TSTP Solution File: REL002-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL002-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 19:42:56 EDT 2022
% Result : Unsatisfiable 0.60s 0.75s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 97
% Number of leaves : 215
% Syntax : Number of clauses : 910 ( 454 unt; 0 nHn; 629 RR)
% Number of literals : 1564 (1563 equ; 656 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 837 ( 12 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(converse_idempotence_8,axiom,
converse(converse(A)) = A ).
cnf(converse_additivity_9,axiom,
converse(join(A,B)) = join(converse(A),converse(B)) ).
cnf(def_top_12,axiom,
top = join(A,complement(A)) ).
cnf(def_zero_13,axiom,
zero = meet(A,complement(A)) ).
cnf(goals_14,negated_conjecture,
join(sk1,top) != top ).
cnf(refute_0_0,plain,
join(X_15,join(complement(X_15),X_17)) = join(join(X_15,complement(X_15)),X_17),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_15)),bind(B,$fot(complement(X_15))),bind(C,$fot(X_17))]]) ).
cnf(refute_0_1,plain,
top = join(X_15,complement(X_15)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_15))]]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( top != join(X_15,complement(X_15))
| join(X_15,complement(X_15)) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(X_15,complement(X_15))))]]) ).
cnf(refute_0_6,plain,
join(X_15,complement(X_15)) = top,
inference(resolve,[$cnf( $equal(top,join(X_15,complement(X_15))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( join(X_15,complement(X_15)) != top
| join(X_15,join(complement(X_15),X_17)) != join(join(X_15,complement(X_15)),X_17)
| join(X_15,join(complement(X_15),X_17)) = join(top,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_15,join(complement(X_15),X_17)),join(join(X_15,complement(X_15)),X_17)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_8,plain,
( join(X_15,join(complement(X_15),X_17)) != join(join(X_15,complement(X_15)),X_17)
| join(X_15,join(complement(X_15),X_17)) = join(top,X_17) ),
inference(resolve,[$cnf( $equal(join(X_15,complement(X_15)),top) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
join(X_15,join(complement(X_15),X_17)) = join(top,X_17),
inference(resolve,[$cnf( $equal(join(X_15,join(complement(X_15),X_17)),join(join(X_15,complement(X_15)),X_17)) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
join(X_15,join(complement(X_15),join(complement(complement(X_15)),X_19))) = join(top,join(complement(complement(X_15)),X_19)),
inference(subst,[],[refute_0_9:[bind(X_17,$fot(join(complement(complement(X_15)),X_19)))]]) ).
cnf(refute_0_11,plain,
join(complement(X_15),join(complement(complement(X_15)),X_19)) = join(top,X_19),
inference(subst,[],[refute_0_9:[bind(X_15,$fot(complement(X_15))),bind(X_17,$fot(X_19))]]) ).
cnf(refute_0_12,plain,
( join(X_15,join(complement(X_15),join(complement(complement(X_15)),X_19))) != join(top,join(complement(complement(X_15)),X_19))
| join(complement(X_15),join(complement(complement(X_15)),X_19)) != join(top,X_19)
| join(X_15,join(top,X_19)) = join(top,join(complement(complement(X_15)),X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_15,join(complement(X_15),join(complement(complement(X_15)),X_19))),join(top,join(complement(complement(X_15)),X_19))) ),[0,1],$fot(join(top,X_19))]]) ).
cnf(refute_0_13,plain,
( join(X_15,join(complement(X_15),join(complement(complement(X_15)),X_19))) != join(top,join(complement(complement(X_15)),X_19))
| join(X_15,join(top,X_19)) = join(top,join(complement(complement(X_15)),X_19)) ),
inference(resolve,[$cnf( $equal(join(complement(X_15),join(complement(complement(X_15)),X_19)),join(top,X_19)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
join(X_15,join(top,X_19)) = join(top,join(complement(complement(X_15)),X_19)),
inference(resolve,[$cnf( $equal(join(X_15,join(complement(X_15),join(complement(complement(X_15)),X_19))),join(top,join(complement(complement(X_15)),X_19))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
join(X_18,join(complement(X_18),X_19)) = join(top,X_19),
inference(subst,[],[refute_0_9:[bind(X_15,$fot(X_18)),bind(X_17,$fot(X_19))]]) ).
cnf(refute_0_16,plain,
join(X_19,complement(X_18)) = join(complement(X_18),X_19),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_19)),bind(B,$fot(complement(X_18)))]]) ).
cnf(refute_0_17,plain,
( join(X_19,complement(X_18)) != join(complement(X_18),X_19)
| join(complement(X_18),X_19) = join(X_19,complement(X_18)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_19,complement(X_18)))),bind(Y,$fot(join(complement(X_18),X_19)))]]) ).
cnf(refute_0_18,plain,
join(complement(X_18),X_19) = join(X_19,complement(X_18)),
inference(resolve,[$cnf( $equal(join(X_19,complement(X_18)),join(complement(X_18),X_19)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( join(X_18,join(complement(X_18),X_19)) != join(top,X_19)
| join(complement(X_18),X_19) != join(X_19,complement(X_18))
| join(X_18,join(X_19,complement(X_18))) = join(top,X_19) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_18,join(complement(X_18),X_19)),join(top,X_19)) ),[0,1],$fot(join(X_19,complement(X_18)))]]) ).
cnf(refute_0_20,plain,
( join(X_18,join(complement(X_18),X_19)) != join(top,X_19)
| join(X_18,join(X_19,complement(X_18))) = join(top,X_19) ),
inference(resolve,[$cnf( $equal(join(complement(X_18),X_19),join(X_19,complement(X_18))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
join(X_18,join(X_19,complement(X_18))) = join(top,X_19),
inference(resolve,[$cnf( $equal(join(X_18,join(complement(X_18),X_19)),join(top,X_19)) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
join(join(zero,X_32),join(meet(top,X_32),complement(join(zero,X_32)))) = join(top,meet(top,X_32)),
inference(subst,[],[refute_0_21:[bind(X_18,$fot(join(zero,X_32))),bind(X_19,$fot(meet(top,X_32)))]]) ).
cnf(refute_0_23,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_24,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_23]) ).
cnf(refute_0_25,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_24:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_26,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$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_27,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( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_27]) ).
cnf(refute_0_29,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_24:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_30,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_31,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_30]) ).
cnf(refute_0_32,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_33,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_34,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_37,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_36]) ).
cnf(refute_0_38,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_37:[bind(X,$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_39,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_29,refute_0_39]) ).
cnf(refute_0_41,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$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_42,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_28,refute_0_42]) ).
cnf(refute_0_44,plain,
top = join(meet(top,X_32),complement(join(complement(top),X_32))),
inference(subst,[],[refute_0_43:[bind(A,$fot(top)),bind(B,$fot(X_32))]]) ).
cnf(refute_0_45,plain,
zero = meet(join(complement(X_22),complement(X_23)),complement(join(complement(X_22),complement(X_23)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_22),complement(X_23))))]]) ).
cnf(refute_0_46,plain,
meet(X_22,X_23) = complement(join(complement(X_22),complement(X_23))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_22)),bind(B,$fot(X_23))]]) ).
cnf(refute_0_47,plain,
( meet(X_22,X_23) != complement(join(complement(X_22),complement(X_23)))
| complement(join(complement(X_22),complement(X_23))) = meet(X_22,X_23) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_22,X_23))),bind(Y,$fot(complement(join(complement(X_22),complement(X_23)))))]]) ).
cnf(refute_0_48,plain,
complement(join(complement(X_22),complement(X_23))) = meet(X_22,X_23),
inference(resolve,[$cnf( $equal(meet(X_22,X_23),complement(join(complement(X_22),complement(X_23)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( complement(join(complement(X_22),complement(X_23))) != meet(X_22,X_23)
| zero != meet(join(complement(X_22),complement(X_23)),complement(join(complement(X_22),complement(X_23))))
| zero = meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_22),complement(X_23)),complement(join(complement(X_22),complement(X_23))))) ),[1,1],$fot(meet(X_22,X_23))]]) ).
cnf(refute_0_50,plain,
( zero != meet(join(complement(X_22),complement(X_23)),complement(join(complement(X_22),complement(X_23))))
| zero = meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_22),complement(X_23))),meet(X_22,X_23)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
zero = meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_22),complement(X_23)),complement(join(complement(X_22),complement(X_23))))) )],[refute_0_45,refute_0_50]) ).
cnf(refute_0_52,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_53,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_52]) ).
cnf(refute_0_54,plain,
join(meet(X_22,X_23),complement(meet(X_22,X_23))) = top,
inference(subst,[],[refute_0_53:[bind(A,$fot(meet(X_22,X_23)))]]) ).
cnf(refute_0_55,plain,
complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))) = complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))))]]) ).
cnf(refute_0_56,plain,
( complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))) != complement(join(meet(X_22,X_23),complement(meet(X_22,X_23))))
| join(meet(X_22,X_23),complement(meet(X_22,X_23))) != top
| complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))),complement(join(meet(X_22,X_23),complement(meet(X_22,X_23))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_57,plain,
( join(meet(X_22,X_23),complement(meet(X_22,X_23))) != top
| complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))),complement(join(meet(X_22,X_23),complement(meet(X_22,X_23))))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_23),complement(meet(X_22,X_23))),top) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
meet(join(complement(X_22),complement(X_23)),B) = complement(join(complement(join(complement(X_22),complement(X_23))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_22),complement(X_23))))]]) ).
cnf(refute_0_60,plain,
( complement(join(complement(X_22),complement(X_23))) != meet(X_22,X_23)
| meet(join(complement(X_22),complement(X_23)),B) != complement(join(complement(join(complement(X_22),complement(X_23))),complement(B)))
| meet(join(complement(X_22),complement(X_23)),B) = complement(join(meet(X_22,X_23),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_22),complement(X_23)),B),complement(join(complement(join(complement(X_22),complement(X_23))),complement(B)))) ),[1,0,0],$fot(meet(X_22,X_23))]]) ).
cnf(refute_0_61,plain,
( meet(join(complement(X_22),complement(X_23)),B) != complement(join(complement(join(complement(X_22),complement(X_23))),complement(B)))
| meet(join(complement(X_22),complement(X_23)),B) = complement(join(meet(X_22,X_23),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_22),complement(X_23))),meet(X_22,X_23)) )],[refute_0_48,refute_0_60]) ).
cnf(refute_0_62,plain,
meet(join(complement(X_22),complement(X_23)),B) = complement(join(meet(X_22,X_23),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_22),complement(X_23)),B),complement(join(complement(join(complement(X_22),complement(X_23))),complement(B)))) )],[refute_0_59,refute_0_61]) ).
cnf(refute_0_63,plain,
meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) = complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))),
inference(subst,[],[refute_0_62:[bind(B,$fot(meet(X_22,X_23)))]]) ).
cnf(refute_0_64,plain,
( complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))) != complement(top)
| meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) != complement(join(meet(X_22,X_23),complement(meet(X_22,X_23))))
| meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) = complement(top) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)))),bind(Y,$fot(complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_65,plain,
( complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))) != complement(top)
| meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)),complement(join(meet(X_22,X_23),complement(meet(X_22,X_23))))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_22,X_23),complement(meet(X_22,X_23)))),complement(top)) )],[refute_0_58,refute_0_65]) ).
cnf(refute_0_67,plain,
( meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) != complement(top)
| zero != meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_68,plain,
( zero != meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23)),complement(top)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_22),complement(X_23)),meet(X_22,X_23))) )],[refute_0_51,refute_0_68]) ).
cnf(refute_0_70,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_71,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( complement(top) != zero
| top != join(meet(top,X_32),complement(join(complement(top),X_32)))
| top = join(meet(top,X_32),complement(join(zero,X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,X_32),complement(join(complement(top),X_32)))) ),[1,1,0,0],$fot(zero)]]) ).
cnf(refute_0_73,plain,
( top != join(meet(top,X_32),complement(join(complement(top),X_32)))
| top = join(meet(top,X_32),complement(join(zero,X_32))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
top = join(meet(top,X_32),complement(join(zero,X_32))),
inference(resolve,[$cnf( $equal(top,join(meet(top,X_32),complement(join(complement(top),X_32)))) )],[refute_0_44,refute_0_73]) ).
cnf(refute_0_75,plain,
( top != join(meet(top,X_32),complement(join(zero,X_32)))
| join(meet(top,X_32),complement(join(zero,X_32))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(meet(top,X_32),complement(join(zero,X_32)))))]]) ).
cnf(refute_0_76,plain,
join(meet(top,X_32),complement(join(zero,X_32))) = top,
inference(resolve,[$cnf( $equal(top,join(meet(top,X_32),complement(join(zero,X_32)))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( join(join(zero,X_32),join(meet(top,X_32),complement(join(zero,X_32)))) != join(top,meet(top,X_32))
| join(meet(top,X_32),complement(join(zero,X_32))) != top
| join(join(zero,X_32),top) = join(top,meet(top,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(zero,X_32),join(meet(top,X_32),complement(join(zero,X_32)))),join(top,meet(top,X_32))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_78,plain,
( join(join(zero,X_32),join(meet(top,X_32),complement(join(zero,X_32)))) != join(top,meet(top,X_32))
| join(join(zero,X_32),top) = join(top,meet(top,X_32)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_32),complement(join(zero,X_32))),top) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
join(join(zero,X_32),top) = join(top,meet(top,X_32)),
inference(resolve,[$cnf( $equal(join(join(zero,X_32),join(meet(top,X_32),complement(join(zero,X_32)))),join(top,meet(top,X_32))) )],[refute_0_22,refute_0_78]) ).
cnf(refute_0_80,plain,
join(top,join(complement(top),X_17)) = join(top,X_17),
inference(subst,[],[refute_0_9:[bind(X_15,$fot(top))]]) ).
cnf(refute_0_81,plain,
( complement(top) != zero
| join(top,join(complement(top),X_17)) != join(top,X_17)
| join(top,join(zero,X_17)) = join(top,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(complement(top),X_17)),join(top,X_17)) ),[0,1,0],$fot(zero)]]) ).
cnf(refute_0_82,plain,
( join(top,join(complement(top),X_17)) != join(top,X_17)
| join(top,join(zero,X_17)) = join(top,X_17) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_81]) ).
cnf(refute_0_83,plain,
join(top,join(zero,X_17)) = join(top,X_17),
inference(resolve,[$cnf( $equal(join(top,join(complement(top),X_17)),join(top,X_17)) )],[refute_0_80,refute_0_82]) ).
cnf(refute_0_84,plain,
join(top,join(zero,X_32)) = join(top,X_32),
inference(subst,[],[refute_0_83:[bind(X_17,$fot(X_32))]]) ).
cnf(refute_0_85,plain,
join(X_15,join(converse(complement(converse(X_15))),X_17)) = join(join(X_15,converse(complement(converse(X_15)))),X_17),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_15)),bind(B,$fot(converse(complement(converse(X_15))))),bind(C,$fot(X_17))]]) ).
cnf(refute_0_86,plain,
converse(join(converse(A),X_7)) = join(converse(converse(A)),converse(X_7)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(A))),bind(B,$fot(X_7))]]) ).
cnf(refute_0_87,plain,
( converse(converse(A)) != A
| converse(join(converse(A),X_7)) != join(converse(converse(A)),converse(X_7))
| converse(join(converse(A),X_7)) = join(A,converse(X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),X_7)),join(converse(converse(A)),converse(X_7))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_88,plain,
( converse(join(converse(A),X_7)) != join(converse(converse(A)),converse(X_7))
| converse(join(converse(A),X_7)) = join(A,converse(X_7)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_87]) ).
cnf(refute_0_89,plain,
converse(join(converse(A),X_7)) = join(A,converse(X_7)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_7)),join(converse(converse(A)),converse(X_7))) )],[refute_0_86,refute_0_88]) ).
cnf(refute_0_90,plain,
converse(join(converse(X_8),complement(converse(X_8)))) = join(X_8,converse(complement(converse(X_8)))),
inference(subst,[],[refute_0_89:[bind(A,$fot(X_8)),bind(X_7,$fot(complement(converse(X_8))))]]) ).
cnf(refute_0_91,plain,
top = join(converse(X_8),complement(converse(X_8))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_8)))]]) ).
cnf(refute_0_92,plain,
( top != join(converse(X_8),complement(converse(X_8)))
| join(converse(X_8),complement(converse(X_8))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_8),complement(converse(X_8)))))]]) ).
cnf(refute_0_93,plain,
join(converse(X_8),complement(converse(X_8))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_8),complement(converse(X_8)))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
( converse(join(converse(X_8),complement(converse(X_8)))) != join(X_8,converse(complement(converse(X_8))))
| join(converse(X_8),complement(converse(X_8))) != top
| converse(top) = join(X_8,converse(complement(converse(X_8)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_8),complement(converse(X_8)))),join(X_8,converse(complement(converse(X_8))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_95,plain,
( converse(join(converse(X_8),complement(converse(X_8)))) != join(X_8,converse(complement(converse(X_8))))
| converse(top) = join(X_8,converse(complement(converse(X_8)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_8),complement(converse(X_8))),top) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
converse(top) = join(X_8,converse(complement(converse(X_8)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_8),complement(converse(X_8)))),join(X_8,converse(complement(converse(X_8))))) )],[refute_0_90,refute_0_95]) ).
cnf(refute_0_97,plain,
converse(top) = join(X_15,converse(complement(converse(X_15)))),
inference(subst,[],[refute_0_96:[bind(X_8,$fot(X_15))]]) ).
cnf(refute_0_98,plain,
( converse(top) != join(X_15,converse(complement(converse(X_15))))
| join(X_15,converse(complement(converse(X_15)))) = converse(top) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(converse(top))),bind(Y,$fot(join(X_15,converse(complement(converse(X_15))))))]]) ).
cnf(refute_0_99,plain,
join(X_15,converse(complement(converse(X_15)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(X_15,converse(complement(converse(X_15))))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( join(X_15,converse(complement(converse(X_15)))) != converse(top)
| join(X_15,join(converse(complement(converse(X_15))),X_17)) != join(join(X_15,converse(complement(converse(X_15)))),X_17)
| join(X_15,join(converse(complement(converse(X_15))),X_17)) = join(converse(top),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_15,join(converse(complement(converse(X_15))),X_17)),join(join(X_15,converse(complement(converse(X_15)))),X_17)) ),[1,0],$fot(converse(top))]]) ).
cnf(refute_0_101,plain,
( join(X_15,join(converse(complement(converse(X_15))),X_17)) != join(join(X_15,converse(complement(converse(X_15)))),X_17)
| join(X_15,join(converse(complement(converse(X_15))),X_17)) = join(converse(top),X_17) ),
inference(resolve,[$cnf( $equal(join(X_15,converse(complement(converse(X_15)))),converse(top)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
join(X_15,join(converse(complement(converse(X_15))),X_17)) = join(converse(top),X_17),
inference(resolve,[$cnf( $equal(join(X_15,join(converse(complement(converse(X_15))),X_17)),join(join(X_15,converse(complement(converse(X_15)))),X_17)) )],[refute_0_85,refute_0_101]) ).
cnf(refute_0_103,plain,
join(X_54,join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54)))))) = join(converse(top),complement(converse(complement(converse(X_54))))),
inference(subst,[],[refute_0_102:[bind(X_15,$fot(X_54)),bind(X_17,$fot(complement(converse(complement(converse(X_54))))))]]) ).
cnf(refute_0_104,plain,
top = join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54))))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(complement(converse(X_54)))))]]) ).
cnf(refute_0_105,plain,
( top != join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54)))))
| join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54))))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54)))))))]]) ).
cnf(refute_0_106,plain,
join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54))))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54)))))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( join(X_54,join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54)))))) != join(converse(top),complement(converse(complement(converse(X_54)))))
| join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54))))) != top
| join(X_54,top) = join(converse(top),complement(converse(complement(converse(X_54))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_54,join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54)))))),join(converse(top),complement(converse(complement(converse(X_54)))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_108,plain,
( join(X_54,join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54)))))) != join(converse(top),complement(converse(complement(converse(X_54)))))
| join(X_54,top) = join(converse(top),complement(converse(complement(converse(X_54))))) ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54))))),top) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
join(X_54,top) = join(converse(top),complement(converse(complement(converse(X_54))))),
inference(resolve,[$cnf( $equal(join(X_54,join(converse(complement(converse(X_54))),complement(converse(complement(converse(X_54)))))),join(converse(top),complement(converse(complement(converse(X_54)))))) )],[refute_0_103,refute_0_108]) ).
cnf(refute_0_110,plain,
converse(converse(X_54)) = X_54,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_54))]]) ).
cnf(refute_0_111,plain,
join(top,converse(converse(X_54))) = join(top,converse(converse(X_54))),
introduced(tautology,[refl,[$fot(join(top,converse(converse(X_54))))]]) ).
cnf(refute_0_112,plain,
( converse(converse(X_54)) != X_54
| join(top,converse(converse(X_54))) != join(top,converse(converse(X_54)))
| join(top,converse(converse(X_54))) = join(top,X_54) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,converse(converse(X_54))),join(top,converse(converse(X_54)))) ),[1,1],$fot(X_54)]]) ).
cnf(refute_0_113,plain,
( converse(converse(X_54)) != X_54
| join(top,converse(converse(X_54))) = join(top,X_54) ),
inference(resolve,[$cnf( $equal(join(top,converse(converse(X_54))),join(top,converse(converse(X_54)))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
join(top,converse(converse(X_54))) = join(top,X_54),
inference(resolve,[$cnf( $equal(converse(converse(X_54)),X_54) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
join(converse(X_7),converse(X_6)) = join(converse(X_6),converse(X_7)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(converse(X_7))),bind(B,$fot(converse(X_6)))]]) ).
cnf(refute_0_116,plain,
converse(join(X_6,X_7)) = join(converse(X_6),converse(X_7)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_6)),bind(B,$fot(X_7))]]) ).
cnf(refute_0_117,plain,
( converse(join(X_6,X_7)) != join(converse(X_6),converse(X_7))
| join(converse(X_6),converse(X_7)) = converse(join(X_6,X_7)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(converse(join(X_6,X_7)))),bind(Y,$fot(join(converse(X_6),converse(X_7))))]]) ).
cnf(refute_0_118,plain,
join(converse(X_6),converse(X_7)) = converse(join(X_6,X_7)),
inference(resolve,[$cnf( $equal(converse(join(X_6,X_7)),join(converse(X_6),converse(X_7))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
( join(converse(X_6),converse(X_7)) != converse(join(X_6,X_7))
| join(converse(X_7),converse(X_6)) != join(converse(X_6),converse(X_7))
| join(converse(X_7),converse(X_6)) = converse(join(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(X_7),converse(X_6)),join(converse(X_6),converse(X_7))) ),[1],$fot(converse(join(X_6,X_7)))]]) ).
cnf(refute_0_120,plain,
( join(converse(X_7),converse(X_6)) != join(converse(X_6),converse(X_7))
| join(converse(X_7),converse(X_6)) = converse(join(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(join(converse(X_6),converse(X_7)),converse(join(X_6,X_7))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
join(converse(X_7),converse(X_6)) = converse(join(X_6,X_7)),
inference(resolve,[$cnf( $equal(join(converse(X_7),converse(X_6)),join(converse(X_6),converse(X_7))) )],[refute_0_115,refute_0_120]) ).
cnf(refute_0_122,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(join(converse(A),converse(B))))]]) ).
cnf(refute_0_123,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_122]) ).
cnf(refute_0_124,plain,
join(converse(X_7),converse(X_6)) = converse(join(X_7,X_6)),
inference(subst,[],[refute_0_123:[bind(A,$fot(X_7)),bind(B,$fot(X_6))]]) ).
