)),bind(B,$fot(complement(X_38)))]]) ).
cnf(refute_0_288,plain,
join(complement(X_38),complement(X_38)) = complement(X_38),
inference(subst,[],[refute_0_183:[bind(X_15,$fot(X_38))]]) ).
cnf(refute_0_289,plain,
( X_38 != join(meet(X_38,complement(X_38)),complement(join(complement(X_38),complement(X_38))))
| join(complement(X_38),complement(X_38)) != complement(X_38)
| X_38 = join(meet(X_38,complement(X_38)),complement(complement(X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(X_38,join(meet(X_38,complement(X_38)),complement(join(complement(X_38),complement(X_38))))) ),[1,1,0],$fot(complement(X_38))]]) ).
cnf(refute_0_290,plain,
( X_38 != join(meet(X_38,complement(X_38)),complement(join(complement(X_38),complement(X_38))))
| X_38 = join(meet(X_38,complement(X_38)),complement(complement(X_38))) ),
inference(resolve,[$cnf( $equal(join(complement(X_38),complement(X_38)),complement(X_38)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
X_38 = join(meet(X_38,complement(X_38)),complement(complement(X_38))),
inference(resolve,[$cnf( $equal(X_38,join(meet(X_38,complement(X_38)),complement(join(complement(X_38),complement(X_38))))) )],[refute_0_287,refute_0_290]) ).
cnf(refute_0_292,plain,
join(complement(complement(X_38)),zero) = join(zero,complement(complement(X_38))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(complement(X_38))))]]) ).
cnf(refute_0_293,plain,
( zero != meet(A,complement(A))
| meet(A,complement(A)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(A,complement(A))))]]) ).
cnf(refute_0_294,plain,
meet(A,complement(A)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(A,complement(A))) )],[def_zero_13,refute_0_293]) ).
cnf(refute_0_295,plain,
meet(X_38,complement(X_38)) = zero,
inference(subst,[],[refute_0_294:[bind(A,$fot(X_38))]]) ).
cnf(refute_0_296,plain,
join(complement(complement(X_38)),meet(X_38,complement(X_38))) = join(complement(complement(X_38)),meet(X_38,complement(X_38))),
introduced(tautology,[refl,[$fot(join(complement(complement(X_38)),meet(X_38,complement(X_38))))]]) ).
cnf(refute_0_297,plain,
( join(complement(complement(X_38)),meet(X_38,complement(X_38))) != join(complement(complement(X_38)),meet(X_38,complement(X_38)))
| meet(X_38,complement(X_38)) != zero
| join(complement(complement(X_38)),meet(X_38,complement(X_38))) = join(complement(complement(X_38)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_38)),meet(X_38,complement(X_38))),join(complement(complement(X_38)),meet(X_38,complement(X_38)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_298,plain,
( meet(X_38,complement(X_38)) != zero
| join(complement(complement(X_38)),meet(X_38,complement(X_38))) = join(complement(complement(X_38)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_38)),meet(X_38,complement(X_38))),join(complement(complement(X_38)),meet(X_38,complement(X_38)))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
join(complement(complement(X_38)),meet(X_38,complement(X_38))) = join(complement(complement(X_38)),zero),
inference(resolve,[$cnf( $equal(meet(X_38,complement(X_38)),zero) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
( join(complement(complement(X_38)),meet(X_38,complement(X_38))) != join(complement(complement(X_38)),zero)
| join(complement(complement(X_38)),zero) != join(zero,complement(complement(X_38)))
| join(complement(complement(X_38)),meet(X_38,complement(X_38))) = join(zero,complement(complement(X_38))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(complement(X_38)),meet(X_38,complement(X_38))))),bind(Y,$fot(join(complement(complement(X_38)),zero))),bind(Z,$fot(join(zero,complement(complement(X_38)))))]]) ).
cnf(refute_0_301,plain,
( join(complement(complement(X_38)),zero) != join(zero,complement(complement(X_38)))
| join(complement(complement(X_38)),meet(X_38,complement(X_38))) = join(zero,complement(complement(X_38))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_38)),meet(X_38,complement(X_38))),join(complement(complement(X_38)),zero)) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
join(complement(complement(X_38)),meet(X_38,complement(X_38))) = join(zero,complement(complement(X_38))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_38)),zero),join(zero,complement(complement(X_38)))) )],[refute_0_292,refute_0_301]) ).
cnf(refute_0_303,plain,
join(meet(X_38,complement(X_38)),complement(complement(X_38))) = join(complement(complement(X_38)),meet(X_38,complement(X_38))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(complement(X_38)))),bind(B,$fot(meet(X_38,complement(X_38))))]]) ).
cnf(refute_0_304,plain,
( join(complement(complement(X_38)),meet(X_38,complement(X_38))) != join(zero,complement(complement(X_38)))
| join(meet(X_38,complement(X_38)),complement(complement(X_38))) != join(complement(complement(X_38)),meet(X_38,complement(X_38)))
| join(meet(X_38,complement(X_38)),complement(complement(X_38))) = join(zero,complement(complement(X_38))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(X_38,complement(X_38)),complement(complement(X_38))))),bind(Y,$fot(join(complement(complement(X_38)),meet(X_38,complement(X_38))))),bind(Z,$fot(join(zero,complement(complement(X_38)))))]]) ).
cnf(refute_0_305,plain,
( join(complement(complement(X_38)),meet(X_38,complement(X_38))) != join(zero,complement(complement(X_38)))
| join(meet(X_38,complement(X_38)),complement(complement(X_38))) = join(zero,complement(complement(X_38))) ),
inference(resolve,[$cnf( $equal(join(meet(X_38,complement(X_38)),complement(complement(X_38))),join(complement(complement(X_38)),meet(X_38,complement(X_38)))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
join(meet(X_38,complement(X_38)),complement(complement(X_38))) = join(zero,complement(complement(X_38))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_38)),meet(X_38,complement(X_38))),join(zero,complement(complement(X_38)))) )],[refute_0_302,refute_0_305]) ).
cnf(refute_0_307,plain,
( X_38 != join(meet(X_38,complement(X_38)),complement(complement(X_38)))
| join(meet(X_38,complement(X_38)),complement(complement(X_38))) != join(zero,complement(complement(X_38)))
| X_38 = join(zero,complement(complement(X_38))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_38,join(zero,complement(complement(X_38)))) ),[0],$fot(join(meet(X_38,complement(X_38)),complement(complement(X_38))))]]) ).
cnf(refute_0_308,plain,
( X_38 != join(meet(X_38,complement(X_38)),complement(complement(X_38)))
| X_38 = join(zero,complement(complement(X_38))) ),
inference(resolve,[$cnf( $equal(join(meet(X_38,complement(X_38)),complement(complement(X_38))),join(zero,complement(complement(X_38)))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
X_38 = join(zero,complement(complement(X_38))),
inference(resolve,[$cnf( $equal(X_38,join(meet(X_38,complement(X_38)),complement(complement(X_38)))) )],[refute_0_291,refute_0_308]) ).
cnf(refute_0_310,plain,
( X_38 != join(zero,complement(complement(X_38)))
| join(zero,complement(complement(X_38))) = X_38 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_38)),bind(Y,$fot(join(zero,complement(complement(X_38)))))]]) ).
cnf(refute_0_311,plain,
join(zero,complement(complement(X_38))) = X_38,
inference(resolve,[$cnf( $equal(X_38,join(zero,complement(complement(X_38)))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
( complement(X_38) != join(meet(complement(X_38),zero),complement(join(zero,complement(complement(X_38)))))
| join(zero,complement(complement(X_38))) != X_38
| complement(X_38) = join(meet(complement(X_38),zero),complement(X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_38),join(meet(complement(X_38),zero),complement(join(zero,complement(complement(X_38)))))) ),[1,1,0],$fot(X_38)]]) ).
cnf(refute_0_313,plain,
( complement(X_38) != join(meet(complement(X_38),zero),complement(join(zero,complement(complement(X_38)))))
| complement(X_38) = join(meet(complement(X_38),zero),complement(X_38)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_38))),X_38) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
complement(X_38) = join(meet(complement(X_38),zero),complement(X_38)),
inference(resolve,[$cnf( $equal(complement(X_38),join(meet(complement(X_38),zero),complement(join(zero,complement(complement(X_38)))))) )],[refute_0_286,refute_0_313]) ).
cnf(refute_0_315,plain,
join(complement(X_38),zero) = join(zero,complement(X_38)),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(X_38)))]]) ).
cnf(refute_0_316,plain,
meet(A,zero) = complement(join(complement(A),complement(zero))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(zero))]]) ).
cnf(refute_0_317,plain,
( complement(zero) != top
| meet(A,zero) != complement(join(complement(A),complement(zero)))
| meet(A,zero) = complement(join(complement(A),top)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,zero),complement(join(complement(A),complement(zero)))) ),[1,0,1],$fot(top)]]) ).
cnf(refute_0_318,plain,
( meet(A,zero) != complement(join(complement(A),complement(zero)))
| meet(A,zero) = complement(join(complement(A),top)) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_259,refute_0_317]) ).
cnf(refute_0_319,plain,
meet(A,zero) = complement(join(complement(A),top)),
inference(resolve,[$cnf( $equal(meet(A,zero),complement(join(complement(A),complement(zero)))) )],[refute_0_316,refute_0_318]) ).
cnf(refute_0_320,plain,
join(top,complement(A)) = top,
inference(subst,[],[refute_0_205:[bind(X_32,$fot(A))]]) ).
cnf(refute_0_321,plain,
join(complement(A),top) = join(top,complement(A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(complement(A)))]]) ).
cnf(refute_0_322,plain,
( join(complement(A),top) != join(top,complement(A))
| join(top,complement(A)) != top
| join(complement(A),top) = top ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(A),top))),bind(Y,$fot(join(top,complement(A)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_323,plain,
( join(top,complement(A)) != top
| join(complement(A),top) = top ),
inference(resolve,[$cnf( $equal(join(complement(A),top),join(top,complement(A))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
join(complement(A),top) = top,
inference(resolve,[$cnf( $equal(join(top,complement(A)),top) )],[refute_0_320,refute_0_323]) ).
cnf(refute_0_325,plain,
complement(join(complement(A),top)) = complement(join(complement(A),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),top)))]]) ).
cnf(refute_0_326,plain,
( complement(join(complement(A),top)) != complement(join(complement(A),top))
| join(complement(A),top) != top
| complement(join(complement(A),top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),top)),complement(join(complement(A),top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_327,plain,
( join(complement(A),top) != top
| complement(join(complement(A),top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),top)),complement(join(complement(A),top))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
complement(join(complement(A),top)) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(A),top),top) )],[refute_0_324,refute_0_327]) ).
cnf(refute_0_329,plain,
( complement(join(complement(A),top)) != complement(top)
| complement(top) != zero
| complement(join(complement(A),top)) = zero ),
inference(subst,[],[refute_0_17:[bind(X,$fot(complement(join(complement(A),top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_330,plain,
( complement(top) != zero
| complement(join(complement(A),top)) = zero ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),top)),complement(top)) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
complement(join(complement(A),top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_330]) ).
cnf(refute_0_332,plain,
( complement(join(complement(A),top)) != zero
| meet(A,zero) != complement(join(complement(A),top))
| meet(A,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,zero),complement(join(complement(A),top))) ),[1],$fot(zero)]]) ).
cnf(refute_0_333,plain,
( meet(A,zero) != complement(join(complement(A),top))
| meet(A,zero) = zero ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),top)),zero) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
meet(A,zero) = zero,
inference(resolve,[$cnf( $equal(meet(A,zero),complement(join(complement(A),top))) )],[refute_0_319,refute_0_333]) ).
cnf(refute_0_335,plain,
meet(complement(X_38),zero) = zero,
inference(subst,[],[refute_0_334:[bind(A,$fot(complement(X_38)))]]) ).
cnf(refute_0_336,plain,
join(complement(X_38),meet(complement(X_38),zero)) = join(complement(X_38),meet(complement(X_38),zero)),
introduced(tautology,[refl,[$fot(join(complement(X_38),meet(complement(X_38),zero)))]]) ).
cnf(refute_0_337,plain,
( join(complement(X_38),meet(complement(X_38),zero)) != join(complement(X_38),meet(complement(X_38),zero))
| meet(complement(X_38),zero) != zero
| join(complement(X_38),meet(complement(X_38),zero)) = join(complement(X_38),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_38),meet(complement(X_38),zero)),join(complement(X_38),meet(complement(X_38),zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_338,plain,
( meet(complement(X_38),zero) != zero
| join(complement(X_38),meet(complement(X_38),zero)) = join(complement(X_38),zero) ),
inference(resolve,[$cnf( $equal(join(complement(X_38),meet(complement(X_38),zero)),join(complement(X_38),meet(complement(X_38),zero))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
join(complement(X_38),meet(complement(X_38),zero)) = join(complement(X_38),zero),
inference(resolve,[$cnf( $equal(meet(complement(X_38),zero),zero) )],[refute_0_335,refute_0_338]) ).
cnf(refute_0_340,plain,
( join(complement(X_38),meet(complement(X_38),zero)) != join(complement(X_38),zero)
| join(complement(X_38),zero) != join(zero,complement(X_38))
| join(complement(X_38),meet(complement(X_38),zero)) = join(zero,complement(X_38)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(X_38),meet(complement(X_38),zero)))),bind(Y,$fot(join(complement(X_38),zero))),bind(Z,$fot(join(zero,complement(X_38))))]]) ).
cnf(refute_0_341,plain,
( join(complement(X_38),zero) != join(zero,complement(X_38))
| join(complement(X_38),meet(complement(X_38),zero)) = join(zero,complement(X_38)) ),
inference(resolve,[$cnf( $equal(join(complement(X_38),meet(complement(X_38),zero)),join(complement(X_38),zero)) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
join(complement(X_38),meet(complement(X_38),zero)) = join(zero,complement(X_38)),
inference(resolve,[$cnf( $equal(join(complement(X_38),zero),join(zero,complement(X_38))) )],[refute_0_315,refute_0_341]) ).
cnf(refute_0_343,plain,
join(meet(complement(X_38),zero),complement(X_38)) = join(complement(X_38),meet(complement(X_38),zero)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_38))),bind(B,$fot(meet(complement(X_38),zero)))]]) ).
cnf(refute_0_344,plain,
( join(complement(X_38),meet(complement(X_38),zero)) != join(zero,complement(X_38))
| join(meet(complement(X_38),zero),complement(X_38)) != join(complement(X_38),meet(complement(X_38),zero))
| join(meet(complement(X_38),zero),complement(X_38)) = join(zero,complement(X_38)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(complement(X_38),zero),complement(X_38)))),bind(Y,$fot(join(complement(X_38),meet(complement(X_38),zero)))),bind(Z,$fot(join(zero,complement(X_38))))]]) ).
cnf(refute_0_345,plain,
( join(complement(X_38),meet(complement(X_38),zero)) != join(zero,complement(X_38))
| join(meet(complement(X_38),zero),complement(X_38)) = join(zero,complement(X_38)) ),
inference(resolve,[$cnf( $equal(join(meet(complement(X_38),zero),complement(X_38)),join(complement(X_38),meet(complement(X_38),zero))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
join(meet(complement(X_38),zero),complement(X_38)) = join(zero,complement(X_38)),
inference(resolve,[$cnf( $equal(join(complement(X_38),meet(complement(X_38),zero)),join(zero,complement(X_38))) )],[refute_0_342,refute_0_345]) ).
cnf(refute_0_347,plain,
( complement(X_38) != join(meet(complement(X_38),zero),complement(X_38))
| join(meet(complement(X_38),zero),complement(X_38)) != join(zero,complement(X_38))
| complement(X_38) = join(zero,complement(X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_38),join(zero,complement(X_38))) ),[0],$fot(join(meet(complement(X_38),zero),complement(X_38)))]]) ).
cnf(refute_0_348,plain,
( complement(X_38) != join(meet(complement(X_38),zero),complement(X_38))
| complement(X_38) = join(zero,complement(X_38)) ),
inference(resolve,[$cnf( $equal(join(meet(complement(X_38),zero),complement(X_38)),join(zero,complement(X_38))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
complement(X_38) = join(zero,complement(X_38)),
inference(resolve,[$cnf( $equal(complement(X_38),join(meet(complement(X_38),zero),complement(X_38))) )],[refute_0_314,refute_0_348]) ).
cnf(refute_0_350,plain,
( complement(X_38) != join(zero,complement(X_38))
| join(zero,complement(X_38)) = complement(X_38) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_38))),bind(Y,$fot(join(zero,complement(X_38))))]]) ).
cnf(refute_0_351,plain,
join(zero,complement(X_38)) = complement(X_38),
inference(resolve,[$cnf( $equal(complement(X_38),join(zero,complement(X_38))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
join(zero,complement(join(X_64,complement(zero)))) = complement(join(X_64,complement(zero))),
inference(subst,[],[refute_0_351:[bind(X_38,$fot(join(X_64,complement(zero))))]]) ).
cnf(refute_0_353,plain,
( complement(join(X_64,complement(zero))) != complement(join(X_64,top))
| join(zero,complement(join(X_64,complement(zero)))) != complement(join(X_64,complement(zero)))
| join(zero,complement(join(X_64,complement(zero)))) = complement(join(X_64,top)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(zero,complement(join(X_64,complement(zero)))))),bind(Y,$fot(complement(join(X_64,complement(zero))))),bind(Z,$fot(complement(join(X_64,top))))]]) ).
cnf(refute_0_354,plain,
( complement(join(X_64,complement(zero))) != complement(join(X_64,top))
| join(zero,complement(join(X_64,complement(zero)))) = complement(join(X_64,top)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(X_64,complement(zero)))),complement(join(X_64,complement(zero)))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
join(zero,complement(join(X_64,complement(zero)))) = complement(join(X_64,top)),
inference(resolve,[$cnf( $equal(complement(join(X_64,complement(zero))),complement(join(X_64,top))) )],[refute_0_285,refute_0_354]) ).
cnf(refute_0_356,plain,
( join(zero,complement(join(X_64,complement(zero)))) != complement(join(X_64,top))
| zero != join(zero,complement(join(X_64,complement(zero))))
| zero = complement(join(X_64,top)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(zero,complement(join(X_64,complement(zero))))) ),[1],$fot(complement(join(X_64,top)))]]) ).
cnf(refute_0_357,plain,
( zero != join(zero,complement(join(X_64,complement(zero))))
| zero = complement(join(X_64,top)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(X_64,complement(zero)))),complement(join(X_64,top))) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
zero = complement(join(X_64,top)),
inference(resolve,[$cnf( $equal(zero,join(zero,complement(join(X_64,complement(zero))))) )],[refute_0_277,refute_0_357]) ).
cnf(refute_0_359,plain,
zero = complement(join(X_69,top)),
inference(subst,[],[refute_0_358:[bind(X_64,$fot(X_69))]]) ).
cnf(refute_0_360,plain,
( zero != complement(join(X_69,top))
| complement(join(X_69,top)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(join(X_69,top))))]]) ).
cnf(refute_0_361,plain,
complement(join(X_69,top)) = zero,
inference(resolve,[$cnf( $equal(zero,complement(join(X_69,top))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
( complement(join(X_69,top)) != zero
| top != join(complement(join(X_69,top)),join(complement(X_19),meet(join(X_69,top),X_19)))
| top = join(zero,join(complement(X_19),meet(join(X_69,top),X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(join(X_69,top)),join(complement(X_19),meet(join(X_69,top),X_19)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_363,plain,
( top != join(complement(join(X_69,top)),join(complement(X_19),meet(join(X_69,top),X_19)))
| top = join(zero,join(complement(X_19),meet(join(X_69,top),X_19))) ),
inference(resolve,[$cnf( $equal(complement(join(X_69,top)),zero) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
top = join(zero,join(complement(X_19),meet(join(X_69,top),X_19))),
inference(resolve,[$cnf( $equal(top,join(complement(join(X_69,top)),join(complement(X_19),meet(join(X_69,top),X_19)))) )],[refute_0_70,refute_0_363]) ).
cnf(refute_0_365,plain,
join(X_69,top) = join(meet(join(X_69,top),X_39),complement(join(X_39,complement(join(X_69,top))))),
inference(subst,[],[refute_0_30:[bind(X_38,$fot(join(X_69,top)))]]) ).
cnf(refute_0_366,plain,
( complement(join(X_69,top)) != zero
| join(X_69,top) != join(meet(join(X_69,top),X_39),complement(join(X_39,complement(join(X_69,top)))))
| join(X_69,top) = join(meet(join(X_69,top),X_39),complement(join(X_39,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_69,top),join(meet(join(X_69,top),X_39),complement(join(X_39,complement(join(X_69,top)))))) ),[1,1,0,1],$fot(zero)]]) ).
cnf(refute_0_367,plain,
( join(X_69,top) != join(meet(join(X_69,top),X_39),complement(join(X_39,complement(join(X_69,top)))))
| join(X_69,top) = join(meet(join(X_69,top),X_39),complement(join(X_39,zero))) ),
inference(resolve,[$cnf( $equal(complement(join(X_69,top)),zero) )],[refute_0_361,refute_0_366]) ).
cnf(refute_0_368,plain,
join(X_69,top) = join(meet(join(X_69,top),X_39),complement(join(X_39,zero))),
inference(resolve,[$cnf( $equal(join(X_69,top),join(meet(join(X_69,top),X_39),complement(join(X_39,complement(join(X_69,top)))))) )],[refute_0_365,refute_0_367]) ).
cnf(refute_0_369,plain,
X_64 = join(meet(X_64,X_64),complement(join(X_64,complement(X_64)))),
inference(subst,[],[refute_0_30:[bind(X_38,$fot(X_64)),bind(X_39,$fot(X_64))]]) ).
cnf(refute_0_370,plain,
meet(X_64,X_64) = complement(complement(X_64)),
inference(subst,[],[refute_0_187:[bind(X_19,$fot(X_64))]]) ).
cnf(refute_0_371,plain,
( X_64 != join(meet(X_64,X_64),complement(join(X_64,complement(X_64))))
| meet(X_64,X_64) != complement(complement(X_64))
| X_64 = join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_64,join(meet(X_64,X_64),complement(join(X_64,complement(X_64))))) ),[1,0],$fot(complement(complement(X_64)))]]) ).
cnf(refute_0_372,plain,
( X_64 != join(meet(X_64,X_64),complement(join(X_64,complement(X_64))))
| X_64 = join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) ),
inference(resolve,[$cnf( $equal(meet(X_64,X_64),complement(complement(X_64))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
X_64 = join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))),
inference(resolve,[$cnf( $equal(X_64,join(meet(X_64,X_64),complement(join(X_64,complement(X_64))))) )],[refute_0_369,refute_0_372]) ).
cnf(refute_0_374,plain,
join(X_64,complement(X_64)) = top,
inference(subst,[],[refute_0_80:[bind(A,$fot(X_64))]]) ).
cnf(refute_0_375,plain,
complement(join(X_64,complement(X_64))) = complement(join(X_64,complement(X_64))),
introduced(tautology,[refl,[$fot(complement(join(X_64,complement(X_64))))]]) ).