cnf(refute_0_125,plain,
( join(converse(X_7),converse(X_6)) != converse(join(X_6,X_7))
| join(converse(X_7),converse(X_6)) != converse(join(X_7,X_6))
| converse(join(X_7,X_6)) = converse(join(X_6,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(X_7),converse(X_6)),converse(join(X_6,X_7))) ),[0],$fot(converse(join(X_7,X_6)))]]) ).
cnf(refute_0_126,plain,
( join(converse(X_7),converse(X_6)) != converse(join(X_6,X_7))
| converse(join(X_7,X_6)) = converse(join(X_6,X_7)) ),
inference(resolve,[$cnf( $equal(join(converse(X_7),converse(X_6)),converse(join(X_7,X_6))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
converse(join(X_7,X_6)) = converse(join(X_6,X_7)),
inference(resolve,[$cnf( $equal(join(converse(X_7),converse(X_6)),converse(join(X_6,X_7))) )],[refute_0_121,refute_0_126]) ).
cnf(refute_0_128,plain,
converse(join(converse(complement(converse(complement(X_65)))),top)) = converse(join(top,converse(complement(converse(complement(X_65)))))),
inference(subst,[],[refute_0_127:[bind(X_6,$fot(top)),bind(X_7,$fot(converse(complement(converse(complement(X_65))))))]]) ).
cnf(refute_0_129,plain,
join(X_18,join(complement(X_18),converse(complement(converse(complement(X_18)))))) = join(top,converse(complement(converse(complement(X_18))))),
inference(subst,[],[refute_0_9:[bind(X_15,$fot(X_18)),bind(X_17,$fot(converse(complement(converse(complement(X_18))))))]]) ).
cnf(refute_0_130,plain,
converse(top) = join(complement(X_18),converse(complement(converse(complement(X_18))))),
inference(subst,[],[refute_0_96:[bind(X_8,$fot(complement(X_18)))]]) ).
cnf(refute_0_131,plain,
( converse(top) != join(complement(X_18),converse(complement(converse(complement(X_18)))))
| join(complement(X_18),converse(complement(converse(complement(X_18))))) = converse(top) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(converse(top))),bind(Y,$fot(join(complement(X_18),converse(complement(converse(complement(X_18)))))))]]) ).
cnf(refute_0_132,plain,
join(complement(X_18),converse(complement(converse(complement(X_18))))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(complement(X_18),converse(complement(converse(complement(X_18)))))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
( join(X_18,join(complement(X_18),converse(complement(converse(complement(X_18)))))) != join(top,converse(complement(converse(complement(X_18)))))
| join(complement(X_18),converse(complement(converse(complement(X_18))))) != converse(top)
| join(X_18,converse(top)) = join(top,converse(complement(converse(complement(X_18))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_18,join(complement(X_18),converse(complement(converse(complement(X_18)))))),join(top,converse(complement(converse(complement(X_18)))))) ),[0,1],$fot(converse(top))]]) ).
cnf(refute_0_134,plain,
( join(X_18,join(complement(X_18),converse(complement(converse(complement(X_18)))))) != join(top,converse(complement(converse(complement(X_18)))))
| join(X_18,converse(top)) = join(top,converse(complement(converse(complement(X_18))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_18),converse(complement(converse(complement(X_18))))),converse(top)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
join(X_18,converse(top)) = join(top,converse(complement(converse(complement(X_18))))),
inference(resolve,[$cnf( $equal(join(X_18,join(complement(X_18),converse(complement(converse(complement(X_18)))))),join(top,converse(complement(converse(complement(X_18)))))) )],[refute_0_129,refute_0_134]) ).
cnf(refute_0_136,plain,
join(X_65,converse(top)) = join(top,converse(complement(converse(complement(X_65))))),
inference(subst,[],[refute_0_135:[bind(X_18,$fot(X_65))]]) ).
cnf(refute_0_137,plain,
( join(X_65,converse(top)) != join(top,converse(complement(converse(complement(X_65)))))
| join(top,converse(complement(converse(complement(X_65))))) = join(X_65,converse(top)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_65,converse(top)))),bind(Y,$fot(join(top,converse(complement(converse(complement(X_65)))))))]]) ).
cnf(refute_0_138,plain,
join(top,converse(complement(converse(complement(X_65))))) = join(X_65,converse(top)),
inference(resolve,[$cnf( $equal(join(X_65,converse(top)),join(top,converse(complement(converse(complement(X_65)))))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
( converse(join(converse(complement(converse(complement(X_65)))),top)) != converse(join(top,converse(complement(converse(complement(X_65))))))
| join(top,converse(complement(converse(complement(X_65))))) != join(X_65,converse(top))
| converse(join(converse(complement(converse(complement(X_65)))),top)) = converse(join(X_65,converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(converse(complement(X_65)))),top)),converse(join(top,converse(complement(converse(complement(X_65))))))) ),[1,0],$fot(join(X_65,converse(top)))]]) ).
cnf(refute_0_140,plain,
( converse(join(converse(complement(converse(complement(X_65)))),top)) != converse(join(top,converse(complement(converse(complement(X_65))))))
| converse(join(converse(complement(converse(complement(X_65)))),top)) = converse(join(X_65,converse(top))) ),
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(complement(X_65))))),join(X_65,converse(top))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
converse(join(converse(complement(converse(complement(X_65)))),top)) = converse(join(X_65,converse(top))),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(complement(X_65)))),top)),converse(join(top,converse(complement(converse(complement(X_65))))))) )],[refute_0_128,refute_0_140]) ).
cnf(refute_0_142,plain,
join(complement(converse(complement(X_65))),converse(top)) = join(converse(top),complement(converse(complement(X_65)))),
inference(subst,[],[refute_0_24:[bind(A,$fot(converse(top))),bind(B,$fot(complement(converse(complement(X_65)))))]]) ).
cnf(refute_0_143,plain,
converse(join(converse(complement(converse(complement(X_65)))),top)) = join(complement(converse(complement(X_65))),converse(top)),
inference(subst,[],[refute_0_89:[bind(A,$fot(complement(converse(complement(X_65))))),bind(X_7,$fot(top))]]) ).
cnf(refute_0_144,plain,
( converse(join(converse(complement(converse(complement(X_65)))),top)) != join(complement(converse(complement(X_65))),converse(top))
| join(complement(converse(complement(X_65))),converse(top)) != join(converse(top),complement(converse(complement(X_65))))
| converse(join(converse(complement(converse(complement(X_65)))),top)) = join(converse(top),complement(converse(complement(X_65)))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(converse(join(converse(complement(converse(complement(X_65)))),top)))),bind(Y,$fot(join(complement(converse(complement(X_65))),converse(top)))),bind(Z,$fot(join(converse(top),complement(converse(complement(X_65))))))]]) ).
cnf(refute_0_145,plain,
( join(complement(converse(complement(X_65))),converse(top)) != join(converse(top),complement(converse(complement(X_65))))
| converse(join(converse(complement(converse(complement(X_65)))),top)) = join(converse(top),complement(converse(complement(X_65)))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(complement(X_65)))),top)),join(complement(converse(complement(X_65))),converse(top))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
converse(join(converse(complement(converse(complement(X_65)))),top)) = join(converse(top),complement(converse(complement(X_65)))),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(X_65))),converse(top)),join(converse(top),complement(converse(complement(X_65))))) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
( converse(join(converse(complement(converse(complement(X_65)))),top)) != converse(join(X_65,converse(top)))
| converse(join(converse(complement(converse(complement(X_65)))),top)) != join(converse(top),complement(converse(complement(X_65))))
| join(converse(top),complement(converse(complement(X_65)))) = converse(join(X_65,converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(converse(complement(X_65)))),top)),converse(join(X_65,converse(top)))) ),[0],$fot(join(converse(top),complement(converse(complement(X_65)))))]]) ).
cnf(refute_0_148,plain,
( converse(join(converse(complement(converse(complement(X_65)))),top)) != converse(join(X_65,converse(top)))
| join(converse(top),complement(converse(complement(X_65)))) = converse(join(X_65,converse(top))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(complement(X_65)))),top)),join(converse(top),complement(converse(complement(X_65))))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
join(A,join(zero,join(zero,meet(top,top)))) = join(join(A,zero),join(zero,meet(top,top))),
inference(subst,[],[maddux2_join_associativity_2:[bind(B,$fot(zero)),bind(C,$fot(join(zero,meet(top,top))))]]) ).
cnf(refute_0_150,plain,
top = join(join(complement(X_22),complement(X_23)),complement(join(complement(X_22),complement(X_23)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(complement(X_22),complement(X_23))))]]) ).
cnf(refute_0_151,plain,
( complement(join(complement(X_22),complement(X_23))) != meet(X_22,X_23)
| top != join(join(complement(X_22),complement(X_23)),complement(join(complement(X_22),complement(X_23))))
| top = join(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_22),complement(X_23)),complement(join(complement(X_22),complement(X_23))))) ),[1,1],$fot(meet(X_22,X_23))]]) ).
cnf(refute_0_152,plain,
( top != join(join(complement(X_22),complement(X_23)),complement(join(complement(X_22),complement(X_23))))
| top = join(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_22),complement(X_23))),meet(X_22,X_23)) )],[refute_0_48,refute_0_151]) ).
cnf(refute_0_153,plain,
top = join(join(complement(X_22),complement(X_23)),meet(X_22,X_23)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_22),complement(X_23)),complement(join(complement(X_22),complement(X_23))))) )],[refute_0_150,refute_0_152]) ).
cnf(refute_0_154,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_155,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_154]) ).
cnf(refute_0_156,plain,
join(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) = join(complement(X_22),join(complement(X_23),meet(X_22,X_23))),
inference(subst,[],[refute_0_155:[bind(A,$fot(complement(X_22))),bind(B,$fot(complement(X_23))),bind(C,$fot(meet(X_22,X_23)))]]) ).
cnf(refute_0_157,plain,
( join(join(complement(X_22),complement(X_23)),meet(X_22,X_23)) != join(complement(X_22),join(complement(X_23),meet(X_22,X_23)))
| top != join(join(complement(X_22),complement(X_23)),meet(X_22,X_23))
| top = join(complement(X_22),join(complement(X_23),meet(X_22,X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_22),complement(X_23)),meet(X_22,X_23))) ),[1],$fot(join(complement(X_22),join(complement(X_23),meet(X_22,X_23))))]]) ).
cnf(refute_0_158,plain,
( top != join(join(complement(X_22),complement(X_23)),meet(X_22,X_23))
| top = join(complement(X_22),join(complement(X_23),meet(X_22,X_23))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_22),complement(X_23)),meet(X_22,X_23)),join(complement(X_22),join(complement(X_23),meet(X_22,X_23)))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
top = join(complement(X_22),join(complement(X_23),meet(X_22,X_23))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_22),complement(X_23)),meet(X_22,X_23))) )],[refute_0_153,refute_0_158]) ).
cnf(refute_0_160,plain,
top = join(complement(X_26),join(complement(top),meet(X_26,top))),
inference(subst,[],[refute_0_159:[bind(X_22,$fot(X_26)),bind(X_23,$fot(top))]]) ).
cnf(refute_0_161,plain,
( complement(top) != zero
| top != join(complement(X_26),join(complement(top),meet(X_26,top)))
| top = join(complement(X_26),join(zero,meet(X_26,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_26),join(complement(top),meet(X_26,top)))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_162,plain,
( top != join(complement(X_26),join(complement(top),meet(X_26,top)))
| top = join(complement(X_26),join(zero,meet(X_26,top))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_161]) ).
cnf(refute_0_163,plain,
top = join(complement(X_26),join(zero,meet(X_26,top))),
inference(resolve,[$cnf( $equal(top,join(complement(X_26),join(complement(top),meet(X_26,top)))) )],[refute_0_160,refute_0_162]) ).
cnf(refute_0_164,plain,
join(X_15,join(X_16,X_17)) = join(join(X_15,X_16),X_17),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_15)),bind(B,$fot(X_16)),bind(C,$fot(X_17))]]) ).
cnf(refute_0_165,plain,
join(X_16,X_15) = join(X_15,X_16),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_16)),bind(B,$fot(X_15))]]) ).
cnf(refute_0_166,plain,
( join(X_16,X_15) != join(X_15,X_16)
| join(X_15,X_16) = join(X_16,X_15) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_16,X_15))),bind(Y,$fot(join(X_15,X_16)))]]) ).
cnf(refute_0_167,plain,
join(X_15,X_16) = join(X_16,X_15),
inference(resolve,[$cnf( $equal(join(X_16,X_15),join(X_15,X_16)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
( join(X_15,X_16) != join(X_16,X_15)
| join(X_15,join(X_16,X_17)) != join(join(X_15,X_16),X_17)
| join(X_15,join(X_16,X_17)) = join(join(X_16,X_15),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_15,join(X_16,X_17)),join(join(X_15,X_16),X_17)) ),[1,0],$fot(join(X_16,X_15))]]) ).
cnf(refute_0_169,plain,
( join(X_15,join(X_16,X_17)) != join(join(X_15,X_16),X_17)
| join(X_15,join(X_16,X_17)) = join(join(X_16,X_15),X_17) ),
inference(resolve,[$cnf( $equal(join(X_15,X_16),join(X_16,X_15)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
join(X_15,join(X_16,X_17)) = join(join(X_16,X_15),X_17),
inference(resolve,[$cnf( $equal(join(X_15,join(X_16,X_17)),join(join(X_15,X_16),X_17)) )],[refute_0_164,refute_0_169]) ).
cnf(refute_0_171,plain,
join(join(X_16,X_15),X_17) = join(X_16,join(X_15,X_17)),
inference(subst,[],[refute_0_155:[bind(A,$fot(X_16)),bind(B,$fot(X_15)),bind(C,$fot(X_17))]]) ).
cnf(refute_0_172,plain,
( join(X_15,join(X_16,X_17)) != join(join(X_16,X_15),X_17)
| join(join(X_16,X_15),X_17) != join(X_16,join(X_15,X_17))
| join(X_15,join(X_16,X_17)) = join(X_16,join(X_15,X_17)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_15,join(X_16,X_17)),join(X_16,join(X_15,X_17))) ),[0],$fot(join(join(X_16,X_15),X_17))]]) ).
cnf(refute_0_173,plain,
( join(X_15,join(X_16,X_17)) != join(join(X_16,X_15),X_17)
| join(X_15,join(X_16,X_17)) = join(X_16,join(X_15,X_17)) ),
inference(resolve,[$cnf( $equal(join(join(X_16,X_15),X_17),join(X_16,join(X_15,X_17))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
join(X_15,join(X_16,X_17)) = join(X_16,join(X_15,X_17)),
inference(resolve,[$cnf( $equal(join(X_15,join(X_16,X_17)),join(join(X_16,X_15),X_17)) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
( join(X_15,join(X_16,X_17)) != join(X_16,join(X_15,X_17))
| join(X_16,join(X_15,X_17)) = join(X_15,join(X_16,X_17)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_15,join(X_16,X_17)))),bind(Y,$fot(join(X_16,join(X_15,X_17))))]]) ).
cnf(refute_0_176,plain,
join(X_16,join(X_15,X_17)) = join(X_15,join(X_16,X_17)),
inference(resolve,[$cnf( $equal(join(X_15,join(X_16,X_17)),join(X_16,join(X_15,X_17))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
join(complement(X_26),join(zero,meet(X_26,top))) = join(zero,join(complement(X_26),meet(X_26,top))),
inference(subst,[],[refute_0_176:[bind(X_15,$fot(zero)),bind(X_16,$fot(complement(X_26))),bind(X_17,$fot(meet(X_26,top)))]]) ).
cnf(refute_0_178,plain,
( join(complement(X_26),join(zero,meet(X_26,top))) != join(zero,join(complement(X_26),meet(X_26,top)))
| top != join(complement(X_26),join(zero,meet(X_26,top)))
| top = join(zero,join(complement(X_26),meet(X_26,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_26),join(zero,meet(X_26,top)))) ),[1],$fot(join(zero,join(complement(X_26),meet(X_26,top))))]]) ).
cnf(refute_0_179,plain,
( top != join(complement(X_26),join(zero,meet(X_26,top)))
| top = join(zero,join(complement(X_26),meet(X_26,top))) ),
inference(resolve,[$cnf( $equal(join(complement(X_26),join(zero,meet(X_26,top))),join(zero,join(complement(X_26),meet(X_26,top)))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
top = join(zero,join(complement(X_26),meet(X_26,top))),
inference(resolve,[$cnf( $equal(top,join(complement(X_26),join(zero,meet(X_26,top)))) )],[refute_0_163,refute_0_179]) ).
cnf(refute_0_181,plain,
top = join(zero,join(complement(top),meet(top,top))),
inference(subst,[],[refute_0_180:[bind(X_26,$fot(top))]]) ).
cnf(refute_0_182,plain,
( complement(top) != zero
| top != join(zero,join(complement(top),meet(top,top)))
| top = join(zero,join(zero,meet(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,join(complement(top),meet(top,top)))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_183,plain,
( top != join(zero,join(complement(top),meet(top,top)))
| top = join(zero,join(zero,meet(top,top))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_182]) ).
cnf(refute_0_184,plain,
top = join(zero,join(zero,meet(top,top))),
inference(resolve,[$cnf( $equal(top,join(zero,join(complement(top),meet(top,top)))) )],[refute_0_181,refute_0_183]) ).
cnf(refute_0_185,plain,
( top != join(zero,join(zero,meet(top,top)))
| join(zero,join(zero,meet(top,top))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(zero,join(zero,meet(top,top)))))]]) ).
cnf(refute_0_186,plain,
join(zero,join(zero,meet(top,top))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,join(zero,meet(top,top)))) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
( join(A,join(zero,join(zero,meet(top,top)))) != join(join(A,zero),join(zero,meet(top,top)))
| join(zero,join(zero,meet(top,top))) != top
| join(A,top) = join(join(A,zero),join(zero,meet(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(zero,join(zero,meet(top,top)))),join(join(A,zero),join(zero,meet(top,top)))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_188,plain,
( join(A,join(zero,join(zero,meet(top,top)))) != join(join(A,zero),join(zero,meet(top,top)))
| join(A,top) = join(join(A,zero),join(zero,meet(top,top))) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(top,top))),top) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
join(A,top) = join(join(A,zero),join(zero,meet(top,top))),
inference(resolve,[$cnf( $equal(join(A,join(zero,join(zero,meet(top,top)))),join(join(A,zero),join(zero,meet(top,top)))) )],[refute_0_149,refute_0_188]) ).
cnf(refute_0_190,plain,
join(join(A,zero),meet(top,top)) = join(A,join(zero,meet(top,top))),
inference(subst,[],[refute_0_155:[bind(B,$fot(zero)),bind(C,$fot(meet(top,top)))]]) ).
cnf(refute_0_191,plain,
join(zero,join(join(A,zero),meet(top,top))) = join(zero,join(join(A,zero),meet(top,top))),
introduced(tautology,[refl,[$fot(join(zero,join(join(A,zero),meet(top,top))))]]) ).
cnf(refute_0_192,plain,
( join(join(A,zero),meet(top,top)) != join(A,join(zero,meet(top,top)))
| join(zero,join(join(A,zero),meet(top,top))) != join(zero,join(join(A,zero),meet(top,top)))
| join(zero,join(join(A,zero),meet(top,top))) = join(zero,join(A,join(zero,meet(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(join(A,zero),meet(top,top))),join(zero,join(join(A,zero),meet(top,top)))) ),[1,1],$fot(join(A,join(zero,meet(top,top))))]]) ).
cnf(refute_0_193,plain,
( join(join(A,zero),meet(top,top)) != join(A,join(zero,meet(top,top)))
| join(zero,join(join(A,zero),meet(top,top))) = join(zero,join(A,join(zero,meet(top,top)))) ),
inference(resolve,[$cnf( $equal(join(zero,join(join(A,zero),meet(top,top))),join(zero,join(join(A,zero),meet(top,top)))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
join(zero,join(join(A,zero),meet(top,top))) = join(zero,join(A,join(zero,meet(top,top)))),
inference(resolve,[$cnf( $equal(join(join(A,zero),meet(top,top)),join(A,join(zero,meet(top,top)))) )],[refute_0_190,refute_0_193]) ).
cnf(refute_0_195,plain,
join(join(A,zero),join(zero,meet(top,top))) = join(zero,join(join(A,zero),meet(top,top))),
inference(subst,[],[refute_0_176:[bind(X_15,$fot(zero)),bind(X_16,$fot(join(A,zero))),bind(X_17,$fot(meet(top,top)))]]) ).
cnf(refute_0_196,plain,
( join(join(A,zero),join(zero,meet(top,top))) != join(zero,join(join(A,zero),meet(top,top)))
| join(zero,join(join(A,zero),meet(top,top))) != join(zero,join(A,join(zero,meet(top,top))))
| join(join(A,zero),join(zero,meet(top,top))) = join(zero,join(A,join(zero,meet(top,top)))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(join(A,zero),join(zero,meet(top,top))))),bind(Y,$fot(join(zero,join(join(A,zero),meet(top,top))))),bind(Z,$fot(join(zero,join(A,join(zero,meet(top,top))))))]]) ).
cnf(refute_0_197,plain,
( join(zero,join(join(A,zero),meet(top,top))) != join(zero,join(A,join(zero,meet(top,top))))
| join(join(A,zero),join(zero,meet(top,top))) = join(zero,join(A,join(zero,meet(top,top)))) ),
inference(resolve,[$cnf( $equal(join(join(A,zero),join(zero,meet(top,top))),join(zero,join(join(A,zero),meet(top,top)))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
join(join(A,zero),join(zero,meet(top,top))) = join(zero,join(A,join(zero,meet(top,top)))),
inference(resolve,[$cnf( $equal(join(zero,join(join(A,zero),meet(top,top))),join(zero,join(A,join(zero,meet(top,top))))) )],[refute_0_194,refute_0_197]) ).
cnf(refute_0_199,plain,
( join(A,top) != join(join(A,zero),join(zero,meet(top,top)))
| join(join(A,zero),join(zero,meet(top,top))) != join(zero,join(A,join(zero,meet(top,top))))
| join(A,top) = join(zero,join(A,join(zero,meet(top,top)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,top),join(zero,join(A,join(zero,meet(top,top))))) ),[0],$fot(join(join(A,zero),join(zero,meet(top,top))))]]) ).
cnf(refute_0_200,plain,
( join(A,top) != join(join(A,zero),join(zero,meet(top,top)))
| join(A,top) = join(zero,join(A,join(zero,meet(top,top)))) ),
inference(resolve,[$cnf( $equal(join(join(A,zero),join(zero,meet(top,top))),join(zero,join(A,join(zero,meet(top,top))))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
join(A,top) = join(zero,join(A,join(zero,meet(top,top)))),
inference(resolve,[$cnf( $equal(join(A,top),join(join(A,zero),join(zero,meet(top,top)))) )],[refute_0_189,refute_0_200]) ).
cnf(refute_0_202,plain,
join(top,join(zero,A)) = join(top,A),
inference(subst,[],[refute_0_83:[bind(X_17,$fot(A))]]) ).
cnf(refute_0_203,plain,
join(A,join(X_15,X_16)) = join(join(X_15,X_16),A),
inference(subst,[],[maddux1_join_commutativity_1:[bind(B,$fot(join(X_15,X_16)))]]) ).
cnf(refute_0_204,plain,
join(X_15,join(X_16,A)) = join(join(X_15,X_16),A),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_15)),bind(B,$fot(X_16)),bind(C,$fot(A))]]) ).
cnf(refute_0_205,plain,
( join(X_15,join(X_16,A)) != join(join(X_15,X_16),A)
| join(join(X_15,X_16),A) = join(X_15,join(X_16,A)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_15,join(X_16,A)))),bind(Y,$fot(join(join(X_15,X_16),A)))]]) ).
cnf(refute_0_206,plain,
join(join(X_15,X_16),A) = join(X_15,join(X_16,A)),
inference(resolve,[$cnf( $equal(join(X_15,join(X_16,A)),join(join(X_15,X_16),A)) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
( join(A,join(X_15,X_16)) != join(join(X_15,X_16),A)
| join(join(X_15,X_16),A) != join(X_15,join(X_16,A))
| join(A,join(X_15,X_16)) = join(X_15,join(X_16,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_15,X_16)),join(X_15,join(X_16,A))) ),[0],$fot(join(join(X_15,X_16),A))]]) ).
cnf(refute_0_208,plain,
( join(A,join(X_15,X_16)) != join(join(X_15,X_16),A)
| join(A,join(X_15,X_16)) = join(X_15,join(X_16,A)) ),
inference(resolve,[$cnf( $equal(join(join(X_15,X_16),A),join(X_15,join(X_16,A))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
join(A,join(X_15,X_16)) = join(X_15,join(X_16,A)),
inference(resolve,[$cnf( $equal(join(A,join(X_15,X_16)),join(join(X_15,X_16),A)) )],[refute_0_203,refute_0_208]) ).
cnf(refute_0_210,plain,
( join(A,join(X_15,X_16)) != join(X_15,join(X_16,A))
| join(X_15,join(X_16,A)) = join(A,join(X_15,X_16)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(A,join(X_15,X_16)))),bind(Y,$fot(join(X_15,join(X_16,A))))]]) ).
cnf(refute_0_211,plain,
join(X_15,join(X_16,A)) = join(A,join(X_15,X_16)),
inference(resolve,[$cnf( $equal(join(A,join(X_15,X_16)),join(X_15,join(X_16,A))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
join(zero,join(A,top)) = join(top,join(zero,A)),
inference(subst,[],[refute_0_211:[bind(A,$fot(top)),bind(X_15,$fot(zero)),bind(X_16,$fot(A))]]) ).
cnf(refute_0_213,plain,
( join(top,join(zero,A)) != join(top,A)
| join(zero,join(A,top)) != join(top,join(zero,A))
| join(zero,join(A,top)) = join(top,A) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(zero,join(A,top)))),bind(Y,$fot(join(top,join(zero,A)))),bind(Z,$fot(join(top,A)))]]) ).
cnf(refute_0_214,plain,
( join(top,join(zero,A)) != join(top,A)
| join(zero,join(A,top)) = join(top,A) ),
inference(resolve,[$cnf( $equal(join(zero,join(A,top)),join(top,join(zero,A))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
join(zero,join(A,top)) = join(top,A),
inference(resolve,[$cnf( $equal(join(top,join(zero,A)),join(top,A)) )],[refute_0_202,refute_0_214]) ).
cnf(refute_0_216,plain,
X_31 = join(meet(X_31,complement(X_31)),complement(join(complement(X_31),complement(X_31)))),
inference(subst,[],[refute_0_43:[bind(A,$fot(X_31)),bind(B,$fot(complement(X_31)))]]) ).
cnf(refute_0_217,plain,
zero = meet(X_31,complement(X_31)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_31))]]) ).
cnf(refute_0_218,plain,
( zero != meet(X_31,complement(X_31))
| meet(X_31,complement(X_31)) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_31,complement(X_31))))]]) ).
cnf(refute_0_219,plain,
meet(X_31,complement(X_31)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_31,complement(X_31))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
( X_31 != join(meet(X_31,complement(X_31)),complement(join(complement(X_31),complement(X_31))))
| meet(X_31,complement(X_31)) != zero
| X_31 = join(zero,complement(join(complement(X_31),complement(X_31)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,join(meet(X_31,complement(X_31)),complement(join(complement(X_31),complement(X_31))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_221,plain,
( X_31 != join(meet(X_31,complement(X_31)),complement(join(complement(X_31),complement(X_31))))
| X_31 = join(zero,complement(join(complement(X_31),complement(X_31)))) ),
inference(resolve,[$cnf( $equal(meet(X_31,complement(X_31)),zero) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
X_31 = join(zero,complement(join(complement(X_31),complement(X_31)))),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,complement(X_31)),complement(join(complement(X_31),complement(X_31))))) )],[refute_0_216,refute_0_221]) ).
cnf(refute_0_223,plain,
complement(join(complement(X_31),complement(X_31))) = meet(X_31,X_31),
inference(subst,[],[refute_0_31:[bind(A,$fot(X_31)),bind(B,$fot(X_31))]]) ).
cnf(refute_0_224,plain,
join(zero,complement(join(complement(X_31),complement(X_31)))) = join(zero,complement(join(complement(X_31),complement(X_31)))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(X_31),complement(X_31)))))]]) ).
cnf(refute_0_225,plain,
( complement(join(complement(X_31),complement(X_31))) != meet(X_31,X_31)
| join(zero,complement(join(complement(X_31),complement(X_31)))) != join(zero,complement(join(complement(X_31),complement(X_31))))
| join(zero,complement(join(complement(X_31),complement(X_31)))) = join(zero,meet(X_31,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(X_31),complement(X_31)))),join(zero,complement(join(complement(X_31),complement(X_31))))) ),[1,1],$fot(meet(X_31,X_31))]]) ).
cnf(refute_0_226,plain,
( complement(join(complement(X_31),complement(X_31))) != meet(X_31,X_31)
| join(zero,complement(join(complement(X_31),complement(X_31)))) = join(zero,meet(X_31,X_31)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(X_31),complement(X_31)))),join(zero,complement(join(complement(X_31),complement(X_31))))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
join(zero,complement(join(complement(X_31),complement(X_31)))) = join(zero,meet(X_31,X_31)),
inference(resolve,[$cnf( $equal(complement(join(complement(X_31),complement(X_31))),meet(X_31,X_31)) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
( X_31 != join(zero,complement(join(complement(X_31),complement(X_31))))
| join(zero,complement(join(complement(X_31),complement(X_31)))) != join(zero,meet(X_31,X_31))
| X_31 = join(zero,meet(X_31,X_31)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_31,join(zero,meet(X_31,X_31))) ),[0],$fot(join(zero,complement(join(complement(X_31),complement(X_31)))))]]) ).
cnf(refute_0_229,plain,
( X_31 != join(zero,complement(join(complement(X_31),complement(X_31))))
| X_31 = join(zero,meet(X_31,X_31)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(X_31),complement(X_31)))),join(zero,meet(X_31,X_31))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
X_31 = join(zero,meet(X_31,X_31)),
inference(resolve,[$cnf( $equal(X_31,join(zero,complement(join(complement(X_31),complement(X_31))))) )],[refute_0_222,refute_0_229]) ).
cnf(refute_0_231,plain,
( X_31 != join(zero,meet(X_31,X_31))
| join(zero,meet(X_31,X_31)) = X_31 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_31)),bind(Y,$fot(join(zero,meet(X_31,X_31))))]]) ).
cnf(refute_0_232,plain,
join(zero,meet(X_31,X_31)) = X_31,
inference(resolve,[$cnf( $equal(X_31,join(zero,meet(X_31,X_31))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
join(zero,meet(top,top)) = top,
inference(subst,[],[refute_0_232:[bind(X_31,$fot(top))]]) ).
cnf(refute_0_234,plain,
join(A,join(zero,meet(top,top))) = join(A,join(zero,meet(top,top))),
introduced(tautology,[refl,[$fot(join(A,join(zero,meet(top,top))))]]) ).
cnf(refute_0_235,plain,
( join(A,join(zero,meet(top,top))) != join(A,join(zero,meet(top,top)))
| join(zero,meet(top,top)) != top
| join(A,join(zero,meet(top,top))) = join(A,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(zero,meet(top,top))),join(A,join(zero,meet(top,top)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_236,plain,
( join(zero,meet(top,top)) != top
| join(A,join(zero,meet(top,top))) = join(A,top) ),
inference(resolve,[$cnf( $equal(join(A,join(zero,meet(top,top))),join(A,join(zero,meet(top,top)))) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
join(A,join(zero,meet(top,top))) = join(A,top),
inference(resolve,[$cnf( $equal(join(zero,meet(top,top)),top) )],[refute_0_233,refute_0_236]) ).
cnf(refute_0_238,plain,
join(zero,join(A,join(zero,meet(top,top)))) = join(zero,join(A,join(zero,meet(top,top)))),
introduced(tautology,[refl,[$fot(join(zero,join(A,join(zero,meet(top,top)))))]]) ).
cnf(refute_0_239,plain,
( join(A,join(zero,meet(top,top))) != join(A,top)
| join(zero,join(A,join(zero,meet(top,top)))) != join(zero,join(A,join(zero,meet(top,top))))
| join(zero,join(A,join(zero,meet(top,top)))) = join(zero,join(A,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(A,join(zero,meet(top,top)))),join(zero,join(A,join(zero,meet(top,top))))) ),[1,1],$fot(join(A,top))]]) ).
cnf(refute_0_240,plain,
( join(A,join(zero,meet(top,top))) != join(A,top)
| join(zero,join(A,join(zero,meet(top,top)))) = join(zero,join(A,top)) ),
inference(resolve,[$cnf( $equal(join(zero,join(A,join(zero,meet(top,top)))),join(zero,join(A,join(zero,meet(top,top))))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
join(zero,join(A,join(zero,meet(top,top)))) = join(zero,join(A,top)),
inference(resolve,[$cnf( $equal(join(A,join(zero,meet(top,top))),join(A,top)) )],[refute_0_237,refute_0_240]) ).
cnf(refute_0_242,plain,
( join(zero,join(A,join(zero,meet(top,top)))) != join(zero,join(A,top))
| join(zero,join(A,top)) != join(top,A)
| join(zero,join(A,join(zero,meet(top,top)))) = join(top,A) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(zero,join(A,join(zero,meet(top,top)))))),bind(Y,$fot(join(zero,join(A,top)))),bind(Z,$fot(join(top,A)))]]) ).
cnf(refute_0_243,plain,
( join(zero,join(A,top)) != join(top,A)
| join(zero,join(A,join(zero,meet(top,top)))) = join(top,A) ),
inference(resolve,[$cnf( $equal(join(zero,join(A,join(zero,meet(top,top)))),join(zero,join(A,top))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
join(zero,join(A,join(zero,meet(top,top)))) = join(top,A),
inference(resolve,[$cnf( $equal(join(zero,join(A,top)),join(top,A)) )],[refute_0_215,refute_0_243]) ).
cnf(refute_0_245,plain,
( join(A,top) != join(zero,join(A,join(zero,meet(top,top))))
| join(zero,join(A,join(zero,meet(top,top)))) != join(top,A)
| join(A,top) = join(top,A) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,top),join(top,A)) ),[0],$fot(join(zero,join(A,join(zero,meet(top,top)))))]]) ).
cnf(refute_0_246,plain,
( join(A,top) != join(zero,join(A,join(zero,meet(top,top))))
| join(A,top) = join(top,A) ),
inference(resolve,[$cnf( $equal(join(zero,join(A,join(zero,meet(top,top)))),join(top,A)) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
join(A,top) = join(top,A),
inference(resolve,[$cnf( $equal(join(A,top),join(zero,join(A,join(zero,meet(top,top))))) )],[refute_0_201,refute_0_246]) ).
cnf(refute_0_248,plain,
join(converse(X_65),top) = join(top,converse(X_65)),
inference(subst,[],[refute_0_247:[bind(A,$fot(converse(X_65)))]]) ).
cnf(refute_0_249,plain,
converse(join(X_6,converse(A))) = join(converse(X_6),converse(converse(A))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_6)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_250,plain,
( converse(converse(A)) != A
| converse(join(X_6,converse(A))) != join(converse(X_6),converse(converse(A)))
| converse(join(X_6,converse(A))) = join(converse(X_6),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_6,converse(A))),join(converse(X_6),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_251,plain,
( converse(join(X_6,converse(A))) != join(converse(X_6),converse(converse(A)))
| converse(join(X_6,converse(A))) = join(converse(X_6),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_250]) ).
cnf(refute_0_252,plain,
converse(join(X_6,converse(A))) = join(converse(X_6),A),
inference(resolve,[$cnf( $equal(converse(join(X_6,converse(A))),join(converse(X_6),converse(converse(A)))) )],[refute_0_249,refute_0_251]) ).
cnf(refute_0_253,plain,
converse(join(X_65,converse(top))) = join(converse(X_65),top),
inference(subst,[],[refute_0_252:[bind(A,$fot(top)),bind(X_6,$fot(X_65))]]) ).
cnf(refute_0_254,plain,
( converse(join(X_65,converse(top))) != join(converse(X_65),top)
| join(converse(X_65),top) != join(top,converse(X_65))
| converse(join(X_65,converse(top))) = join(top,converse(X_65)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(converse(join(X_65,converse(top))))),bind(Y,$fot(join(converse(X_65),top))),bind(Z,$fot(join(top,converse(X_65))))]]) ).
cnf(refute_0_255,plain,
( join(converse(X_65),top) != join(top,converse(X_65))
| converse(join(X_65,converse(top))) = join(top,converse(X_65)) ),
inference(resolve,[$cnf( $equal(converse(join(X_65,converse(top))),join(converse(X_65),top)) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
converse(join(X_65,converse(top))) = join(top,converse(X_65)),
inference(resolve,[$cnf( $equal(join(converse(X_65),top),join(top,converse(X_65))) )],[refute_0_248,refute_0_255]) ).
cnf(refute_0_257,plain,
( converse(join(X_65,converse(top))) != join(top,converse(X_65))
| join(converse(top),complement(converse(complement(X_65)))) != converse(join(X_65,converse(top)))
| join(converse(top),complement(converse(complement(X_65)))) = join(top,converse(X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(top),complement(converse(complement(X_65)))),converse(join(X_65,converse(top)))) ),[1],$fot(join(top,converse(X_65)))]]) ).
cnf(refute_0_258,plain,
( join(converse(top),complement(converse(complement(X_65)))) != converse(join(X_65,converse(top)))
| join(converse(top),complement(converse(complement(X_65)))) = join(top,converse(X_65)) ),
inference(resolve,[$cnf( $equal(converse(join(X_65,converse(top))),join(top,converse(X_65))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
( converse(join(converse(complement(converse(complement(X_65)))),top)) != converse(join(X_65,converse(top)))
| join(converse(top),complement(converse(complement(X_65)))) = join(top,converse(X_65)) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(complement(X_65)))),converse(join(X_65,converse(top)))) )],[refute_0_148,refute_0_258]) ).
cnf(refute_0_260,plain,
join(converse(top),complement(converse(complement(X_65)))) = join(top,converse(X_65)),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(complement(X_65)))),top)),converse(join(X_65,converse(top)))) )],[refute_0_141,refute_0_259]) ).
cnf(refute_0_261,plain,
join(converse(top),complement(converse(complement(converse(X_54))))) = join(top,converse(converse(X_54))),
inference(subst,[],[refute_0_260:[bind(X_65,$fot(converse(X_54)))]]) ).
cnf(refute_0_262,plain,
( join(converse(top),complement(converse(complement(converse(X_54))))) != join(top,converse(converse(X_54)))
| join(top,converse(converse(X_54))) != join(top,X_54)
| join(converse(top),complement(converse(complement(converse(X_54))))) = join(top,X_54) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(converse(top),complement(converse(complement(converse(X_54))))))),bind(Y,$fot(join(top,converse(converse(X_54))))),bind(Z,$fot(join(top,X_54)))]]) ).
cnf(refute_0_263,plain,
( join(top,converse(converse(X_54))) != join(top,X_54)
| join(converse(top),complement(converse(complement(converse(X_54))))) = join(top,X_54) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(complement(converse(X_54))))),join(top,converse(converse(X_54)))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
join(converse(top),complement(converse(complement(converse(X_54))))) = join(top,X_54),
inference(resolve,[$cnf( $equal(join(top,converse(converse(X_54))),join(top,X_54)) )],[refute_0_114,refute_0_263]) ).
cnf(refute_0_265,plain,
( join(X_54,top) != join(converse(top),complement(converse(complement(converse(X_54)))))
| join(converse(top),complement(converse(complement(converse(X_54))))) != join(top,X_54)
| join(X_54,top) = join(top,X_54) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_54,top),join(top,X_54)) ),[0],$fot(join(converse(top),complement(converse(complement(converse(X_54))))))]]) ).
cnf(refute_0_266,plain,
( join(X_54,top) != join(converse(top),complement(converse(complement(converse(X_54)))))
| join(X_54,top) = join(top,X_54) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(complement(converse(X_54))))),join(top,X_54)) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
join(X_54,top) = join(top,X_54),
inference(resolve,[$cnf( $equal(join(X_54,top),join(converse(top),complement(converse(complement(converse(X_54)))))) )],[refute_0_109,refute_0_266]) ).
cnf(refute_0_268,plain,
join(join(zero,X_32),top) = join(top,join(zero,X_32)),
inference(subst,[],[refute_0_267:[bind(X_54,$fot(join(zero,X_32)))]]) ).
cnf(refute_0_269,plain,
( join(join(zero,X_32),top) != join(top,join(zero,X_32))
| join(top,join(zero,X_32)) != join(top,X_32)
| join(join(zero,X_32),top) = join(top,X_32) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(join(zero,X_32),top))),bind(Y,$fot(join(top,join(zero,X_32)))),bind(Z,$fot(join(top,X_32)))]]) ).
cnf(refute_0_270,plain,
( join(top,join(zero,X_32)) != join(top,X_32)
| join(join(zero,X_32),top) = join(top,X_32) ),
inference(resolve,[$cnf( $equal(join(join(zero,X_32),top),join(top,join(zero,X_32))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
join(join(zero,X_32),top) = join(top,X_32),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_32)),join(top,X_32)) )],[refute_0_84,refute_0_270]) ).
cnf(refute_0_272,plain,
( join(join(zero,X_32),top) != join(top,X_32)
| join(join(zero,X_32),top) != join(top,meet(top,X_32))
| join(top,X_32) = join(top,meet(top,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(zero,X_32),top),join(top,meet(top,X_32))) ),[0],$fot(join(top,X_32))]]) ).
cnf(refute_0_273,plain,
( join(join(zero,X_32),top) != join(top,meet(top,X_32))
| join(top,X_32) = join(top,meet(top,X_32)) ),
inference(resolve,[$cnf( $equal(join(join(zero,X_32),top),join(top,X_32)) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
join(top,X_32) = join(top,meet(top,X_32)),
inference(resolve,[$cnf( $equal(join(join(zero,X_32),top),join(top,meet(top,X_32))) )],[refute_0_79,refute_0_273]) ).
cnf(refute_0_275,plain,
X_31 = join(meet(X_31,X_32),complement(join(complement(X_31),X_32))),
inference(subst,[],[refute_0_43:[bind(A,$fot(X_31)),bind(B,$fot(X_32))]]) ).
cnf(refute_0_276,plain,
join(complement(X_23),complement(X_22)) = join(complement(X_22),complement(X_23)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_23))),bind(B,$fot(complement(X_22)))]]) ).
cnf(refute_0_277,plain,
( join(complement(X_23),complement(X_22)) != join(complement(X_22),complement(X_23))
| join(complement(X_22),complement(X_23)) = join(complement(X_23),complement(X_22)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(complement(X_23),complement(X_22)))),bind(Y,$fot(join(complement(X_22),complement(X_23))))]]) ).
cnf(refute_0_278,plain,
join(complement(X_22),complement(X_23)) = join(complement(X_23),complement(X_22)),
inference(resolve,[$cnf( $equal(join(complement(X_23),complement(X_22)),join(complement(X_22),complement(X_23))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
( join(complement(X_22),complement(X_23)) != join(complement(X_23),complement(X_22))
| meet(X_22,X_23) != complement(join(complement(X_22),complement(X_23)))
| meet(X_22,X_23) = complement(join(complement(X_23),complement(X_22))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_22,X_23),complement(join(complement(X_22),complement(X_23)))) ),[1,0],$fot(join(complement(X_23),complement(X_22)))]]) ).
cnf(refute_0_280,plain,
( meet(X_22,X_23) != complement(join(complement(X_22),complement(X_23)))
| meet(X_22,X_23) = complement(join(complement(X_23),complement(X_22))) ),
inference(resolve,[$cnf( $equal(join(complement(X_22),complement(X_23)),join(complement(X_23),complement(X_22))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
meet(X_22,X_23) = complement(join(complement(X_23),complement(X_22))),
inference(resolve,[$cnf( $equal(meet(X_22,X_23),complement(join(complement(X_22),complement(X_23)))) )],[refute_0_46,refute_0_280]) ).
cnf(refute_0_282,plain,
complement(join(complement(X_23),complement(X_22))) = meet(X_23,X_22),
inference(subst,[],[refute_0_31:[bind(A,$fot(X_23)),bind(B,$fot(X_22))]]) ).
cnf(refute_0_283,plain,
( complement(join(complement(X_23),complement(X_22))) != meet(X_23,X_22)
| meet(X_22,X_23) != complement(join(complement(X_23),complement(X_22)))
| meet(X_22,X_23) = meet(X_23,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_22,X_23),complement(join(complement(X_23),complement(X_22)))) ),[1],$fot(meet(X_23,X_22))]]) ).
cnf(refute_0_284,plain,
( meet(X_22,X_23) != complement(join(complement(X_23),complement(X_22)))
| meet(X_22,X_23) = meet(X_23,X_22) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_23),complement(X_22))),meet(X_23,X_22)) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
meet(X_22,X_23) = meet(X_23,X_22),
inference(resolve,[$cnf( $equal(meet(X_22,X_23),complement(join(complement(X_23),complement(X_22)))) )],[refute_0_281,refute_0_284]) ).
cnf(refute_0_286,plain,
meet(X_32,X_31) = meet(X_31,X_32),
inference(subst,[],[refute_0_285:[bind(X_22,$fot(X_32)),bind(X_23,$fot(X_31))]]) ).
cnf(refute_0_287,plain,
( meet(X_32,X_31) != meet(X_31,X_32)
| meet(X_31,X_32) = meet(X_32,X_31) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_32,X_31))),bind(Y,$fot(meet(X_31,X_32)))]]) ).
cnf(refute_0_288,plain,
meet(X_31,X_32) = meet(X_32,X_31),
inference(resolve,[$cnf( $equal(meet(X_32,X_31),meet(X_31,X_32)) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
( X_31 != join(meet(X_31,X_32),complement(join(complement(X_31),X_32)))
| meet(X_31,X_32) != meet(X_32,X_31)
| X_31 = join(meet(X_32,X_31),complement(join(complement(X_31),X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,join(meet(X_31,X_32),complement(join(complement(X_31),X_32)))) ),[1,0],$fot(meet(X_32,X_31))]]) ).
cnf(refute_0_290,plain,
( X_31 != join(meet(X_31,X_32),complement(join(complement(X_31),X_32)))
| X_31 = join(meet(X_32,X_31),complement(join(complement(X_31),X_32))) ),
inference(resolve,[$cnf( $equal(meet(X_31,X_32),meet(X_32,X_31)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
X_31 = join(meet(X_32,X_31),complement(join(complement(X_31),X_32))),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,X_32),complement(join(complement(X_31),X_32)))) )],[refute_0_275,refute_0_290]) ).
cnf(refute_0_292,plain,
join(top,top) = join(meet(top,join(top,top)),complement(join(complement(join(top,top)),top))),
inference(subst,[],[refute_0_291:[bind(X_31,$fot(join(top,top))),bind(X_32,$fot(top))]]) ).
cnf(refute_0_293,plain,
X_31 = join(meet(X_31,complement(complement(X_31))),complement(join(complement(X_31),complement(complement(X_31))))),
inference(subst,[],[refute_0_43:[bind(A,$fot(X_31)),bind(B,$fot(complement(complement(X_31))))]]) ).