cnf(refute_0_376,plain,
( complement(join(X_64,complement(X_64))) != complement(join(X_64,complement(X_64)))
| join(X_64,complement(X_64)) != top
| complement(join(X_64,complement(X_64))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(X_64,complement(X_64))),complement(join(X_64,complement(X_64)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_377,plain,
( join(X_64,complement(X_64)) != top
| complement(join(X_64,complement(X_64))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(X_64,complement(X_64))),complement(join(X_64,complement(X_64)))) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
complement(join(X_64,complement(X_64))) = complement(top),
inference(resolve,[$cnf( $equal(join(X_64,complement(X_64)),top) )],[refute_0_374,refute_0_377]) ).
cnf(refute_0_379,plain,
( complement(join(X_64,complement(X_64))) != complement(top)
| complement(top) != zero
| complement(join(X_64,complement(X_64))) = zero ),
inference(subst,[],[refute_0_17:[bind(X,$fot(complement(join(X_64,complement(X_64))))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_380,plain,
( complement(top) != zero
| complement(join(X_64,complement(X_64))) = zero ),
inference(resolve,[$cnf( $equal(complement(join(X_64,complement(X_64))),complement(top)) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
complement(join(X_64,complement(X_64))) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_380]) ).
cnf(refute_0_382,plain,
join(X_64,complement(join(X_64,complement(X_64)))) = join(X_64,complement(join(X_64,complement(X_64)))),
introduced(tautology,[refl,[$fot(join(X_64,complement(join(X_64,complement(X_64)))))]]) ).
cnf(refute_0_383,plain,
( complement(join(X_64,complement(X_64))) != zero
| join(X_64,complement(join(X_64,complement(X_64)))) != join(X_64,complement(join(X_64,complement(X_64))))
| join(X_64,complement(join(X_64,complement(X_64)))) = join(X_64,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_64,complement(join(X_64,complement(X_64)))),join(X_64,complement(join(X_64,complement(X_64))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_384,plain,
( complement(join(X_64,complement(X_64))) != zero
| join(X_64,complement(join(X_64,complement(X_64)))) = join(X_64,zero) ),
inference(resolve,[$cnf( $equal(join(X_64,complement(join(X_64,complement(X_64)))),join(X_64,complement(join(X_64,complement(X_64))))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
join(X_64,complement(join(X_64,complement(X_64)))) = join(X_64,zero),
inference(resolve,[$cnf( $equal(complement(join(X_64,complement(X_64))),zero) )],[refute_0_381,refute_0_384]) ).
cnf(refute_0_386,plain,
X_63 = join(meet(X_63,X_63),complement(join(X_63,complement(X_63)))),
inference(subst,[],[refute_0_30:[bind(X_38,$fot(X_63)),bind(X_39,$fot(X_63))]]) ).
cnf(refute_0_387,plain,
top = join(X_63,complement(X_63)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_63))]]) ).
cnf(refute_0_388,plain,
( top != join(X_63,complement(X_63))
| join(X_63,complement(X_63)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(X_63,complement(X_63))))]]) ).
cnf(refute_0_389,plain,
join(X_63,complement(X_63)) = top,
inference(resolve,[$cnf( $equal(top,join(X_63,complement(X_63))) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
( X_63 != join(meet(X_63,X_63),complement(join(X_63,complement(X_63))))
| join(X_63,complement(X_63)) != top
| X_63 = join(meet(X_63,X_63),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_63,join(meet(X_63,X_63),complement(join(X_63,complement(X_63))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_391,plain,
( X_63 != join(meet(X_63,X_63),complement(join(X_63,complement(X_63))))
| X_63 = join(meet(X_63,X_63),complement(top)) ),
inference(resolve,[$cnf( $equal(join(X_63,complement(X_63)),top) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
X_63 = join(meet(X_63,X_63),complement(top)),
inference(resolve,[$cnf( $equal(X_63,join(meet(X_63,X_63),complement(join(X_63,complement(X_63))))) )],[refute_0_386,refute_0_391]) ).
cnf(refute_0_393,plain,
join(zero,complement(complement(X_63))) = complement(complement(X_63)),
inference(subst,[],[refute_0_351:[bind(X_38,$fot(complement(X_63)))]]) ).
cnf(refute_0_394,plain,
meet(X_63,X_63) = complement(complement(X_63)),
inference(subst,[],[refute_0_187:[bind(X_19,$fot(X_63))]]) ).
cnf(refute_0_395,plain,
join(zero,meet(X_63,X_63)) = join(zero,meet(X_63,X_63)),
introduced(tautology,[refl,[$fot(join(zero,meet(X_63,X_63)))]]) ).
cnf(refute_0_396,plain,
( join(zero,meet(X_63,X_63)) != join(zero,meet(X_63,X_63))
| meet(X_63,X_63) != complement(complement(X_63))
| join(zero,meet(X_63,X_63)) = join(zero,complement(complement(X_63))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(X_63,X_63)),join(zero,meet(X_63,X_63))) ),[1,1],$fot(complement(complement(X_63)))]]) ).
cnf(refute_0_397,plain,
( meet(X_63,X_63) != complement(complement(X_63))
| join(zero,meet(X_63,X_63)) = join(zero,complement(complement(X_63))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_63,X_63)),join(zero,meet(X_63,X_63))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
join(zero,meet(X_63,X_63)) = join(zero,complement(complement(X_63))),
inference(resolve,[$cnf( $equal(meet(X_63,X_63),complement(complement(X_63))) )],[refute_0_394,refute_0_397]) ).
cnf(refute_0_399,plain,
join(complement(top),meet(X_63,X_63)) = join(complement(top),meet(X_63,X_63)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_63,X_63)))]]) ).
cnf(refute_0_400,plain,
( complement(top) != zero
| join(complement(top),meet(X_63,X_63)) != join(complement(top),meet(X_63,X_63))
| join(complement(top),meet(X_63,X_63)) = join(zero,meet(X_63,X_63)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_63,X_63)),join(complement(top),meet(X_63,X_63))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_401,plain,
( complement(top) != zero
| join(complement(top),meet(X_63,X_63)) = join(zero,meet(X_63,X_63)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_63,X_63)),join(complement(top),meet(X_63,X_63))) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
join(complement(top),meet(X_63,X_63)) = join(zero,meet(X_63,X_63)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_401]) ).
cnf(refute_0_403,plain,
( join(complement(top),meet(X_63,X_63)) != join(zero,meet(X_63,X_63))
| join(zero,meet(X_63,X_63)) != join(zero,complement(complement(X_63)))
| join(complement(top),meet(X_63,X_63)) = join(zero,complement(complement(X_63))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(top),meet(X_63,X_63)))),bind(Y,$fot(join(zero,meet(X_63,X_63)))),bind(Z,$fot(join(zero,complement(complement(X_63)))))]]) ).
cnf(refute_0_404,plain,
( join(zero,meet(X_63,X_63)) != join(zero,complement(complement(X_63)))
| join(complement(top),meet(X_63,X_63)) = join(zero,complement(complement(X_63))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_63,X_63)),join(zero,meet(X_63,X_63))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
join(complement(top),meet(X_63,X_63)) = join(zero,complement(complement(X_63))),
inference(resolve,[$cnf( $equal(join(zero,meet(X_63,X_63)),join(zero,complement(complement(X_63)))) )],[refute_0_398,refute_0_404]) ).
cnf(refute_0_406,plain,
( join(complement(top),meet(X_63,X_63)) != join(zero,complement(complement(X_63)))
| join(zero,complement(complement(X_63))) != complement(complement(X_63))
| join(complement(top),meet(X_63,X_63)) = complement(complement(X_63)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(top),meet(X_63,X_63)))),bind(Y,$fot(join(zero,complement(complement(X_63))))),bind(Z,$fot(complement(complement(X_63))))]]) ).
cnf(refute_0_407,plain,
( join(zero,complement(complement(X_63))) != complement(complement(X_63))
| join(complement(top),meet(X_63,X_63)) = complement(complement(X_63)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_63,X_63)),join(zero,complement(complement(X_63)))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
join(complement(top),meet(X_63,X_63)) = complement(complement(X_63)),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_63))),complement(complement(X_63))) )],[refute_0_393,refute_0_407]) ).
cnf(refute_0_409,plain,
join(meet(X_63,X_63),complement(top)) = join(complement(top),meet(X_63,X_63)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_63,X_63)))]]) ).
cnf(refute_0_410,plain,
( join(complement(top),meet(X_63,X_63)) != complement(complement(X_63))
| join(meet(X_63,X_63),complement(top)) != join(complement(top),meet(X_63,X_63))
| join(meet(X_63,X_63),complement(top)) = complement(complement(X_63)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(X_63,X_63),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_63,X_63)))),bind(Z,$fot(complement(complement(X_63))))]]) ).
cnf(refute_0_411,plain,
( join(complement(top),meet(X_63,X_63)) != complement(complement(X_63))
| join(meet(X_63,X_63),complement(top)) = complement(complement(X_63)) ),
inference(resolve,[$cnf( $equal(join(meet(X_63,X_63),complement(top)),join(complement(top),meet(X_63,X_63))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
join(meet(X_63,X_63),complement(top)) = complement(complement(X_63)),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_63,X_63)),complement(complement(X_63))) )],[refute_0_408,refute_0_411]) ).
cnf(refute_0_413,plain,
( X_63 != join(meet(X_63,X_63),complement(top))
| join(meet(X_63,X_63),complement(top)) != complement(complement(X_63))
| X_63 = complement(complement(X_63)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_63,complement(complement(X_63))) ),[0],$fot(join(meet(X_63,X_63),complement(top)))]]) ).
cnf(refute_0_414,plain,
( X_63 != join(meet(X_63,X_63),complement(top))
| X_63 = complement(complement(X_63)) ),
inference(resolve,[$cnf( $equal(join(meet(X_63,X_63),complement(top)),complement(complement(X_63))) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
X_63 = complement(complement(X_63)),
inference(resolve,[$cnf( $equal(X_63,join(meet(X_63,X_63),complement(top))) )],[refute_0_392,refute_0_414]) ).
cnf(refute_0_416,plain,
( X_63 != complement(complement(X_63))
| complement(complement(X_63)) = X_63 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_63)),bind(Y,$fot(complement(complement(X_63))))]]) ).
cnf(refute_0_417,plain,
complement(complement(X_63)) = X_63,
inference(resolve,[$cnf( $equal(X_63,complement(complement(X_63))) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
complement(complement(X_64)) = X_64,
inference(subst,[],[refute_0_417:[bind(X_63,$fot(X_64))]]) ).
cnf(refute_0_419,plain,
join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) = join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))),
introduced(tautology,[refl,[$fot(join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))))]]) ).
cnf(refute_0_420,plain,
( complement(complement(X_64)) != X_64
| join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) != join(complement(complement(X_64)),complement(join(X_64,complement(X_64))))
| join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) = join(X_64,complement(join(X_64,complement(X_64)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))),join(complement(complement(X_64)),complement(join(X_64,complement(X_64))))) ),[1,0],$fot(X_64)]]) ).
cnf(refute_0_421,plain,
( complement(complement(X_64)) != X_64
| join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) = join(X_64,complement(join(X_64,complement(X_64)))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))),join(complement(complement(X_64)),complement(join(X_64,complement(X_64))))) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) = join(X_64,complement(join(X_64,complement(X_64)))),
inference(resolve,[$cnf( $equal(complement(complement(X_64)),X_64) )],[refute_0_418,refute_0_421]) ).
cnf(refute_0_423,plain,
( join(X_64,complement(join(X_64,complement(X_64)))) != join(X_64,zero)
| join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) != join(X_64,complement(join(X_64,complement(X_64))))
| join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) = join(X_64,zero) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))))),bind(Y,$fot(join(X_64,complement(join(X_64,complement(X_64)))))),bind(Z,$fot(join(X_64,zero)))]]) ).
cnf(refute_0_424,plain,
( join(X_64,complement(join(X_64,complement(X_64)))) != join(X_64,zero)
| join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) = join(X_64,zero) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))),join(X_64,complement(join(X_64,complement(X_64))))) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) = join(X_64,zero),
inference(resolve,[$cnf( $equal(join(X_64,complement(join(X_64,complement(X_64)))),join(X_64,zero)) )],[refute_0_385,refute_0_424]) ).
cnf(refute_0_426,plain,
( X_64 != join(complement(complement(X_64)),complement(join(X_64,complement(X_64))))
| join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))) != join(X_64,zero)
| X_64 = join(X_64,zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_64,join(X_64,zero)) ),[0],$fot(join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))))]]) ).
cnf(refute_0_427,plain,
( X_64 != join(complement(complement(X_64)),complement(join(X_64,complement(X_64))))
| X_64 = join(X_64,zero) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_64)),complement(join(X_64,complement(X_64)))),join(X_64,zero)) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
X_64 = join(X_64,zero),
inference(resolve,[$cnf( $equal(X_64,join(complement(complement(X_64)),complement(join(X_64,complement(X_64))))) )],[refute_0_373,refute_0_427]) ).
cnf(refute_0_429,plain,
( X_64 != join(X_64,zero)
| join(X_64,zero) = X_64 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_64)),bind(Y,$fot(join(X_64,zero)))]]) ).
cnf(refute_0_430,plain,
join(X_64,zero) = X_64,
inference(resolve,[$cnf( $equal(X_64,join(X_64,zero)) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
join(X_39,zero) = X_39,
inference(subst,[],[refute_0_430:[bind(X_64,$fot(X_39))]]) ).
cnf(refute_0_432,plain,
complement(join(X_39,zero)) = complement(join(X_39,zero)),
introduced(tautology,[refl,[$fot(complement(join(X_39,zero)))]]) ).
cnf(refute_0_433,plain,
( complement(join(X_39,zero)) != complement(join(X_39,zero))
| join(X_39,zero) != X_39
| complement(join(X_39,zero)) = complement(X_39) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(X_39,zero)),complement(join(X_39,zero))) ),[1,0],$fot(X_39)]]) ).
cnf(refute_0_434,plain,
( join(X_39,zero) != X_39
| complement(join(X_39,zero)) = complement(X_39) ),
inference(resolve,[$cnf( $equal(complement(join(X_39,zero)),complement(join(X_39,zero))) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
complement(join(X_39,zero)) = complement(X_39),
inference(resolve,[$cnf( $equal(join(X_39,zero),X_39) )],[refute_0_431,refute_0_434]) ).
cnf(refute_0_436,plain,
join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)) = join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)),
introduced(tautology,[refl,[$fot(join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)))]]) ).
cnf(refute_0_437,plain,
( complement(join(X_39,zero)) != complement(X_39)
| join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)) != join(complement(join(X_39,zero)),meet(join(X_69,top),X_39))
| join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)) = join(complement(X_39),meet(join(X_69,top),X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)),join(complement(join(X_39,zero)),meet(join(X_69,top),X_39))) ),[1,0],$fot(complement(X_39))]]) ).
cnf(refute_0_438,plain,
( complement(join(X_39,zero)) != complement(X_39)
| join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)) = join(complement(X_39),meet(join(X_69,top),X_39)) ),
inference(resolve,[$cnf( $equal(join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)),join(complement(join(X_39,zero)),meet(join(X_69,top),X_39))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)) = join(complement(X_39),meet(join(X_69,top),X_39)),
inference(resolve,[$cnf( $equal(complement(join(X_39,zero)),complement(X_39)) )],[refute_0_435,refute_0_438]) ).
cnf(refute_0_440,plain,
join(meet(join(X_69,top),X_39),complement(join(X_39,zero))) = join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(X_39,zero)))),bind(B,$fot(meet(join(X_69,top),X_39)))]]) ).
cnf(refute_0_441,plain,
( join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)) != join(complement(X_39),meet(join(X_69,top),X_39))
| join(meet(join(X_69,top),X_39),complement(join(X_39,zero))) != join(complement(join(X_39,zero)),meet(join(X_69,top),X_39))
| join(meet(join(X_69,top),X_39),complement(join(X_39,zero))) = join(complement(X_39),meet(join(X_69,top),X_39)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(join(X_69,top),X_39),complement(join(X_39,zero))))),bind(Y,$fot(join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)))),bind(Z,$fot(join(complement(X_39),meet(join(X_69,top),X_39))))]]) ).
cnf(refute_0_442,plain,
( join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)) != join(complement(X_39),meet(join(X_69,top),X_39))
| join(meet(join(X_69,top),X_39),complement(join(X_39,zero))) = join(complement(X_39),meet(join(X_69,top),X_39)) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_69,top),X_39),complement(join(X_39,zero))),join(complement(join(X_39,zero)),meet(join(X_69,top),X_39))) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
join(meet(join(X_69,top),X_39),complement(join(X_39,zero))) = join(complement(X_39),meet(join(X_69,top),X_39)),
inference(resolve,[$cnf( $equal(join(complement(join(X_39,zero)),meet(join(X_69,top),X_39)),join(complement(X_39),meet(join(X_69,top),X_39))) )],[refute_0_439,refute_0_442]) ).
cnf(refute_0_444,plain,
( join(X_69,top) != join(meet(join(X_69,top),X_39),complement(join(X_39,zero)))
| join(meet(join(X_69,top),X_39),complement(join(X_39,zero))) != join(complement(X_39),meet(join(X_69,top),X_39))
| join(X_69,top) = join(complement(X_39),meet(join(X_69,top),X_39)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_69,top),join(complement(X_39),meet(join(X_69,top),X_39))) ),[0],$fot(join(meet(join(X_69,top),X_39),complement(join(X_39,zero))))]]) ).
cnf(refute_0_445,plain,
( join(X_69,top) != join(meet(join(X_69,top),X_39),complement(join(X_39,zero)))
| join(X_69,top) = join(complement(X_39),meet(join(X_69,top),X_39)) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_69,top),X_39),complement(join(X_39,zero))),join(complement(X_39),meet(join(X_69,top),X_39))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
join(X_69,top) = join(complement(X_39),meet(join(X_69,top),X_39)),
inference(resolve,[$cnf( $equal(join(X_69,top),join(meet(join(X_69,top),X_39),complement(join(X_39,zero)))) )],[refute_0_368,refute_0_445]) ).
cnf(refute_0_447,plain,
( join(X_69,top) != join(complement(X_39),meet(join(X_69,top),X_39))
| join(complement(X_39),meet(join(X_69,top),X_39)) = join(X_69,top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_69,top))),bind(Y,$fot(join(complement(X_39),meet(join(X_69,top),X_39))))]]) ).
cnf(refute_0_448,plain,
join(complement(X_39),meet(join(X_69,top),X_39)) = join(X_69,top),
inference(resolve,[$cnf( $equal(join(X_69,top),join(complement(X_39),meet(join(X_69,top),X_39))) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
join(complement(X_19),meet(join(X_69,top),X_19)) = join(X_69,top),
inference(subst,[],[refute_0_448:[bind(X_39,$fot(X_19))]]) ).
cnf(refute_0_450,plain,
join(X_52,zero) = join(meet(join(X_52,zero),meet(top,X_52)),complement(join(meet(top,X_52),complement(join(X_52,zero))))),
inference(subst,[],[refute_0_30:[bind(X_38,$fot(join(X_52,zero))),bind(X_39,$fot(meet(top,X_52)))]]) ).
cnf(refute_0_451,plain,
top = join(meet(top,X_39),complement(join(complement(top),X_39))),
inference(subst,[],[refute_0_23:[bind(A,$fot(top)),bind(B,$fot(X_39))]]) ).
cnf(refute_0_452,plain,
( complement(top) != zero
| top != join(meet(top,X_39),complement(join(complement(top),X_39)))
| top = join(meet(top,X_39),complement(join(zero,X_39))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,X_39),complement(join(complement(top),X_39)))) ),[1,1,0,0],$fot(zero)]]) ).
cnf(refute_0_453,plain,
( top != join(meet(top,X_39),complement(join(complement(top),X_39)))
| top = join(meet(top,X_39),complement(join(zero,X_39))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_452]) ).
cnf(refute_0_454,plain,
top = join(meet(top,X_39),complement(join(zero,X_39))),
inference(resolve,[$cnf( $equal(top,join(meet(top,X_39),complement(join(complement(top),X_39)))) )],[refute_0_451,refute_0_453]) ).
cnf(refute_0_455,plain,
top = join(meet(top,X_52),complement(join(zero,X_52))),
inference(subst,[],[refute_0_454:[bind(X_39,$fot(X_52))]]) ).
cnf(refute_0_456,plain,
join(X_52,zero) = join(zero,X_52),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_52)),bind(B,$fot(zero))]]) ).
cnf(refute_0_457,plain,
( join(X_52,zero) != join(zero,X_52)
| join(zero,X_52) = join(X_52,zero) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_52,zero))),bind(Y,$fot(join(zero,X_52)))]]) ).
cnf(refute_0_458,plain,
join(zero,X_52) = join(X_52,zero),
inference(resolve,[$cnf( $equal(join(X_52,zero),join(zero,X_52)) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
( join(zero,X_52) != join(X_52,zero)
| top != join(meet(top,X_52),complement(join(zero,X_52)))
| top = join(meet(top,X_52),complement(join(X_52,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,X_52),complement(join(zero,X_52)))) ),[1,1,0],$fot(join(X_52,zero))]]) ).
cnf(refute_0_460,plain,
( top != join(meet(top,X_52),complement(join(zero,X_52)))
| top = join(meet(top,X_52),complement(join(X_52,zero))) ),
inference(resolve,[$cnf( $equal(join(zero,X_52),join(X_52,zero)) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
top = join(meet(top,X_52),complement(join(X_52,zero))),
inference(resolve,[$cnf( $equal(top,join(meet(top,X_52),complement(join(zero,X_52)))) )],[refute_0_455,refute_0_460]) ).
cnf(refute_0_462,plain,
( top != join(meet(top,X_52),complement(join(X_52,zero)))
| join(meet(top,X_52),complement(join(X_52,zero))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(meet(top,X_52),complement(join(X_52,zero)))))]]) ).
cnf(refute_0_463,plain,
join(meet(top,X_52),complement(join(X_52,zero))) = top,
inference(resolve,[$cnf( $equal(top,join(meet(top,X_52),complement(join(X_52,zero)))) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
( join(X_52,zero) != join(meet(join(X_52,zero),meet(top,X_52)),complement(join(meet(top,X_52),complement(join(X_52,zero)))))
| join(meet(top,X_52),complement(join(X_52,zero))) != top
| join(X_52,zero) = join(meet(join(X_52,zero),meet(top,X_52)),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_52,zero),join(meet(join(X_52,zero),meet(top,X_52)),complement(join(meet(top,X_52),complement(join(X_52,zero)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_465,plain,
( join(X_52,zero) != join(meet(join(X_52,zero),meet(top,X_52)),complement(join(meet(top,X_52),complement(join(X_52,zero)))))
| join(X_52,zero) = join(meet(join(X_52,zero),meet(top,X_52)),complement(top)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_52),complement(join(X_52,zero))),top) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
join(X_52,zero) = join(meet(join(X_52,zero),meet(top,X_52)),complement(top)),
inference(resolve,[$cnf( $equal(join(X_52,zero),join(meet(join(X_52,zero),meet(top,X_52)),complement(join(meet(top,X_52),complement(join(X_52,zero)))))) )],[refute_0_450,refute_0_465]) ).