cnf(refute_0_294,plain,
top = join(complement(X_31),complement(complement(X_31))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_31)))]]) ).
cnf(refute_0_295,plain,
( top != join(complement(X_31),complement(complement(X_31)))
| join(complement(X_31),complement(complement(X_31))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_31),complement(complement(X_31)))))]]) ).
cnf(refute_0_296,plain,
join(complement(X_31),complement(complement(X_31))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_31),complement(complement(X_31)))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
( X_31 != join(meet(X_31,complement(complement(X_31))),complement(join(complement(X_31),complement(complement(X_31)))))
| join(complement(X_31),complement(complement(X_31))) != top
| X_31 = join(meet(X_31,complement(complement(X_31))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_31,join(meet(X_31,complement(complement(X_31))),complement(join(complement(X_31),complement(complement(X_31)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_298,plain,
( X_31 != join(meet(X_31,complement(complement(X_31))),complement(join(complement(X_31),complement(complement(X_31)))))
| X_31 = join(meet(X_31,complement(complement(X_31))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_31),complement(complement(X_31))),top) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
X_31 = join(meet(X_31,complement(complement(X_31))),complement(top)),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,complement(complement(X_31))),complement(join(complement(X_31),complement(complement(X_31)))))) )],[refute_0_293,refute_0_298]) ).
cnf(refute_0_300,plain,
join(complement(top),meet(X_31,complement(complement(X_31)))) = join(complement(top),meet(X_31,complement(complement(X_31)))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_31,complement(complement(X_31)))))]]) ).
cnf(refute_0_301,plain,
( complement(top) != zero
| join(complement(top),meet(X_31,complement(complement(X_31)))) != join(complement(top),meet(X_31,complement(complement(X_31))))
| join(complement(top),meet(X_31,complement(complement(X_31)))) = join(zero,meet(X_31,complement(complement(X_31)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_31,complement(complement(X_31)))),join(complement(top),meet(X_31,complement(complement(X_31))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_302,plain,
( complement(top) != zero
| join(complement(top),meet(X_31,complement(complement(X_31)))) = join(zero,meet(X_31,complement(complement(X_31)))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_31,complement(complement(X_31)))),join(complement(top),meet(X_31,complement(complement(X_31))))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
join(complement(top),meet(X_31,complement(complement(X_31)))) = join(zero,meet(X_31,complement(complement(X_31)))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_302]) ).
cnf(refute_0_304,plain,
join(meet(X_31,complement(complement(X_31))),complement(top)) = join(complement(top),meet(X_31,complement(complement(X_31)))),
inference(subst,[],[refute_0_24:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_31,complement(complement(X_31)))))]]) ).
cnf(refute_0_305,plain,
( join(complement(top),meet(X_31,complement(complement(X_31)))) != join(zero,meet(X_31,complement(complement(X_31))))
| join(meet(X_31,complement(complement(X_31))),complement(top)) != join(complement(top),meet(X_31,complement(complement(X_31))))
| join(meet(X_31,complement(complement(X_31))),complement(top)) = join(zero,meet(X_31,complement(complement(X_31)))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(meet(X_31,complement(complement(X_31))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_31,complement(complement(X_31)))))),bind(Z,$fot(join(zero,meet(X_31,complement(complement(X_31))))))]]) ).
cnf(refute_0_306,plain,
( join(complement(top),meet(X_31,complement(complement(X_31)))) != join(zero,meet(X_31,complement(complement(X_31))))
| join(meet(X_31,complement(complement(X_31))),complement(top)) = join(zero,meet(X_31,complement(complement(X_31)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_31,complement(complement(X_31))),complement(top)),join(complement(top),meet(X_31,complement(complement(X_31))))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
join(meet(X_31,complement(complement(X_31))),complement(top)) = join(zero,meet(X_31,complement(complement(X_31)))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_31,complement(complement(X_31)))),join(zero,meet(X_31,complement(complement(X_31))))) )],[refute_0_303,refute_0_306]) ).
cnf(refute_0_308,plain,
( X_31 != join(meet(X_31,complement(complement(X_31))),complement(top))
| join(meet(X_31,complement(complement(X_31))),complement(top)) != join(zero,meet(X_31,complement(complement(X_31))))
| X_31 = join(zero,meet(X_31,complement(complement(X_31)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_31,join(zero,meet(X_31,complement(complement(X_31))))) ),[0],$fot(join(meet(X_31,complement(complement(X_31))),complement(top)))]]) ).
cnf(refute_0_309,plain,
( X_31 != join(meet(X_31,complement(complement(X_31))),complement(top))
| X_31 = join(zero,meet(X_31,complement(complement(X_31)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_31,complement(complement(X_31))),complement(top)),join(zero,meet(X_31,complement(complement(X_31))))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
X_31 = join(zero,meet(X_31,complement(complement(X_31)))),
inference(resolve,[$cnf( $equal(X_31,join(meet(X_31,complement(complement(X_31))),complement(top))) )],[refute_0_299,refute_0_309]) ).
cnf(refute_0_311,plain,
meet(top,join(top,top)) = join(zero,meet(meet(top,join(top,top)),complement(complement(meet(top,join(top,top)))))),
inference(subst,[],[refute_0_310:[bind(X_31,$fot(meet(top,join(top,top))))]]) ).
cnf(refute_0_312,plain,
join(zero,join(zero,zero)) = join(meet(top,join(zero,join(zero,zero))),complement(join(complement(join(zero,join(zero,zero))),top))),
inference(subst,[],[refute_0_291:[bind(X_31,$fot(join(zero,join(zero,zero)))),bind(X_32,$fot(top))]]) ).
cnf(refute_0_313,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_314,plain,
( complement(top) != zero
| meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_0_315,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_314]) ).
cnf(refute_0_316,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_313,refute_0_315]) ).
cnf(refute_0_317,plain,
meet(top,join(zero,join(zero,zero))) = complement(join(zero,complement(join(zero,join(zero,zero))))),
inference(subst,[],[refute_0_316:[bind(B,$fot(join(zero,join(zero,zero))))]]) ).
cnf(refute_0_318,plain,
top = join(meet(top,join(zero,zero)),complement(join(complement(top),join(zero,zero)))),
inference(subst,[],[refute_0_43:[bind(A,$fot(top)),bind(B,$fot(join(zero,zero)))]]) ).
cnf(refute_0_319,plain,
meet(top,join(zero,zero)) = complement(join(zero,complement(join(zero,zero)))),
inference(subst,[],[refute_0_316:[bind(B,$fot(join(zero,zero)))]]) ).
cnf(refute_0_320,plain,
meet(top,top) = complement(join(zero,complement(top))),
inference(subst,[],[refute_0_316:[bind(B,$fot(top))]]) ).
cnf(refute_0_321,plain,
( complement(top) != zero
| meet(top,top) != complement(join(zero,complement(top)))
| meet(top,top) = complement(join(zero,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,top),complement(join(zero,complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_322,plain,
( meet(top,top) != complement(join(zero,complement(top)))
| meet(top,top) = complement(join(zero,zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_321]) ).
cnf(refute_0_323,plain,
meet(top,top) = complement(join(zero,zero)),
inference(resolve,[$cnf( $equal(meet(top,top),complement(join(zero,complement(top)))) )],[refute_0_320,refute_0_322]) ).
cnf(refute_0_324,plain,
( meet(top,top) != complement(join(zero,zero))
| complement(join(zero,zero)) = meet(top,top) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(top,top))),bind(Y,$fot(complement(join(zero,zero))))]]) ).
cnf(refute_0_325,plain,
complement(join(zero,zero)) = meet(top,top),
inference(resolve,[$cnf( $equal(meet(top,top),complement(join(zero,zero))) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
( complement(join(zero,zero)) != meet(top,top)
| meet(top,join(zero,zero)) != complement(join(zero,complement(join(zero,zero))))
| meet(top,join(zero,zero)) = complement(join(zero,meet(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,zero)),complement(join(zero,complement(join(zero,zero))))) ),[1,0,1],$fot(meet(top,top))]]) ).
cnf(refute_0_327,plain,
( meet(top,join(zero,zero)) != complement(join(zero,complement(join(zero,zero))))
| meet(top,join(zero,zero)) = complement(join(zero,meet(top,top))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),meet(top,top)) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
meet(top,join(zero,zero)) = complement(join(zero,meet(top,top))),
inference(resolve,[$cnf( $equal(meet(top,join(zero,zero)),complement(join(zero,complement(join(zero,zero))))) )],[refute_0_319,refute_0_327]) ).
cnf(refute_0_329,plain,
complement(join(zero,meet(top,top))) = complement(join(zero,meet(top,top))),
introduced(tautology,[refl,[$fot(complement(join(zero,meet(top,top))))]]) ).
cnf(refute_0_330,plain,
( complement(join(zero,meet(top,top))) != complement(join(zero,meet(top,top)))
| join(zero,meet(top,top)) != top
| complement(join(zero,meet(top,top))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,meet(top,top))),complement(join(zero,meet(top,top)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_331,plain,
( join(zero,meet(top,top)) != top
| complement(join(zero,meet(top,top))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,top))),complement(join(zero,meet(top,top)))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
complement(join(zero,meet(top,top))) = complement(top),
inference(resolve,[$cnf( $equal(join(zero,meet(top,top)),top) )],[refute_0_233,refute_0_331]) ).
cnf(refute_0_333,plain,
( complement(join(zero,meet(top,top))) != complement(top)
| complement(top) != zero
| complement(join(zero,meet(top,top))) = zero ),
inference(subst,[],[refute_0_37:[bind(X,$fot(complement(join(zero,meet(top,top))))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_334,plain,
( complement(top) != zero
| complement(join(zero,meet(top,top))) = zero ),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,top))),complement(top)) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
complement(join(zero,meet(top,top))) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_334]) ).
cnf(refute_0_336,plain,
( complement(join(zero,meet(top,top))) != zero
| meet(top,join(zero,zero)) != complement(join(zero,meet(top,top)))
| meet(top,join(zero,zero)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,zero)),complement(join(zero,meet(top,top)))) ),[1],$fot(zero)]]) ).
cnf(refute_0_337,plain,
( meet(top,join(zero,zero)) != complement(join(zero,meet(top,top)))
| meet(top,join(zero,zero)) = zero ),
inference(resolve,[$cnf( $equal(complement(join(zero,meet(top,top))),zero) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
meet(top,join(zero,zero)) = zero,
inference(resolve,[$cnf( $equal(meet(top,join(zero,zero)),complement(join(zero,meet(top,top)))) )],[refute_0_328,refute_0_337]) ).
cnf(refute_0_339,plain,
( meet(top,join(zero,zero)) != zero
| top != join(meet(top,join(zero,zero)),complement(join(complement(top),join(zero,zero))))
| top = join(zero,complement(join(complement(top),join(zero,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,join(zero,zero)),complement(join(complement(top),join(zero,zero))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_340,plain,
( top != join(meet(top,join(zero,zero)),complement(join(complement(top),join(zero,zero))))
| top = join(zero,complement(join(complement(top),join(zero,zero)))) ),
inference(resolve,[$cnf( $equal(meet(top,join(zero,zero)),zero) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
top = join(zero,complement(join(complement(top),join(zero,zero)))),
inference(resolve,[$cnf( $equal(top,join(meet(top,join(zero,zero)),complement(join(complement(top),join(zero,zero))))) )],[refute_0_318,refute_0_340]) ).
cnf(refute_0_342,plain,
join(zero,complement(top)) = join(zero,complement(top)),
introduced(tautology,[refl,[$fot(join(zero,complement(top)))]]) ).
cnf(refute_0_343,plain,
( complement(top) != zero
| join(zero,complement(top)) != join(zero,complement(top))
| join(zero,complement(top)) = join(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_344,plain,
( complement(top) != zero
| join(zero,complement(top)) = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
join(zero,complement(top)) = join(zero,zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_344]) ).
cnf(refute_0_346,plain,
join(zero,join(zero,complement(top))) = join(zero,join(zero,complement(top))),
introduced(tautology,[refl,[$fot(join(zero,join(zero,complement(top))))]]) ).
cnf(refute_0_347,plain,
( join(zero,complement(top)) != join(zero,zero)
| join(zero,join(zero,complement(top))) != join(zero,join(zero,complement(top)))
| join(zero,join(zero,complement(top))) = join(zero,join(zero,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,complement(top))),join(zero,join(zero,complement(top)))) ),[1,1],$fot(join(zero,zero))]]) ).
cnf(refute_0_348,plain,
( join(zero,complement(top)) != join(zero,zero)
| join(zero,join(zero,complement(top))) = join(zero,join(zero,zero)) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,complement(top))),join(zero,join(zero,complement(top)))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
join(zero,join(zero,complement(top))) = join(zero,join(zero,zero)),
inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,zero)) )],[refute_0_345,refute_0_348]) ).
cnf(refute_0_350,plain,
join(X_17,X_16) = join(X_16,X_17),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_17)),bind(B,$fot(X_16))]]) ).
cnf(refute_0_351,plain,
( join(X_17,X_16) != join(X_16,X_17)
| join(X_16,X_17) = join(X_17,X_16) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_17,X_16))),bind(Y,$fot(join(X_16,X_17)))]]) ).
cnf(refute_0_352,plain,
join(X_16,X_17) = join(X_17,X_16),
inference(resolve,[$cnf( $equal(join(X_17,X_16),join(X_16,X_17)) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
( join(X_15,join(X_16,X_17)) != join(join(X_15,X_16),X_17)
| join(X_16,X_17) != join(X_17,X_16)
| join(X_15,join(X_17,X_16)) = join(join(X_15,X_16),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_15,join(X_16,X_17)),join(join(X_15,X_16),X_17)) ),[0,1],$fot(join(X_17,X_16))]]) ).
cnf(refute_0_354,plain,
( join(X_15,join(X_16,X_17)) != join(join(X_15,X_16),X_17)
| join(X_15,join(X_17,X_16)) = join(join(X_15,X_16),X_17) ),
inference(resolve,[$cnf( $equal(join(X_16,X_17),join(X_17,X_16)) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
join(X_15,join(X_17,X_16)) = join(join(X_15,X_16),X_17),
inference(resolve,[$cnf( $equal(join(X_15,join(X_16,X_17)),join(join(X_15,X_16),X_17)) )],[refute_0_164,refute_0_354]) ).
cnf(refute_0_356,plain,
join(join(X_15,X_16),X_17) = join(X_15,join(X_16,X_17)),
inference(subst,[],[refute_0_155:[bind(A,$fot(X_15)),bind(B,$fot(X_16)),bind(C,$fot(X_17))]]) ).
cnf(refute_0_357,plain,
( join(X_15,join(X_17,X_16)) != join(join(X_15,X_16),X_17)
| join(join(X_15,X_16),X_17) != join(X_15,join(X_16,X_17))
| join(X_15,join(X_17,X_16)) = join(X_15,join(X_16,X_17)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_15,join(X_17,X_16)),join(X_15,join(X_16,X_17))) ),[0],$fot(join(join(X_15,X_16),X_17))]]) ).
cnf(refute_0_358,plain,
( join(X_15,join(X_17,X_16)) != join(join(X_15,X_16),X_17)
| join(X_15,join(X_17,X_16)) = join(X_15,join(X_16,X_17)) ),
inference(resolve,[$cnf( $equal(join(join(X_15,X_16),X_17),join(X_15,join(X_16,X_17))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
join(X_15,join(X_17,X_16)) = join(X_15,join(X_16,X_17)),
inference(resolve,[$cnf( $equal(join(X_15,join(X_17,X_16)),join(join(X_15,X_16),X_17)) )],[refute_0_355,refute_0_358]) ).
cnf(refute_0_360,plain,
( join(X_15,join(X_17,X_16)) != join(X_15,join(X_16,X_17))
| join(X_15,join(X_16,X_17)) = join(X_15,join(X_17,X_16)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_15,join(X_17,X_16)))),bind(Y,$fot(join(X_15,join(X_16,X_17))))]]) ).
cnf(refute_0_361,plain,
join(X_15,join(X_16,X_17)) = join(X_15,join(X_17,X_16)),
inference(resolve,[$cnf( $equal(join(X_15,join(X_17,X_16)),join(X_15,join(X_16,X_17))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
join(zero,join(complement(top),zero)) = join(zero,join(zero,complement(top))),
inference(subst,[],[refute_0_361:[bind(X_15,$fot(zero)),bind(X_16,$fot(complement(top))),bind(X_17,$fot(zero))]]) ).
cnf(refute_0_363,plain,
join(complement(top),join(zero,zero)) = join(zero,join(complement(top),zero)),
inference(subst,[],[refute_0_176:[bind(X_15,$fot(zero)),bind(X_16,$fot(complement(top))),bind(X_17,$fot(zero))]]) ).
cnf(refute_0_364,plain,
( join(complement(top),join(zero,zero)) != join(zero,join(complement(top),zero))
| join(zero,join(complement(top),zero)) != join(zero,join(zero,complement(top)))
| join(complement(top),join(zero,zero)) = join(zero,join(zero,complement(top))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(complement(top),join(zero,zero)))),bind(Y,$fot(join(zero,join(complement(top),zero)))),bind(Z,$fot(join(zero,join(zero,complement(top)))))]]) ).
cnf(refute_0_365,plain,
( join(zero,join(complement(top),zero)) != join(zero,join(zero,complement(top)))
| join(complement(top),join(zero,zero)) = join(zero,join(zero,complement(top))) ),
inference(resolve,[$cnf( $equal(join(complement(top),join(zero,zero)),join(zero,join(complement(top),zero))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
join(complement(top),join(zero,zero)) = join(zero,join(zero,complement(top))),
inference(resolve,[$cnf( $equal(join(zero,join(complement(top),zero)),join(zero,join(zero,complement(top)))) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
( join(complement(top),join(zero,zero)) != join(zero,join(zero,complement(top)))
| join(zero,join(zero,complement(top))) != join(zero,join(zero,zero))
| join(complement(top),join(zero,zero)) = join(zero,join(zero,zero)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(complement(top),join(zero,zero)))),bind(Y,$fot(join(zero,join(zero,complement(top))))),bind(Z,$fot(join(zero,join(zero,zero))))]]) ).
cnf(refute_0_368,plain,
( join(zero,join(zero,complement(top))) != join(zero,join(zero,zero))
| join(complement(top),join(zero,zero)) = join(zero,join(zero,zero)) ),
inference(resolve,[$cnf( $equal(join(complement(top),join(zero,zero)),join(zero,join(zero,complement(top)))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
join(complement(top),join(zero,zero)) = join(zero,join(zero,zero)),
inference(resolve,[$cnf( $equal(join(zero,join(zero,complement(top))),join(zero,join(zero,zero))) )],[refute_0_349,refute_0_368]) ).
cnf(refute_0_370,plain,
complement(join(complement(top),join(zero,zero))) = complement(join(complement(top),join(zero,zero))),
introduced(tautology,[refl,[$fot(complement(join(complement(top),join(zero,zero))))]]) ).
cnf(refute_0_371,plain,
( complement(join(complement(top),join(zero,zero))) != complement(join(complement(top),join(zero,zero)))
| join(complement(top),join(zero,zero)) != join(zero,join(zero,zero))
| complement(join(complement(top),join(zero,zero))) = complement(join(zero,join(zero,zero))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(top),join(zero,zero))),complement(join(complement(top),join(zero,zero)))) ),[1,0],$fot(join(zero,join(zero,zero)))]]) ).
cnf(refute_0_372,plain,
( join(complement(top),join(zero,zero)) != join(zero,join(zero,zero))
| complement(join(complement(top),join(zero,zero))) = complement(join(zero,join(zero,zero))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(top),join(zero,zero))),complement(join(complement(top),join(zero,zero)))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
complement(join(complement(top),join(zero,zero))) = complement(join(zero,join(zero,zero))),
inference(resolve,[$cnf( $equal(join(complement(top),join(zero,zero)),join(zero,join(zero,zero))) )],[refute_0_369,refute_0_372]) ).
cnf(refute_0_374,plain,
join(zero,complement(join(complement(top),join(zero,zero)))) = join(zero,complement(join(complement(top),join(zero,zero)))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(top),join(zero,zero)))))]]) ).
cnf(refute_0_375,plain,
( complement(join(complement(top),join(zero,zero))) != complement(join(zero,join(zero,zero)))
| join(zero,complement(join(complement(top),join(zero,zero)))) != join(zero,complement(join(complement(top),join(zero,zero))))
| join(zero,complement(join(complement(top),join(zero,zero)))) = join(zero,complement(join(zero,join(zero,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(top),join(zero,zero)))),join(zero,complement(join(complement(top),join(zero,zero))))) ),[1,1],$fot(complement(join(zero,join(zero,zero))))]]) ).
cnf(refute_0_376,plain,
( complement(join(complement(top),join(zero,zero))) != complement(join(zero,join(zero,zero)))
| join(zero,complement(join(complement(top),join(zero,zero)))) = join(zero,complement(join(zero,join(zero,zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(top),join(zero,zero)))),join(zero,complement(join(complement(top),join(zero,zero))))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
join(zero,complement(join(complement(top),join(zero,zero)))) = join(zero,complement(join(zero,join(zero,zero)))),
inference(resolve,[$cnf( $equal(complement(join(complement(top),join(zero,zero))),complement(join(zero,join(zero,zero)))) )],[refute_0_373,refute_0_376]) ).
cnf(refute_0_378,plain,
( join(zero,complement(join(complement(top),join(zero,zero)))) != join(zero,complement(join(zero,join(zero,zero))))
| top != join(zero,complement(join(complement(top),join(zero,zero))))
| top = join(zero,complement(join(zero,join(zero,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,complement(join(complement(top),join(zero,zero))))) ),[1],$fot(join(zero,complement(join(zero,join(zero,zero)))))]]) ).
cnf(refute_0_379,plain,
( top != join(zero,complement(join(complement(top),join(zero,zero))))
| top = join(zero,complement(join(zero,join(zero,zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(top),join(zero,zero)))),join(zero,complement(join(zero,join(zero,zero))))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
top = join(zero,complement(join(zero,join(zero,zero)))),
inference(resolve,[$cnf( $equal(top,join(zero,complement(join(complement(top),join(zero,zero))))) )],[refute_0_341,refute_0_379]) ).
cnf(refute_0_381,plain,
( top != join(zero,complement(join(zero,join(zero,zero))))
| join(zero,complement(join(zero,join(zero,zero)))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(zero,complement(join(zero,join(zero,zero))))))]]) ).
cnf(refute_0_382,plain,
join(zero,complement(join(zero,join(zero,zero)))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,complement(join(zero,join(zero,zero))))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
( join(zero,complement(join(zero,join(zero,zero)))) != top
| meet(top,join(zero,join(zero,zero))) != complement(join(zero,complement(join(zero,join(zero,zero)))))
| meet(top,join(zero,join(zero,zero))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,join(zero,zero))),complement(join(zero,complement(join(zero,join(zero,zero)))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_384,plain,
( meet(top,join(zero,join(zero,zero))) != complement(join(zero,complement(join(zero,join(zero,zero)))))
| meet(top,join(zero,join(zero,zero))) = complement(top) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(zero,join(zero,zero)))),top) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
meet(top,join(zero,join(zero,zero))) = complement(top),
inference(resolve,[$cnf( $equal(meet(top,join(zero,join(zero,zero))),complement(join(zero,complement(join(zero,join(zero,zero)))))) )],[refute_0_317,refute_0_384]) ).
cnf(refute_0_386,plain,
( complement(top) != zero
| meet(top,join(zero,join(zero,zero))) != complement(top)
| meet(top,join(zero,join(zero,zero))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(zero,join(zero,zero))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_387,plain,
( meet(top,join(zero,join(zero,zero))) != complement(top)
| meet(top,join(zero,join(zero,zero))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_386]) ).
cnf(refute_0_388,plain,
meet(top,join(zero,join(zero,zero))) = zero,
inference(resolve,[$cnf( $equal(meet(top,join(zero,join(zero,zero))),complement(top)) )],[refute_0_385,refute_0_387]) ).
cnf(refute_0_389,plain,
( join(zero,join(zero,zero)) != join(meet(top,join(zero,join(zero,zero))),complement(join(complement(join(zero,join(zero,zero))),top)))
| meet(top,join(zero,join(zero,zero))) != zero
| join(zero,join(zero,zero)) = join(zero,complement(join(complement(join(zero,join(zero,zero))),top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,zero)),join(meet(top,join(zero,join(zero,zero))),complement(join(complement(join(zero,join(zero,zero))),top)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_390,plain,
( join(zero,join(zero,zero)) != join(meet(top,join(zero,join(zero,zero))),complement(join(complement(join(zero,join(zero,zero))),top)))
| join(zero,join(zero,zero)) = join(zero,complement(join(complement(join(zero,join(zero,zero))),top))) ),
inference(resolve,[$cnf( $equal(meet(top,join(zero,join(zero,zero))),zero) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
join(zero,join(zero,zero)) = join(zero,complement(join(complement(join(zero,join(zero,zero))),top))),
inference(resolve,[$cnf( $equal(join(zero,join(zero,zero)),join(meet(top,join(zero,join(zero,zero))),complement(join(complement(join(zero,join(zero,zero))),top)))) )],[refute_0_312,refute_0_390]) ).
cnf(refute_0_392,plain,
join(top,join(zero,complement(join(zero,join(zero,zero))))) = join(top,complement(join(zero,join(zero,zero)))),
inference(subst,[],[refute_0_83:[bind(X_17,$fot(complement(join(zero,join(zero,zero)))))]]) ).
cnf(refute_0_393,plain,
( join(top,join(zero,complement(join(zero,join(zero,zero))))) != join(top,complement(join(zero,join(zero,zero))))
| join(zero,complement(join(zero,join(zero,zero)))) != top
| join(top,top) = join(top,complement(join(zero,join(zero,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,complement(join(zero,join(zero,zero))))),join(top,complement(join(zero,join(zero,zero))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_394,plain,
( join(top,join(zero,complement(join(zero,join(zero,zero))))) != join(top,complement(join(zero,join(zero,zero))))
| join(top,top) = join(top,complement(join(zero,join(zero,zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(zero,join(zero,zero)))),top) )],[refute_0_382,refute_0_393]) ).
cnf(refute_0_395,plain,
join(top,top) = join(top,complement(join(zero,join(zero,zero)))),
inference(resolve,[$cnf( $equal(join(top,join(zero,complement(join(zero,join(zero,zero))))),join(top,complement(join(zero,join(zero,zero))))) )],[refute_0_392,refute_0_394]) ).
cnf(refute_0_396,plain,
( join(top,top) != join(top,complement(join(zero,join(zero,zero))))
| join(top,complement(join(zero,join(zero,zero)))) = join(top,top) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(top,top))),bind(Y,$fot(join(top,complement(join(zero,join(zero,zero))))))]]) ).
cnf(refute_0_397,plain,
join(top,complement(join(zero,join(zero,zero)))) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,top),join(top,complement(join(zero,join(zero,zero))))) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
join(complement(join(zero,join(zero,zero))),top) = join(top,complement(join(zero,join(zero,zero)))),
inference(subst,[],[refute_0_247:[bind(A,$fot(complement(join(zero,join(zero,zero)))))]]) ).
cnf(refute_0_399,plain,
( join(complement(join(zero,join(zero,zero))),top) != join(top,complement(join(zero,join(zero,zero))))
| join(top,complement(join(zero,join(zero,zero)))) != join(top,top)
| join(complement(join(zero,join(zero,zero))),top) = join(top,top) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(complement(join(zero,join(zero,zero))),top))),bind(Y,$fot(join(top,complement(join(zero,join(zero,zero)))))),bind(Z,$fot(join(top,top)))]]) ).
cnf(refute_0_400,plain,
( join(top,complement(join(zero,join(zero,zero)))) != join(top,top)
| join(complement(join(zero,join(zero,zero))),top) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(complement(join(zero,join(zero,zero))),top),join(top,complement(join(zero,join(zero,zero))))) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
join(complement(join(zero,join(zero,zero))),top) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,complement(join(zero,join(zero,zero)))),join(top,top)) )],[refute_0_397,refute_0_400]) ).
cnf(refute_0_402,plain,
complement(join(complement(join(zero,join(zero,zero))),top)) = complement(join(complement(join(zero,join(zero,zero))),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(join(zero,join(zero,zero))),top)))]]) ).
cnf(refute_0_403,plain,
( complement(join(complement(join(zero,join(zero,zero))),top)) != complement(join(complement(join(zero,join(zero,zero))),top))
| join(complement(join(zero,join(zero,zero))),top) != join(top,top)
| complement(join(complement(join(zero,join(zero,zero))),top)) = complement(join(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(join(zero,join(zero,zero))),top)),complement(join(complement(join(zero,join(zero,zero))),top))) ),[1,0],$fot(join(top,top))]]) ).
cnf(refute_0_404,plain,
( join(complement(join(zero,join(zero,zero))),top) != join(top,top)
| complement(join(complement(join(zero,join(zero,zero))),top)) = complement(join(top,top)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(join(zero,join(zero,zero))),top)),complement(join(complement(join(zero,join(zero,zero))),top))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
complement(join(complement(join(zero,join(zero,zero))),top)) = complement(join(top,top)),
inference(resolve,[$cnf( $equal(join(complement(join(zero,join(zero,zero))),top),join(top,top)) )],[refute_0_401,refute_0_404]) ).
cnf(refute_0_406,plain,
join(zero,complement(join(complement(join(zero,join(zero,zero))),top))) = join(zero,complement(join(complement(join(zero,join(zero,zero))),top))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(join(zero,join(zero,zero))),top))))]]) ).
cnf(refute_0_407,plain,
( complement(join(complement(join(zero,join(zero,zero))),top)) != complement(join(top,top))
| join(zero,complement(join(complement(join(zero,join(zero,zero))),top))) != join(zero,complement(join(complement(join(zero,join(zero,zero))),top)))
| join(zero,complement(join(complement(join(zero,join(zero,zero))),top))) = join(zero,complement(join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(join(zero,join(zero,zero))),top))),join(zero,complement(join(complement(join(zero,join(zero,zero))),top)))) ),[1,1],$fot(complement(join(top,top)))]]) ).
cnf(refute_0_408,plain,
( complement(join(complement(join(zero,join(zero,zero))),top)) != complement(join(top,top))
| join(zero,complement(join(complement(join(zero,join(zero,zero))),top))) = join(zero,complement(join(top,top))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(join(zero,join(zero,zero))),top))),join(zero,complement(join(complement(join(zero,join(zero,zero))),top)))) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
join(zero,complement(join(complement(join(zero,join(zero,zero))),top))) = join(zero,complement(join(top,top))),
inference(resolve,[$cnf( $equal(complement(join(complement(join(zero,join(zero,zero))),top)),complement(join(top,top))) )],[refute_0_405,refute_0_408]) ).
cnf(refute_0_410,plain,
( join(zero,complement(join(complement(join(zero,join(zero,zero))),top))) != join(zero,complement(join(top,top)))
| join(zero,join(zero,zero)) != join(zero,complement(join(complement(join(zero,join(zero,zero))),top)))
| join(zero,join(zero,zero)) = join(zero,complement(join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,zero)),join(zero,complement(join(complement(join(zero,join(zero,zero))),top)))) ),[1],$fot(join(zero,complement(join(top,top))))]]) ).
cnf(refute_0_411,plain,
( join(zero,join(zero,zero)) != join(zero,complement(join(complement(join(zero,join(zero,zero))),top)))
| join(zero,join(zero,zero)) = join(zero,complement(join(top,top))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(join(zero,join(zero,zero))),top))),join(zero,complement(join(top,top)))) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
join(zero,join(zero,zero)) = join(zero,complement(join(top,top))),
inference(resolve,[$cnf( $equal(join(zero,join(zero,zero)),join(zero,complement(join(complement(join(zero,join(zero,zero))),top)))) )],[refute_0_391,refute_0_411]) ).
cnf(refute_0_413,plain,
zero = join(meet(top,zero),complement(join(complement(zero),top))),
inference(subst,[],[refute_0_291:[bind(X_31,$fot(zero)),bind(X_32,$fot(top))]]) ).
cnf(refute_0_414,plain,
zero = meet(top,complement(top)),
inference(subst,[],[def_zero_13:[bind(A,$fot(top))]]) ).
cnf(refute_0_415,plain,
( complement(top) != zero
| zero != meet(top,complement(top))
| zero = meet(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(top,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_416,plain,
( zero != meet(top,complement(top))
| zero = meet(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_415]) ).
cnf(refute_0_417,plain,
zero = meet(top,zero),
inference(resolve,[$cnf( $equal(zero,meet(top,complement(top))) )],[refute_0_414,refute_0_416]) ).
cnf(refute_0_418,plain,
( zero != meet(top,zero)
| meet(top,zero) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(meet(top,zero)))]]) ).
cnf(refute_0_419,plain,
meet(top,zero) = zero,
inference(resolve,[$cnf( $equal(zero,meet(top,zero)) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
( meet(top,zero) != zero
| zero != join(meet(top,zero),complement(join(complement(zero),top)))
| zero = join(zero,complement(join(complement(zero),top))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(meet(top,zero),complement(join(complement(zero),top)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_421,plain,
( zero != join(meet(top,zero),complement(join(complement(zero),top)))
| zero = join(zero,complement(join(complement(zero),top))) ),
inference(resolve,[$cnf( $equal(meet(top,zero),zero) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
zero = join(zero,complement(join(complement(zero),top))),
inference(resolve,[$cnf( $equal(zero,join(meet(top,zero),complement(join(complement(zero),top)))) )],[refute_0_413,refute_0_421]) ).
cnf(refute_0_423,plain,
join(zero,zero) = join(meet(top,join(zero,zero)),complement(join(complement(join(zero,zero)),top))),
inference(subst,[],[refute_0_291:[bind(X_31,$fot(join(zero,zero))),bind(X_32,$fot(top))]]) ).
cnf(refute_0_424,plain,
( join(zero,zero) != join(meet(top,join(zero,zero)),complement(join(complement(join(zero,zero)),top)))
| meet(top,join(zero,zero)) != zero
| join(zero,zero) = join(zero,complement(join(complement(join(zero,zero)),top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,zero),join(meet(top,join(zero,zero)),complement(join(complement(join(zero,zero)),top)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_425,plain,
( join(zero,zero) != join(meet(top,join(zero,zero)),complement(join(complement(join(zero,zero)),top)))
| join(zero,zero) = join(zero,complement(join(complement(join(zero,zero)),top))) ),
inference(resolve,[$cnf( $equal(meet(top,join(zero,zero)),zero) )],[refute_0_338,refute_0_424]) ).
cnf(refute_0_426,plain,
join(zero,zero) = join(zero,complement(join(complement(join(zero,zero)),top))),
inference(resolve,[$cnf( $equal(join(zero,zero),join(meet(top,join(zero,zero)),complement(join(complement(join(zero,zero)),top)))) )],[refute_0_423,refute_0_425]) ).
cnf(refute_0_427,plain,
( join(zero,join(zero,zero)) != join(zero,complement(join(top,top)))
| join(zero,complement(join(top,top))) = join(zero,join(zero,zero)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(zero,join(zero,zero)))),bind(Y,$fot(join(zero,complement(join(top,top)))))]]) ).
cnf(refute_0_428,plain,
join(zero,complement(join(top,top))) = join(zero,join(zero,zero)),
inference(resolve,[$cnf( $equal(join(zero,join(zero,zero)),join(zero,complement(join(top,top)))) )],[refute_0_412,refute_0_427]) ).
cnf(refute_0_429,plain,
join(top,join(zero,meet(X_33,X_33))) = join(top,meet(X_33,X_33)),
inference(subst,[],[refute_0_83:[bind(X_17,$fot(meet(X_33,X_33)))]]) ).
cnf(refute_0_430,plain,
X_33 = join(zero,meet(X_33,X_33)),
inference(subst,[],[refute_0_230:[bind(X_31,$fot(X_33))]]) ).
cnf(refute_0_431,plain,
( X_33 != join(zero,meet(X_33,X_33))
| join(zero,meet(X_33,X_33)) = X_33 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_33)),bind(Y,$fot(join(zero,meet(X_33,X_33))))]]) ).
cnf(refute_0_432,plain,
join(zero,meet(X_33,X_33)) = X_33,
inference(resolve,[$cnf( $equal(X_33,join(zero,meet(X_33,X_33))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
( join(top,join(zero,meet(X_33,X_33))) != join(top,meet(X_33,X_33))
| join(zero,meet(X_33,X_33)) != X_33
| join(top,X_33) = join(top,meet(X_33,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,meet(X_33,X_33))),join(top,meet(X_33,X_33))) ),[0,1],$fot(X_33)]]) ).
cnf(refute_0_434,plain,
( join(top,join(zero,meet(X_33,X_33))) != join(top,meet(X_33,X_33))
| join(top,X_33) = join(top,meet(X_33,X_33)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_33,X_33)),X_33) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
join(top,X_33) = join(top,meet(X_33,X_33)),
inference(resolve,[$cnf( $equal(join(top,join(zero,meet(X_33,X_33))),join(top,meet(X_33,X_33))) )],[refute_0_429,refute_0_434]) ).
cnf(refute_0_436,plain,
( join(top,X_33) != join(top,meet(X_33,X_33))
| join(top,meet(X_33,X_33)) = join(top,X_33) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(top,X_33))),bind(Y,$fot(join(top,meet(X_33,X_33))))]]) ).
cnf(refute_0_437,plain,
join(top,meet(X_33,X_33)) = join(top,X_33),
inference(resolve,[$cnf( $equal(join(top,X_33),join(top,meet(X_33,X_33))) )],[refute_0_435,refute_0_436]) ).
cnf(refute_0_438,plain,
join(top,meet(top,top)) = join(top,top),
inference(subst,[],[refute_0_437:[bind(X_33,$fot(top))]]) ).
cnf(refute_0_439,plain,
join(top,complement(join(zero,zero))) = join(top,complement(join(zero,zero))),
introduced(tautology,[refl,[$fot(join(top,complement(join(zero,zero))))]]) ).
cnf(refute_0_440,plain,
( complement(join(zero,zero)) != meet(top,top)
| join(top,complement(join(zero,zero))) != join(top,complement(join(zero,zero)))
| join(top,complement(join(zero,zero))) = join(top,meet(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,complement(join(zero,zero))),join(top,complement(join(zero,zero)))) ),[1,1],$fot(meet(top,top))]]) ).
cnf(refute_0_441,plain,
( complement(join(zero,zero)) != meet(top,top)
| join(top,complement(join(zero,zero))) = join(top,meet(top,top)) ),
inference(resolve,[$cnf( $equal(join(top,complement(join(zero,zero))),join(top,complement(join(zero,zero)))) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
join(top,complement(join(zero,zero))) = join(top,meet(top,top)),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),meet(top,top)) )],[refute_0_325,refute_0_441]) ).
cnf(refute_0_443,plain,
( join(top,complement(join(zero,zero))) != join(top,meet(top,top))
| join(top,meet(top,top)) != join(top,top)
| join(top,complement(join(zero,zero))) = join(top,top) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(top,complement(join(zero,zero))))),bind(Y,$fot(join(top,meet(top,top)))),bind(Z,$fot(join(top,top)))]]) ).
cnf(refute_0_444,plain,
( join(top,meet(top,top)) != join(top,top)
| join(top,complement(join(zero,zero))) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(top,complement(join(zero,zero))),join(top,meet(top,top))) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
join(top,complement(join(zero,zero))) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,meet(top,top)),join(top,top)) )],[refute_0_438,refute_0_444]) ).
cnf(refute_0_446,plain,
join(complement(join(zero,zero)),top) = join(top,complement(join(zero,zero))),
inference(subst,[],[refute_0_247:[bind(A,$fot(complement(join(zero,zero))))]]) ).
cnf(refute_0_447,plain,
( join(complement(join(zero,zero)),top) != join(top,complement(join(zero,zero)))
| join(top,complement(join(zero,zero))) != join(top,top)
| join(complement(join(zero,zero)),top) = join(top,top) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(complement(join(zero,zero)),top))),bind(Y,$fot(join(top,complement(join(zero,zero))))),bind(Z,$fot(join(top,top)))]]) ).
cnf(refute_0_448,plain,
( join(top,complement(join(zero,zero))) != join(top,top)
| join(complement(join(zero,zero)),top) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(complement(join(zero,zero)),top),join(top,complement(join(zero,zero)))) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
join(complement(join(zero,zero)),top) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,complement(join(zero,zero))),join(top,top)) )],[refute_0_445,refute_0_448]) ).
cnf(refute_0_450,plain,
complement(join(complement(join(zero,zero)),top)) = complement(join(complement(join(zero,zero)),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(join(zero,zero)),top)))]]) ).
cnf(refute_0_451,plain,
( complement(join(complement(join(zero,zero)),top)) != complement(join(complement(join(zero,zero)),top))
| join(complement(join(zero,zero)),top) != join(top,top)
| complement(join(complement(join(zero,zero)),top)) = complement(join(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(join(zero,zero)),top)),complement(join(complement(join(zero,zero)),top))) ),[1,0],$fot(join(top,top))]]) ).
cnf(refute_0_452,plain,
( join(complement(join(zero,zero)),top) != join(top,top)
| complement(join(complement(join(zero,zero)),top)) = complement(join(top,top)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(join(zero,zero)),top)),complement(join(complement(join(zero,zero)),top))) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
complement(join(complement(join(zero,zero)),top)) = complement(join(top,top)),
inference(resolve,[$cnf( $equal(join(complement(join(zero,zero)),top),join(top,top)) )],[refute_0_449,refute_0_452]) ).
cnf(refute_0_454,plain,
join(zero,complement(join(complement(join(zero,zero)),top))) = join(zero,complement(join(complement(join(zero,zero)),top))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(join(zero,zero)),top))))]]) ).
cnf(refute_0_455,plain,
( complement(join(complement(join(zero,zero)),top)) != complement(join(top,top))
| join(zero,complement(join(complement(join(zero,zero)),top))) != join(zero,complement(join(complement(join(zero,zero)),top)))
| join(zero,complement(join(complement(join(zero,zero)),top))) = join(zero,complement(join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(join(zero,zero)),top))),join(zero,complement(join(complement(join(zero,zero)),top)))) ),[1,1],$fot(complement(join(top,top)))]]) ).
cnf(refute_0_456,plain,
( complement(join(complement(join(zero,zero)),top)) != complement(join(top,top))
| join(zero,complement(join(complement(join(zero,zero)),top))) = join(zero,complement(join(top,top))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(join(zero,zero)),top))),join(zero,complement(join(complement(join(zero,zero)),top)))) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
join(zero,complement(join(complement(join(zero,zero)),top))) = join(zero,complement(join(top,top))),
inference(resolve,[$cnf( $equal(complement(join(complement(join(zero,zero)),top)),complement(join(top,top))) )],[refute_0_453,refute_0_456]) ).
cnf(refute_0_458,plain,
( join(zero,complement(join(complement(join(zero,zero)),top))) != join(zero,complement(join(top,top)))
| join(zero,complement(join(top,top))) != join(zero,join(zero,zero))
| join(zero,complement(join(complement(join(zero,zero)),top))) = join(zero,join(zero,zero)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(zero,complement(join(complement(join(zero,zero)),top))))),bind(Y,$fot(join(zero,complement(join(top,top))))),bind(Z,$fot(join(zero,join(zero,zero))))]]) ).
cnf(refute_0_459,plain,
( join(zero,complement(join(top,top))) != join(zero,join(zero,zero))
| join(zero,complement(join(complement(join(zero,zero)),top))) = join(zero,join(zero,zero)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(join(zero,zero)),top))),join(zero,complement(join(top,top)))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
join(zero,complement(join(complement(join(zero,zero)),top))) = join(zero,join(zero,zero)),
inference(resolve,[$cnf( $equal(join(zero,complement(join(top,top))),join(zero,join(zero,zero))) )],[refute_0_428,refute_0_459]) ).
cnf(refute_0_461,plain,
( join(zero,complement(join(complement(join(zero,zero)),top))) != join(zero,join(zero,zero))
| join(zero,zero) != join(zero,complement(join(complement(join(zero,zero)),top)))
| join(zero,zero) = join(zero,join(zero,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,zero),join(zero,complement(join(complement(join(zero,zero)),top)))) ),[1],$fot(join(zero,join(zero,zero)))]]) ).
cnf(refute_0_462,plain,
( join(zero,zero) != join(zero,complement(join(complement(join(zero,zero)),top)))
| join(zero,zero) = join(zero,join(zero,zero)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(join(zero,zero)),top))),join(zero,join(zero,zero))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
join(zero,zero) = join(zero,join(zero,zero)),
inference(resolve,[$cnf( $equal(join(zero,zero),join(zero,complement(join(complement(join(zero,zero)),top)))) )],[refute_0_426,refute_0_462]) ).
cnf(refute_0_464,plain,
( join(zero,zero) != join(zero,join(zero,zero))
| join(zero,join(zero,zero)) = join(zero,zero) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(zero,zero))),bind(Y,$fot(join(zero,join(zero,zero))))]]) ).
cnf(refute_0_465,plain,
join(zero,join(zero,zero)) = join(zero,zero),
inference(resolve,[$cnf( $equal(join(zero,zero),join(zero,join(zero,zero))) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
( join(zero,complement(join(top,top))) != join(zero,join(zero,zero))
| join(zero,join(zero,zero)) != join(zero,zero)
| join(zero,complement(join(top,top))) = join(zero,zero) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(zero,complement(join(top,top))))),bind(Y,$fot(join(zero,join(zero,zero)))),bind(Z,$fot(join(zero,zero)))]]) ).
cnf(refute_0_467,plain,
( join(zero,join(zero,zero)) != join(zero,zero)
| join(zero,complement(join(top,top))) = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(top,top))),join(zero,join(zero,zero))) )],[refute_0_428,refute_0_466]) ).
cnf(refute_0_468,plain,
join(zero,complement(join(top,top))) = join(zero,zero),
inference(resolve,[$cnf( $equal(join(zero,join(zero,zero)),join(zero,zero)) )],[refute_0_465,refute_0_467]) ).
cnf(refute_0_469,plain,
join(top,join(zero,complement(zero))) = join(top,complement(zero)),
inference(subst,[],[refute_0_83:[bind(X_17,$fot(complement(zero)))]]) ).
cnf(refute_0_470,plain,
top = join(zero,complement(zero)),
inference(subst,[],[def_top_12:[bind(A,$fot(zero))]]) ).
cnf(refute_0_471,plain,
( top != join(zero,complement(zero))
| join(zero,complement(zero)) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(zero,complement(zero))))]]) ).
cnf(refute_0_472,plain,
join(zero,complement(zero)) = top,
inference(resolve,[$cnf( $equal(top,join(zero,complement(zero))) )],[refute_0_470,refute_0_471]) ).
cnf(refute_0_473,plain,
( join(top,join(zero,complement(zero))) != join(top,complement(zero))
| join(zero,complement(zero)) != top
| join(top,top) = join(top,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,complement(zero))),join(top,complement(zero))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_474,plain,
( join(top,join(zero,complement(zero))) != join(top,complement(zero))
| join(top,top) = join(top,complement(zero)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(zero)),top) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
join(top,top) = join(top,complement(zero)),
inference(resolve,[$cnf( $equal(join(top,join(zero,complement(zero))),join(top,complement(zero))) )],[refute_0_469,refute_0_474]) ).