cnf(refute_0_467,plain,
join(complement(top),meet(join(X_52,zero),meet(top,X_52))) = join(complement(top),meet(join(X_52,zero),meet(top,X_52))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(join(X_52,zero),meet(top,X_52))))]]) ).
cnf(refute_0_468,plain,
( complement(top) != zero
| join(complement(top),meet(join(X_52,zero),meet(top,X_52))) != join(complement(top),meet(join(X_52,zero),meet(top,X_52)))
| join(complement(top),meet(join(X_52,zero),meet(top,X_52))) = join(zero,meet(join(X_52,zero),meet(top,X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(join(X_52,zero),meet(top,X_52))),join(complement(top),meet(join(X_52,zero),meet(top,X_52)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_469,plain,
( complement(top) != zero
| join(complement(top),meet(join(X_52,zero),meet(top,X_52))) = join(zero,meet(join(X_52,zero),meet(top,X_52))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(X_52,zero),meet(top,X_52))),join(complement(top),meet(join(X_52,zero),meet(top,X_52)))) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
join(complement(top),meet(join(X_52,zero),meet(top,X_52))) = join(zero,meet(join(X_52,zero),meet(top,X_52))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_469]) ).
cnf(refute_0_471,plain,
join(meet(join(X_52,zero),meet(top,X_52)),complement(top)) = join(complement(top),meet(join(X_52,zero),meet(top,X_52))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(join(X_52,zero),meet(top,X_52))))]]) ).
cnf(refute_0_472,plain,
( join(complement(top),meet(join(X_52,zero),meet(top,X_52))) != join(zero,meet(join(X_52,zero),meet(top,X_52)))
| join(meet(join(X_52,zero),meet(top,X_52)),complement(top)) != join(complement(top),meet(join(X_52,zero),meet(top,X_52)))
| join(meet(join(X_52,zero),meet(top,X_52)),complement(top)) = join(zero,meet(join(X_52,zero),meet(top,X_52))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(join(X_52,zero),meet(top,X_52)),complement(top)))),bind(Y,$fot(join(complement(top),meet(join(X_52,zero),meet(top,X_52))))),bind(Z,$fot(join(zero,meet(join(X_52,zero),meet(top,X_52)))))]]) ).
cnf(refute_0_473,plain,
( join(complement(top),meet(join(X_52,zero),meet(top,X_52))) != join(zero,meet(join(X_52,zero),meet(top,X_52)))
| join(meet(join(X_52,zero),meet(top,X_52)),complement(top)) = join(zero,meet(join(X_52,zero),meet(top,X_52))) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_52,zero),meet(top,X_52)),complement(top)),join(complement(top),meet(join(X_52,zero),meet(top,X_52)))) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
join(meet(join(X_52,zero),meet(top,X_52)),complement(top)) = join(zero,meet(join(X_52,zero),meet(top,X_52))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(X_52,zero),meet(top,X_52))),join(zero,meet(join(X_52,zero),meet(top,X_52)))) )],[refute_0_470,refute_0_473]) ).
cnf(refute_0_475,plain,
( join(X_52,zero) != join(meet(join(X_52,zero),meet(top,X_52)),complement(top))
| join(meet(join(X_52,zero),meet(top,X_52)),complement(top)) != join(zero,meet(join(X_52,zero),meet(top,X_52)))
| join(X_52,zero) = join(zero,meet(join(X_52,zero),meet(top,X_52))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_52,zero),join(zero,meet(join(X_52,zero),meet(top,X_52)))) ),[0],$fot(join(meet(join(X_52,zero),meet(top,X_52)),complement(top)))]]) ).
cnf(refute_0_476,plain,
( join(X_52,zero) != join(meet(join(X_52,zero),meet(top,X_52)),complement(top))
| join(X_52,zero) = join(zero,meet(join(X_52,zero),meet(top,X_52))) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_52,zero),meet(top,X_52)),complement(top)),join(zero,meet(join(X_52,zero),meet(top,X_52)))) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
join(X_52,zero) = join(zero,meet(join(X_52,zero),meet(top,X_52))),
inference(resolve,[$cnf( $equal(join(X_52,zero),join(meet(join(X_52,zero),meet(top,X_52)),complement(top))) )],[refute_0_466,refute_0_476]) ).
cnf(refute_0_478,plain,
join(X_52,zero) = X_52,
inference(subst,[],[refute_0_430:[bind(X_64,$fot(X_52))]]) ).
cnf(refute_0_479,plain,
( join(X_52,zero) != X_52
| join(X_52,zero) != join(zero,meet(join(X_52,zero),meet(top,X_52)))
| X_52 = join(zero,meet(join(X_52,zero),meet(top,X_52))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_52,zero),join(zero,meet(join(X_52,zero),meet(top,X_52)))) ),[0],$fot(X_52)]]) ).
cnf(refute_0_480,plain,
( join(X_52,zero) != join(zero,meet(join(X_52,zero),meet(top,X_52)))
| X_52 = join(zero,meet(join(X_52,zero),meet(top,X_52))) ),
inference(resolve,[$cnf( $equal(join(X_52,zero),X_52) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
complement(complement(X_52)) = X_52,
inference(subst,[],[refute_0_417:[bind(X_63,$fot(X_52))]]) ).
cnf(refute_0_482,plain,
meet(X_52,X_52) = complement(complement(X_52)),
inference(subst,[],[refute_0_187:[bind(X_19,$fot(X_52))]]) ).
cnf(refute_0_483,plain,
( complement(complement(X_52)) != X_52
| meet(X_52,X_52) != complement(complement(X_52))
| meet(X_52,X_52) = X_52 ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(X_52,X_52))),bind(Y,$fot(complement(complement(X_52)))),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_484,plain,
( complement(complement(X_52)) != X_52
| meet(X_52,X_52) = X_52 ),
inference(resolve,[$cnf( $equal(meet(X_52,X_52),complement(complement(X_52))) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
meet(X_52,X_52) = X_52,
inference(resolve,[$cnf( $equal(complement(complement(X_52)),X_52) )],[refute_0_481,refute_0_484]) ).
cnf(refute_0_486,plain,
X_63 = join(meet(X_63,zero),complement(join(zero,complement(X_63)))),
inference(subst,[],[refute_0_30:[bind(X_38,$fot(X_63)),bind(X_39,$fot(zero))]]) ).
cnf(refute_0_487,plain,
meet(X_63,zero) = zero,
inference(subst,[],[refute_0_334:[bind(A,$fot(X_63))]]) ).
cnf(refute_0_488,plain,
( X_63 != join(meet(X_63,zero),complement(join(zero,complement(X_63))))
| meet(X_63,zero) != zero
| X_63 = join(zero,complement(join(zero,complement(X_63)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_63,join(meet(X_63,zero),complement(join(zero,complement(X_63))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_489,plain,
( X_63 != join(meet(X_63,zero),complement(join(zero,complement(X_63))))
| X_63 = join(zero,complement(join(zero,complement(X_63)))) ),
inference(resolve,[$cnf( $equal(meet(X_63,zero),zero) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
X_63 = join(zero,complement(join(zero,complement(X_63)))),
inference(resolve,[$cnf( $equal(X_63,join(meet(X_63,zero),complement(join(zero,complement(X_63))))) )],[refute_0_486,refute_0_489]) ).
cnf(refute_0_491,plain,
complement(join(zero,complement(X_63))) = meet(top,X_63),
inference(subst,[],[refute_0_107:[bind(B,$fot(X_63))]]) ).
cnf(refute_0_492,plain,
join(zero,complement(join(zero,complement(X_63)))) = complement(join(zero,complement(X_63))),
inference(subst,[],[refute_0_351:[bind(X_38,$fot(join(zero,complement(X_63))))]]) ).
cnf(refute_0_493,plain,
( complement(join(zero,complement(X_63))) != meet(top,X_63)
| join(zero,complement(join(zero,complement(X_63)))) != complement(join(zero,complement(X_63)))
| join(zero,complement(join(zero,complement(X_63)))) = meet(top,X_63) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(zero,complement(join(zero,complement(X_63)))))),bind(Y,$fot(complement(join(zero,complement(X_63))))),bind(Z,$fot(meet(top,X_63)))]]) ).
cnf(refute_0_494,plain,
( complement(join(zero,complement(X_63))) != meet(top,X_63)
| join(zero,complement(join(zero,complement(X_63)))) = meet(top,X_63) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(zero,complement(X_63)))),complement(join(zero,complement(X_63)))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
join(zero,complement(join(zero,complement(X_63)))) = meet(top,X_63),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_63))),meet(top,X_63)) )],[refute_0_491,refute_0_494]) ).
cnf(refute_0_496,plain,
( X_63 != join(zero,complement(join(zero,complement(X_63))))
| join(zero,complement(join(zero,complement(X_63)))) != meet(top,X_63)
| X_63 = meet(top,X_63) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_63,meet(top,X_63)) ),[0],$fot(join(zero,complement(join(zero,complement(X_63)))))]]) ).
cnf(refute_0_497,plain,
( X_63 != join(zero,complement(join(zero,complement(X_63))))
| X_63 = meet(top,X_63) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(zero,complement(X_63)))),meet(top,X_63)) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
X_63 = meet(top,X_63),
inference(resolve,[$cnf( $equal(X_63,join(zero,complement(join(zero,complement(X_63))))) )],[refute_0_490,refute_0_497]) ).
cnf(refute_0_499,plain,
( X_63 != meet(top,X_63)
| meet(top,X_63) = X_63 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_63)),bind(Y,$fot(meet(top,X_63)))]]) ).
cnf(refute_0_500,plain,
meet(top,X_63) = X_63,
inference(resolve,[$cnf( $equal(X_63,meet(top,X_63)) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
meet(top,X_52) = X_52,
inference(subst,[],[refute_0_500:[bind(X_63,$fot(X_52))]]) ).
cnf(refute_0_502,plain,
meet(X_52,meet(top,X_52)) = meet(X_52,meet(top,X_52)),
introduced(tautology,[refl,[$fot(meet(X_52,meet(top,X_52)))]]) ).
cnf(refute_0_503,plain,
( meet(X_52,meet(top,X_52)) != meet(X_52,meet(top,X_52))
| meet(top,X_52) != X_52
| meet(X_52,meet(top,X_52)) = meet(X_52,X_52) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_52,meet(top,X_52)),meet(X_52,meet(top,X_52))) ),[1,1],$fot(X_52)]]) ).
cnf(refute_0_504,plain,
( meet(top,X_52) != X_52
| meet(X_52,meet(top,X_52)) = meet(X_52,X_52) ),
inference(resolve,[$cnf( $equal(meet(X_52,meet(top,X_52)),meet(X_52,meet(top,X_52))) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
meet(X_52,meet(top,X_52)) = meet(X_52,X_52),
inference(resolve,[$cnf( $equal(meet(top,X_52),X_52) )],[refute_0_501,refute_0_504]) ).
cnf(refute_0_506,plain,
meet(join(X_52,zero),meet(top,X_52)) = meet(join(X_52,zero),meet(top,X_52)),
introduced(tautology,[refl,[$fot(meet(join(X_52,zero),meet(top,X_52)))]]) ).
cnf(refute_0_507,plain,
( join(X_52,zero) != X_52
| meet(join(X_52,zero),meet(top,X_52)) != meet(join(X_52,zero),meet(top,X_52))
| meet(join(X_52,zero),meet(top,X_52)) = meet(X_52,meet(top,X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_52,zero),meet(top,X_52)),meet(join(X_52,zero),meet(top,X_52))) ),[1,0],$fot(X_52)]]) ).
cnf(refute_0_508,plain,
( join(X_52,zero) != X_52
| meet(join(X_52,zero),meet(top,X_52)) = meet(X_52,meet(top,X_52)) ),
inference(resolve,[$cnf( $equal(meet(join(X_52,zero),meet(top,X_52)),meet(join(X_52,zero),meet(top,X_52))) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
meet(join(X_52,zero),meet(top,X_52)) = meet(X_52,meet(top,X_52)),
inference(resolve,[$cnf( $equal(join(X_52,zero),X_52) )],[refute_0_478,refute_0_508]) ).
cnf(refute_0_510,plain,
( meet(X_52,meet(top,X_52)) != meet(X_52,X_52)
| meet(join(X_52,zero),meet(top,X_52)) != meet(X_52,meet(top,X_52))
| meet(join(X_52,zero),meet(top,X_52)) = meet(X_52,X_52) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(join(X_52,zero),meet(top,X_52)))),bind(Y,$fot(meet(X_52,meet(top,X_52)))),bind(Z,$fot(meet(X_52,X_52)))]]) ).
cnf(refute_0_511,plain,
( meet(X_52,meet(top,X_52)) != meet(X_52,X_52)
| meet(join(X_52,zero),meet(top,X_52)) = meet(X_52,X_52) ),
inference(resolve,[$cnf( $equal(meet(join(X_52,zero),meet(top,X_52)),meet(X_52,meet(top,X_52))) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
meet(join(X_52,zero),meet(top,X_52)) = meet(X_52,X_52),
inference(resolve,[$cnf( $equal(meet(X_52,meet(top,X_52)),meet(X_52,X_52)) )],[refute_0_505,refute_0_511]) ).
cnf(refute_0_513,plain,
( meet(X_52,X_52) != X_52
| meet(join(X_52,zero),meet(top,X_52)) != meet(X_52,X_52)
| meet(join(X_52,zero),meet(top,X_52)) = X_52 ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(join(X_52,zero),meet(top,X_52)))),bind(Y,$fot(meet(X_52,X_52))),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_514,plain,
( meet(X_52,X_52) != X_52
| meet(join(X_52,zero),meet(top,X_52)) = X_52 ),
inference(resolve,[$cnf( $equal(meet(join(X_52,zero),meet(top,X_52)),meet(X_52,X_52)) )],[refute_0_512,refute_0_513]) ).
cnf(refute_0_515,plain,
meet(join(X_52,zero),meet(top,X_52)) = X_52,
inference(resolve,[$cnf( $equal(meet(X_52,X_52),X_52) )],[refute_0_485,refute_0_514]) ).
cnf(refute_0_516,plain,
join(zero,meet(join(X_52,zero),meet(top,X_52))) = join(zero,meet(join(X_52,zero),meet(top,X_52))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(X_52,zero),meet(top,X_52))))]]) ).
cnf(refute_0_517,plain,
( join(zero,meet(join(X_52,zero),meet(top,X_52))) != join(zero,meet(join(X_52,zero),meet(top,X_52)))
| meet(join(X_52,zero),meet(top,X_52)) != X_52
| join(zero,meet(join(X_52,zero),meet(top,X_52))) = join(zero,X_52) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(X_52,zero),meet(top,X_52))),join(zero,meet(join(X_52,zero),meet(top,X_52)))) ),[1,1],$fot(X_52)]]) ).
cnf(refute_0_518,plain,
( meet(join(X_52,zero),meet(top,X_52)) != X_52
| join(zero,meet(join(X_52,zero),meet(top,X_52))) = join(zero,X_52) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(X_52,zero),meet(top,X_52))),join(zero,meet(join(X_52,zero),meet(top,X_52)))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
join(zero,meet(join(X_52,zero),meet(top,X_52))) = join(zero,X_52),
inference(resolve,[$cnf( $equal(meet(join(X_52,zero),meet(top,X_52)),X_52) )],[refute_0_515,refute_0_518]) ).
cnf(refute_0_520,plain,
( X_52 != join(zero,meet(join(X_52,zero),meet(top,X_52)))
| join(zero,meet(join(X_52,zero),meet(top,X_52))) != join(zero,X_52)
| X_52 = join(zero,X_52) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_52,join(zero,X_52)) ),[0],$fot(join(zero,meet(join(X_52,zero),meet(top,X_52))))]]) ).
cnf(refute_0_521,plain,
( X_52 != join(zero,meet(join(X_52,zero),meet(top,X_52)))
| X_52 = join(zero,X_52) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(X_52,zero),meet(top,X_52))),join(zero,X_52)) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
( join(X_52,zero) != join(zero,meet(join(X_52,zero),meet(top,X_52)))
| X_52 = join(zero,X_52) ),
inference(resolve,[$cnf( $equal(X_52,join(zero,meet(join(X_52,zero),meet(top,X_52)))) )],[refute_0_480,refute_0_521]) ).
cnf(refute_0_523,plain,
X_52 = join(zero,X_52),
inference(resolve,[$cnf( $equal(join(X_52,zero),join(zero,meet(join(X_52,zero),meet(top,X_52)))) )],[refute_0_477,refute_0_522]) ).
cnf(refute_0_524,plain,
( X_52 != join(zero,X_52)
| join(zero,X_52) = X_52 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_52)),bind(Y,$fot(join(zero,X_52)))]]) ).
cnf(refute_0_525,plain,
join(zero,X_52) = X_52,
inference(resolve,[$cnf( $equal(X_52,join(zero,X_52)) )],[refute_0_523,refute_0_524]) ).
cnf(refute_0_526,plain,
join(zero,join(complement(X_19),meet(join(X_69,top),X_19))) = join(complement(X_19),meet(join(X_69,top),X_19)),
inference(subst,[],[refute_0_525:[bind(X_52,$fot(join(complement(X_19),meet(join(X_69,top),X_19))))]]) ).
cnf(refute_0_527,plain,
( join(complement(X_19),meet(join(X_69,top),X_19)) != join(X_69,top)
| join(zero,join(complement(X_19),meet(join(X_69,top),X_19))) != join(complement(X_19),meet(join(X_69,top),X_19))
| join(zero,join(complement(X_19),meet(join(X_69,top),X_19))) = join(X_69,top) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(zero,join(complement(X_19),meet(join(X_69,top),X_19))))),bind(Y,$fot(join(complement(X_19),meet(join(X_69,top),X_19)))),bind(Z,$fot(join(X_69,top)))]]) ).
cnf(refute_0_528,plain,
( join(complement(X_19),meet(join(X_69,top),X_19)) != join(X_69,top)
| join(zero,join(complement(X_19),meet(join(X_69,top),X_19))) = join(X_69,top) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_19),meet(join(X_69,top),X_19))),join(complement(X_19),meet(join(X_69,top),X_19))) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
join(zero,join(complement(X_19),meet(join(X_69,top),X_19))) = join(X_69,top),
inference(resolve,[$cnf( $equal(join(complement(X_19),meet(join(X_69,top),X_19)),join(X_69,top)) )],[refute_0_449,refute_0_528]) ).
cnf(refute_0_530,plain,
( join(zero,join(complement(X_19),meet(join(X_69,top),X_19))) != join(X_69,top)
| top != join(zero,join(complement(X_19),meet(join(X_69,top),X_19)))
| top = join(X_69,top) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,join(complement(X_19),meet(join(X_69,top),X_19)))) ),[1],$fot(join(X_69,top))]]) ).
cnf(refute_0_531,plain,
( top != join(zero,join(complement(X_19),meet(join(X_69,top),X_19)))
| top = join(X_69,top) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_19),meet(join(X_69,top),X_19))),join(X_69,top)) )],[refute_0_529,refute_0_530]) ).
cnf(refute_0_532,plain,
top = join(X_69,top),
inference(resolve,[$cnf( $equal(top,join(zero,join(complement(X_19),meet(join(X_69,top),X_19)))) )],[refute_0_364,refute_0_531]) ).
cnf(refute_0_533,plain,
top = join(B,top),
inference(subst,[],[refute_0_532:[bind(X_69,$fot(B))]]) ).
cnf(refute_0_534,plain,
( top != join(B,top)
| join(B,top) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(B,top)))]]) ).
cnf(refute_0_535,plain,
join(B,top) = top,
inference(resolve,[$cnf( $equal(top,join(B,top)) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
( join(B,top) != top
| join(top,B) != join(B,top)
| join(top,B) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(top,B),join(B,top)) ),[1],$fot(top)]]) ).
cnf(refute_0_537,plain,
( join(top,B) != join(B,top)
| join(top,B) = top ),
inference(resolve,[$cnf( $equal(join(B,top),top) )],[refute_0_535,refute_0_536]) ).
cnf(refute_0_538,plain,
join(top,B) = top,
inference(resolve,[$cnf( $equal(join(top,B),join(B,top)) )],[refute_0_57,refute_0_537]) ).
cnf(refute_0_539,plain,
join(top,X_104) = top,
inference(subst,[],[refute_0_538:[bind(B,$fot(X_104))]]) ).
cnf(refute_0_540,plain,
( join(X_102,join(complement(X_102),X_104)) != join(top,X_104)
| join(top,X_104) != top
| join(X_102,join(complement(X_102),X_104)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_102,join(complement(X_102),X_104)),top) ),[0],$fot(join(top,X_104))]]) ).
cnf(refute_0_541,plain,
( join(X_102,join(complement(X_102),X_104)) != join(top,X_104)
| join(X_102,join(complement(X_102),X_104)) = top ),
inference(resolve,[$cnf( $equal(join(top,X_104),top) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
join(X_102,join(complement(X_102),X_104)) = top,
inference(resolve,[$cnf( $equal(join(X_102,join(complement(X_102),X_104)),join(top,X_104)) )],[refute_0_56,refute_0_541]) ).
cnf(refute_0_543,plain,
join(complement(X_38),join(complement(complement(X_38)),X_107)) = top,
inference(subst,[],[refute_0_542:[bind(X_102,$fot(complement(X_38))),bind(X_104,$fot(X_107))]]) ).
cnf(refute_0_544,plain,
( X_38 != join(meet(join(complement(complement(X_38)),X_107),X_38),complement(join(complement(X_38),join(complement(complement(X_38)),X_107))))
| join(complement(X_38),join(complement(complement(X_38)),X_107)) != top
| X_38 = join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_38,join(meet(join(complement(complement(X_38)),X_107),X_38),complement(join(complement(X_38),join(complement(complement(X_38)),X_107))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_545,plain,
( X_38 != join(meet(join(complement(complement(X_38)),X_107),X_38),complement(join(complement(X_38),join(complement(complement(X_38)),X_107))))
| X_38 = join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_38),join(complement(complement(X_38)),X_107)),top) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
X_38 = join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)),
inference(resolve,[$cnf( $equal(X_38,join(meet(join(complement(complement(X_38)),X_107),X_38),complement(join(complement(X_38),join(complement(complement(X_38)),X_107))))) )],[refute_0_49,refute_0_545]) ).
cnf(refute_0_547,plain,
join(zero,meet(X_38,join(X_38,X_107))) = meet(X_38,join(X_38,X_107)),
inference(subst,[],[refute_0_525:[bind(X_52,$fot(meet(X_38,join(X_38,X_107))))]]) ).
cnf(refute_0_548,plain,
complement(complement(X_38)) = X_38,
inference(subst,[],[refute_0_417:[bind(X_63,$fot(X_38))]]) ).
cnf(refute_0_549,plain,
join(complement(complement(X_38)),X_107) = join(complement(complement(X_38)),X_107),
introduced(tautology,[refl,[$fot(join(complement(complement(X_38)),X_107))]]) ).
cnf(refute_0_550,plain,
( complement(complement(X_38)) != X_38
| join(complement(complement(X_38)),X_107) != join(complement(complement(X_38)),X_107)
| join(complement(complement(X_38)),X_107) = join(X_38,X_107) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_38)),X_107),join(complement(complement(X_38)),X_107)) ),[1,0],$fot(X_38)]]) ).
cnf(refute_0_551,plain,
( complement(complement(X_38)) != X_38
| join(complement(complement(X_38)),X_107) = join(X_38,X_107) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_38)),X_107),join(complement(complement(X_38)),X_107)) )],[refute_0_549,refute_0_550]) ).
cnf(refute_0_552,plain,
join(complement(complement(X_38)),X_107) = join(X_38,X_107),
inference(resolve,[$cnf( $equal(complement(complement(X_38)),X_38) )],[refute_0_548,refute_0_551]) ).
cnf(refute_0_553,plain,
meet(X_38,join(complement(complement(X_38)),X_107)) = meet(X_38,join(complement(complement(X_38)),X_107)),
introduced(tautology,[refl,[$fot(meet(X_38,join(complement(complement(X_38)),X_107)))]]) ).
cnf(refute_0_554,plain,
( join(complement(complement(X_38)),X_107) != join(X_38,X_107)
| meet(X_38,join(complement(complement(X_38)),X_107)) != meet(X_38,join(complement(complement(X_38)),X_107))
| meet(X_38,join(complement(complement(X_38)),X_107)) = meet(X_38,join(X_38,X_107)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_38,join(complement(complement(X_38)),X_107)),meet(X_38,join(complement(complement(X_38)),X_107))) ),[1,1],$fot(join(X_38,X_107))]]) ).
cnf(refute_0_555,plain,
( join(complement(complement(X_38)),X_107) != join(X_38,X_107)
| meet(X_38,join(complement(complement(X_38)),X_107)) = meet(X_38,join(X_38,X_107)) ),
inference(resolve,[$cnf( $equal(meet(X_38,join(complement(complement(X_38)),X_107)),meet(X_38,join(complement(complement(X_38)),X_107))) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
meet(X_38,join(complement(complement(X_38)),X_107)) = meet(X_38,join(X_38,X_107)),
inference(resolve,[$cnf( $equal(join(complement(complement(X_38)),X_107),join(X_38,X_107)) )],[refute_0_552,refute_0_555]) ).
cnf(refute_0_557,plain,
( meet(X_18,X_19) != meet(X_19,X_18)
| meet(X_19,X_18) = meet(X_18,X_19) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_18,X_19))),bind(Y,$fot(meet(X_19,X_18)))]]) ).
cnf(refute_0_558,plain,
meet(X_19,X_18) = meet(X_18,X_19),
inference(resolve,[$cnf( $equal(meet(X_18,X_19),meet(X_19,X_18)) )],[refute_0_42,refute_0_557]) ).
cnf(refute_0_559,plain,
meet(join(complement(complement(X_38)),X_107),X_38) = meet(X_38,join(complement(complement(X_38)),X_107)),
inference(subst,[],[refute_0_558:[bind(X_18,$fot(X_38)),bind(X_19,$fot(join(complement(complement(X_38)),X_107)))]]) ).
cnf(refute_0_560,plain,
( meet(X_38,join(complement(complement(X_38)),X_107)) != meet(X_38,join(X_38,X_107))
| meet(join(complement(complement(X_38)),X_107),X_38) != meet(X_38,join(complement(complement(X_38)),X_107))
| meet(join(complement(complement(X_38)),X_107),X_38) = meet(X_38,join(X_38,X_107)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(join(complement(complement(X_38)),X_107),X_38))),bind(Y,$fot(meet(X_38,join(complement(complement(X_38)),X_107)))),bind(Z,$fot(meet(X_38,join(X_38,X_107))))]]) ).
cnf(refute_0_561,plain,
( meet(X_38,join(complement(complement(X_38)),X_107)) != meet(X_38,join(X_38,X_107))
| meet(join(complement(complement(X_38)),X_107),X_38) = meet(X_38,join(X_38,X_107)) ),
inference(resolve,[$cnf( $equal(meet(join(complement(complement(X_38)),X_107),X_38),meet(X_38,join(complement(complement(X_38)),X_107))) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
meet(join(complement(complement(X_38)),X_107),X_38) = meet(X_38,join(X_38,X_107)),
inference(resolve,[$cnf( $equal(meet(X_38,join(complement(complement(X_38)),X_107)),meet(X_38,join(X_38,X_107))) )],[refute_0_556,refute_0_561]) ).
cnf(refute_0_563,plain,
join(zero,meet(join(complement(complement(X_38)),X_107),X_38)) = join(zero,meet(join(complement(complement(X_38)),X_107),X_38)),
introduced(tautology,[refl,[$fot(join(zero,meet(join(complement(complement(X_38)),X_107),X_38)))]]) ).
cnf(refute_0_564,plain,
( join(zero,meet(join(complement(complement(X_38)),X_107),X_38)) != join(zero,meet(join(complement(complement(X_38)),X_107),X_38))
| meet(join(complement(complement(X_38)),X_107),X_38) != meet(X_38,join(X_38,X_107))
| join(zero,meet(join(complement(complement(X_38)),X_107),X_38)) = join(zero,meet(X_38,join(X_38,X_107))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(complement(complement(X_38)),X_107),X_38)),join(zero,meet(join(complement(complement(X_38)),X_107),X_38))) ),[1,1],$fot(meet(X_38,join(X_38,X_107)))]]) ).
cnf(refute_0_565,plain,
( meet(join(complement(complement(X_38)),X_107),X_38) != meet(X_38,join(X_38,X_107))
| join(zero,meet(join(complement(complement(X_38)),X_107),X_38)) = join(zero,meet(X_38,join(X_38,X_107))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(complement(X_38)),X_107),X_38)),join(zero,meet(join(complement(complement(X_38)),X_107),X_38))) )],[refute_0_563,refute_0_564]) ).
cnf(refute_0_566,plain,
join(zero,meet(join(complement(complement(X_38)),X_107),X_38)) = join(zero,meet(X_38,join(X_38,X_107))),
inference(resolve,[$cnf( $equal(meet(join(complement(complement(X_38)),X_107),X_38),meet(X_38,join(X_38,X_107))) )],[refute_0_562,refute_0_565]) ).
cnf(refute_0_567,plain,
join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) = join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)))]]) ).
cnf(refute_0_568,plain,
( complement(top) != zero
| join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) != join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38))
| join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) = join(zero,meet(join(complement(complement(X_38)),X_107),X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)),join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_569,plain,
( complement(top) != zero
| join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) = join(zero,meet(join(complement(complement(X_38)),X_107),X_38)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)),join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38))) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) = join(zero,meet(join(complement(complement(X_38)),X_107),X_38)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_569]) ).
cnf(refute_0_571,plain,
( join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) != join(zero,meet(join(complement(complement(X_38)),X_107),X_38))
| join(zero,meet(join(complement(complement(X_38)),X_107),X_38)) != join(zero,meet(X_38,join(X_38,X_107)))
| join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) = join(zero,meet(X_38,join(X_38,X_107))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)))),bind(Y,$fot(join(zero,meet(join(complement(complement(X_38)),X_107),X_38)))),bind(Z,$fot(join(zero,meet(X_38,join(X_38,X_107)))))]]) ).
cnf(refute_0_572,plain,
( join(zero,meet(join(complement(complement(X_38)),X_107),X_38)) != join(zero,meet(X_38,join(X_38,X_107)))
| join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) = join(zero,meet(X_38,join(X_38,X_107))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)),join(zero,meet(join(complement(complement(X_38)),X_107),X_38))) )],[refute_0_570,refute_0_571]) ).
cnf(refute_0_573,plain,
join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) = join(zero,meet(X_38,join(X_38,X_107))),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(complement(X_38)),X_107),X_38)),join(zero,meet(X_38,join(X_38,X_107)))) )],[refute_0_566,refute_0_572]) ).
cnf(refute_0_574,plain,
( join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) != join(zero,meet(X_38,join(X_38,X_107)))
| join(zero,meet(X_38,join(X_38,X_107))) != meet(X_38,join(X_38,X_107))
| join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) = meet(X_38,join(X_38,X_107)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)))),bind(Y,$fot(join(zero,meet(X_38,join(X_38,X_107))))),bind(Z,$fot(meet(X_38,join(X_38,X_107))))]]) ).
cnf(refute_0_575,plain,
( join(zero,meet(X_38,join(X_38,X_107))) != meet(X_38,join(X_38,X_107))
| join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) = meet(X_38,join(X_38,X_107)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)),join(zero,meet(X_38,join(X_38,X_107)))) )],[refute_0_573,refute_0_574]) ).
cnf(refute_0_576,plain,
join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) = meet(X_38,join(X_38,X_107)),
inference(resolve,[$cnf( $equal(join(zero,meet(X_38,join(X_38,X_107))),meet(X_38,join(X_38,X_107))) )],[refute_0_547,refute_0_575]) ).
cnf(refute_0_577,plain,
join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)) = join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(join(complement(complement(X_38)),X_107),X_38)))]]) ).
cnf(refute_0_578,plain,
( join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) != meet(X_38,join(X_38,X_107))
| join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)) != join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38))
| join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)) = meet(X_38,join(X_38,X_107)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)))),bind(Y,$fot(join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)))),bind(Z,$fot(meet(X_38,join(X_38,X_107))))]]) ).
cnf(refute_0_579,plain,
( join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)) != meet(X_38,join(X_38,X_107))
| join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)) = meet(X_38,join(X_38,X_107)) ),
inference(resolve,[$cnf( $equal(join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)),join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38))) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)) = meet(X_38,join(X_38,X_107)),
inference(resolve,[$cnf( $equal(join(complement(top),meet(join(complement(complement(X_38)),X_107),X_38)),meet(X_38,join(X_38,X_107))) )],[refute_0_576,refute_0_579]) ).
cnf(refute_0_581,plain,
( X_38 != join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top))
| join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)) != meet(X_38,join(X_38,X_107))
| X_38 = meet(X_38,join(X_38,X_107)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_38,meet(X_38,join(X_38,X_107))) ),[0],$fot(join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)))]]) ).
cnf(refute_0_582,plain,
( X_38 != join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top))
| X_38 = meet(X_38,join(X_38,X_107)) ),
inference(resolve,[$cnf( $equal(join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top)),meet(X_38,join(X_38,X_107))) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
X_38 = meet(X_38,join(X_38,X_107)),
inference(resolve,[$cnf( $equal(X_38,join(meet(join(complement(complement(X_38)),X_107),X_38),complement(top))) )],[refute_0_546,refute_0_582]) ).
cnf(refute_0_584,plain,
X_109 = meet(X_109,join(X_109,X_108)),
inference(subst,[],[refute_0_583:[bind(X_107,$fot(X_108)),bind(X_38,$fot(X_109))]]) ).
cnf(refute_0_585,plain,
join(X_108,X_109) = join(X_109,X_108),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_108)),bind(B,$fot(X_109))]]) ).
cnf(refute_0_586,plain,
( join(X_108,X_109) != join(X_109,X_108)
| join(X_109,X_108) = join(X_108,X_109) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_108,X_109))),bind(Y,$fot(join(X_109,X_108)))]]) ).
cnf(refute_0_587,plain,
join(X_109,X_108) = join(X_108,X_109),
inference(resolve,[$cnf( $equal(join(X_108,X_109),join(X_109,X_108)) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
( X_109 != meet(X_109,join(X_109,X_108))
| join(X_109,X_108) != join(X_108,X_109)
| X_109 = meet(X_109,join(X_108,X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(X_109,meet(X_109,join(X_109,X_108))) ),[1,1],$fot(join(X_108,X_109))]]) ).
cnf(refute_0_589,plain,
( X_109 != meet(X_109,join(X_109,X_108))
| X_109 = meet(X_109,join(X_108,X_109)) ),
inference(resolve,[$cnf( $equal(join(X_109,X_108),join(X_108,X_109)) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
X_109 = meet(X_109,join(X_108,X_109)),
inference(resolve,[$cnf( $equal(X_109,meet(X_109,join(X_109,X_108))) )],[refute_0_584,refute_0_589]) ).
cnf(refute_0_591,plain,
composition(complement(sk1),top) = meet(composition(complement(sk1),top),join(complement(sk1),composition(complement(sk1),top))),
inference(subst,[],[refute_0_590:[bind(X_108,$fot(complement(sk1))),bind(X_109,$fot(composition(complement(sk1),top)))]]) ).
cnf(refute_0_592,plain,
join(complement(sk1),composition(converse(converse(complement(sk1))),complement(composition(converse(complement(sk1)),sk1)))) = complement(sk1),
inference(subst,[],[refute_0_130:[bind(A,$fot(converse(complement(sk1)))),bind(B,$fot(sk1))]]) ).
cnf(refute_0_593,plain,
converse(composition(converse(sk1),complement(sk1))) = composition(converse(complement(sk1)),converse(converse(sk1))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(sk1))),bind(B,$fot(complement(sk1)))]]) ).
cnf(refute_0_594,plain,
join(complement(top),composition(converse(sk1),complement(composition(sk1,top)))) = complement(top),
inference(subst,[],[refute_0_130:[bind(A,$fot(sk1)),bind(B,$fot(top))]]) ).
cnf(refute_0_595,plain,
( composition(sk1,top) != sk1
| join(complement(top),composition(converse(sk1),complement(composition(sk1,top)))) != complement(top)
| join(complement(top),composition(converse(sk1),complement(sk1))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(sk1),complement(composition(sk1,top)))),complement(top)) ),[0,1,1,0],$fot(sk1)]]) ).
cnf(refute_0_596,plain,
( join(complement(top),composition(converse(sk1),complement(composition(sk1,top)))) != complement(top)
| join(complement(top),composition(converse(sk1),complement(sk1))) = complement(top) ),
inference(resolve,[$cnf( $equal(composition(sk1,top),sk1) )],[goals_14,refute_0_595]) ).
cnf(refute_0_597,plain,
join(complement(top),composition(converse(sk1),complement(sk1))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(sk1),complement(composition(sk1,top)))),complement(top)) )],[refute_0_594,refute_0_596]) ).
cnf(refute_0_598,plain,
join(complement(top),composition(converse(sk1),complement(sk1))) = join(complement(top),composition(converse(sk1),complement(sk1))),
introduced(tautology,[refl,[$fot(join(complement(top),composition(converse(sk1),complement(sk1))))]]) ).
cnf(refute_0_599,plain,
( complement(top) != zero
| join(complement(top),composition(converse(sk1),complement(sk1))) != join(complement(top),composition(converse(sk1),complement(sk1)))
| join(complement(top),composition(converse(sk1),complement(sk1))) = join(zero,composition(converse(sk1),complement(sk1))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(sk1),complement(sk1))),join(complement(top),composition(converse(sk1),complement(sk1)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_600,plain,
( complement(top) != zero
| join(complement(top),composition(converse(sk1),complement(sk1))) = join(zero,composition(converse(sk1),complement(sk1))) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(sk1),complement(sk1))),join(complement(top),composition(converse(sk1),complement(sk1)))) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
join(complement(top),composition(converse(sk1),complement(sk1))) = join(zero,composition(converse(sk1),complement(sk1))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_600]) ).
cnf(refute_0_602,plain,
( join(complement(top),composition(converse(sk1),complement(sk1))) != complement(top)
| join(complement(top),composition(converse(sk1),complement(sk1))) != join(zero,composition(converse(sk1),complement(sk1)))
| join(zero,composition(converse(sk1),complement(sk1))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(sk1),complement(sk1))),complement(top)) ),[0],$fot(join(zero,composition(converse(sk1),complement(sk1))))]]) ).
cnf(refute_0_603,plain,
( join(complement(top),composition(converse(sk1),complement(sk1))) != complement(top)
| join(zero,composition(converse(sk1),complement(sk1))) = complement(top) ),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(sk1),complement(sk1))),join(zero,composition(converse(sk1),complement(sk1)))) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
( complement(top) != zero
| join(zero,composition(converse(sk1),complement(sk1))) != complement(top)
| join(zero,composition(converse(sk1),complement(sk1))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(sk1),complement(sk1))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_605,plain,
( join(zero,composition(converse(sk1),complement(sk1))) != complement(top)
| join(zero,composition(converse(sk1),complement(sk1))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_604]) ).
cnf(refute_0_606,plain,
( join(complement(top),composition(converse(sk1),complement(sk1))) != complement(top)
| join(zero,composition(converse(sk1),complement(sk1))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(sk1),complement(sk1))),complement(top)) )],[refute_0_603,refute_0_605]) ).
cnf(refute_0_607,plain,
join(zero,composition(converse(sk1),complement(sk1))) = zero,
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(sk1),complement(sk1))),complement(top)) )],[refute_0_597,refute_0_606]) ).
cnf(refute_0_608,plain,
join(zero,composition(converse(sk1),complement(sk1))) = composition(converse(sk1),complement(sk1)),
inference(subst,[],[refute_0_525:[bind(X_52,$fot(composition(converse(sk1),complement(sk1))))]]) ).
cnf(refute_0_609,plain,
( join(zero,composition(converse(sk1),complement(sk1))) != composition(converse(sk1),complement(sk1))
| join(zero,composition(converse(sk1),complement(sk1))) != zero
| composition(converse(sk1),complement(sk1)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(sk1),complement(sk1))),zero) ),[0],$fot(composition(converse(sk1),complement(sk1)))]]) ).
cnf(refute_0_610,plain,
( join(zero,composition(converse(sk1),complement(sk1))) != zero
| composition(converse(sk1),complement(sk1)) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(sk1),complement(sk1))),composition(converse(sk1),complement(sk1))) )],[refute_0_608,refute_0_609]) ).
cnf(refute_0_611,plain,
composition(converse(sk1),complement(sk1)) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(sk1),complement(sk1))),zero) )],[refute_0_607,refute_0_610]) ).
cnf(refute_0_612,plain,
( composition(converse(sk1),complement(sk1)) != zero
| converse(composition(converse(sk1),complement(sk1))) != composition(converse(complement(sk1)),converse(converse(sk1)))
| converse(zero) = composition(converse(complement(sk1)),converse(converse(sk1))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(sk1),complement(sk1))),composition(converse(complement(sk1)),converse(converse(sk1)))) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_613,plain,
( converse(composition(converse(sk1),complement(sk1))) != composition(converse(complement(sk1)),converse(converse(sk1)))
| converse(zero) = composition(converse(complement(sk1)),converse(converse(sk1))) ),
inference(resolve,[$cnf( $equal(composition(converse(sk1),complement(sk1)),zero) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
converse(zero) = composition(converse(complement(sk1)),converse(converse(sk1))),
inference(resolve,[$cnf( $equal(converse(composition(converse(sk1),complement(sk1))),composition(converse(complement(sk1)),converse(converse(sk1)))) )],[refute_0_593,refute_0_613]) ).
cnf(refute_0_615,plain,
converse(composition(converse(sk1),complement(sk1))) = composition(converse(complement(sk1)),sk1),
inference(subst,[],[refute_0_135:[bind(A,$fot(sk1)),bind(X_5,$fot(complement(sk1)))]]) ).
cnf(refute_0_616,plain,
( converse(composition(A,B)) != composition(converse(B),converse(A))
| composition(converse(B),converse(A)) = converse(composition(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(A,B)))),bind(Y,$fot(composition(converse(B),converse(A))))]]) ).
cnf(refute_0_617,plain,
composition(converse(B),converse(A)) = converse(composition(A,B)),
inference(resolve,[$cnf( $equal(converse(composition(A,B)),composition(converse(B),converse(A))) )],[converse_multiplicativity_10,refute_0_616]) ).
cnf(refute_0_618,plain,
composition(converse(complement(sk1)),converse(converse(sk1))) = converse(composition(converse(sk1),complement(sk1))),
inference(subst,[],[refute_0_617:[bind(A,$fot(converse(sk1))),bind(B,$fot(complement(sk1)))]]) ).
cnf(refute_0_619,plain,
( composition(converse(complement(sk1)),converse(converse(sk1))) != converse(composition(converse(sk1),complement(sk1)))
| converse(composition(converse(sk1),complement(sk1))) != composition(converse(complement(sk1)),sk1)
| composition(converse(complement(sk1)),converse(converse(sk1))) = composition(converse(complement(sk1)),sk1) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(composition(converse(complement(sk1)),converse(converse(sk1))))),bind(Y,$fot(converse(composition(converse(sk1),complement(sk1))))),bind(Z,$fot(composition(converse(complement(sk1)),sk1)))]]) ).
cnf(refute_0_620,plain,
( converse(composition(converse(sk1),complement(sk1))) != composition(converse(complement(sk1)),sk1)
| composition(converse(complement(sk1)),converse(converse(sk1))) = composition(converse(complement(sk1)),sk1) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(sk1)),converse(converse(sk1))),converse(composition(converse(sk1),complement(sk1)))) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
composition(converse(complement(sk1)),converse(converse(sk1))) = composition(converse(complement(sk1)),sk1),
inference(resolve,[$cnf( $equal(converse(composition(converse(sk1),complement(sk1))),composition(converse(complement(sk1)),sk1)) )],[refute_0_615,refute_0_620]) ).
cnf(refute_0_622,plain,
( composition(converse(complement(sk1)),converse(converse(sk1))) != composition(converse(complement(sk1)),sk1)
| converse(zero) != composition(converse(complement(sk1)),converse(converse(sk1)))
| converse(zero) = composition(converse(complement(sk1)),sk1) ),
introduced(tautology,[equality,[$cnf( $equal(converse(zero),composition(converse(complement(sk1)),converse(converse(sk1)))) ),[1],$fot(composition(converse(complement(sk1)),sk1))]]) ).
cnf(refute_0_623,plain,
( converse(zero) != composition(converse(complement(sk1)),converse(converse(sk1)))
| converse(zero) = composition(converse(complement(sk1)),sk1) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(sk1)),converse(converse(sk1))),composition(converse(complement(sk1)),sk1)) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
converse(zero) = composition(converse(complement(sk1)),sk1),
inference(resolve,[$cnf( $equal(converse(zero),composition(converse(complement(sk1)),converse(converse(sk1)))) )],[refute_0_614,refute_0_623]) ).
cnf(refute_0_625,plain,
( converse(zero) != composition(converse(complement(sk1)),sk1)
| composition(converse(complement(sk1)),sk1) = converse(zero) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(zero))),bind(Y,$fot(composition(converse(complement(sk1)),sk1)))]]) ).
cnf(refute_0_626,plain,
composition(converse(complement(sk1)),sk1) = converse(zero),
inference(resolve,[$cnf( $equal(converse(zero),composition(converse(complement(sk1)),sk1)) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
( composition(converse(complement(sk1)),sk1) != converse(zero)
| join(complement(sk1),composition(converse(converse(complement(sk1))),complement(composition(converse(complement(sk1)),sk1)))) != complement(sk1)
| join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))) = complement(sk1) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(sk1),composition(converse(converse(complement(sk1))),complement(composition(converse(complement(sk1)),sk1)))),complement(sk1)) ),[0,1,1,0],$fot(converse(zero))]]) ).