cnf(refute_0_476,plain,
( join(top,top) != join(top,complement(zero))
| join(top,complement(zero)) = join(top,top) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(top,top))),bind(Y,$fot(join(top,complement(zero))))]]) ).
cnf(refute_0_477,plain,
join(top,complement(zero)) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,top),join(top,complement(zero))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
join(complement(zero),top) = join(top,complement(zero)),
inference(subst,[],[refute_0_247:[bind(A,$fot(complement(zero)))]]) ).
cnf(refute_0_479,plain,
( join(complement(zero),top) != join(top,complement(zero))
| join(top,complement(zero)) != join(top,top)
| join(complement(zero),top) = join(top,top) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(complement(zero),top))),bind(Y,$fot(join(top,complement(zero)))),bind(Z,$fot(join(top,top)))]]) ).
cnf(refute_0_480,plain,
( join(top,complement(zero)) != join(top,top)
| join(complement(zero),top) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(complement(zero),top),join(top,complement(zero))) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
join(complement(zero),top) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,complement(zero)),join(top,top)) )],[refute_0_477,refute_0_480]) ).
cnf(refute_0_482,plain,
complement(join(complement(zero),top)) = complement(join(complement(zero),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(zero),top)))]]) ).
cnf(refute_0_483,plain,
( complement(join(complement(zero),top)) != complement(join(complement(zero),top))
| join(complement(zero),top) != join(top,top)
| complement(join(complement(zero),top)) = complement(join(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(zero),top)),complement(join(complement(zero),top))) ),[1,0],$fot(join(top,top))]]) ).
cnf(refute_0_484,plain,
( join(complement(zero),top) != join(top,top)
| complement(join(complement(zero),top)) = complement(join(top,top)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(zero),top)),complement(join(complement(zero),top))) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
complement(join(complement(zero),top)) = complement(join(top,top)),
inference(resolve,[$cnf( $equal(join(complement(zero),top),join(top,top)) )],[refute_0_481,refute_0_484]) ).
cnf(refute_0_486,plain,
join(zero,complement(join(complement(zero),top))) = join(zero,complement(join(complement(zero),top))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(zero),top))))]]) ).
cnf(refute_0_487,plain,
( complement(join(complement(zero),top)) != complement(join(top,top))
| join(zero,complement(join(complement(zero),top))) != join(zero,complement(join(complement(zero),top)))
| join(zero,complement(join(complement(zero),top))) = join(zero,complement(join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(zero),top))),join(zero,complement(join(complement(zero),top)))) ),[1,1],$fot(complement(join(top,top)))]]) ).
cnf(refute_0_488,plain,
( complement(join(complement(zero),top)) != complement(join(top,top))
| join(zero,complement(join(complement(zero),top))) = join(zero,complement(join(top,top))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(zero),top))),join(zero,complement(join(complement(zero),top)))) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
join(zero,complement(join(complement(zero),top))) = join(zero,complement(join(top,top))),
inference(resolve,[$cnf( $equal(complement(join(complement(zero),top)),complement(join(top,top))) )],[refute_0_485,refute_0_488]) ).
cnf(refute_0_490,plain,
( join(zero,complement(join(complement(zero),top))) != join(zero,complement(join(top,top)))
| join(zero,complement(join(top,top))) != join(zero,zero)
| join(zero,complement(join(complement(zero),top))) = join(zero,zero) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(zero,complement(join(complement(zero),top))))),bind(Y,$fot(join(zero,complement(join(top,top))))),bind(Z,$fot(join(zero,zero)))]]) ).
cnf(refute_0_491,plain,
( join(zero,complement(join(top,top))) != join(zero,zero)
| join(zero,complement(join(complement(zero),top))) = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(zero),top))),join(zero,complement(join(top,top)))) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
join(zero,complement(join(complement(zero),top))) = join(zero,zero),
inference(resolve,[$cnf( $equal(join(zero,complement(join(top,top))),join(zero,zero)) )],[refute_0_468,refute_0_491]) ).
cnf(refute_0_493,plain,
( join(zero,complement(join(complement(zero),top))) != join(zero,zero)
| zero != join(zero,complement(join(complement(zero),top)))
| zero = join(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(zero,complement(join(complement(zero),top)))) ),[1],$fot(join(zero,zero))]]) ).
cnf(refute_0_494,plain,
( zero != join(zero,complement(join(complement(zero),top)))
| zero = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(zero),top))),join(zero,zero)) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
zero = join(zero,zero),
inference(resolve,[$cnf( $equal(zero,join(zero,complement(join(complement(zero),top)))) )],[refute_0_422,refute_0_494]) ).
cnf(refute_0_496,plain,
( zero != join(zero,zero)
| join(zero,zero) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(join(zero,zero)))]]) ).
cnf(refute_0_497,plain,
join(zero,zero) = zero,
inference(resolve,[$cnf( $equal(zero,join(zero,zero)) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
( join(zero,join(zero,zero)) != join(zero,zero)
| join(zero,zero) != zero
| join(zero,join(zero,zero)) = zero ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(zero,join(zero,zero)))),bind(Y,$fot(join(zero,zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_499,plain,
( join(zero,zero) != zero
| join(zero,join(zero,zero)) = zero ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,zero)),join(zero,zero)) )],[refute_0_465,refute_0_498]) ).
cnf(refute_0_500,plain,
join(zero,join(zero,zero)) = zero,
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_497,refute_0_499]) ).
cnf(refute_0_501,plain,
( join(zero,join(zero,zero)) != join(zero,complement(join(top,top)))
| join(zero,join(zero,zero)) != zero
| zero = join(zero,complement(join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,zero)),join(zero,complement(join(top,top)))) ),[0],$fot(zero)]]) ).
cnf(refute_0_502,plain,
( join(zero,join(zero,zero)) != join(zero,complement(join(top,top)))
| zero = join(zero,complement(join(top,top))) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,zero)),zero) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
zero = join(zero,complement(join(top,top))),
inference(resolve,[$cnf( $equal(join(zero,join(zero,zero)),join(zero,complement(join(top,top)))) )],[refute_0_412,refute_0_502]) ).
cnf(refute_0_504,plain,
join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B)))))),
inference(subst,[],[refute_0_310:[bind(X_31,$fot(join(zero,complement(B))))]]) ).
cnf(refute_0_505,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) = meet(top,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(top,B))),bind(Y,$fot(complement(join(zero,complement(B)))))]]) ).
cnf(refute_0_506,plain,
complement(join(zero,complement(B))) = meet(top,B),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_316,refute_0_505]) ).
cnf(refute_0_507,plain,
( complement(join(zero,complement(B))) != meet(top,B)
| join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))
| join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))) ),[1,1,1,0],$fot(meet(top,B))]]) ).
cnf(refute_0_508,plain,
( join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))
| join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),meet(top,B)) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
join(zero,complement(B)) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(join(zero,complement(B)),complement(complement(join(zero,complement(B))))))) )],[refute_0_504,refute_0_508]) ).
cnf(refute_0_510,plain,
( meet(X_22,X_23) != meet(X_23,X_22)
| meet(X_23,X_22) = meet(X_22,X_23) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_22,X_23))),bind(Y,$fot(meet(X_23,X_22)))]]) ).
cnf(refute_0_511,plain,
meet(X_23,X_22) = meet(X_22,X_23),
inference(resolve,[$cnf( $equal(meet(X_22,X_23),meet(X_23,X_22)) )],[refute_0_285,refute_0_510]) ).
cnf(refute_0_512,plain,
meet(join(zero,complement(B)),complement(meet(top,B))) = meet(complement(meet(top,B)),join(zero,complement(B))),
inference(subst,[],[refute_0_511:[bind(X_22,$fot(complement(meet(top,B)))),bind(X_23,$fot(join(zero,complement(B))))]]) ).
cnf(refute_0_513,plain,
join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))))]]) ).
cnf(refute_0_514,plain,
( join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) != join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))
| meet(join(zero,complement(B)),complement(meet(top,B))) != meet(complement(meet(top,B)),join(zero,complement(B)))
| join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))) ),[1,1],$fot(meet(complement(meet(top,B)),join(zero,complement(B))))]]) ).
cnf(refute_0_515,plain,
( meet(join(zero,complement(B)),complement(meet(top,B))) != meet(complement(meet(top,B)),join(zero,complement(B)))
| join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(B)),complement(meet(top,B))),meet(complement(meet(top,B)),join(zero,complement(B)))) )],[refute_0_512,refute_0_515]) ).
cnf(refute_0_517,plain,
( join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))
| join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| join(zero,complement(B)) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,complement(B)),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) ),[0],$fot(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))))]]) ).
cnf(refute_0_518,plain,
( join(zero,complement(B)) != join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))
| join(zero,complement(B)) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,complement(B)),complement(meet(top,B)))),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
join(zero,complement(B)) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(join(zero,complement(B)),complement(meet(top,B))))) )],[refute_0_509,refute_0_518]) ).
cnf(refute_0_520,plain,
join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))) = complement(meet(top,B)),
inference(subst,[],[refute_0_232:[bind(X_31,$fot(complement(meet(top,B))))]]) ).
cnf(refute_0_521,plain,
meet(A,join(zero,complement(X_29))) = complement(join(complement(A),complement(join(zero,complement(X_29))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(zero,complement(X_29))))]]) ).
cnf(refute_0_522,plain,
meet(top,X_29) = complement(join(zero,complement(X_29))),
inference(subst,[],[refute_0_316:[bind(B,$fot(X_29))]]) ).
cnf(refute_0_523,plain,
( meet(top,X_29) != complement(join(zero,complement(X_29)))
| complement(join(zero,complement(X_29))) = meet(top,X_29) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(top,X_29))),bind(Y,$fot(complement(join(zero,complement(X_29)))))]]) ).
cnf(refute_0_524,plain,
complement(join(zero,complement(X_29))) = meet(top,X_29),
inference(resolve,[$cnf( $equal(meet(top,X_29),complement(join(zero,complement(X_29)))) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
( complement(join(zero,complement(X_29))) != meet(top,X_29)
| meet(A,join(zero,complement(X_29))) != complement(join(complement(A),complement(join(zero,complement(X_29)))))
| meet(A,join(zero,complement(X_29))) = complement(join(complement(A),meet(top,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_29))),complement(join(complement(A),complement(join(zero,complement(X_29)))))) ),[1,0,1],$fot(meet(top,X_29))]]) ).
cnf(refute_0_526,plain,
( meet(A,join(zero,complement(X_29))) != complement(join(complement(A),complement(join(zero,complement(X_29)))))
| meet(A,join(zero,complement(X_29))) = complement(join(complement(A),meet(top,X_29))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_29))),meet(top,X_29)) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
meet(A,join(zero,complement(X_29))) = complement(join(complement(A),meet(top,X_29))),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_29))),complement(join(complement(A),complement(join(zero,complement(X_29)))))) )],[refute_0_521,refute_0_526]) ).
cnf(refute_0_528,plain,
meet(A,join(complement(X_22),complement(X_23))) = complement(join(complement(A),complement(join(complement(X_22),complement(X_23))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(complement(X_22),complement(X_23))))]]) ).
cnf(refute_0_529,plain,
( complement(join(complement(X_22),complement(X_23))) != meet(X_22,X_23)
| meet(A,join(complement(X_22),complement(X_23))) != complement(join(complement(A),complement(join(complement(X_22),complement(X_23)))))
| meet(A,join(complement(X_22),complement(X_23))) = complement(join(complement(A),meet(X_22,X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_22),complement(X_23))),complement(join(complement(A),complement(join(complement(X_22),complement(X_23)))))) ),[1,0,1],$fot(meet(X_22,X_23))]]) ).
cnf(refute_0_530,plain,
( meet(A,join(complement(X_22),complement(X_23))) != complement(join(complement(A),complement(join(complement(X_22),complement(X_23)))))
| meet(A,join(complement(X_22),complement(X_23))) = complement(join(complement(A),meet(X_22,X_23))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_22),complement(X_23))),meet(X_22,X_23)) )],[refute_0_48,refute_0_529]) ).
cnf(refute_0_531,plain,
meet(A,join(complement(X_22),complement(X_23))) = complement(join(complement(A),meet(X_22,X_23))),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_22),complement(X_23))),complement(join(complement(A),complement(join(complement(X_22),complement(X_23)))))) )],[refute_0_528,refute_0_530]) ).
cnf(refute_0_532,plain,
join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B)))))),
inference(subst,[],[refute_0_310:[bind(X_31,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_533,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))
| join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))) ),[1,1,1,0],$fot(meet(A,B))]]) ).
cnf(refute_0_534,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))
| join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_31,refute_0_533]) ).
cnf(refute_0_535,plain,
join(complement(A),complement(B)) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(complement(join(complement(A),complement(B))))))) )],[refute_0_532,refute_0_534]) ).
cnf(refute_0_536,plain,
join(complement(complement(meet(A,B))),meet(A,B)) = join(meet(A,B),complement(complement(meet(A,B)))),
inference(subst,[],[refute_0_24:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(complement(meet(A,B)))))]]) ).
cnf(refute_0_537,plain,
complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(meet(A,B))),meet(A,B))))]]) ).
cnf(refute_0_538,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| join(complement(complement(meet(A,B))),meet(A,B)) != join(meet(A,B),complement(complement(meet(A,B))))
| complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) ),[1,0],$fot(join(meet(A,B),complement(complement(meet(A,B)))))]]) ).
cnf(refute_0_539,plain,
( join(complement(complement(meet(A,B))),meet(A,B)) != join(meet(A,B),complement(complement(meet(A,B))))
| complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
complement(join(complement(complement(meet(A,B))),meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))),
inference(resolve,[$cnf( $equal(join(complement(complement(meet(A,B))),meet(A,B)),join(meet(A,B),complement(complement(meet(A,B))))) )],[refute_0_536,refute_0_539]) ).
cnf(refute_0_541,plain,
meet(complement(meet(A,B)),join(complement(A),complement(B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
inference(subst,[],[refute_0_531:[bind(A,$fot(complement(meet(A,B)))),bind(X_22,$fot(A)),bind(X_23,$fot(B))]]) ).
cnf(refute_0_542,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = meet(complement(meet(A,B)),join(complement(A),complement(B))),
inference(subst,[],[refute_0_511:[bind(X_22,$fot(complement(meet(A,B)))),bind(X_23,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_543,plain,
( meet(complement(meet(A,B)),join(complement(A),complement(B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != meet(complement(meet(A,B)),join(complement(A),complement(B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(meet(join(complement(A),complement(B)),complement(meet(A,B))))),bind(Y,$fot(meet(complement(meet(A,B)),join(complement(A),complement(B))))),bind(Z,$fot(complement(join(complement(complement(meet(A,B))),meet(A,B)))))]]) ).
cnf(refute_0_544,plain,
( meet(complement(meet(A,B)),join(complement(A),complement(B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),meet(complement(meet(A,B)),join(complement(A),complement(B)))) )],[refute_0_542,refute_0_543]) ).
cnf(refute_0_545,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(complement(complement(meet(A,B))),meet(A,B))),
inference(resolve,[$cnf( $equal(meet(complement(meet(A,B)),join(complement(A),complement(B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_541,refute_0_544]) ).
cnf(refute_0_546,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(complement(complement(meet(A,B))),meet(A,B)))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(meet(join(complement(A),complement(B)),complement(meet(A,B))))),bind(Y,$fot(complement(join(complement(complement(meet(A,B))),meet(A,B))))),bind(Z,$fot(complement(join(meet(A,B),complement(complement(meet(A,B)))))))]]) ).
cnf(refute_0_547,plain,
( complement(join(complement(complement(meet(A,B))),meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))) ),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),complement(join(complement(complement(meet(A,B))),meet(A,B)))) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
meet(join(complement(A),complement(B)),complement(meet(A,B))) = complement(join(meet(A,B),complement(complement(meet(A,B))))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(meet(A,B))),meet(A,B))),complement(join(meet(A,B),complement(complement(meet(A,B)))))) )],[refute_0_540,refute_0_547]) ).
cnf(refute_0_549,plain,
join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),
introduced(tautology,[refl,[$fot(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))))]]) ).
cnf(refute_0_550,plain,
( join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) ),[1,1],$fot(complement(join(meet(A,B),complement(complement(meet(A,B))))))]]) ).
cnf(refute_0_551,plain,
( meet(join(complement(A),complement(B)),complement(meet(A,B))) != complement(join(meet(A,B),complement(complement(meet(A,B)))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) )],[refute_0_549,refute_0_550]) ).
cnf(refute_0_552,plain,
join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),complement(meet(A,B))),complement(join(meet(A,B),complement(complement(meet(A,B)))))) )],[refute_0_548,refute_0_551]) ).
cnf(refute_0_553,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) ),[0],$fot(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))))]]) ).
cnf(refute_0_554,plain,
( join(complement(A),complement(B)) != join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))
| join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B)))),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) )],[refute_0_552,refute_0_553]) ).
cnf(refute_0_555,plain,
join(complement(A),complement(B)) = join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,meet(join(complement(A),complement(B)),complement(meet(A,B))))) )],[refute_0_535,refute_0_554]) ).
cnf(refute_0_556,plain,
complement(X_51) = join(meet(X_51,complement(X_51)),complement(join(complement(complement(X_51)),X_51))),
inference(subst,[],[refute_0_291:[bind(X_31,$fot(complement(X_51))),bind(X_32,$fot(X_51))]]) ).
cnf(refute_0_557,plain,
zero = meet(X_51,complement(X_51)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_51))]]) ).
cnf(refute_0_558,plain,
( zero != meet(X_51,complement(X_51))
| meet(X_51,complement(X_51)) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_51,complement(X_51))))]]) ).
cnf(refute_0_559,plain,
meet(X_51,complement(X_51)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_51,complement(X_51))) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
( complement(X_51) != join(meet(X_51,complement(X_51)),complement(join(complement(complement(X_51)),X_51)))
| meet(X_51,complement(X_51)) != zero
| complement(X_51) = join(zero,complement(join(complement(complement(X_51)),X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_51),join(meet(X_51,complement(X_51)),complement(join(complement(complement(X_51)),X_51)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_561,plain,
( complement(X_51) != join(meet(X_51,complement(X_51)),complement(join(complement(complement(X_51)),X_51)))
| complement(X_51) = join(zero,complement(join(complement(complement(X_51)),X_51))) ),
inference(resolve,[$cnf( $equal(meet(X_51,complement(X_51)),zero) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
complement(X_51) = join(zero,complement(join(complement(complement(X_51)),X_51))),
inference(resolve,[$cnf( $equal(complement(X_51),join(meet(X_51,complement(X_51)),complement(join(complement(complement(X_51)),X_51)))) )],[refute_0_556,refute_0_561]) ).
cnf(refute_0_563,plain,
join(complement(complement(X_51)),X_51) = join(X_51,complement(complement(X_51))),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_51)),bind(B,$fot(complement(complement(X_51))))]]) ).
cnf(refute_0_564,plain,
complement(join(complement(complement(X_51)),X_51)) = complement(join(complement(complement(X_51)),X_51)),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(X_51)),X_51)))]]) ).
cnf(refute_0_565,plain,
( complement(join(complement(complement(X_51)),X_51)) != complement(join(complement(complement(X_51)),X_51))
| join(complement(complement(X_51)),X_51) != join(X_51,complement(complement(X_51)))
| complement(join(complement(complement(X_51)),X_51)) = complement(join(X_51,complement(complement(X_51)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(X_51)),X_51)),complement(join(complement(complement(X_51)),X_51))) ),[1,0],$fot(join(X_51,complement(complement(X_51))))]]) ).
cnf(refute_0_566,plain,
( join(complement(complement(X_51)),X_51) != join(X_51,complement(complement(X_51)))
| complement(join(complement(complement(X_51)),X_51)) = complement(join(X_51,complement(complement(X_51)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_51)),X_51)),complement(join(complement(complement(X_51)),X_51))) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
complement(join(complement(complement(X_51)),X_51)) = complement(join(X_51,complement(complement(X_51)))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_51)),X_51),join(X_51,complement(complement(X_51)))) )],[refute_0_563,refute_0_566]) ).
cnf(refute_0_568,plain,
join(zero,complement(join(complement(complement(X_51)),X_51))) = join(zero,complement(join(complement(complement(X_51)),X_51))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(complement(X_51)),X_51))))]]) ).
cnf(refute_0_569,plain,
( complement(join(complement(complement(X_51)),X_51)) != complement(join(X_51,complement(complement(X_51))))
| join(zero,complement(join(complement(complement(X_51)),X_51))) != join(zero,complement(join(complement(complement(X_51)),X_51)))
| join(zero,complement(join(complement(complement(X_51)),X_51))) = join(zero,complement(join(X_51,complement(complement(X_51))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(complement(X_51)),X_51))),join(zero,complement(join(complement(complement(X_51)),X_51)))) ),[1,1],$fot(complement(join(X_51,complement(complement(X_51)))))]]) ).
cnf(refute_0_570,plain,
( complement(join(complement(complement(X_51)),X_51)) != complement(join(X_51,complement(complement(X_51))))
| join(zero,complement(join(complement(complement(X_51)),X_51))) = join(zero,complement(join(X_51,complement(complement(X_51))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(complement(X_51)),X_51))),join(zero,complement(join(complement(complement(X_51)),X_51)))) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
join(zero,complement(join(complement(complement(X_51)),X_51))) = join(zero,complement(join(X_51,complement(complement(X_51))))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_51)),X_51)),complement(join(X_51,complement(complement(X_51))))) )],[refute_0_567,refute_0_570]) ).
cnf(refute_0_572,plain,
( complement(X_51) != join(zero,complement(join(complement(complement(X_51)),X_51)))
| join(zero,complement(join(complement(complement(X_51)),X_51))) != join(zero,complement(join(X_51,complement(complement(X_51)))))
| complement(X_51) = join(zero,complement(join(X_51,complement(complement(X_51))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_51),join(zero,complement(join(X_51,complement(complement(X_51)))))) ),[0],$fot(join(zero,complement(join(complement(complement(X_51)),X_51))))]]) ).
cnf(refute_0_573,plain,
( complement(X_51) != join(zero,complement(join(complement(complement(X_51)),X_51)))
| complement(X_51) = join(zero,complement(join(X_51,complement(complement(X_51))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(complement(X_51)),X_51))),join(zero,complement(join(X_51,complement(complement(X_51)))))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
complement(X_51) = join(zero,complement(join(X_51,complement(complement(X_51))))),
inference(resolve,[$cnf( $equal(complement(X_51),join(zero,complement(join(complement(complement(X_51)),X_51)))) )],[refute_0_562,refute_0_573]) ).
cnf(refute_0_575,plain,
( complement(X_51) != join(zero,complement(join(X_51,complement(complement(X_51)))))
| join(zero,complement(join(X_51,complement(complement(X_51))))) = complement(X_51) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(complement(X_51))),bind(Y,$fot(join(zero,complement(join(X_51,complement(complement(X_51)))))))]]) ).
cnf(refute_0_576,plain,
join(zero,complement(join(X_51,complement(complement(X_51))))) = complement(X_51),
inference(resolve,[$cnf( $equal(complement(X_51),join(zero,complement(join(X_51,complement(complement(X_51)))))) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) = complement(meet(A,B)),
inference(subst,[],[refute_0_576:[bind(X_51,$fot(meet(A,B)))]]) ).
cnf(refute_0_578,plain,
( join(complement(A),complement(B)) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))) != complement(meet(A,B))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),complement(meet(A,B))) ),[0],$fot(join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))))]]) ).