cnf(refute_0_628,plain,
( join(complement(sk1),composition(converse(converse(complement(sk1))),complement(composition(converse(complement(sk1)),sk1)))) != complement(sk1)
| join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))) = complement(sk1) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(sk1)),sk1),converse(zero)) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))) = complement(sk1),
inference(resolve,[$cnf( $equal(join(complement(sk1),composition(converse(converse(complement(sk1))),complement(composition(converse(complement(sk1)),sk1)))),complement(sk1)) )],[refute_0_592,refute_0_628]) ).
cnf(refute_0_630,plain,
converse(converse(complement(converse(zero)))) = complement(converse(zero)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_631,plain,
converse(top) = join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(join(complement(converse(top)),meet(top,converse(complement(converse(zero))))))),
inference(subst,[],[refute_0_23:[bind(A,$fot(converse(top))),bind(B,$fot(meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_632,plain,
X_38 = join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(join(complement(X_38),converse(complement(converse(complement(X_38))))))),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_38)),bind(B,$fot(converse(complement(converse(complement(X_38))))))]]) ).
cnf(refute_0_633,plain,
converse(join(converse(A),X_25)) = join(converse(converse(A)),converse(X_25)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(A))),bind(B,$fot(X_25))]]) ).
cnf(refute_0_634,plain,
( converse(converse(A)) != A
| converse(join(converse(A),X_25)) != join(converse(converse(A)),converse(X_25))
| converse(join(converse(A),X_25)) = join(A,converse(X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),X_25)),join(converse(converse(A)),converse(X_25))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_635,plain,
( converse(join(converse(A),X_25)) != join(converse(converse(A)),converse(X_25))
| converse(join(converse(A),X_25)) = join(A,converse(X_25)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_634]) ).
cnf(refute_0_636,plain,
converse(join(converse(A),X_25)) = join(A,converse(X_25)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_25)),join(converse(converse(A)),converse(X_25))) )],[refute_0_633,refute_0_635]) ).
cnf(refute_0_637,plain,
converse(join(converse(X_27),complement(converse(X_27)))) = join(X_27,converse(complement(converse(X_27)))),
inference(subst,[],[refute_0_636:[bind(A,$fot(X_27)),bind(X_25,$fot(complement(converse(X_27))))]]) ).
cnf(refute_0_638,plain,
top = join(converse(X_27),complement(converse(X_27))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_27)))]]) ).
cnf(refute_0_639,plain,
( top != join(converse(X_27),complement(converse(X_27)))
| join(converse(X_27),complement(converse(X_27))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_27),complement(converse(X_27)))))]]) ).
cnf(refute_0_640,plain,
join(converse(X_27),complement(converse(X_27))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_27),complement(converse(X_27)))) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
( converse(join(converse(X_27),complement(converse(X_27)))) != join(X_27,converse(complement(converse(X_27))))
| join(converse(X_27),complement(converse(X_27))) != top
| converse(top) = join(X_27,converse(complement(converse(X_27)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_27),complement(converse(X_27)))),join(X_27,converse(complement(converse(X_27))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_642,plain,
( converse(join(converse(X_27),complement(converse(X_27)))) != join(X_27,converse(complement(converse(X_27))))
| converse(top) = join(X_27,converse(complement(converse(X_27)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_27),complement(converse(X_27))),top) )],[refute_0_640,refute_0_641]) ).
cnf(refute_0_643,plain,
converse(top) = join(X_27,converse(complement(converse(X_27)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_27),complement(converse(X_27)))),join(X_27,converse(complement(converse(X_27))))) )],[refute_0_637,refute_0_642]) ).
cnf(refute_0_644,plain,
converse(top) = join(complement(X_38),converse(complement(converse(complement(X_38))))),
inference(subst,[],[refute_0_643:[bind(X_27,$fot(complement(X_38)))]]) ).
cnf(refute_0_645,plain,
( converse(top) != join(complement(X_38),converse(complement(converse(complement(X_38)))))
| join(complement(X_38),converse(complement(converse(complement(X_38))))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(complement(X_38),converse(complement(converse(complement(X_38)))))))]]) ).
cnf(refute_0_646,plain,
join(complement(X_38),converse(complement(converse(complement(X_38))))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(complement(X_38),converse(complement(converse(complement(X_38)))))) )],[refute_0_644,refute_0_645]) ).
cnf(refute_0_647,plain,
( X_38 != join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(join(complement(X_38),converse(complement(converse(complement(X_38)))))))
| join(complement(X_38),converse(complement(converse(complement(X_38))))) != converse(top)
| X_38 = join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_38,join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(join(complement(X_38),converse(complement(converse(complement(X_38)))))))) ),[1,1,0],$fot(converse(top))]]) ).
cnf(refute_0_648,plain,
( X_38 != join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(join(complement(X_38),converse(complement(converse(complement(X_38)))))))
| X_38 = join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(converse(top))) ),
inference(resolve,[$cnf( $equal(join(complement(X_38),converse(complement(converse(complement(X_38))))),converse(top)) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
X_38 = join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(converse(top))),
inference(resolve,[$cnf( $equal(X_38,join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(join(complement(X_38),converse(complement(converse(complement(X_38)))))))) )],[refute_0_632,refute_0_648]) ).
cnf(refute_0_650,plain,
join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(converse(top))) = join(complement(converse(top)),meet(X_38,converse(complement(converse(complement(X_38)))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(converse(top)))),bind(B,$fot(meet(X_38,converse(complement(converse(complement(X_38)))))))]]) ).
cnf(refute_0_651,plain,
( X_38 != join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(converse(top)))
| join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(converse(top))) != join(complement(converse(top)),meet(X_38,converse(complement(converse(complement(X_38))))))
| X_38 = join(complement(converse(top)),meet(X_38,converse(complement(converse(complement(X_38)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_38,join(complement(converse(top)),meet(X_38,converse(complement(converse(complement(X_38))))))) ),[0],$fot(join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(converse(top))))]]) ).
cnf(refute_0_652,plain,
( X_38 != join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(converse(top)))
| X_38 = join(complement(converse(top)),meet(X_38,converse(complement(converse(complement(X_38)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(converse(top))),join(complement(converse(top)),meet(X_38,converse(complement(converse(complement(X_38))))))) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
X_38 = join(complement(converse(top)),meet(X_38,converse(complement(converse(complement(X_38)))))),
inference(resolve,[$cnf( $equal(X_38,join(meet(X_38,converse(complement(converse(complement(X_38))))),complement(converse(top)))) )],[refute_0_649,refute_0_652]) ).
cnf(refute_0_654,plain,
top = join(complement(converse(top)),meet(top,converse(complement(converse(complement(top)))))),
inference(subst,[],[refute_0_653:[bind(X_38,$fot(top))]]) ).
cnf(refute_0_655,plain,
( complement(top) != zero
| top != join(complement(converse(top)),meet(top,converse(complement(converse(complement(top))))))
| top = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(converse(top)),meet(top,converse(complement(converse(complement(top))))))) ),[1,1,1,0,0,0],$fot(zero)]]) ).
cnf(refute_0_656,plain,
( top != join(complement(converse(top)),meet(top,converse(complement(converse(complement(top))))))
| top = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_655]) ).
cnf(refute_0_657,plain,
top = join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),
inference(resolve,[$cnf( $equal(top,join(complement(converse(top)),meet(top,converse(complement(converse(complement(top))))))) )],[refute_0_654,refute_0_656]) ).
cnf(refute_0_658,plain,
( top != join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))
| join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_659,plain,
join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))) )],[refute_0_657,refute_0_658]) ).
cnf(refute_0_660,plain,
( converse(top) != join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))))
| join(complement(converse(top)),meet(top,converse(complement(converse(zero))))) != top
| converse(top) = join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_661,plain,
( converse(top) != join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))))
| converse(top) = join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(top,converse(complement(converse(zero))))),top) )],[refute_0_659,refute_0_660]) ).
cnf(refute_0_662,plain,
converse(top) = join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)),
inference(resolve,[$cnf( $equal(converse(top),join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(join(complement(converse(top)),meet(top,converse(complement(converse(zero)))))))) )],[refute_0_631,refute_0_661]) ).
cnf(refute_0_663,plain,
join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) = join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_664,plain,
( complement(top) != zero
| join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) != join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero))))))
| join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))),join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_665,plain,
( complement(top) != zero
| join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))),join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero))))))) )],[refute_0_663,refute_0_664]) ).
cnf(refute_0_666,plain,
join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_665]) ).
cnf(refute_0_667,plain,
join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) = join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(converse(top),meet(top,converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_668,plain,
( join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) != join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero))))))
| join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)))),bind(Y,$fot(join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))))),bind(Z,$fot(join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))))]]) ).
cnf(refute_0_669,plain,
( join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))) != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)),join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero))))))) )],[refute_0_667,refute_0_668]) ).
cnf(refute_0_670,plain,
join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(top),meet(top,converse(complement(converse(zero)))))),join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))) )],[refute_0_666,refute_0_669]) ).
cnf(refute_0_671,plain,
( converse(top) != join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top))
| join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)) != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| converse(top) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))) ),[0],$fot(join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)))]]) ).
cnf(refute_0_672,plain,
( converse(top) != join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top))
| converse(top) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top)),join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))) )],[refute_0_670,refute_0_671]) ).
cnf(refute_0_673,plain,
converse(top) = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))),
inference(resolve,[$cnf( $equal(converse(top),join(meet(converse(top),meet(top,converse(complement(converse(zero))))),complement(top))) )],[refute_0_662,refute_0_672]) ).
cnf(refute_0_674,plain,
converse(top) = join(meet(converse(top),zero),complement(join(zero,complement(converse(top))))),
inference(subst,[],[refute_0_30:[bind(X_38,$fot(converse(top))),bind(X_39,$fot(zero))]]) ).
cnf(refute_0_675,plain,
zero = join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero)))))),
inference(subst,[],[refute_0_653:[bind(X_38,$fot(zero))]]) ).
cnf(refute_0_676,plain,
( complement(zero) != top
| zero != join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))
| zero = join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))) ),[1,1,1,0,0,0],$fot(top)]]) ).
cnf(refute_0_677,plain,
( zero != join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))
| zero = join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) ),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_259,refute_0_676]) ).
cnf(refute_0_678,plain,
zero = join(complement(converse(top)),meet(zero,converse(complement(converse(top))))),
inference(resolve,[$cnf( $equal(zero,join(complement(converse(top)),meet(zero,converse(complement(converse(complement(zero))))))) )],[refute_0_675,refute_0_677]) ).
cnf(refute_0_679,plain,
join(complement(converse(top)),zero) = join(zero,complement(converse(top))),
inference(subst,[],[refute_0_4:[bind(A,$fot(zero)),bind(B,$fot(complement(converse(top))))]]) ).
cnf(refute_0_680,plain,
meet(zero,converse(complement(converse(top)))) = zero,
inference(subst,[],[refute_0_273:[bind(B,$fot(converse(complement(converse(top)))))]]) ).
cnf(refute_0_681,plain,
join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) = join(complement(converse(top)),meet(zero,converse(complement(converse(top))))),
introduced(tautology,[refl,[$fot(join(complement(converse(top)),meet(zero,converse(complement(converse(top))))))]]) ).
cnf(refute_0_682,plain,
( join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) != join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))
| meet(zero,converse(complement(converse(top)))) != zero
| join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) = join(complement(converse(top)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(top)),meet(zero,converse(complement(converse(top))))),join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_683,plain,
( meet(zero,converse(complement(converse(top)))) != zero
| join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) = join(complement(converse(top)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(zero,converse(complement(converse(top))))),join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) = join(complement(converse(top)),zero),
inference(resolve,[$cnf( $equal(meet(zero,converse(complement(converse(top)))),zero) )],[refute_0_680,refute_0_683]) ).
cnf(refute_0_685,plain,
( join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) != join(complement(converse(top)),zero)
| join(complement(converse(top)),zero) != join(zero,complement(converse(top)))
| join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) = join(zero,complement(converse(top))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(converse(top)),meet(zero,converse(complement(converse(top))))))),bind(Y,$fot(join(complement(converse(top)),zero))),bind(Z,$fot(join(zero,complement(converse(top)))))]]) ).
cnf(refute_0_686,plain,
( join(complement(converse(top)),zero) != join(zero,complement(converse(top)))
| join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) = join(zero,complement(converse(top))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(zero,converse(complement(converse(top))))),join(complement(converse(top)),zero)) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) = join(zero,complement(converse(top))),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),zero),join(zero,complement(converse(top)))) )],[refute_0_679,refute_0_686]) ).
cnf(refute_0_688,plain,
( join(complement(converse(top)),meet(zero,converse(complement(converse(top))))) != join(zero,complement(converse(top)))
| zero != join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))
| zero = join(zero,complement(converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))) ),[1],$fot(join(zero,complement(converse(top))))]]) ).
cnf(refute_0_689,plain,
( zero != join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))
| zero = join(zero,complement(converse(top))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(top)),meet(zero,converse(complement(converse(top))))),join(zero,complement(converse(top)))) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
zero = join(zero,complement(converse(top))),
inference(resolve,[$cnf( $equal(zero,join(complement(converse(top)),meet(zero,converse(complement(converse(top)))))) )],[refute_0_678,refute_0_689]) ).
cnf(refute_0_691,plain,
( zero != join(zero,complement(converse(top)))
| join(zero,complement(converse(top))) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(join(zero,complement(converse(top)))))]]) ).
cnf(refute_0_692,plain,
join(zero,complement(converse(top))) = zero,
inference(resolve,[$cnf( $equal(zero,join(zero,complement(converse(top)))) )],[refute_0_690,refute_0_691]) ).
cnf(refute_0_693,plain,
( converse(top) != join(meet(converse(top),zero),complement(join(zero,complement(converse(top)))))
| join(zero,complement(converse(top))) != zero
| converse(top) = join(meet(converse(top),zero),complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(meet(converse(top),zero),complement(join(zero,complement(converse(top)))))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_694,plain,
( converse(top) != join(meet(converse(top),zero),complement(join(zero,complement(converse(top)))))
| converse(top) = join(meet(converse(top),zero),complement(zero)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(converse(top))),zero) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
converse(top) = join(meet(converse(top),zero),complement(zero)),
inference(resolve,[$cnf( $equal(converse(top),join(meet(converse(top),zero),complement(join(zero,complement(converse(top)))))) )],[refute_0_674,refute_0_694]) ).
cnf(refute_0_696,plain,
top = join(top,complement(top)),
inference(subst,[],[def_top_12:[bind(A,$fot(top))]]) ).
cnf(refute_0_697,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_698,plain,
( top != join(top,complement(top))
| top = join(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_697]) ).
cnf(refute_0_699,plain,
top = join(top,zero),
inference(resolve,[$cnf( $equal(top,join(top,complement(top))) )],[refute_0_696,refute_0_698]) ).
cnf(refute_0_700,plain,
( top != join(top,zero)
| join(top,zero) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,zero)))]]) ).
cnf(refute_0_701,plain,
join(top,zero) = top,
inference(resolve,[$cnf( $equal(top,join(top,zero)) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
meet(converse(top),zero) = zero,
inference(subst,[],[refute_0_334:[bind(A,$fot(converse(top)))]]) ).
cnf(refute_0_703,plain,
join(top,meet(converse(top),zero)) = join(top,meet(converse(top),zero)),
introduced(tautology,[refl,[$fot(join(top,meet(converse(top),zero)))]]) ).
cnf(refute_0_704,plain,
( join(top,meet(converse(top),zero)) != join(top,meet(converse(top),zero))
| meet(converse(top),zero) != zero
| join(top,meet(converse(top),zero)) = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,meet(converse(top),zero)),join(top,meet(converse(top),zero))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_705,plain,
( meet(converse(top),zero) != zero
| join(top,meet(converse(top),zero)) = join(top,zero) ),
inference(resolve,[$cnf( $equal(join(top,meet(converse(top),zero)),join(top,meet(converse(top),zero))) )],[refute_0_703,refute_0_704]) ).
cnf(refute_0_706,plain,
join(top,meet(converse(top),zero)) = join(top,zero),
inference(resolve,[$cnf( $equal(meet(converse(top),zero),zero) )],[refute_0_702,refute_0_705]) ).
cnf(refute_0_707,plain,
join(complement(zero),meet(converse(top),zero)) = join(complement(zero),meet(converse(top),zero)),
introduced(tautology,[refl,[$fot(join(complement(zero),meet(converse(top),zero)))]]) ).
cnf(refute_0_708,plain,
( complement(zero) != top
| join(complement(zero),meet(converse(top),zero)) != join(complement(zero),meet(converse(top),zero))
| join(complement(zero),meet(converse(top),zero)) = join(top,meet(converse(top),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(zero),meet(converse(top),zero)),join(complement(zero),meet(converse(top),zero))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_709,plain,
( complement(zero) != top
| join(complement(zero),meet(converse(top),zero)) = join(top,meet(converse(top),zero)) ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(converse(top),zero)),join(complement(zero),meet(converse(top),zero))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
join(complement(zero),meet(converse(top),zero)) = join(top,meet(converse(top),zero)),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_259,refute_0_709]) ).
cnf(refute_0_711,plain,
( join(complement(zero),meet(converse(top),zero)) != join(top,meet(converse(top),zero))
| join(top,meet(converse(top),zero)) != join(top,zero)
| join(complement(zero),meet(converse(top),zero)) = join(top,zero) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(zero),meet(converse(top),zero)))),bind(Y,$fot(join(top,meet(converse(top),zero)))),bind(Z,$fot(join(top,zero)))]]) ).
cnf(refute_0_712,plain,
( join(top,meet(converse(top),zero)) != join(top,zero)
| join(complement(zero),meet(converse(top),zero)) = join(top,zero) ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(converse(top),zero)),join(top,meet(converse(top),zero))) )],[refute_0_710,refute_0_711]) ).
cnf(refute_0_713,plain,
join(complement(zero),meet(converse(top),zero)) = join(top,zero),
inference(resolve,[$cnf( $equal(join(top,meet(converse(top),zero)),join(top,zero)) )],[refute_0_706,refute_0_712]) ).
cnf(refute_0_714,plain,
( join(complement(zero),meet(converse(top),zero)) != join(top,zero)
| join(top,zero) != top
| join(complement(zero),meet(converse(top),zero)) = top ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(zero),meet(converse(top),zero)))),bind(Y,$fot(join(top,zero))),bind(Z,$fot(top))]]) ).
cnf(refute_0_715,plain,
( join(top,zero) != top
| join(complement(zero),meet(converse(top),zero)) = top ),
inference(resolve,[$cnf( $equal(join(complement(zero),meet(converse(top),zero)),join(top,zero)) )],[refute_0_713,refute_0_714]) ).
cnf(refute_0_716,plain,
join(complement(zero),meet(converse(top),zero)) = top,
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_701,refute_0_715]) ).
cnf(refute_0_717,plain,
join(meet(converse(top),zero),complement(zero)) = join(complement(zero),meet(converse(top),zero)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(zero))),bind(B,$fot(meet(converse(top),zero)))]]) ).
cnf(refute_0_718,plain,
( join(complement(zero),meet(converse(top),zero)) != top
| join(meet(converse(top),zero),complement(zero)) != join(complement(zero),meet(converse(top),zero))
| join(meet(converse(top),zero),complement(zero)) = top ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(meet(converse(top),zero),complement(zero)))),bind(Y,$fot(join(complement(zero),meet(converse(top),zero)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_719,plain,
( join(complement(zero),meet(converse(top),zero)) != top
| join(meet(converse(top),zero),complement(zero)) = top ),
inference(resolve,[$cnf( $equal(join(meet(converse(top),zero),complement(zero)),join(complement(zero),meet(converse(top),zero))) )],[refute_0_717,refute_0_718]) ).
cnf(refute_0_720,plain,
join(meet(converse(top),zero),complement(zero)) = top,
inference(resolve,[$cnf( $equal(join(complement(zero),meet(converse(top),zero)),top) )],[refute_0_716,refute_0_719]) ).
cnf(refute_0_721,plain,
( converse(top) != join(meet(converse(top),zero),complement(zero))
| join(meet(converse(top),zero),complement(zero)) != top
| converse(top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),top) ),[0],$fot(join(meet(converse(top),zero),complement(zero)))]]) ).
cnf(refute_0_722,plain,
( converse(top) != join(meet(converse(top),zero),complement(zero))
| converse(top) = top ),
inference(resolve,[$cnf( $equal(join(meet(converse(top),zero),complement(zero)),top) )],[refute_0_720,refute_0_721]) ).
cnf(refute_0_723,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(converse(top),join(meet(converse(top),zero),complement(zero))) )],[refute_0_695,refute_0_722]) ).
cnf(refute_0_724,plain,
( converse(top) != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| converse(top) != top
| top = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))) ),[0],$fot(top)]]) ).
cnf(refute_0_725,plain,
( converse(top) != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| top = join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_723,refute_0_724]) ).
cnf(refute_0_726,plain,
meet(top,converse(complement(converse(zero)))) = converse(complement(converse(zero))),
inference(subst,[],[refute_0_500:[bind(X_63,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_727,plain,
meet(top,meet(top,converse(complement(converse(zero))))) = meet(top,meet(top,converse(complement(converse(zero))))),
introduced(tautology,[refl,[$fot(meet(top,meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_728,plain,
( meet(top,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| meet(top,meet(top,converse(complement(converse(zero))))) != meet(top,meet(top,converse(complement(converse(zero)))))
| meet(top,meet(top,converse(complement(converse(zero))))) = meet(top,converse(complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,meet(top,converse(complement(converse(zero))))),meet(top,meet(top,converse(complement(converse(zero)))))) ),[1,1],$fot(converse(complement(converse(zero))))]]) ).
cnf(refute_0_729,plain,
( meet(top,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| meet(top,meet(top,converse(complement(converse(zero))))) = meet(top,converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(meet(top,meet(top,converse(complement(converse(zero))))),meet(top,meet(top,converse(complement(converse(zero)))))) )],[refute_0_727,refute_0_728]) ).
cnf(refute_0_730,plain,
meet(top,meet(top,converse(complement(converse(zero))))) = meet(top,converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(meet(top,converse(complement(converse(zero)))),converse(complement(converse(zero)))) )],[refute_0_726,refute_0_729]) ).
cnf(refute_0_731,plain,
meet(converse(top),meet(top,converse(complement(converse(zero))))) = meet(converse(top),meet(top,converse(complement(converse(zero))))),
introduced(tautology,[refl,[$fot(meet(converse(top),meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_732,plain,
( converse(top) != top
| meet(converse(top),meet(top,converse(complement(converse(zero))))) != meet(converse(top),meet(top,converse(complement(converse(zero)))))
| meet(converse(top),meet(top,converse(complement(converse(zero))))) = meet(top,meet(top,converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(converse(top),meet(top,converse(complement(converse(zero))))),meet(converse(top),meet(top,converse(complement(converse(zero)))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_733,plain,
( converse(top) != top
| meet(converse(top),meet(top,converse(complement(converse(zero))))) = meet(top,meet(top,converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(meet(converse(top),meet(top,converse(complement(converse(zero))))),meet(converse(top),meet(top,converse(complement(converse(zero)))))) )],[refute_0_731,refute_0_732]) ).
cnf(refute_0_734,plain,
meet(converse(top),meet(top,converse(complement(converse(zero))))) = meet(top,meet(top,converse(complement(converse(zero))))),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_723,refute_0_733]) ).
cnf(refute_0_735,plain,
( meet(converse(top),meet(top,converse(complement(converse(zero))))) != meet(top,meet(top,converse(complement(converse(zero)))))
| meet(top,meet(top,converse(complement(converse(zero))))) != meet(top,converse(complement(converse(zero))))
| meet(converse(top),meet(top,converse(complement(converse(zero))))) = meet(top,converse(complement(converse(zero)))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(converse(top),meet(top,converse(complement(converse(zero))))))),bind(Y,$fot(meet(top,meet(top,converse(complement(converse(zero))))))),bind(Z,$fot(meet(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_736,plain,
( meet(top,meet(top,converse(complement(converse(zero))))) != meet(top,converse(complement(converse(zero))))
| meet(converse(top),meet(top,converse(complement(converse(zero))))) = meet(top,converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(meet(converse(top),meet(top,converse(complement(converse(zero))))),meet(top,meet(top,converse(complement(converse(zero)))))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
meet(converse(top),meet(top,converse(complement(converse(zero))))) = meet(top,converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(meet(top,meet(top,converse(complement(converse(zero))))),meet(top,converse(complement(converse(zero))))) )],[refute_0_730,refute_0_736]) ).
cnf(refute_0_738,plain,
( meet(converse(top),meet(top,converse(complement(converse(zero))))) != meet(top,converse(complement(converse(zero))))
| meet(top,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| meet(converse(top),meet(top,converse(complement(converse(zero))))) = converse(complement(converse(zero))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(meet(converse(top),meet(top,converse(complement(converse(zero))))))),bind(Y,$fot(meet(top,converse(complement(converse(zero)))))),bind(Z,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_739,plain,
( meet(top,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| meet(converse(top),meet(top,converse(complement(converse(zero))))) = converse(complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(meet(converse(top),meet(top,converse(complement(converse(zero))))),meet(top,converse(complement(converse(zero))))) )],[refute_0_737,refute_0_738]) ).
cnf(refute_0_740,plain,
meet(converse(top),meet(top,converse(complement(converse(zero))))) = converse(complement(converse(zero))),
inference(resolve,[$cnf( $equal(meet(top,converse(complement(converse(zero)))),converse(complement(converse(zero)))) )],[refute_0_726,refute_0_739]) ).
cnf(refute_0_741,plain,
join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) = meet(converse(top),meet(top,converse(complement(converse(zero))))),
inference(subst,[],[refute_0_525:[bind(X_52,$fot(meet(converse(top),meet(top,converse(complement(converse(zero)))))))]]) ).
cnf(refute_0_742,plain,
( join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) != meet(converse(top),meet(top,converse(complement(converse(zero)))))
| meet(converse(top),meet(top,converse(complement(converse(zero))))) != converse(complement(converse(zero)))
| join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) = converse(complement(converse(zero))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))))),bind(Y,$fot(meet(converse(top),meet(top,converse(complement(converse(zero))))))),bind(Z,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_743,plain,
( meet(converse(top),meet(top,converse(complement(converse(zero))))) != converse(complement(converse(zero)))
| join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) = converse(complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))),meet(converse(top),meet(top,converse(complement(converse(zero)))))) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) = converse(complement(converse(zero))),
inference(resolve,[$cnf( $equal(meet(converse(top),meet(top,converse(complement(converse(zero))))),converse(complement(converse(zero)))) )],[refute_0_740,refute_0_743]) ).
cnf(refute_0_745,plain,
( join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))) != converse(complement(converse(zero)))
| top != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| top = converse(complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))) ),[1],$fot(converse(complement(converse(zero))))]]) ).
cnf(refute_0_746,plain,
( top != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| top = converse(complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(converse(top),meet(top,converse(complement(converse(zero)))))),converse(complement(converse(zero)))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
( converse(top) != join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))
| top = converse(complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(top,join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))) )],[refute_0_725,refute_0_746]) ).
cnf(refute_0_748,plain,
top = converse(complement(converse(zero))),
inference(resolve,[$cnf( $equal(converse(top),join(zero,meet(converse(top),meet(top,converse(complement(converse(zero))))))) )],[refute_0_673,refute_0_747]) ).
cnf(refute_0_749,plain,
( top != converse(complement(converse(zero)))
| converse(complement(converse(zero))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_750,plain,
converse(complement(converse(zero))) = top,
inference(resolve,[$cnf( $equal(top,converse(complement(converse(zero)))) )],[refute_0_748,refute_0_749]) ).
cnf(refute_0_751,plain,
( converse(complement(converse(zero))) != top
| converse(converse(complement(converse(zero)))) != complement(converse(zero))
| converse(top) = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(complement(converse(zero)))),complement(converse(zero))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_752,plain,
( converse(converse(complement(converse(zero)))) != complement(converse(zero))
| converse(top) = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(zero))),top) )],[refute_0_750,refute_0_751]) ).
cnf(refute_0_753,plain,
converse(top) = complement(converse(zero)),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(zero)))),complement(converse(zero))) )],[refute_0_630,refute_0_752]) ).
cnf(refute_0_754,plain,
( converse(top) != complement(converse(zero))
| converse(top) != top
| top = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),complement(converse(zero))) ),[0],$fot(top)]]) ).
cnf(refute_0_755,plain,
( converse(top) != complement(converse(zero))
| top = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_723,refute_0_754]) ).
cnf(refute_0_756,plain,
top = complement(converse(zero)),
inference(resolve,[$cnf( $equal(converse(top),complement(converse(zero))) )],[refute_0_753,refute_0_755]) ).
cnf(refute_0_757,plain,
( top != complement(converse(zero))
| complement(converse(zero)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_758,plain,
complement(converse(zero)) = top,
inference(resolve,[$cnf( $equal(top,complement(converse(zero))) )],[refute_0_756,refute_0_757]) ).
cnf(refute_0_759,plain,
composition(complement(sk1),complement(converse(zero))) = composition(complement(sk1),complement(converse(zero))),
introduced(tautology,[refl,[$fot(composition(complement(sk1),complement(converse(zero))))]]) ).
cnf(refute_0_760,plain,
( complement(converse(zero)) != top
| composition(complement(sk1),complement(converse(zero))) != composition(complement(sk1),complement(converse(zero)))
| composition(complement(sk1),complement(converse(zero))) = composition(complement(sk1),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(sk1),complement(converse(zero))),composition(complement(sk1),complement(converse(zero)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_761,plain,
( complement(converse(zero)) != top
| composition(complement(sk1),complement(converse(zero))) = composition(complement(sk1),top) ),
inference(resolve,[$cnf( $equal(composition(complement(sk1),complement(converse(zero))),composition(complement(sk1),complement(converse(zero)))) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
composition(complement(sk1),complement(converse(zero))) = composition(complement(sk1),top),
inference(resolve,[$cnf( $equal(complement(converse(zero)),top) )],[refute_0_758,refute_0_761]) ).
cnf(refute_0_763,plain,
converse(converse(complement(sk1))) = complement(sk1),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(sk1)))]]) ).
cnf(refute_0_764,plain,
composition(converse(converse(complement(sk1))),complement(converse(zero))) = composition(converse(converse(complement(sk1))),complement(converse(zero))),
introduced(tautology,[refl,[$fot(composition(converse(converse(complement(sk1))),complement(converse(zero))))]]) ).
cnf(refute_0_765,plain,
( composition(converse(converse(complement(sk1))),complement(converse(zero))) != composition(converse(converse(complement(sk1))),complement(converse(zero)))
| converse(converse(complement(sk1))) != complement(sk1)
| composition(converse(converse(complement(sk1))),complement(converse(zero))) = composition(complement(sk1),complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(converse(complement(sk1))),complement(converse(zero))),composition(converse(converse(complement(sk1))),complement(converse(zero)))) ),[1,0],$fot(complement(sk1))]]) ).
cnf(refute_0_766,plain,
( converse(converse(complement(sk1))) != complement(sk1)
| composition(converse(converse(complement(sk1))),complement(converse(zero))) = composition(complement(sk1),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(complement(sk1))),complement(converse(zero))),composition(converse(converse(complement(sk1))),complement(converse(zero)))) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
composition(converse(converse(complement(sk1))),complement(converse(zero))) = composition(complement(sk1),complement(converse(zero))),
inference(resolve,[$cnf( $equal(converse(converse(complement(sk1))),complement(sk1)) )],[refute_0_763,refute_0_766]) ).
cnf(refute_0_768,plain,
( composition(complement(sk1),complement(converse(zero))) != composition(complement(sk1),top)
| composition(converse(converse(complement(sk1))),complement(converse(zero))) != composition(complement(sk1),complement(converse(zero)))
| composition(converse(converse(complement(sk1))),complement(converse(zero))) = composition(complement(sk1),top) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(composition(converse(converse(complement(sk1))),complement(converse(zero))))),bind(Y,$fot(composition(complement(sk1),complement(converse(zero))))),bind(Z,$fot(composition(complement(sk1),top)))]]) ).
cnf(refute_0_769,plain,
( composition(complement(sk1),complement(converse(zero))) != composition(complement(sk1),top)
| composition(converse(converse(complement(sk1))),complement(converse(zero))) = composition(complement(sk1),top) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(complement(sk1))),complement(converse(zero))),composition(complement(sk1),complement(converse(zero)))) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
composition(converse(converse(complement(sk1))),complement(converse(zero))) = composition(complement(sk1),top),
inference(resolve,[$cnf( $equal(composition(complement(sk1),complement(converse(zero))),composition(complement(sk1),top)) )],[refute_0_762,refute_0_769]) ).
cnf(refute_0_771,plain,
join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))) = join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))),
introduced(tautology,[refl,[$fot(join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))))]]) ).
cnf(refute_0_772,plain,
( composition(converse(converse(complement(sk1))),complement(converse(zero))) != composition(complement(sk1),top)
| join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))) != join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero))))
| join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))) = join(complement(sk1),composition(complement(sk1),top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))),join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero))))) ),[1,1],$fot(composition(complement(sk1),top))]]) ).
cnf(refute_0_773,plain,
( composition(converse(converse(complement(sk1))),complement(converse(zero))) != composition(complement(sk1),top)
| join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))) = join(complement(sk1),composition(complement(sk1),top)) ),
inference(resolve,[$cnf( $equal(join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))),join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero))))) )],[refute_0_771,refute_0_772]) ).
cnf(refute_0_774,plain,
join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))) = join(complement(sk1),composition(complement(sk1),top)),
inference(resolve,[$cnf( $equal(composition(converse(converse(complement(sk1))),complement(converse(zero))),composition(complement(sk1),top)) )],[refute_0_770,refute_0_773]) ).
cnf(refute_0_775,plain,
( join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))) != complement(sk1)
| join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))) != join(complement(sk1),composition(complement(sk1),top))
| join(complement(sk1),composition(complement(sk1),top)) = complement(sk1) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))),complement(sk1)) ),[0],$fot(join(complement(sk1),composition(complement(sk1),top)))]]) ).
cnf(refute_0_776,plain,
( join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))) != complement(sk1)
| join(complement(sk1),composition(complement(sk1),top)) = complement(sk1) ),
inference(resolve,[$cnf( $equal(join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))),join(complement(sk1),composition(complement(sk1),top))) )],[refute_0_774,refute_0_775]) ).
cnf(refute_0_777,plain,
join(complement(sk1),composition(complement(sk1),top)) = complement(sk1),
inference(resolve,[$cnf( $equal(join(complement(sk1),composition(converse(converse(complement(sk1))),complement(converse(zero)))),complement(sk1)) )],[refute_0_629,refute_0_776]) ).
cnf(refute_0_778,plain,
( composition(complement(sk1),top) != meet(composition(complement(sk1),top),join(complement(sk1),composition(complement(sk1),top)))
| join(complement(sk1),composition(complement(sk1),top)) != complement(sk1)
| composition(complement(sk1),top) = meet(composition(complement(sk1),top),complement(sk1)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(sk1),top),meet(composition(complement(sk1),top),join(complement(sk1),composition(complement(sk1),top)))) ),[1,1],$fot(complement(sk1))]]) ).
cnf(refute_0_779,plain,
( composition(complement(sk1),top) != meet(composition(complement(sk1),top),join(complement(sk1),composition(complement(sk1),top)))
| composition(complement(sk1),top) = meet(composition(complement(sk1),top),complement(sk1)) ),
inference(resolve,[$cnf( $equal(join(complement(sk1),composition(complement(sk1),top)),complement(sk1)) )],[refute_0_777,refute_0_778]) ).
cnf(refute_0_780,plain,
composition(complement(sk1),top) = meet(composition(complement(sk1),top),complement(sk1)),
inference(resolve,[$cnf( $equal(composition(complement(sk1),top),meet(composition(complement(sk1),top),join(complement(sk1),composition(complement(sk1),top)))) )],[refute_0_591,refute_0_779]) ).
cnf(refute_0_781,plain,
meet(composition(complement(sk1),top),complement(sk1)) = meet(complement(sk1),composition(complement(sk1),top)),
inference(subst,[],[refute_0_558:[bind(X_18,$fot(complement(sk1))),bind(X_19,$fot(composition(complement(sk1),top)))]]) ).
cnf(refute_0_782,plain,
( composition(complement(sk1),top) != meet(composition(complement(sk1),top),complement(sk1))
| meet(composition(complement(sk1),top),complement(sk1)) != meet(complement(sk1),composition(complement(sk1),top))
| composition(complement(sk1),top) = meet(complement(sk1),composition(complement(sk1),top)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(complement(sk1),top),meet(complement(sk1),composition(complement(sk1),top))) ),[0],$fot(meet(composition(complement(sk1),top),complement(sk1)))]]) ).
cnf(refute_0_783,plain,
( composition(complement(sk1),top) != meet(composition(complement(sk1),top),complement(sk1))
| composition(complement(sk1),top) = meet(complement(sk1),composition(complement(sk1),top)) ),
inference(resolve,[$cnf( $equal(meet(composition(complement(sk1),top),complement(sk1)),meet(complement(sk1),composition(complement(sk1),top))) )],[refute_0_781,refute_0_782]) ).
cnf(refute_0_784,plain,
composition(complement(sk1),top) = meet(complement(sk1),composition(complement(sk1),top)),
inference(resolve,[$cnf( $equal(composition(complement(sk1),top),meet(composition(complement(sk1),top),complement(sk1))) )],[refute_0_780,refute_0_783]) ).
cnf(refute_0_785,plain,
( composition(complement(sk1),top) != meet(complement(sk1),composition(complement(sk1),top))
| meet(complement(sk1),composition(complement(sk1),top)) = composition(complement(sk1),top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(complement(sk1),top))),bind(Y,$fot(meet(complement(sk1),composition(complement(sk1),top))))]]) ).
cnf(refute_0_786,plain,
meet(complement(sk1),composition(complement(sk1),top)) = composition(complement(sk1),top),
inference(resolve,[$cnf( $equal(composition(complement(sk1),top),meet(complement(sk1),composition(complement(sk1),top))) )],[refute_0_784,refute_0_785]) ).
cnf(refute_0_787,plain,
( complement(sk1) != join(meet(complement(sk1),composition(complement(sk1),top)),complement(join(composition(complement(sk1),top),complement(complement(sk1)))))
| meet(complement(sk1),composition(complement(sk1),top)) != composition(complement(sk1),top)
| complement(sk1) = join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(sk1),join(meet(complement(sk1),composition(complement(sk1),top)),complement(join(composition(complement(sk1),top),complement(complement(sk1)))))) ),[1,0],$fot(composition(complement(sk1),top))]]) ).
cnf(refute_0_788,plain,
( complement(sk1) != join(meet(complement(sk1),composition(complement(sk1),top)),complement(join(composition(complement(sk1),top),complement(complement(sk1)))))
| complement(sk1) = join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))) ),
inference(resolve,[$cnf( $equal(meet(complement(sk1),composition(complement(sk1),top)),composition(complement(sk1),top)) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
complement(sk1) = join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))),
inference(resolve,[$cnf( $equal(complement(sk1),join(meet(complement(sk1),composition(complement(sk1),top)),complement(join(composition(complement(sk1),top),complement(complement(sk1)))))) )],[refute_0_31,refute_0_788]) ).
cnf(refute_0_790,plain,
complement(complement(sk1)) = sk1,
inference(subst,[],[refute_0_417:[bind(X_63,$fot(sk1))]]) ).
cnf(refute_0_791,plain,
join(complement(complement(sk1)),composition(complement(sk1),top)) = join(complement(complement(sk1)),composition(complement(sk1),top)),
introduced(tautology,[refl,[$fot(join(complement(complement(sk1)),composition(complement(sk1),top)))]]) ).
cnf(refute_0_792,plain,
( complement(complement(sk1)) != sk1
| join(complement(complement(sk1)),composition(complement(sk1),top)) != join(complement(complement(sk1)),composition(complement(sk1),top))
| join(complement(complement(sk1)),composition(complement(sk1),top)) = join(sk1,composition(complement(sk1),top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(sk1)),composition(complement(sk1),top)),join(complement(complement(sk1)),composition(complement(sk1),top))) ),[1,0],$fot(sk1)]]) ).
cnf(refute_0_793,plain,
( complement(complement(sk1)) != sk1
| join(complement(complement(sk1)),composition(complement(sk1),top)) = join(sk1,composition(complement(sk1),top)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(sk1)),composition(complement(sk1),top)),join(complement(complement(sk1)),composition(complement(sk1),top))) )],[refute_0_791,refute_0_792]) ).
cnf(refute_0_794,plain,
join(complement(complement(sk1)),composition(complement(sk1),top)) = join(sk1,composition(complement(sk1),top)),
inference(resolve,[$cnf( $equal(complement(complement(sk1)),sk1) )],[refute_0_790,refute_0_793]) ).
cnf(refute_0_795,plain,
join(composition(complement(sk1),top),complement(complement(sk1))) = join(complement(complement(sk1)),composition(complement(sk1),top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(complement(sk1)))),bind(B,$fot(composition(complement(sk1),top)))]]) ).
cnf(refute_0_796,plain,
( join(complement(complement(sk1)),composition(complement(sk1),top)) != join(sk1,composition(complement(sk1),top))
| join(composition(complement(sk1),top),complement(complement(sk1))) != join(complement(complement(sk1)),composition(complement(sk1),top))
| join(composition(complement(sk1),top),complement(complement(sk1))) = join(sk1,composition(complement(sk1),top)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(composition(complement(sk1),top),complement(complement(sk1))))),bind(Y,$fot(join(complement(complement(sk1)),composition(complement(sk1),top)))),bind(Z,$fot(join(sk1,composition(complement(sk1),top))))]]) ).
cnf(refute_0_797,plain,
( join(complement(complement(sk1)),composition(complement(sk1),top)) != join(sk1,composition(complement(sk1),top))
| join(composition(complement(sk1),top),complement(complement(sk1))) = join(sk1,composition(complement(sk1),top)) ),
inference(resolve,[$cnf( $equal(join(composition(complement(sk1),top),complement(complement(sk1))),join(complement(complement(sk1)),composition(complement(sk1),top))) )],[refute_0_795,refute_0_796]) ).
cnf(refute_0_798,plain,
join(composition(complement(sk1),top),complement(complement(sk1))) = join(sk1,composition(complement(sk1),top)),
inference(resolve,[$cnf( $equal(join(complement(complement(sk1)),composition(complement(sk1),top)),join(sk1,composition(complement(sk1),top))) )],[refute_0_794,refute_0_797]) ).
cnf(refute_0_799,plain,
complement(join(composition(complement(sk1),top),complement(complement(sk1)))) = complement(join(composition(complement(sk1),top),complement(complement(sk1)))),
introduced(tautology,[refl,[$fot(complement(join(composition(complement(sk1),top),complement(complement(sk1)))))]]) ).
cnf(refute_0_800,plain,
( complement(join(composition(complement(sk1),top),complement(complement(sk1)))) != complement(join(composition(complement(sk1),top),complement(complement(sk1))))
| join(composition(complement(sk1),top),complement(complement(sk1))) != join(sk1,composition(complement(sk1),top))
| complement(join(composition(complement(sk1),top),complement(complement(sk1)))) = complement(join(sk1,composition(complement(sk1),top))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(composition(complement(sk1),top),complement(complement(sk1)))),complement(join(composition(complement(sk1),top),complement(complement(sk1))))) ),[1,0],$fot(join(sk1,composition(complement(sk1),top)))]]) ).
cnf(refute_0_801,plain,
( join(composition(complement(sk1),top),complement(complement(sk1))) != join(sk1,composition(complement(sk1),top))
| complement(join(composition(complement(sk1),top),complement(complement(sk1)))) = complement(join(sk1,composition(complement(sk1),top))) ),
inference(resolve,[$cnf( $equal(complement(join(composition(complement(sk1),top),complement(complement(sk1)))),complement(join(composition(complement(sk1),top),complement(complement(sk1))))) )],[refute_0_799,refute_0_800]) ).
cnf(refute_0_802,plain,
complement(join(composition(complement(sk1),top),complement(complement(sk1)))) = complement(join(sk1,composition(complement(sk1),top))),
inference(resolve,[$cnf( $equal(join(composition(complement(sk1),top),complement(complement(sk1))),join(sk1,composition(complement(sk1),top))) )],[refute_0_798,refute_0_801]) ).
cnf(refute_0_803,plain,
join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))) = join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))),
introduced(tautology,[refl,[$fot(join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))))]]) ).
cnf(refute_0_804,plain,
( complement(join(composition(complement(sk1),top),complement(complement(sk1)))) != complement(join(sk1,composition(complement(sk1),top)))
| join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))) != join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1)))))
| join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))) = join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))),join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1)))))) ),[1,1],$fot(complement(join(sk1,composition(complement(sk1),top))))]]) ).
cnf(refute_0_805,plain,
( complement(join(composition(complement(sk1),top),complement(complement(sk1)))) != complement(join(sk1,composition(complement(sk1),top)))
| join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))) = join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) ),
inference(resolve,[$cnf( $equal(join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))),join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1)))))) )],[refute_0_803,refute_0_804]) ).
cnf(refute_0_806,plain,
join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))) = join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))),
inference(resolve,[$cnf( $equal(complement(join(composition(complement(sk1),top),complement(complement(sk1)))),complement(join(sk1,composition(complement(sk1),top)))) )],[refute_0_802,refute_0_805]) ).
cnf(refute_0_807,plain,
( complement(sk1) != join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1)))))
| join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))) != join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top))))
| complement(sk1) = join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(sk1),join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top))))) ),[0],$fot(join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))))]]) ).
cnf(refute_0_808,plain,
( complement(sk1) != join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1)))))
| complement(sk1) = join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) ),
inference(resolve,[$cnf( $equal(join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1))))),join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top))))) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
complement(sk1) = join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))),
inference(resolve,[$cnf( $equal(complement(sk1),join(composition(complement(sk1),top),complement(join(composition(complement(sk1),top),complement(complement(sk1)))))) )],[refute_0_789,refute_0_808]) ).
cnf(refute_0_810,plain,
join(composition(complement(sk1),top),complement(composition(top,top))) = join(complement(composition(top,top)),composition(complement(sk1),top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(composition(top,top)))),bind(B,$fot(composition(complement(sk1),top)))]]) ).