cnf(refute_0_579,plain,
( join(complement(A),complement(B)) != join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(meet(A,B),complement(complement(meet(A,B)))))),complement(meet(A,B))) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
join(complement(A),complement(B)) = complement(meet(A,B)),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(join(meet(A,B),complement(complement(meet(A,B))))))) )],[refute_0_555,refute_0_579]) ).
cnf(refute_0_581,plain,
join(complement(X_22),complement(X_23)) = complement(meet(X_22,X_23)),
inference(subst,[],[refute_0_580:[bind(A,$fot(X_22)),bind(B,$fot(X_23))]]) ).
cnf(refute_0_582,plain,
meet(A,join(complement(X_22),complement(X_23))) = meet(A,join(complement(X_22),complement(X_23))),
introduced(tautology,[refl,[$fot(meet(A,join(complement(X_22),complement(X_23))))]]) ).
cnf(refute_0_583,plain,
( join(complement(X_22),complement(X_23)) != complement(meet(X_22,X_23))
| meet(A,join(complement(X_22),complement(X_23))) != meet(A,join(complement(X_22),complement(X_23)))
| meet(A,join(complement(X_22),complement(X_23))) = meet(A,complement(meet(X_22,X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_22),complement(X_23))),meet(A,join(complement(X_22),complement(X_23)))) ),[1,1],$fot(complement(meet(X_22,X_23)))]]) ).
cnf(refute_0_584,plain,
( join(complement(X_22),complement(X_23)) != complement(meet(X_22,X_23))
| meet(A,join(complement(X_22),complement(X_23))) = meet(A,complement(meet(X_22,X_23))) ),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_22),complement(X_23))),meet(A,join(complement(X_22),complement(X_23)))) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
meet(A,join(complement(X_22),complement(X_23))) = meet(A,complement(meet(X_22,X_23))),
inference(resolve,[$cnf( $equal(join(complement(X_22),complement(X_23)),complement(meet(X_22,X_23))) )],[refute_0_581,refute_0_584]) ).
cnf(refute_0_586,plain,
( meet(A,join(complement(X_22),complement(X_23))) != complement(join(complement(A),meet(X_22,X_23)))
| meet(A,join(complement(X_22),complement(X_23))) != meet(A,complement(meet(X_22,X_23)))
| meet(A,complement(meet(X_22,X_23))) = complement(join(complement(A),meet(X_22,X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(complement(X_22),complement(X_23))),complement(join(complement(A),meet(X_22,X_23)))) ),[0],$fot(meet(A,complement(meet(X_22,X_23))))]]) ).
cnf(refute_0_587,plain,
( meet(A,join(complement(X_22),complement(X_23))) != complement(join(complement(A),meet(X_22,X_23)))
| meet(A,complement(meet(X_22,X_23))) = complement(join(complement(A),meet(X_22,X_23))) ),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_22),complement(X_23))),meet(A,complement(meet(X_22,X_23)))) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
meet(A,complement(meet(X_22,X_23))) = complement(join(complement(A),meet(X_22,X_23))),
inference(resolve,[$cnf( $equal(meet(A,join(complement(X_22),complement(X_23))),complement(join(complement(A),meet(X_22,X_23)))) )],[refute_0_531,refute_0_587]) ).
cnf(refute_0_589,plain,
( meet(A,complement(meet(X_22,X_23))) != complement(join(complement(A),meet(X_22,X_23)))
| complement(join(complement(A),meet(X_22,X_23))) = meet(A,complement(meet(X_22,X_23))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(A,complement(meet(X_22,X_23))))),bind(Y,$fot(complement(join(complement(A),meet(X_22,X_23)))))]]) ).
cnf(refute_0_590,plain,
complement(join(complement(A),meet(X_22,X_23))) = meet(A,complement(meet(X_22,X_23))),
inference(resolve,[$cnf( $equal(meet(A,complement(meet(X_22,X_23))),complement(join(complement(A),meet(X_22,X_23)))) )],[refute_0_588,refute_0_589]) ).
cnf(refute_0_591,plain,
complement(join(complement(A),meet(top,X_29))) = meet(A,complement(meet(top,X_29))),
inference(subst,[],[refute_0_590:[bind(X_22,$fot(top)),bind(X_23,$fot(X_29))]]) ).
cnf(refute_0_592,plain,
( complement(join(complement(A),meet(top,X_29))) != meet(A,complement(meet(top,X_29)))
| meet(A,join(zero,complement(X_29))) != complement(join(complement(A),meet(top,X_29)))
| meet(A,join(zero,complement(X_29))) = meet(A,complement(meet(top,X_29))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_29))),complement(join(complement(A),meet(top,X_29)))) ),[1],$fot(meet(A,complement(meet(top,X_29))))]]) ).
cnf(refute_0_593,plain,
( meet(A,join(zero,complement(X_29))) != complement(join(complement(A),meet(top,X_29)))
| meet(A,join(zero,complement(X_29))) = meet(A,complement(meet(top,X_29))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),meet(top,X_29))),meet(A,complement(meet(top,X_29)))) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
meet(A,join(zero,complement(X_29))) = meet(A,complement(meet(top,X_29))),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_29))),complement(join(complement(A),meet(top,X_29)))) )],[refute_0_527,refute_0_593]) ).
cnf(refute_0_595,plain,
meet(complement(meet(top,B)),join(zero,complement(B))) = meet(complement(meet(top,B)),complement(meet(top,B))),
inference(subst,[],[refute_0_594:[bind(A,$fot(complement(meet(top,B)))),bind(X_29,$fot(B))]]) ).
cnf(refute_0_596,plain,
join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),
introduced(tautology,[refl,[$fot(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))))]]) ).
cnf(refute_0_597,plain,
( join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| meet(complement(meet(top,B)),join(zero,complement(B))) != meet(complement(meet(top,B)),complement(meet(top,B)))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) ),[1,1],$fot(meet(complement(meet(top,B)),complement(meet(top,B))))]]) ).
cnf(refute_0_598,plain,
( meet(complement(meet(top,B)),join(zero,complement(B))) != meet(complement(meet(top,B)),complement(meet(top,B)))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))),
inference(resolve,[$cnf( $equal(meet(complement(meet(top,B)),join(zero,complement(B))),meet(complement(meet(top,B)),complement(meet(top,B)))) )],[refute_0_595,refute_0_598]) ).
cnf(refute_0_600,plain,
( join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))) != complement(meet(top,B))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) != join(zero,meet(complement(meet(top,B)),complement(meet(top,B))))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = complement(meet(top,B)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))))),bind(Y,$fot(join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))))),bind(Z,$fot(complement(meet(top,B))))]]) ).
cnf(refute_0_601,plain,
( join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))) != complement(meet(top,B))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = complement(meet(top,B)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),join(zero,meet(complement(meet(top,B)),complement(meet(top,B))))) )],[refute_0_599,refute_0_600]) ).
cnf(refute_0_602,plain,
join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) = complement(meet(top,B)),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),complement(meet(top,B)))),complement(meet(top,B))) )],[refute_0_520,refute_0_601]) ).
cnf(refute_0_603,plain,
( join(zero,complement(B)) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))) != complement(meet(top,B))
| join(zero,complement(B)) = complement(meet(top,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,complement(B)),complement(meet(top,B))) ),[0],$fot(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))))]]) ).
cnf(refute_0_604,plain,
( join(zero,complement(B)) != join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))
| join(zero,complement(B)) = complement(meet(top,B)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(complement(meet(top,B)),join(zero,complement(B)))),complement(meet(top,B))) )],[refute_0_602,refute_0_603]) ).
cnf(refute_0_605,plain,
join(zero,complement(B)) = complement(meet(top,B)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(zero,meet(complement(meet(top,B)),join(zero,complement(B))))) )],[refute_0_519,refute_0_604]) ).
cnf(refute_0_606,plain,
join(zero,complement(join(top,top))) = complement(meet(top,join(top,top))),
inference(subst,[],[refute_0_605:[bind(B,$fot(join(top,top)))]]) ).
cnf(refute_0_607,plain,
( join(zero,complement(join(top,top))) != complement(meet(top,join(top,top)))
| zero != join(zero,complement(join(top,top)))
| zero = complement(meet(top,join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,join(zero,complement(join(top,top)))) ),[1],$fot(complement(meet(top,join(top,top))))]]) ).
cnf(refute_0_608,plain,
( zero != join(zero,complement(join(top,top)))
| zero = complement(meet(top,join(top,top))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(top,top))),complement(meet(top,join(top,top)))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
zero = complement(meet(top,join(top,top))),
inference(resolve,[$cnf( $equal(zero,join(zero,complement(join(top,top)))) )],[refute_0_503,refute_0_608]) ).
cnf(refute_0_610,plain,
( zero != complement(meet(top,join(top,top)))
| complement(meet(top,join(top,top))) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(complement(meet(top,join(top,top)))))]]) ).
cnf(refute_0_611,plain,
complement(meet(top,join(top,top))) = zero,
inference(resolve,[$cnf( $equal(zero,complement(meet(top,join(top,top)))) )],[refute_0_609,refute_0_610]) ).
cnf(refute_0_612,plain,
( complement(meet(top,join(top,top))) != zero
| meet(top,join(top,top)) != join(zero,meet(meet(top,join(top,top)),complement(complement(meet(top,join(top,top))))))
| meet(top,join(top,top)) = join(zero,meet(meet(top,join(top,top)),complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(top,top)),join(zero,meet(meet(top,join(top,top)),complement(complement(meet(top,join(top,top))))))) ),[1,1,1,0],$fot(zero)]]) ).
cnf(refute_0_613,plain,
( meet(top,join(top,top)) != join(zero,meet(meet(top,join(top,top)),complement(complement(meet(top,join(top,top))))))
| meet(top,join(top,top)) = join(zero,meet(meet(top,join(top,top)),complement(zero))) ),
inference(resolve,[$cnf( $equal(complement(meet(top,join(top,top))),zero) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
meet(top,join(top,top)) = join(zero,meet(meet(top,join(top,top)),complement(zero))),
inference(resolve,[$cnf( $equal(meet(top,join(top,top)),join(zero,meet(meet(top,join(top,top)),complement(complement(meet(top,join(top,top))))))) )],[refute_0_311,refute_0_613]) ).
cnf(refute_0_615,plain,
top = join(complement(top),join(complement(X_27),meet(top,X_27))),
inference(subst,[],[refute_0_159:[bind(X_22,$fot(top)),bind(X_23,$fot(X_27))]]) ).
cnf(refute_0_616,plain,
( complement(top) != zero
| top != join(complement(top),join(complement(X_27),meet(top,X_27)))
| top = join(zero,join(complement(X_27),meet(top,X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(top),join(complement(X_27),meet(top,X_27)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_617,plain,
( top != join(complement(top),join(complement(X_27),meet(top,X_27)))
| top = join(zero,join(complement(X_27),meet(top,X_27))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_616]) ).
cnf(refute_0_618,plain,
top = join(zero,join(complement(X_27),meet(top,X_27))),
inference(resolve,[$cnf( $equal(top,join(complement(top),join(complement(X_27),meet(top,X_27)))) )],[refute_0_615,refute_0_617]) ).
cnf(refute_0_619,plain,
top = join(zero,join(complement(meet(top,join(top,top))),meet(top,meet(top,join(top,top))))),
inference(subst,[],[refute_0_618:[bind(X_27,$fot(meet(top,join(top,top))))]]) ).
cnf(refute_0_620,plain,
( complement(meet(top,join(top,top))) != zero
| top != join(zero,join(complement(meet(top,join(top,top))),meet(top,meet(top,join(top,top)))))
| top = join(zero,join(zero,meet(top,meet(top,join(top,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,join(complement(meet(top,join(top,top))),meet(top,meet(top,join(top,top)))))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_621,plain,
( top != join(zero,join(complement(meet(top,join(top,top))),meet(top,meet(top,join(top,top)))))
| top = join(zero,join(zero,meet(top,meet(top,join(top,top))))) ),
inference(resolve,[$cnf( $equal(complement(meet(top,join(top,top))),zero) )],[refute_0_611,refute_0_620]) ).
cnf(refute_0_622,plain,
top = join(zero,join(zero,meet(top,meet(top,join(top,top))))),
inference(resolve,[$cnf( $equal(top,join(zero,join(complement(meet(top,join(top,top))),meet(top,meet(top,join(top,top)))))) )],[refute_0_619,refute_0_621]) ).
cnf(refute_0_623,plain,
join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(join(zero,meet(join(zero,zero),complement(meet(top,top)))),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(meet(join(zero,zero),complement(meet(top,top)))))]]) ).
cnf(refute_0_624,plain,
join(zero,zero) = join(zero,meet(join(zero,zero),complement(complement(join(zero,zero))))),
inference(subst,[],[refute_0_310:[bind(X_31,$fot(join(zero,zero)))]]) ).
cnf(refute_0_625,plain,
( complement(join(zero,zero)) != meet(top,top)
| join(zero,zero) != join(zero,meet(join(zero,zero),complement(complement(join(zero,zero)))))
| join(zero,zero) = join(zero,meet(join(zero,zero),complement(meet(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,zero),join(zero,meet(join(zero,zero),complement(complement(join(zero,zero)))))) ),[1,1,1,0],$fot(meet(top,top))]]) ).
cnf(refute_0_626,plain,
( join(zero,zero) != join(zero,meet(join(zero,zero),complement(complement(join(zero,zero)))))
| join(zero,zero) = join(zero,meet(join(zero,zero),complement(meet(top,top)))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),meet(top,top)) )],[refute_0_325,refute_0_625]) ).
cnf(refute_0_627,plain,
join(zero,zero) = join(zero,meet(join(zero,zero),complement(meet(top,top)))),
inference(resolve,[$cnf( $equal(join(zero,zero),join(zero,meet(join(zero,zero),complement(complement(join(zero,zero)))))) )],[refute_0_624,refute_0_626]) ).
cnf(refute_0_628,plain,
( join(zero,zero) != join(zero,meet(join(zero,zero),complement(meet(top,top))))
| join(zero,meet(join(zero,zero),complement(meet(top,top)))) = join(zero,zero) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(zero,zero))),bind(Y,$fot(join(zero,meet(join(zero,zero),complement(meet(top,top))))))]]) ).
cnf(refute_0_629,plain,
join(zero,meet(join(zero,zero),complement(meet(top,top)))) = join(zero,zero),
inference(resolve,[$cnf( $equal(join(zero,zero),join(zero,meet(join(zero,zero),complement(meet(top,top))))) )],[refute_0_627,refute_0_628]) ).
cnf(refute_0_630,plain,
( join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) != join(join(zero,meet(join(zero,zero),complement(meet(top,top)))),C)
| join(zero,meet(join(zero,zero),complement(meet(top,top)))) != join(zero,zero)
| join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(join(zero,zero),C) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)),join(join(zero,meet(join(zero,zero),complement(meet(top,top)))),C)) ),[1,0],$fot(join(zero,zero))]]) ).
cnf(refute_0_631,plain,
( join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) != join(join(zero,meet(join(zero,zero),complement(meet(top,top)))),C)
| join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(join(zero,zero),C) ),
inference(resolve,[$cnf( $equal(join(zero,meet(join(zero,zero),complement(meet(top,top)))),join(zero,zero)) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(join(zero,zero),C),
inference(resolve,[$cnf( $equal(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)),join(join(zero,meet(join(zero,zero),complement(meet(top,top)))),C)) )],[refute_0_623,refute_0_631]) ).
cnf(refute_0_633,plain,
join(join(zero,zero),C) = join(zero,join(zero,C)),
inference(subst,[],[refute_0_155:[bind(A,$fot(zero)),bind(B,$fot(zero))]]) ).
cnf(refute_0_634,plain,
( join(join(zero,zero),C) != join(zero,join(zero,C))
| join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) != join(join(zero,zero),C)
| join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(zero,join(zero,C)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)),join(join(zero,zero),C)) ),[1],$fot(join(zero,join(zero,C)))]]) ).
cnf(refute_0_635,plain,
( join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) != join(join(zero,zero),C)
| join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(zero,join(zero,C)) ),
inference(resolve,[$cnf( $equal(join(join(zero,zero),C),join(zero,join(zero,C))) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(zero,join(zero,C)),
inference(resolve,[$cnf( $equal(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)),join(join(zero,zero),C)) )],[refute_0_632,refute_0_635]) ).
cnf(refute_0_637,plain,
join(zero,join(meet(X_34,complement(complement(X_34))),C)) = join(join(zero,meet(X_34,complement(complement(X_34)))),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(meet(X_34,complement(complement(X_34)))))]]) ).
cnf(refute_0_638,plain,
X_34 = join(zero,meet(X_34,complement(complement(X_34)))),
inference(subst,[],[refute_0_310:[bind(X_31,$fot(X_34))]]) ).
cnf(refute_0_639,plain,
( X_34 != join(zero,meet(X_34,complement(complement(X_34))))
| join(zero,meet(X_34,complement(complement(X_34)))) = X_34 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_34)),bind(Y,$fot(join(zero,meet(X_34,complement(complement(X_34))))))]]) ).
cnf(refute_0_640,plain,
join(zero,meet(X_34,complement(complement(X_34)))) = X_34,
inference(resolve,[$cnf( $equal(X_34,join(zero,meet(X_34,complement(complement(X_34))))) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
( join(zero,join(meet(X_34,complement(complement(X_34))),C)) != join(join(zero,meet(X_34,complement(complement(X_34)))),C)
| join(zero,meet(X_34,complement(complement(X_34)))) != X_34
| join(zero,join(meet(X_34,complement(complement(X_34))),C)) = join(X_34,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(X_34,complement(complement(X_34))),C)),join(join(zero,meet(X_34,complement(complement(X_34)))),C)) ),[1,0],$fot(X_34)]]) ).
cnf(refute_0_642,plain,
( join(zero,join(meet(X_34,complement(complement(X_34))),C)) != join(join(zero,meet(X_34,complement(complement(X_34)))),C)
| join(zero,join(meet(X_34,complement(complement(X_34))),C)) = join(X_34,C) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_34,complement(complement(X_34)))),X_34) )],[refute_0_640,refute_0_641]) ).
cnf(refute_0_643,plain,
join(zero,join(meet(X_34,complement(complement(X_34))),C)) = join(X_34,C),
inference(resolve,[$cnf( $equal(join(zero,join(meet(X_34,complement(complement(X_34))),C)),join(join(zero,meet(X_34,complement(complement(X_34)))),C)) )],[refute_0_637,refute_0_642]) ).
cnf(refute_0_644,plain,
join(zero,join(meet(zero,complement(complement(zero))),C)) = join(zero,C),
inference(subst,[],[refute_0_643:[bind(X_34,$fot(zero))]]) ).
cnf(refute_0_645,plain,
complement(join(zero,zero)) = complement(join(zero,zero)),
introduced(tautology,[refl,[$fot(complement(join(zero,zero)))]]) ).
cnf(refute_0_646,plain,
( complement(join(zero,zero)) != complement(join(zero,zero))
| join(zero,zero) != zero
| complement(join(zero,zero)) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,zero)),complement(join(zero,zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_647,plain,
( join(zero,zero) != zero
| complement(join(zero,zero)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),complement(join(zero,zero))) )],[refute_0_645,refute_0_646]) ).
cnf(refute_0_648,plain,
complement(join(zero,zero)) = complement(zero),
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_497,refute_0_647]) ).
cnf(refute_0_649,plain,
( complement(join(zero,zero)) != complement(zero)
| meet(top,top) != complement(join(zero,zero))
| meet(top,top) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,top),complement(join(zero,zero))) ),[1],$fot(complement(zero))]]) ).
cnf(refute_0_650,plain,
( meet(top,top) != complement(join(zero,zero))
| meet(top,top) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),complement(zero)) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
meet(top,top) = complement(zero),
inference(resolve,[$cnf( $equal(meet(top,top),complement(join(zero,zero))) )],[refute_0_323,refute_0_650]) ).
cnf(refute_0_652,plain,
complement(meet(top,top)) = complement(meet(top,top)),
introduced(tautology,[refl,[$fot(complement(meet(top,top)))]]) ).
cnf(refute_0_653,plain,
( complement(meet(top,top)) != complement(meet(top,top))
| meet(top,top) != complement(zero)
| complement(meet(top,top)) = complement(complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(top,top)),complement(meet(top,top))) ),[1,0],$fot(complement(zero))]]) ).
cnf(refute_0_654,plain,
( meet(top,top) != complement(zero)
| complement(meet(top,top)) = complement(complement(zero)) ),
inference(resolve,[$cnf( $equal(complement(meet(top,top)),complement(meet(top,top))) )],[refute_0_652,refute_0_653]) ).
cnf(refute_0_655,plain,
complement(meet(top,top)) = complement(complement(zero)),
inference(resolve,[$cnf( $equal(meet(top,top),complement(zero)) )],[refute_0_651,refute_0_654]) ).
cnf(refute_0_656,plain,
meet(zero,complement(meet(top,top))) = meet(zero,complement(meet(top,top))),
introduced(tautology,[refl,[$fot(meet(zero,complement(meet(top,top))))]]) ).
cnf(refute_0_657,plain,
( complement(meet(top,top)) != complement(complement(zero))
| meet(zero,complement(meet(top,top))) != meet(zero,complement(meet(top,top)))
| meet(zero,complement(meet(top,top))) = meet(zero,complement(complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(zero,complement(meet(top,top))),meet(zero,complement(meet(top,top)))) ),[1,1],$fot(complement(complement(zero)))]]) ).
cnf(refute_0_658,plain,
( complement(meet(top,top)) != complement(complement(zero))
| meet(zero,complement(meet(top,top))) = meet(zero,complement(complement(zero))) ),
inference(resolve,[$cnf( $equal(meet(zero,complement(meet(top,top))),meet(zero,complement(meet(top,top)))) )],[refute_0_656,refute_0_657]) ).
cnf(refute_0_659,plain,
meet(zero,complement(meet(top,top))) = meet(zero,complement(complement(zero))),
inference(resolve,[$cnf( $equal(complement(meet(top,top)),complement(complement(zero))) )],[refute_0_655,refute_0_658]) ).
cnf(refute_0_660,plain,
meet(join(zero,zero),complement(meet(top,top))) = meet(join(zero,zero),complement(meet(top,top))),
introduced(tautology,[refl,[$fot(meet(join(zero,zero),complement(meet(top,top))))]]) ).
cnf(refute_0_661,plain,
( join(zero,zero) != zero
| meet(join(zero,zero),complement(meet(top,top))) != meet(join(zero,zero),complement(meet(top,top)))
| meet(join(zero,zero),complement(meet(top,top))) = meet(zero,complement(meet(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,zero),complement(meet(top,top))),meet(join(zero,zero),complement(meet(top,top)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_662,plain,
( join(zero,zero) != zero
| meet(join(zero,zero),complement(meet(top,top))) = meet(zero,complement(meet(top,top))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,zero),complement(meet(top,top))),meet(join(zero,zero),complement(meet(top,top)))) )],[refute_0_660,refute_0_661]) ).
cnf(refute_0_663,plain,
meet(join(zero,zero),complement(meet(top,top))) = meet(zero,complement(meet(top,top))),
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_497,refute_0_662]) ).
cnf(refute_0_664,plain,
( meet(join(zero,zero),complement(meet(top,top))) != meet(zero,complement(meet(top,top)))
| meet(zero,complement(meet(top,top))) != meet(zero,complement(complement(zero)))
| meet(join(zero,zero),complement(meet(top,top))) = meet(zero,complement(complement(zero))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(meet(join(zero,zero),complement(meet(top,top))))),bind(Y,$fot(meet(zero,complement(meet(top,top))))),bind(Z,$fot(meet(zero,complement(complement(zero)))))]]) ).