cnf(refute_0_811,plain,
join(sk1,complement(sk1)) = top,
inference(subst,[],[refute_0_80:[bind(A,$fot(sk1))]]) ).
cnf(refute_0_812,plain,
composition(join(sk1,complement(sk1)),top) = composition(join(sk1,complement(sk1)),top),
introduced(tautology,[refl,[$fot(composition(join(sk1,complement(sk1)),top))]]) ).
cnf(refute_0_813,plain,
( composition(join(sk1,complement(sk1)),top) != composition(join(sk1,complement(sk1)),top)
| join(sk1,complement(sk1)) != top
| composition(join(sk1,complement(sk1)),top) = composition(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(sk1,complement(sk1)),top),composition(join(sk1,complement(sk1)),top)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_814,plain,
( join(sk1,complement(sk1)) != top
| composition(join(sk1,complement(sk1)),top) = composition(top,top) ),
inference(resolve,[$cnf( $equal(composition(join(sk1,complement(sk1)),top),composition(join(sk1,complement(sk1)),top)) )],[refute_0_812,refute_0_813]) ).
cnf(refute_0_815,plain,
composition(join(sk1,complement(sk1)),top) = composition(top,top),
inference(resolve,[$cnf( $equal(join(sk1,complement(sk1)),top) )],[refute_0_811,refute_0_814]) ).
cnf(refute_0_816,plain,
join(composition(X_135,X_136),composition(X_134,X_136)) = join(composition(X_134,X_136),composition(X_135,X_136)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(composition(X_135,X_136))),bind(B,$fot(composition(X_134,X_136)))]]) ).
cnf(refute_0_817,plain,
composition(join(X_134,X_135),X_136) = join(composition(X_134,X_136),composition(X_135,X_136)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_134)),bind(B,$fot(X_135)),bind(C,$fot(X_136))]]) ).
cnf(refute_0_818,plain,
( composition(join(X_134,X_135),X_136) != join(composition(X_134,X_136),composition(X_135,X_136))
| join(composition(X_134,X_136),composition(X_135,X_136)) = composition(join(X_134,X_135),X_136) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_134,X_135),X_136))),bind(Y,$fot(join(composition(X_134,X_136),composition(X_135,X_136))))]]) ).
cnf(refute_0_819,plain,
join(composition(X_134,X_136),composition(X_135,X_136)) = composition(join(X_134,X_135),X_136),
inference(resolve,[$cnf( $equal(composition(join(X_134,X_135),X_136),join(composition(X_134,X_136),composition(X_135,X_136))) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
( join(composition(X_134,X_136),composition(X_135,X_136)) != composition(join(X_134,X_135),X_136)
| join(composition(X_135,X_136),composition(X_134,X_136)) != join(composition(X_134,X_136),composition(X_135,X_136))
| join(composition(X_135,X_136),composition(X_134,X_136)) = composition(join(X_134,X_135),X_136) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_135,X_136),composition(X_134,X_136)),join(composition(X_134,X_136),composition(X_135,X_136))) ),[1],$fot(composition(join(X_134,X_135),X_136))]]) ).
cnf(refute_0_821,plain,
( join(composition(X_135,X_136),composition(X_134,X_136)) != join(composition(X_134,X_136),composition(X_135,X_136))
| join(composition(X_135,X_136),composition(X_134,X_136)) = composition(join(X_134,X_135),X_136) ),
inference(resolve,[$cnf( $equal(join(composition(X_134,X_136),composition(X_135,X_136)),composition(join(X_134,X_135),X_136)) )],[refute_0_819,refute_0_820]) ).
cnf(refute_0_822,plain,
join(composition(X_135,X_136),composition(X_134,X_136)) = composition(join(X_134,X_135),X_136),
inference(resolve,[$cnf( $equal(join(composition(X_135,X_136),composition(X_134,X_136)),join(composition(X_134,X_136),composition(X_135,X_136))) )],[refute_0_816,refute_0_821]) ).
cnf(refute_0_823,plain,
( composition(join(A,B),C) != join(composition(A,C),composition(B,C))
| join(composition(A,C),composition(B,C)) = composition(join(A,B),C) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(A,B),C))),bind(Y,$fot(join(composition(A,C),composition(B,C))))]]) ).
cnf(refute_0_824,plain,
join(composition(A,C),composition(B,C)) = composition(join(A,B),C),
inference(resolve,[$cnf( $equal(composition(join(A,B),C),join(composition(A,C),composition(B,C))) )],[composition_distributivity_7,refute_0_823]) ).
cnf(refute_0_825,plain,
join(composition(X_135,X_136),composition(X_134,X_136)) = composition(join(X_135,X_134),X_136),
inference(subst,[],[refute_0_824:[bind(A,$fot(X_135)),bind(B,$fot(X_134)),bind(C,$fot(X_136))]]) ).
cnf(refute_0_826,plain,
( join(composition(X_135,X_136),composition(X_134,X_136)) != composition(join(X_134,X_135),X_136)
| join(composition(X_135,X_136),composition(X_134,X_136)) != composition(join(X_135,X_134),X_136)
| composition(join(X_135,X_134),X_136) = composition(join(X_134,X_135),X_136) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_135,X_136),composition(X_134,X_136)),composition(join(X_134,X_135),X_136)) ),[0],$fot(composition(join(X_135,X_134),X_136))]]) ).
cnf(refute_0_827,plain,
( join(composition(X_135,X_136),composition(X_134,X_136)) != composition(join(X_134,X_135),X_136)
| composition(join(X_135,X_134),X_136) = composition(join(X_134,X_135),X_136) ),
inference(resolve,[$cnf( $equal(join(composition(X_135,X_136),composition(X_134,X_136)),composition(join(X_135,X_134),X_136)) )],[refute_0_825,refute_0_826]) ).
cnf(refute_0_828,plain,
composition(join(X_135,X_134),X_136) = composition(join(X_134,X_135),X_136),
inference(resolve,[$cnf( $equal(join(composition(X_135,X_136),composition(X_134,X_136)),composition(join(X_134,X_135),X_136)) )],[refute_0_822,refute_0_827]) ).
cnf(refute_0_829,plain,
( composition(join(X_135,X_134),X_136) != composition(join(X_134,X_135),X_136)
| composition(join(X_134,X_135),X_136) = composition(join(X_135,X_134),X_136) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_135,X_134),X_136))),bind(Y,$fot(composition(join(X_134,X_135),X_136)))]]) ).
cnf(refute_0_830,plain,
composition(join(X_134,X_135),X_136) = composition(join(X_135,X_134),X_136),
inference(resolve,[$cnf( $equal(composition(join(X_135,X_134),X_136),composition(join(X_134,X_135),X_136)) )],[refute_0_828,refute_0_829]) ).
cnf(refute_0_831,plain,
composition(join(complement(sk1),sk1),top) = composition(join(sk1,complement(sk1)),top),
inference(subst,[],[refute_0_830:[bind(X_134,$fot(complement(sk1))),bind(X_135,$fot(sk1)),bind(X_136,$fot(top))]]) ).
cnf(refute_0_832,plain,
composition(join(X_134,sk1),top) = join(composition(X_134,top),composition(sk1,top)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_134)),bind(B,$fot(sk1)),bind(C,$fot(top))]]) ).
cnf(refute_0_833,plain,
( composition(join(X_134,sk1),top) != join(composition(X_134,top),composition(sk1,top))
| composition(sk1,top) != sk1
| composition(join(X_134,sk1),top) = join(composition(X_134,top),sk1) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_134,sk1),top),join(composition(X_134,top),composition(sk1,top))) ),[1,1],$fot(sk1)]]) ).
cnf(refute_0_834,plain,
( composition(join(X_134,sk1),top) != join(composition(X_134,top),composition(sk1,top))
| composition(join(X_134,sk1),top) = join(composition(X_134,top),sk1) ),
inference(resolve,[$cnf( $equal(composition(sk1,top),sk1) )],[goals_14,refute_0_833]) ).
cnf(refute_0_835,plain,
composition(join(X_134,sk1),top) = join(composition(X_134,top),sk1),
inference(resolve,[$cnf( $equal(composition(join(X_134,sk1),top),join(composition(X_134,top),composition(sk1,top))) )],[refute_0_832,refute_0_834]) ).
cnf(refute_0_836,plain,
join(composition(X_134,top),sk1) = join(sk1,composition(X_134,top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(sk1)),bind(B,$fot(composition(X_134,top)))]]) ).
cnf(refute_0_837,plain,
( composition(join(X_134,sk1),top) != join(composition(X_134,top),sk1)
| join(composition(X_134,top),sk1) != join(sk1,composition(X_134,top))
| composition(join(X_134,sk1),top) = join(sk1,composition(X_134,top)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_134,sk1),top),join(sk1,composition(X_134,top))) ),[0],$fot(join(composition(X_134,top),sk1))]]) ).
cnf(refute_0_838,plain,
( composition(join(X_134,sk1),top) != join(composition(X_134,top),sk1)
| composition(join(X_134,sk1),top) = join(sk1,composition(X_134,top)) ),
inference(resolve,[$cnf( $equal(join(composition(X_134,top),sk1),join(sk1,composition(X_134,top))) )],[refute_0_836,refute_0_837]) ).
cnf(refute_0_839,plain,
composition(join(X_134,sk1),top) = join(sk1,composition(X_134,top)),
inference(resolve,[$cnf( $equal(composition(join(X_134,sk1),top),join(composition(X_134,top),sk1)) )],[refute_0_835,refute_0_838]) ).
cnf(refute_0_840,plain,
( composition(join(X_134,sk1),top) != join(sk1,composition(X_134,top))
| join(sk1,composition(X_134,top)) = composition(join(X_134,sk1),top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_134,sk1),top))),bind(Y,$fot(join(sk1,composition(X_134,top))))]]) ).
cnf(refute_0_841,plain,
join(sk1,composition(X_134,top)) = composition(join(X_134,sk1),top),
inference(resolve,[$cnf( $equal(composition(join(X_134,sk1),top),join(sk1,composition(X_134,top))) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
join(sk1,composition(complement(sk1),top)) = composition(join(complement(sk1),sk1),top),
inference(subst,[],[refute_0_841:[bind(X_134,$fot(complement(sk1)))]]) ).
cnf(refute_0_843,plain,
( composition(join(complement(sk1),sk1),top) != composition(join(sk1,complement(sk1)),top)
| join(sk1,composition(complement(sk1),top)) != composition(join(complement(sk1),sk1),top)
| join(sk1,composition(complement(sk1),top)) = composition(join(sk1,complement(sk1)),top) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(sk1,composition(complement(sk1),top)))),bind(Y,$fot(composition(join(complement(sk1),sk1),top))),bind(Z,$fot(composition(join(sk1,complement(sk1)),top)))]]) ).
cnf(refute_0_844,plain,
( composition(join(complement(sk1),sk1),top) != composition(join(sk1,complement(sk1)),top)
| join(sk1,composition(complement(sk1),top)) = composition(join(sk1,complement(sk1)),top) ),
inference(resolve,[$cnf( $equal(join(sk1,composition(complement(sk1),top)),composition(join(complement(sk1),sk1),top)) )],[refute_0_842,refute_0_843]) ).
cnf(refute_0_845,plain,
join(sk1,composition(complement(sk1),top)) = composition(join(sk1,complement(sk1)),top),
inference(resolve,[$cnf( $equal(composition(join(complement(sk1),sk1),top),composition(join(sk1,complement(sk1)),top)) )],[refute_0_831,refute_0_844]) ).
cnf(refute_0_846,plain,
( composition(join(sk1,complement(sk1)),top) != composition(top,top)
| join(sk1,composition(complement(sk1),top)) != composition(join(sk1,complement(sk1)),top)
| join(sk1,composition(complement(sk1),top)) = composition(top,top) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(sk1,composition(complement(sk1),top)))),bind(Y,$fot(composition(join(sk1,complement(sk1)),top))),bind(Z,$fot(composition(top,top)))]]) ).
cnf(refute_0_847,plain,
( composition(join(sk1,complement(sk1)),top) != composition(top,top)
| join(sk1,composition(complement(sk1),top)) = composition(top,top) ),
inference(resolve,[$cnf( $equal(join(sk1,composition(complement(sk1),top)),composition(join(sk1,complement(sk1)),top)) )],[refute_0_845,refute_0_846]) ).
cnf(refute_0_848,plain,
join(sk1,composition(complement(sk1),top)) = composition(top,top),
inference(resolve,[$cnf( $equal(composition(join(sk1,complement(sk1)),top),composition(top,top)) )],[refute_0_815,refute_0_847]) ).
cnf(refute_0_849,plain,
complement(join(sk1,composition(complement(sk1),top))) = complement(join(sk1,composition(complement(sk1),top))),
introduced(tautology,[refl,[$fot(complement(join(sk1,composition(complement(sk1),top))))]]) ).
cnf(refute_0_850,plain,
( complement(join(sk1,composition(complement(sk1),top))) != complement(join(sk1,composition(complement(sk1),top)))
| join(sk1,composition(complement(sk1),top)) != composition(top,top)
| complement(join(sk1,composition(complement(sk1),top))) = complement(composition(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(sk1,composition(complement(sk1),top))),complement(join(sk1,composition(complement(sk1),top)))) ),[1,0],$fot(composition(top,top))]]) ).
cnf(refute_0_851,plain,
( join(sk1,composition(complement(sk1),top)) != composition(top,top)
| complement(join(sk1,composition(complement(sk1),top))) = complement(composition(top,top)) ),
inference(resolve,[$cnf( $equal(complement(join(sk1,composition(complement(sk1),top))),complement(join(sk1,composition(complement(sk1),top)))) )],[refute_0_849,refute_0_850]) ).
cnf(refute_0_852,plain,
complement(join(sk1,composition(complement(sk1),top))) = complement(composition(top,top)),
inference(resolve,[$cnf( $equal(join(sk1,composition(complement(sk1),top)),composition(top,top)) )],[refute_0_848,refute_0_851]) ).
cnf(refute_0_853,plain,
join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) = join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))),
introduced(tautology,[refl,[$fot(join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))))]]) ).
cnf(refute_0_854,plain,
( complement(join(sk1,composition(complement(sk1),top))) != complement(composition(top,top))
| join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) != join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top))))
| join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) = join(composition(complement(sk1),top),complement(composition(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))),join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top))))) ),[1,1],$fot(complement(composition(top,top)))]]) ).
cnf(refute_0_855,plain,
( complement(join(sk1,composition(complement(sk1),top))) != complement(composition(top,top))
| join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) = join(composition(complement(sk1),top),complement(composition(top,top))) ),
inference(resolve,[$cnf( $equal(join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))),join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top))))) )],[refute_0_853,refute_0_854]) ).
cnf(refute_0_856,plain,
join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) = join(composition(complement(sk1),top),complement(composition(top,top))),
inference(resolve,[$cnf( $equal(complement(join(sk1,composition(complement(sk1),top))),complement(composition(top,top))) )],[refute_0_852,refute_0_855]) ).
cnf(refute_0_857,plain,
( join(composition(complement(sk1),top),complement(composition(top,top))) != join(complement(composition(top,top)),composition(complement(sk1),top))
| join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) != join(composition(complement(sk1),top),complement(composition(top,top)))
| join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) = join(complement(composition(top,top)),composition(complement(sk1),top)) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))))),bind(Y,$fot(join(composition(complement(sk1),top),complement(composition(top,top))))),bind(Z,$fot(join(complement(composition(top,top)),composition(complement(sk1),top))))]]) ).
cnf(refute_0_858,plain,
( join(composition(complement(sk1),top),complement(composition(top,top))) != join(complement(composition(top,top)),composition(complement(sk1),top))
| join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) = join(complement(composition(top,top)),composition(complement(sk1),top)) ),
inference(resolve,[$cnf( $equal(join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))),join(composition(complement(sk1),top),complement(composition(top,top)))) )],[refute_0_856,refute_0_857]) ).
cnf(refute_0_859,plain,
join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) = join(complement(composition(top,top)),composition(complement(sk1),top)),
inference(resolve,[$cnf( $equal(join(composition(complement(sk1),top),complement(composition(top,top))),join(complement(composition(top,top)),composition(complement(sk1),top))) )],[refute_0_810,refute_0_858]) ).
cnf(refute_0_860,plain,
( complement(sk1) != join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top))))
| join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))) != join(complement(composition(top,top)),composition(complement(sk1),top))
| complement(sk1) = join(complement(composition(top,top)),composition(complement(sk1),top)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(sk1),join(complement(composition(top,top)),composition(complement(sk1),top))) ),[0],$fot(join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))))]]) ).
cnf(refute_0_861,plain,
( complement(sk1) != join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top))))
| complement(sk1) = join(complement(composition(top,top)),composition(complement(sk1),top)) ),
inference(resolve,[$cnf( $equal(join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top)))),join(complement(composition(top,top)),composition(complement(sk1),top))) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
complement(sk1) = join(complement(composition(top,top)),composition(complement(sk1),top)),
inference(resolve,[$cnf( $equal(complement(sk1),join(composition(complement(sk1),top),complement(join(sk1,composition(complement(sk1),top))))) )],[refute_0_809,refute_0_861]) ).
cnf(refute_0_863,plain,
join(zero,composition(complement(sk1),top)) = composition(complement(sk1),top),
inference(subst,[],[refute_0_525:[bind(X_52,$fot(composition(complement(sk1),top)))]]) ).
cnf(refute_0_864,plain,
composition(join(X_134,one),X_136) = join(composition(X_134,X_136),composition(one,X_136)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_134)),bind(B,$fot(one)),bind(C,$fot(X_136))]]) ).
cnf(refute_0_865,plain,
X_136 = composition(one,X_136),
inference(subst,[],[refute_0_160:[bind(X_8,$fot(X_136))]]) ).
cnf(refute_0_866,plain,
( X_136 != composition(one,X_136)
| composition(one,X_136) = X_136 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_136)),bind(Y,$fot(composition(one,X_136)))]]) ).
cnf(refute_0_867,plain,
composition(one,X_136) = X_136,
inference(resolve,[$cnf( $equal(X_136,composition(one,X_136)) )],[refute_0_865,refute_0_866]) ).
cnf(refute_0_868,plain,
( composition(join(X_134,one),X_136) != join(composition(X_134,X_136),composition(one,X_136))
| composition(one,X_136) != X_136
| composition(join(X_134,one),X_136) = join(composition(X_134,X_136),X_136) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_134,one),X_136),join(composition(X_134,X_136),composition(one,X_136))) ),[1,1],$fot(X_136)]]) ).
cnf(refute_0_869,plain,
( composition(join(X_134,one),X_136) != join(composition(X_134,X_136),composition(one,X_136))
| composition(join(X_134,one),X_136) = join(composition(X_134,X_136),X_136) ),
inference(resolve,[$cnf( $equal(composition(one,X_136),X_136) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
composition(join(X_134,one),X_136) = join(composition(X_134,X_136),X_136),
inference(resolve,[$cnf( $equal(composition(join(X_134,one),X_136),join(composition(X_134,X_136),composition(one,X_136))) )],[refute_0_864,refute_0_869]) ).
cnf(refute_0_871,plain,
join(composition(X_134,X_136),X_136) = join(X_136,composition(X_134,X_136)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_136)),bind(B,$fot(composition(X_134,X_136)))]]) ).
cnf(refute_0_872,plain,
( composition(join(X_134,one),X_136) != join(composition(X_134,X_136),X_136)
| join(composition(X_134,X_136),X_136) != join(X_136,composition(X_134,X_136))
| composition(join(X_134,one),X_136) = join(X_136,composition(X_134,X_136)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_134,one),X_136),join(X_136,composition(X_134,X_136))) ),[0],$fot(join(composition(X_134,X_136),X_136))]]) ).
cnf(refute_0_873,plain,
( composition(join(X_134,one),X_136) != join(composition(X_134,X_136),X_136)
| composition(join(X_134,one),X_136) = join(X_136,composition(X_134,X_136)) ),
inference(resolve,[$cnf( $equal(join(composition(X_134,X_136),X_136),join(X_136,composition(X_134,X_136))) )],[refute_0_871,refute_0_872]) ).
cnf(refute_0_874,plain,
composition(join(X_134,one),X_136) = join(X_136,composition(X_134,X_136)),
inference(resolve,[$cnf( $equal(composition(join(X_134,one),X_136),join(composition(X_134,X_136),X_136)) )],[refute_0_870,refute_0_873]) ).
cnf(refute_0_875,plain,
composition(join(converse(X_5),one),top) = join(top,composition(converse(X_5),top)),
inference(subst,[],[refute_0_874:[bind(X_134,$fot(converse(X_5))),bind(X_136,$fot(top))]]) ).
cnf(refute_0_876,plain,
converse(composition(converse(top),X_5)) = composition(converse(X_5),top),
inference(subst,[],[refute_0_135:[bind(A,$fot(top))]]) ).
cnf(refute_0_877,plain,
( converse(composition(converse(top),X_5)) != composition(converse(X_5),top)
| converse(top) != top
| converse(composition(top,X_5)) = composition(converse(X_5),top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(top),X_5)),composition(converse(X_5),top)) ),[0,0,0],$fot(top)]]) ).
cnf(refute_0_878,plain,
( converse(composition(converse(top),X_5)) != composition(converse(X_5),top)
| converse(composition(top,X_5)) = composition(converse(X_5),top) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_723,refute_0_877]) ).
cnf(refute_0_879,plain,
converse(composition(top,X_5)) = composition(converse(X_5),top),
inference(resolve,[$cnf( $equal(converse(composition(converse(top),X_5)),composition(converse(X_5),top)) )],[refute_0_876,refute_0_878]) ).
cnf(refute_0_880,plain,
( converse(composition(top,X_5)) != composition(converse(X_5),top)
| composition(converse(X_5),top) = converse(composition(top,X_5)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(top,X_5)))),bind(Y,$fot(composition(converse(X_5),top)))]]) ).
cnf(refute_0_881,plain,
composition(converse(X_5),top) = converse(composition(top,X_5)),
inference(resolve,[$cnf( $equal(converse(composition(top,X_5)),composition(converse(X_5),top)) )],[refute_0_879,refute_0_880]) ).
cnf(refute_0_882,plain,
( composition(converse(X_5),top) != converse(composition(top,X_5))
| composition(join(converse(X_5),one),top) != join(top,composition(converse(X_5),top))
| composition(join(converse(X_5),one),top) = join(top,converse(composition(top,X_5))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(X_5),one),top),join(top,composition(converse(X_5),top))) ),[1,1],$fot(converse(composition(top,X_5)))]]) ).
cnf(refute_0_883,plain,
( composition(join(converse(X_5),one),top) != join(top,composition(converse(X_5),top))
| composition(join(converse(X_5),one),top) = join(top,converse(composition(top,X_5))) ),
inference(resolve,[$cnf( $equal(composition(converse(X_5),top),converse(composition(top,X_5))) )],[refute_0_881,refute_0_882]) ).
cnf(refute_0_884,plain,
composition(join(converse(X_5),one),top) = join(top,converse(composition(top,X_5))),
inference(resolve,[$cnf( $equal(composition(join(converse(X_5),one),top),join(top,composition(converse(X_5),top))) )],[refute_0_875,refute_0_883]) ).
cnf(refute_0_885,plain,
composition(converse(join(X_5,one)),top) = converse(composition(top,join(X_5,one))),
inference(subst,[],[refute_0_881:[bind(X_5,$fot(join(X_5,one)))]]) ).
cnf(refute_0_886,plain,
converse(join(X_24,one)) = join(converse(X_24),converse(one)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_24)),bind(B,$fot(one))]]) ).
cnf(refute_0_887,plain,
( converse(join(X_24,one)) != join(converse(X_24),converse(one))
| converse(one) != one
| converse(join(X_24,one)) = join(converse(X_24),one) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_24,one)),join(converse(X_24),converse(one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_888,plain,
( converse(join(X_24,one)) != join(converse(X_24),converse(one))
| converse(join(X_24,one)) = join(converse(X_24),one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_153,refute_0_887]) ).
cnf(refute_0_889,plain,
converse(join(X_24,one)) = join(converse(X_24),one),
inference(resolve,[$cnf( $equal(converse(join(X_24,one)),join(converse(X_24),converse(one))) )],[refute_0_886,refute_0_888]) ).
cnf(refute_0_890,plain,
join(converse(X_24),one) = join(one,converse(X_24)),
inference(subst,[],[refute_0_4:[bind(A,$fot(one)),bind(B,$fot(converse(X_24)))]]) ).
cnf(refute_0_891,plain,
( converse(join(X_24,one)) != join(converse(X_24),one)
| join(converse(X_24),one) != join(one,converse(X_24))
| converse(join(X_24,one)) = join(one,converse(X_24)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X_24,one)),join(one,converse(X_24))) ),[0],$fot(join(converse(X_24),one))]]) ).
cnf(refute_0_892,plain,
( converse(join(X_24,one)) != join(converse(X_24),one)
| converse(join(X_24,one)) = join(one,converse(X_24)) ),
inference(resolve,[$cnf( $equal(join(converse(X_24),one),join(one,converse(X_24))) )],[refute_0_890,refute_0_891]) ).
cnf(refute_0_893,plain,
converse(join(X_24,one)) = join(one,converse(X_24)),
inference(resolve,[$cnf( $equal(converse(join(X_24,one)),join(converse(X_24),one)) )],[refute_0_889,refute_0_892]) ).
cnf(refute_0_894,plain,
( converse(join(X_24,one)) != join(one,converse(X_24))
| join(one,converse(X_24)) = converse(join(X_24,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_24,one)))),bind(Y,$fot(join(one,converse(X_24))))]]) ).
cnf(refute_0_895,plain,
join(one,converse(X_24)) = converse(join(X_24,one)),
inference(resolve,[$cnf( $equal(converse(join(X_24,one)),join(one,converse(X_24))) )],[refute_0_893,refute_0_894]) ).
cnf(refute_0_896,plain,
join(one,converse(X_5)) = converse(join(X_5,one)),
inference(subst,[],[refute_0_895:[bind(X_24,$fot(X_5))]]) ).
cnf(refute_0_897,plain,
composition(join(one,converse(X_5)),top) = composition(join(one,converse(X_5)),top),
introduced(tautology,[refl,[$fot(composition(join(one,converse(X_5)),top))]]) ).
cnf(refute_0_898,plain,
( composition(join(one,converse(X_5)),top) != composition(join(one,converse(X_5)),top)
| join(one,converse(X_5)) != converse(join(X_5,one))
| composition(join(one,converse(X_5)),top) = composition(converse(join(X_5,one)),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(X_5)),top),composition(join(one,converse(X_5)),top)) ),[1,0],$fot(converse(join(X_5,one)))]]) ).
cnf(refute_0_899,plain,
( join(one,converse(X_5)) != converse(join(X_5,one))
| composition(join(one,converse(X_5)),top) = composition(converse(join(X_5,one)),top) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(X_5)),top),composition(join(one,converse(X_5)),top)) )],[refute_0_897,refute_0_898]) ).
cnf(refute_0_900,plain,
composition(join(one,converse(X_5)),top) = composition(converse(join(X_5,one)),top),
inference(resolve,[$cnf( $equal(join(one,converse(X_5)),converse(join(X_5,one))) )],[refute_0_896,refute_0_899]) ).
cnf(refute_0_901,plain,
( composition(converse(join(X_5,one)),top) != converse(composition(top,join(X_5,one)))
| composition(join(one,converse(X_5)),top) != composition(converse(join(X_5,one)),top)
| composition(join(one,converse(X_5)),top) = converse(composition(top,join(X_5,one))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(composition(join(one,converse(X_5)),top))),bind(Y,$fot(composition(converse(join(X_5,one)),top))),bind(Z,$fot(converse(composition(top,join(X_5,one)))))]]) ).
cnf(refute_0_902,plain,
( composition(converse(join(X_5,one)),top) != converse(composition(top,join(X_5,one)))
| composition(join(one,converse(X_5)),top) = converse(composition(top,join(X_5,one))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(X_5)),top),composition(converse(join(X_5,one)),top)) )],[refute_0_900,refute_0_901]) ).
cnf(refute_0_903,plain,
composition(join(one,converse(X_5)),top) = converse(composition(top,join(X_5,one))),
inference(resolve,[$cnf( $equal(composition(converse(join(X_5,one)),top),converse(composition(top,join(X_5,one)))) )],[refute_0_885,refute_0_902]) ).
cnf(refute_0_904,plain,
composition(join(X_151,one),X_152) = join(X_152,composition(X_151,X_152)),
inference(subst,[],[refute_0_874:[bind(X_134,$fot(X_151)),bind(X_136,$fot(X_152))]]) ).
cnf(refute_0_905,plain,
join(one,X_151) = join(X_151,one),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(one)),bind(B,$fot(X_151))]]) ).
cnf(refute_0_906,plain,
( join(one,X_151) != join(X_151,one)
| join(X_151,one) = join(one,X_151) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,X_151))),bind(Y,$fot(join(X_151,one)))]]) ).
cnf(refute_0_907,plain,
join(X_151,one) = join(one,X_151),
inference(resolve,[$cnf( $equal(join(one,X_151),join(X_151,one)) )],[refute_0_905,refute_0_906]) ).
cnf(refute_0_908,plain,
( composition(join(X_151,one),X_152) != join(X_152,composition(X_151,X_152))
| join(X_151,one) != join(one,X_151)
| composition(join(one,X_151),X_152) = join(X_152,composition(X_151,X_152)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_151,one),X_152),join(X_152,composition(X_151,X_152))) ),[0,0],$fot(join(one,X_151))]]) ).
cnf(refute_0_909,plain,
( composition(join(X_151,one),X_152) != join(X_152,composition(X_151,X_152))
| composition(join(one,X_151),X_152) = join(X_152,composition(X_151,X_152)) ),
inference(resolve,[$cnf( $equal(join(X_151,one),join(one,X_151)) )],[refute_0_907,refute_0_908]) ).
cnf(refute_0_910,plain,
composition(join(one,X_151),X_152) = join(X_152,composition(X_151,X_152)),
inference(resolve,[$cnf( $equal(composition(join(X_151,one),X_152),join(X_152,composition(X_151,X_152))) )],[refute_0_904,refute_0_909]) ).
cnf(refute_0_911,plain,
( composition(join(X_134,one),X_136) != join(X_136,composition(X_134,X_136))
| join(X_136,composition(X_134,X_136)) = composition(join(X_134,one),X_136) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_134,one),X_136))),bind(Y,$fot(join(X_136,composition(X_134,X_136))))]]) ).
cnf(refute_0_912,plain,
join(X_136,composition(X_134,X_136)) = composition(join(X_134,one),X_136),
inference(resolve,[$cnf( $equal(composition(join(X_134,one),X_136),join(X_136,composition(X_134,X_136))) )],[refute_0_874,refute_0_911]) ).
cnf(refute_0_913,plain,
join(X_152,composition(X_151,X_152)) = composition(join(X_151,one),X_152),
inference(subst,[],[refute_0_912:[bind(X_134,$fot(X_151)),bind(X_136,$fot(X_152))]]) ).
cnf(refute_0_914,plain,
( composition(join(one,X_151),X_152) != join(X_152,composition(X_151,X_152))
| join(X_152,composition(X_151,X_152)) != composition(join(X_151,one),X_152)
| composition(join(one,X_151),X_152) = composition(join(X_151,one),X_152) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,X_151),X_152),composition(join(X_151,one),X_152)) ),[0],$fot(join(X_152,composition(X_151,X_152)))]]) ).
cnf(refute_0_915,plain,
( composition(join(one,X_151),X_152) != join(X_152,composition(X_151,X_152))
| composition(join(one,X_151),X_152) = composition(join(X_151,one),X_152) ),
inference(resolve,[$cnf( $equal(join(X_152,composition(X_151,X_152)),composition(join(X_151,one),X_152)) )],[refute_0_913,refute_0_914]) ).
cnf(refute_0_916,plain,
composition(join(one,X_151),X_152) = composition(join(X_151,one),X_152),
inference(resolve,[$cnf( $equal(composition(join(one,X_151),X_152),join(X_152,composition(X_151,X_152))) )],[refute_0_910,refute_0_915]) ).
cnf(refute_0_917,plain,
( composition(join(one,X_151),X_152) != composition(join(X_151,one),X_152)
| composition(join(X_151,one),X_152) = composition(join(one,X_151),X_152) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,X_151),X_152))),bind(Y,$fot(composition(join(X_151,one),X_152)))]]) ).
cnf(refute_0_918,plain,
composition(join(X_151,one),X_152) = composition(join(one,X_151),X_152),
inference(resolve,[$cnf( $equal(composition(join(one,X_151),X_152),composition(join(X_151,one),X_152)) )],[refute_0_916,refute_0_917]) ).
cnf(refute_0_919,plain,
composition(join(converse(X_5),one),top) = composition(join(one,converse(X_5)),top),
inference(subst,[],[refute_0_918:[bind(X_151,$fot(converse(X_5))),bind(X_152,$fot(top))]]) ).
cnf(refute_0_920,plain,
( composition(join(converse(X_5),one),top) != composition(join(one,converse(X_5)),top)
| composition(join(one,converse(X_5)),top) != converse(composition(top,join(X_5,one)))
| composition(join(converse(X_5),one),top) = converse(composition(top,join(X_5,one))) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(composition(join(converse(X_5),one),top))),bind(Y,$fot(composition(join(one,converse(X_5)),top))),bind(Z,$fot(converse(composition(top,join(X_5,one)))))]]) ).
cnf(refute_0_921,plain,
( composition(join(one,converse(X_5)),top) != converse(composition(top,join(X_5,one)))
| composition(join(converse(X_5),one),top) = converse(composition(top,join(X_5,one))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(X_5),one),top),composition(join(one,converse(X_5)),top)) )],[refute_0_919,refute_0_920]) ).
cnf(refute_0_922,plain,
composition(join(converse(X_5),one),top) = converse(composition(top,join(X_5,one))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(X_5)),top),converse(composition(top,join(X_5,one)))) )],[refute_0_903,refute_0_921]) ).
cnf(refute_0_923,plain,
( composition(join(converse(X_5),one),top) != converse(composition(top,join(X_5,one)))
| composition(join(converse(X_5),one),top) != join(top,converse(composition(top,X_5)))
| converse(composition(top,join(X_5,one))) = join(top,converse(composition(top,X_5))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(X_5),one),top),join(top,converse(composition(top,X_5)))) ),[0],$fot(converse(composition(top,join(X_5,one))))]]) ).
cnf(refute_0_924,plain,
( composition(join(converse(X_5),one),top) != join(top,converse(composition(top,X_5)))
| converse(composition(top,join(X_5,one))) = join(top,converse(composition(top,X_5))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(X_5),one),top),converse(composition(top,join(X_5,one)))) )],[refute_0_922,refute_0_923]) ).
cnf(refute_0_925,plain,
join(top,converse(composition(top,X_5))) = top,
inference(subst,[],[refute_0_538:[bind(B,$fot(converse(composition(top,X_5))))]]) ).
cnf(refute_0_926,plain,
( converse(composition(top,join(X_5,one))) != join(top,converse(composition(top,X_5)))
| join(top,converse(composition(top,X_5))) != top
| converse(composition(top,join(X_5,one))) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(composition(top,join(X_5,one))),top) ),[0],$fot(join(top,converse(composition(top,X_5))))]]) ).
cnf(refute_0_927,plain,
( converse(composition(top,join(X_5,one))) != join(top,converse(composition(top,X_5)))
| converse(composition(top,join(X_5,one))) = top ),
inference(resolve,[$cnf( $equal(join(top,converse(composition(top,X_5))),top) )],[refute_0_925,refute_0_926]) ).
cnf(refute_0_928,plain,
( composition(join(converse(X_5),one),top) != join(top,converse(composition(top,X_5)))
| converse(composition(top,join(X_5,one))) = top ),
inference(resolve,[$cnf( $equal(converse(composition(top,join(X_5,one))),join(top,converse(composition(top,X_5)))) )],[refute_0_924,refute_0_927]) ).
cnf(refute_0_929,plain,
converse(composition(top,join(X_5,one))) = top,
inference(resolve,[$cnf( $equal(composition(join(converse(X_5),one),top),join(top,converse(composition(top,X_5)))) )],[refute_0_884,refute_0_928]) ).
cnf(refute_0_930,plain,
converse(composition(top,join(top,one))) = top,
inference(subst,[],[refute_0_929:[bind(X_5,$fot(top))]]) ).
cnf(refute_0_931,plain,
join(top,one) = top,
inference(subst,[],[refute_0_538:[bind(B,$fot(one))]]) ).
cnf(refute_0_932,plain,
( converse(composition(top,join(top,one))) != top
| join(top,one) != top
| converse(composition(top,top)) = top ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(top,join(top,one))),top) ),[0,0,1],$fot(top)]]) ).
cnf(refute_0_933,plain,
( converse(composition(top,join(top,one))) != top
| converse(composition(top,top)) = top ),
inference(resolve,[$cnf( $equal(join(top,one),top) )],[refute_0_931,refute_0_932]) ).
cnf(refute_0_934,plain,
converse(composition(top,top)) = top,
inference(resolve,[$cnf( $equal(converse(composition(top,join(top,one))),top) )],[refute_0_930,refute_0_933]) ).
cnf(refute_0_935,plain,
converse(composition(X_4,converse(A))) = composition(converse(converse(A)),converse(X_4)),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(X_4)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_936,plain,
( converse(composition(X_4,converse(A))) != composition(converse(converse(A)),converse(X_4))
| converse(converse(A)) != A
| converse(composition(X_4,converse(A))) = composition(A,converse(X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_4,converse(A))),composition(converse(converse(A)),converse(X_4))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_937,plain,
( converse(composition(X_4,converse(A))) != composition(converse(converse(A)),converse(X_4))
| converse(composition(X_4,converse(A))) = composition(A,converse(X_4)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_936]) ).
cnf(refute_0_938,plain,
converse(composition(X_4,converse(A))) = composition(A,converse(X_4)),
inference(resolve,[$cnf( $equal(converse(composition(X_4,converse(A))),composition(converse(converse(A)),converse(X_4))) )],[refute_0_935,refute_0_937]) ).
cnf(refute_0_939,plain,
converse(composition(X_4,converse(top))) = composition(top,converse(X_4)),
inference(subst,[],[refute_0_938:[bind(A,$fot(top))]]) ).
cnf(refute_0_940,plain,
( converse(composition(X_4,converse(top))) != composition(top,converse(X_4))
| converse(top) != top
| converse(composition(X_4,top)) = composition(top,converse(X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_4,converse(top))),composition(top,converse(X_4))) ),[0,0,1],$fot(top)]]) ).
cnf(refute_0_941,plain,
( converse(composition(X_4,converse(top))) != composition(top,converse(X_4))
| converse(composition(X_4,top)) = composition(top,converse(X_4)) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_723,refute_0_940]) ).
cnf(refute_0_942,plain,
converse(composition(X_4,top)) = composition(top,converse(X_4)),
inference(resolve,[$cnf( $equal(converse(composition(X_4,converse(top))),composition(top,converse(X_4))) )],[refute_0_939,refute_0_941]) ).
cnf(refute_0_943,plain,
converse(composition(top,top)) = composition(top,converse(top)),
inference(subst,[],[refute_0_942:[bind(X_4,$fot(top))]]) ).
cnf(refute_0_944,plain,
( converse(composition(top,top)) != composition(top,converse(top))
| converse(top) != top
| converse(composition(top,top)) = composition(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(top,top)),composition(top,converse(top))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_945,plain,
( converse(composition(top,top)) != composition(top,converse(top))
| converse(composition(top,top)) = composition(top,top) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_723,refute_0_944]) ).
cnf(refute_0_946,plain,
converse(composition(top,top)) = composition(top,top),
inference(resolve,[$cnf( $equal(converse(composition(top,top)),composition(top,converse(top))) )],[refute_0_943,refute_0_945]) ).
cnf(refute_0_947,plain,
( converse(composition(top,top)) != composition(top,top)
| converse(composition(top,top)) != top
| composition(top,top) = top ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(top,top)),top) ),[0],$fot(composition(top,top))]]) ).
cnf(refute_0_948,plain,
( converse(composition(top,top)) != top
| composition(top,top) = top ),
inference(resolve,[$cnf( $equal(converse(composition(top,top)),composition(top,top)) )],[refute_0_946,refute_0_947]) ).
cnf(refute_0_949,plain,
composition(top,top) = top,
inference(resolve,[$cnf( $equal(converse(composition(top,top)),top) )],[refute_0_934,refute_0_948]) ).
cnf(refute_0_950,plain,
complement(composition(top,top)) = complement(composition(top,top)),
introduced(tautology,[refl,[$fot(complement(composition(top,top)))]]) ).
cnf(refute_0_951,plain,
( complement(composition(top,top)) != complement(composition(top,top))
| composition(top,top) != top
| complement(composition(top,top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(top,top)),complement(composition(top,top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_952,plain,
( composition(top,top) != top
| complement(composition(top,top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(composition(top,top)),complement(composition(top,top))) )],[refute_0_950,refute_0_951]) ).
cnf(refute_0_953,plain,
complement(composition(top,top)) = complement(top),
inference(resolve,[$cnf( $equal(composition(top,top),top) )],[refute_0_949,refute_0_952]) ).
cnf(refute_0_954,plain,
( complement(composition(top,top)) != complement(top)
| complement(top) != zero
| complement(composition(top,top)) = zero ),
inference(subst,[],[refute_0_17:[bind(X,$fot(complement(composition(top,top)))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_955,plain,
( complement(top) != zero
| complement(composition(top,top)) = zero ),
inference(resolve,[$cnf( $equal(complement(composition(top,top)),complement(top)) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
complement(composition(top,top)) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_98,refute_0_955]) ).
cnf(refute_0_957,plain,
join(complement(composition(top,top)),composition(complement(sk1),top)) = join(complement(composition(top,top)),composition(complement(sk1),top)),
introduced(tautology,[refl,[$fot(join(complement(composition(top,top)),composition(complement(sk1),top)))]]) ).
cnf(refute_0_958,plain,
( complement(composition(top,top)) != zero
| join(complement(composition(top,top)),composition(complement(sk1),top)) != join(complement(composition(top,top)),composition(complement(sk1),top))
| join(complement(composition(top,top)),composition(complement(sk1),top)) = join(zero,composition(complement(sk1),top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(top,top)),composition(complement(sk1),top)),join(complement(composition(top,top)),composition(complement(sk1),top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_959,plain,
( complement(composition(top,top)) != zero
| join(complement(composition(top,top)),composition(complement(sk1),top)) = join(zero,composition(complement(sk1),top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,top)),composition(complement(sk1),top)),join(complement(composition(top,top)),composition(complement(sk1),top))) )],[refute_0_957,refute_0_958]) ).
cnf(refute_0_960,plain,
join(complement(composition(top,top)),composition(complement(sk1),top)) = join(zero,composition(complement(sk1),top)),
inference(resolve,[$cnf( $equal(complement(composition(top,top)),zero) )],[refute_0_956,refute_0_959]) ).
cnf(refute_0_961,plain,
( join(complement(composition(top,top)),composition(complement(sk1),top)) != join(zero,composition(complement(sk1),top))
| join(zero,composition(complement(sk1),top)) != composition(complement(sk1),top)
| join(complement(composition(top,top)),composition(complement(sk1),top)) = composition(complement(sk1),top) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(join(complement(composition(top,top)),composition(complement(sk1),top)))),bind(Y,$fot(join(zero,composition(complement(sk1),top)))),bind(Z,$fot(composition(complement(sk1),top)))]]) ).
cnf(refute_0_962,plain,
( join(zero,composition(complement(sk1),top)) != composition(complement(sk1),top)
| join(complement(composition(top,top)),composition(complement(sk1),top)) = composition(complement(sk1),top) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,top)),composition(complement(sk1),top)),join(zero,composition(complement(sk1),top))) )],[refute_0_960,refute_0_961]) ).
cnf(refute_0_963,plain,
join(complement(composition(top,top)),composition(complement(sk1),top)) = composition(complement(sk1),top),
inference(resolve,[$cnf( $equal(join(zero,composition(complement(sk1),top)),composition(complement(sk1),top)) )],[refute_0_863,refute_0_962]) ).
cnf(refute_0_964,plain,
( complement(sk1) != join(complement(composition(top,top)),composition(complement(sk1),top))
| join(complement(composition(top,top)),composition(complement(sk1),top)) != composition(complement(sk1),top)
| complement(sk1) = composition(complement(sk1),top) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(sk1),composition(complement(sk1),top)) ),[0],$fot(join(complement(composition(top,top)),composition(complement(sk1),top)))]]) ).
cnf(refute_0_965,plain,
( complement(sk1) != join(complement(composition(top,top)),composition(complement(sk1),top))
| complement(sk1) = composition(complement(sk1),top) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,top)),composition(complement(sk1),top)),composition(complement(sk1),top)) )],[refute_0_963,refute_0_964]) ).
cnf(refute_0_966,plain,
complement(sk1) = composition(complement(sk1),top),
inference(resolve,[$cnf( $equal(complement(sk1),join(complement(composition(top,top)),composition(complement(sk1),top))) )],[refute_0_862,refute_0_965]) ).
cnf(refute_0_967,plain,
( complement(sk1) != composition(complement(sk1),top)
| composition(complement(sk1),top) = complement(sk1) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(sk1))),bind(Y,$fot(composition(complement(sk1),top)))]]) ).
cnf(refute_0_968,plain,
complement(sk1) != composition(complement(sk1),top),
inference(resolve,[$cnf( $equal(composition(complement(sk1),top),complement(sk1)) )],[refute_0_967,goals_15]) ).
cnf(refute_0_969,plain,
$false,
inference(resolve,[$cnf( $equal(complement(sk1),composition(complement(sk1),top)) )],[refute_0_966,refute_0_968]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : REL018-1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Fri Jul 8 16:08:45 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.07/1.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.07/1.26
% 1.07/1.26 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.17/1.36
%------------------------------------------------------------------------------