cnf(refute_0_665,plain,
( meet(zero,complement(meet(top,top))) != meet(zero,complement(complement(zero)))
| meet(join(zero,zero),complement(meet(top,top))) = meet(zero,complement(complement(zero))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,zero),complement(meet(top,top))),meet(zero,complement(meet(top,top)))) )],[refute_0_663,refute_0_664]) ).
cnf(refute_0_666,plain,
meet(join(zero,zero),complement(meet(top,top))) = meet(zero,complement(complement(zero))),
inference(resolve,[$cnf( $equal(meet(zero,complement(meet(top,top))),meet(zero,complement(complement(zero)))) )],[refute_0_659,refute_0_665]) ).
cnf(refute_0_667,plain,
join(meet(join(zero,zero),complement(meet(top,top))),C) = join(meet(join(zero,zero),complement(meet(top,top))),C),
introduced(tautology,[refl,[$fot(join(meet(join(zero,zero),complement(meet(top,top))),C))]]) ).
cnf(refute_0_668,plain,
( join(meet(join(zero,zero),complement(meet(top,top))),C) != join(meet(join(zero,zero),complement(meet(top,top))),C)
| meet(join(zero,zero),complement(meet(top,top))) != meet(zero,complement(complement(zero)))
| join(meet(join(zero,zero),complement(meet(top,top))),C) = join(meet(zero,complement(complement(zero))),C) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(join(zero,zero),complement(meet(top,top))),C),join(meet(join(zero,zero),complement(meet(top,top))),C)) ),[1,0],$fot(meet(zero,complement(complement(zero))))]]) ).
cnf(refute_0_669,plain,
( meet(join(zero,zero),complement(meet(top,top))) != meet(zero,complement(complement(zero)))
| join(meet(join(zero,zero),complement(meet(top,top))),C) = join(meet(zero,complement(complement(zero))),C) ),
inference(resolve,[$cnf( $equal(join(meet(join(zero,zero),complement(meet(top,top))),C),join(meet(join(zero,zero),complement(meet(top,top))),C)) )],[refute_0_667,refute_0_668]) ).
cnf(refute_0_670,plain,
join(meet(join(zero,zero),complement(meet(top,top))),C) = join(meet(zero,complement(complement(zero))),C),
inference(resolve,[$cnf( $equal(meet(join(zero,zero),complement(meet(top,top))),meet(zero,complement(complement(zero)))) )],[refute_0_666,refute_0_669]) ).
cnf(refute_0_671,plain,
join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)),
introduced(tautology,[refl,[$fot(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)))]]) ).
cnf(refute_0_672,plain,
( join(meet(join(zero,zero),complement(meet(top,top))),C) != join(meet(zero,complement(complement(zero))),C)
| join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) != join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C))
| join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(zero,join(meet(zero,complement(complement(zero))),C)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)),join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C))) ),[1,1],$fot(join(meet(zero,complement(complement(zero))),C))]]) ).
cnf(refute_0_673,plain,
( join(meet(join(zero,zero),complement(meet(top,top))),C) != join(meet(zero,complement(complement(zero))),C)
| join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(zero,join(meet(zero,complement(complement(zero))),C)) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)),join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C))) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(zero,join(meet(zero,complement(complement(zero))),C)),
inference(resolve,[$cnf( $equal(join(meet(join(zero,zero),complement(meet(top,top))),C),join(meet(zero,complement(complement(zero))),C)) )],[refute_0_670,refute_0_673]) ).
cnf(refute_0_675,plain,
( join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) != join(zero,join(meet(zero,complement(complement(zero))),C))
| join(zero,join(meet(zero,complement(complement(zero))),C)) != join(zero,C)
| join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(zero,C) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)))),bind(Y,$fot(join(zero,join(meet(zero,complement(complement(zero))),C)))),bind(Z,$fot(join(zero,C)))]]) ).
cnf(refute_0_676,plain,
( join(zero,join(meet(zero,complement(complement(zero))),C)) != join(zero,C)
| join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(zero,C) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)),join(zero,join(meet(zero,complement(complement(zero))),C))) )],[refute_0_674,refute_0_675]) ).
cnf(refute_0_677,plain,
join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) = join(zero,C),
inference(resolve,[$cnf( $equal(join(zero,join(meet(zero,complement(complement(zero))),C)),join(zero,C)) )],[refute_0_644,refute_0_676]) ).
cnf(refute_0_678,plain,
( join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) != join(zero,C)
| join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) != join(zero,join(zero,C))
| join(zero,C) = join(zero,join(zero,C)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)),join(zero,join(zero,C))) ),[0],$fot(join(zero,C))]]) ).
cnf(refute_0_679,plain,
( join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)) != join(zero,join(zero,C))
| join(zero,C) = join(zero,join(zero,C)) ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)),join(zero,C)) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
join(zero,C) = join(zero,join(zero,C)),
inference(resolve,[$cnf( $equal(join(zero,join(meet(join(zero,zero),complement(meet(top,top))),C)),join(zero,join(zero,C))) )],[refute_0_636,refute_0_679]) ).
cnf(refute_0_681,plain,
( join(zero,C) != join(zero,join(zero,C))
| join(zero,join(zero,C)) = join(zero,C) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(zero,C))),bind(Y,$fot(join(zero,join(zero,C))))]]) ).
cnf(refute_0_682,plain,
join(zero,join(zero,C)) = join(zero,C),
inference(resolve,[$cnf( $equal(join(zero,C),join(zero,join(zero,C))) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
join(zero,join(zero,meet(top,meet(top,join(top,top))))) = join(zero,meet(top,meet(top,join(top,top)))),
inference(subst,[],[refute_0_682:[bind(C,$fot(meet(top,meet(top,join(top,top)))))]]) ).
cnf(refute_0_684,plain,
( join(zero,join(zero,meet(top,meet(top,join(top,top))))) != join(zero,meet(top,meet(top,join(top,top))))
| top != join(zero,join(zero,meet(top,meet(top,join(top,top)))))
| top = join(zero,meet(top,meet(top,join(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,join(zero,meet(top,meet(top,join(top,top)))))) ),[1],$fot(join(zero,meet(top,meet(top,join(top,top)))))]]) ).
cnf(refute_0_685,plain,
( top != join(zero,join(zero,meet(top,meet(top,join(top,top)))))
| top = join(zero,meet(top,meet(top,join(top,top)))) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(top,meet(top,join(top,top))))),join(zero,meet(top,meet(top,join(top,top))))) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
top = join(zero,meet(top,meet(top,join(top,top)))),
inference(resolve,[$cnf( $equal(top,join(zero,join(zero,meet(top,meet(top,join(top,top)))))) )],[refute_0_622,refute_0_685]) ).
cnf(refute_0_687,plain,
( top != join(zero,meet(top,meet(top,join(top,top))))
| join(zero,meet(top,meet(top,join(top,top)))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(zero,meet(top,meet(top,join(top,top))))))]]) ).
cnf(refute_0_688,plain,
join(zero,meet(top,meet(top,join(top,top)))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,meet(top,join(top,top))))) )],[refute_0_686,refute_0_687]) ).
cnf(refute_0_689,plain,
meet(top,top) = join(meet(join(zero,zero),meet(top,top)),complement(join(complement(meet(top,top)),join(zero,zero)))),
inference(subst,[],[refute_0_291:[bind(X_31,$fot(meet(top,top))),bind(X_32,$fot(join(zero,zero)))]]) ).
cnf(refute_0_690,plain,
zero = meet(join(zero,zero),complement(join(zero,zero))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(zero,zero)))]]) ).
cnf(refute_0_691,plain,
( complement(join(zero,zero)) != meet(top,top)
| zero != meet(join(zero,zero),complement(join(zero,zero)))
| zero = meet(join(zero,zero),meet(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(zero,zero),complement(join(zero,zero)))) ),[1,1],$fot(meet(top,top))]]) ).
cnf(refute_0_692,plain,
( zero != meet(join(zero,zero),complement(join(zero,zero)))
| zero = meet(join(zero,zero),meet(top,top)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,zero)),meet(top,top)) )],[refute_0_325,refute_0_691]) ).
cnf(refute_0_693,plain,
zero = meet(join(zero,zero),meet(top,top)),
inference(resolve,[$cnf( $equal(zero,meet(join(zero,zero),complement(join(zero,zero)))) )],[refute_0_690,refute_0_692]) ).
cnf(refute_0_694,plain,
( zero != meet(join(zero,zero),meet(top,top))
| meet(join(zero,zero),meet(top,top)) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(meet(join(zero,zero),meet(top,top))))]]) ).
cnf(refute_0_695,plain,
meet(join(zero,zero),meet(top,top)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(join(zero,zero),meet(top,top))) )],[refute_0_693,refute_0_694]) ).
cnf(refute_0_696,plain,
( meet(join(zero,zero),meet(top,top)) != zero
| meet(top,top) != join(meet(join(zero,zero),meet(top,top)),complement(join(complement(meet(top,top)),join(zero,zero))))
| meet(top,top) = join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,top),join(meet(join(zero,zero),meet(top,top)),complement(join(complement(meet(top,top)),join(zero,zero))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_697,plain,
( meet(top,top) != join(meet(join(zero,zero),meet(top,top)),complement(join(complement(meet(top,top)),join(zero,zero))))
| meet(top,top) = join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,zero),meet(top,top)),zero) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
meet(top,top) = join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),
inference(resolve,[$cnf( $equal(meet(top,top),join(meet(join(zero,zero),meet(top,top)),complement(join(complement(meet(top,top)),join(zero,zero))))) )],[refute_0_689,refute_0_697]) ).
cnf(refute_0_699,plain,
join(zero,join(complement(meet(top,top)),zero)) = join(zero,join(zero,complement(meet(top,top)))),
inference(subst,[],[refute_0_361:[bind(X_15,$fot(zero)),bind(X_16,$fot(complement(meet(top,top)))),bind(X_17,$fot(zero))]]) ).
cnf(refute_0_700,plain,
join(complement(meet(top,top)),join(zero,zero)) = join(zero,join(complement(meet(top,top)),zero)),
inference(subst,[],[refute_0_176:[bind(X_15,$fot(zero)),bind(X_16,$fot(complement(meet(top,top)))),bind(X_17,$fot(zero))]]) ).
cnf(refute_0_701,plain,
( join(complement(meet(top,top)),join(zero,zero)) != join(zero,join(complement(meet(top,top)),zero))
| join(zero,join(complement(meet(top,top)),zero)) != join(zero,join(zero,complement(meet(top,top))))
| join(complement(meet(top,top)),join(zero,zero)) = join(zero,join(zero,complement(meet(top,top)))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(complement(meet(top,top)),join(zero,zero)))),bind(Y,$fot(join(zero,join(complement(meet(top,top)),zero)))),bind(Z,$fot(join(zero,join(zero,complement(meet(top,top))))))]]) ).
cnf(refute_0_702,plain,
( join(zero,join(complement(meet(top,top)),zero)) != join(zero,join(zero,complement(meet(top,top))))
| join(complement(meet(top,top)),join(zero,zero)) = join(zero,join(zero,complement(meet(top,top)))) ),
inference(resolve,[$cnf( $equal(join(complement(meet(top,top)),join(zero,zero)),join(zero,join(complement(meet(top,top)),zero))) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
join(complement(meet(top,top)),join(zero,zero)) = join(zero,join(zero,complement(meet(top,top)))),
inference(resolve,[$cnf( $equal(join(zero,join(complement(meet(top,top)),zero)),join(zero,join(zero,complement(meet(top,top))))) )],[refute_0_699,refute_0_702]) ).
cnf(refute_0_704,plain,
complement(join(complement(meet(top,top)),join(zero,zero))) = complement(join(complement(meet(top,top)),join(zero,zero))),
introduced(tautology,[refl,[$fot(complement(join(complement(meet(top,top)),join(zero,zero))))]]) ).
cnf(refute_0_705,plain,
( complement(join(complement(meet(top,top)),join(zero,zero))) != complement(join(complement(meet(top,top)),join(zero,zero)))
| join(complement(meet(top,top)),join(zero,zero)) != join(zero,join(zero,complement(meet(top,top))))
| complement(join(complement(meet(top,top)),join(zero,zero))) = complement(join(zero,join(zero,complement(meet(top,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(meet(top,top)),join(zero,zero))),complement(join(complement(meet(top,top)),join(zero,zero)))) ),[1,0],$fot(join(zero,join(zero,complement(meet(top,top)))))]]) ).
cnf(refute_0_706,plain,
( join(complement(meet(top,top)),join(zero,zero)) != join(zero,join(zero,complement(meet(top,top))))
| complement(join(complement(meet(top,top)),join(zero,zero))) = complement(join(zero,join(zero,complement(meet(top,top))))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(meet(top,top)),join(zero,zero))),complement(join(complement(meet(top,top)),join(zero,zero)))) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
complement(join(complement(meet(top,top)),join(zero,zero))) = complement(join(zero,join(zero,complement(meet(top,top))))),
inference(resolve,[$cnf( $equal(join(complement(meet(top,top)),join(zero,zero)),join(zero,join(zero,complement(meet(top,top))))) )],[refute_0_703,refute_0_706]) ).
cnf(refute_0_708,plain,
join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))) = join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))))]]) ).
cnf(refute_0_709,plain,
( complement(join(complement(meet(top,top)),join(zero,zero))) != complement(join(zero,join(zero,complement(meet(top,top)))))
| join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))) != join(zero,complement(join(complement(meet(top,top)),join(zero,zero))))
| join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))) = join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),join(zero,complement(join(complement(meet(top,top)),join(zero,zero))))) ),[1,1],$fot(complement(join(zero,join(zero,complement(meet(top,top))))))]]) ).
cnf(refute_0_710,plain,
( complement(join(complement(meet(top,top)),join(zero,zero))) != complement(join(zero,join(zero,complement(meet(top,top)))))
| join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))) = join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),join(zero,complement(join(complement(meet(top,top)),join(zero,zero))))) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))) = join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),
inference(resolve,[$cnf( $equal(complement(join(complement(meet(top,top)),join(zero,zero))),complement(join(zero,join(zero,complement(meet(top,top)))))) )],[refute_0_707,refute_0_710]) ).
cnf(refute_0_712,plain,
( join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))) != join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))
| meet(top,top) != join(zero,complement(join(complement(meet(top,top)),join(zero,zero))))
| meet(top,top) = join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,top),join(zero,complement(join(complement(meet(top,top)),join(zero,zero))))) ),[1],$fot(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))))]]) ).
cnf(refute_0_713,plain,
( meet(top,top) != join(zero,complement(join(complement(meet(top,top)),join(zero,zero))))
| meet(top,top) = join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(meet(top,top)),join(zero,zero)))),join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
meet(top,top) = join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),
inference(resolve,[$cnf( $equal(meet(top,top),join(zero,complement(join(complement(meet(top,top)),join(zero,zero))))) )],[refute_0_698,refute_0_713]) ).
cnf(refute_0_715,plain,
( meet(top,top) != complement(zero)
| meet(top,top) != join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))
| complement(zero) = join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,top),join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))) ),[0],$fot(complement(zero))]]) ).
cnf(refute_0_716,plain,
( meet(top,top) != join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))
| complement(zero) = join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) ),
inference(resolve,[$cnf( $equal(meet(top,top),complement(zero)) )],[refute_0_651,refute_0_715]) ).
cnf(refute_0_717,plain,
top = join(zero,meet(top,complement(complement(top)))),
inference(subst,[],[refute_0_310:[bind(X_31,$fot(top))]]) ).
cnf(refute_0_718,plain,
( complement(top) != zero
| top != join(zero,meet(top,complement(complement(top))))
| top = join(zero,meet(top,complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) ),[1,1,1,0],$fot(zero)]]) ).
cnf(refute_0_719,plain,
( top != join(zero,meet(top,complement(complement(top))))
| top = join(zero,meet(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_718]) ).
cnf(refute_0_720,plain,
top = join(zero,meet(top,complement(zero))),
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(complement(top))))) )],[refute_0_717,refute_0_719]) ).
cnf(refute_0_721,plain,
( top != join(zero,meet(top,complement(zero)))
| join(zero,meet(top,complement(zero))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(zero,meet(top,complement(zero)))))]]) ).
cnf(refute_0_722,plain,
join(zero,meet(top,complement(zero))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,complement(zero)))) )],[refute_0_720,refute_0_721]) ).
cnf(refute_0_723,plain,
complement(join(zero,complement(complement(zero)))) = meet(top,complement(zero)),
inference(subst,[],[refute_0_506:[bind(B,$fot(complement(zero)))]]) ).
cnf(refute_0_724,plain,
join(zero,complement(meet(top,top))) = join(zero,complement(meet(top,top))),
introduced(tautology,[refl,[$fot(join(zero,complement(meet(top,top))))]]) ).
cnf(refute_0_725,plain,
( complement(meet(top,top)) != complement(complement(zero))
| join(zero,complement(meet(top,top))) != join(zero,complement(meet(top,top)))
| join(zero,complement(meet(top,top))) = join(zero,complement(complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(meet(top,top))),join(zero,complement(meet(top,top)))) ),[1,1],$fot(complement(complement(zero)))]]) ).
cnf(refute_0_726,plain,
( complement(meet(top,top)) != complement(complement(zero))
| join(zero,complement(meet(top,top))) = join(zero,complement(complement(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(meet(top,top))),join(zero,complement(meet(top,top)))) )],[refute_0_724,refute_0_725]) ).
cnf(refute_0_727,plain,
join(zero,complement(meet(top,top))) = join(zero,complement(complement(zero))),
inference(resolve,[$cnf( $equal(complement(meet(top,top)),complement(complement(zero))) )],[refute_0_655,refute_0_726]) ).
cnf(refute_0_728,plain,
join(zero,join(zero,complement(meet(top,top)))) = join(zero,complement(meet(top,top))),
inference(subst,[],[refute_0_682:[bind(C,$fot(complement(meet(top,top))))]]) ).
cnf(refute_0_729,plain,
( join(zero,complement(meet(top,top))) != join(zero,complement(complement(zero)))
| join(zero,join(zero,complement(meet(top,top)))) != join(zero,complement(meet(top,top)))
| join(zero,join(zero,complement(meet(top,top)))) = join(zero,complement(complement(zero))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(zero,join(zero,complement(meet(top,top)))))),bind(Y,$fot(join(zero,complement(meet(top,top))))),bind(Z,$fot(join(zero,complement(complement(zero)))))]]) ).
cnf(refute_0_730,plain,
( join(zero,complement(meet(top,top))) != join(zero,complement(complement(zero)))
| join(zero,join(zero,complement(meet(top,top)))) = join(zero,complement(complement(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,complement(meet(top,top)))),join(zero,complement(meet(top,top)))) )],[refute_0_728,refute_0_729]) ).
cnf(refute_0_731,plain,
join(zero,join(zero,complement(meet(top,top)))) = join(zero,complement(complement(zero))),
inference(resolve,[$cnf( $equal(join(zero,complement(meet(top,top))),join(zero,complement(complement(zero)))) )],[refute_0_727,refute_0_730]) ).
cnf(refute_0_732,plain,
complement(join(zero,join(zero,complement(meet(top,top))))) = complement(join(zero,join(zero,complement(meet(top,top))))),
introduced(tautology,[refl,[$fot(complement(join(zero,join(zero,complement(meet(top,top))))))]]) ).
cnf(refute_0_733,plain,
( complement(join(zero,join(zero,complement(meet(top,top))))) != complement(join(zero,join(zero,complement(meet(top,top)))))
| join(zero,join(zero,complement(meet(top,top)))) != join(zero,complement(complement(zero)))
| complement(join(zero,join(zero,complement(meet(top,top))))) = complement(join(zero,complement(complement(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,join(zero,complement(meet(top,top))))),complement(join(zero,join(zero,complement(meet(top,top)))))) ),[1,0],$fot(join(zero,complement(complement(zero))))]]) ).
cnf(refute_0_734,plain,
( join(zero,join(zero,complement(meet(top,top)))) != join(zero,complement(complement(zero)))
| complement(join(zero,join(zero,complement(meet(top,top))))) = complement(join(zero,complement(complement(zero)))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,join(zero,complement(meet(top,top))))),complement(join(zero,join(zero,complement(meet(top,top)))))) )],[refute_0_732,refute_0_733]) ).
cnf(refute_0_735,plain,
complement(join(zero,join(zero,complement(meet(top,top))))) = complement(join(zero,complement(complement(zero)))),
inference(resolve,[$cnf( $equal(join(zero,join(zero,complement(meet(top,top)))),join(zero,complement(complement(zero)))) )],[refute_0_731,refute_0_734]) ).
cnf(refute_0_736,plain,
( complement(join(zero,complement(complement(zero)))) != meet(top,complement(zero))
| complement(join(zero,join(zero,complement(meet(top,top))))) != complement(join(zero,complement(complement(zero))))
| complement(join(zero,join(zero,complement(meet(top,top))))) = meet(top,complement(zero)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(complement(join(zero,join(zero,complement(meet(top,top))))))),bind(Y,$fot(complement(join(zero,complement(complement(zero)))))),bind(Z,$fot(meet(top,complement(zero))))]]) ).
cnf(refute_0_737,plain,
( complement(join(zero,complement(complement(zero)))) != meet(top,complement(zero))
| complement(join(zero,join(zero,complement(meet(top,top))))) = meet(top,complement(zero)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,join(zero,complement(meet(top,top))))),complement(join(zero,complement(complement(zero))))) )],[refute_0_735,refute_0_736]) ).
cnf(refute_0_738,plain,
complement(join(zero,join(zero,complement(meet(top,top))))) = meet(top,complement(zero)),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(complement(zero)))),meet(top,complement(zero))) )],[refute_0_723,refute_0_737]) ).
cnf(refute_0_739,plain,
join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) = join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),
introduced(tautology,[refl,[$fot(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))))]]) ).
cnf(refute_0_740,plain,
( complement(join(zero,join(zero,complement(meet(top,top))))) != meet(top,complement(zero))
| join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) != join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))
| join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) = join(zero,meet(top,complement(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))) ),[1,1],$fot(meet(top,complement(zero)))]]) ).
cnf(refute_0_741,plain,
( complement(join(zero,join(zero,complement(meet(top,top))))) != meet(top,complement(zero))
| join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) = join(zero,meet(top,complement(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))) )],[refute_0_739,refute_0_740]) ).
cnf(refute_0_742,plain,
join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) = join(zero,meet(top,complement(zero))),
inference(resolve,[$cnf( $equal(complement(join(zero,join(zero,complement(meet(top,top))))),meet(top,complement(zero))) )],[refute_0_738,refute_0_741]) ).
cnf(refute_0_743,plain,
( join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) != join(zero,meet(top,complement(zero)))
| join(zero,meet(top,complement(zero))) != top
| join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) = top ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))))),bind(Y,$fot(join(zero,meet(top,complement(zero))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_744,plain,
( join(zero,meet(top,complement(zero))) != top
| join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) = top ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),join(zero,meet(top,complement(zero)))) )],[refute_0_742,refute_0_743]) ).
cnf(refute_0_745,plain,
join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) = top,
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(zero))),top) )],[refute_0_722,refute_0_744]) ).
cnf(refute_0_746,plain,
( complement(zero) != join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))
| join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))) != top
| complement(zero) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(zero),top) ),[0],$fot(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))))]]) ).
cnf(refute_0_747,plain,
( complement(zero) != join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(zero,join(zero,complement(meet(top,top)))))),top) )],[refute_0_745,refute_0_746]) ).
cnf(refute_0_748,plain,
( meet(top,top) != join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))
| complement(zero) = top ),
inference(resolve,[$cnf( $equal(complement(zero),join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))) )],[refute_0_716,refute_0_747]) ).
cnf(refute_0_749,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(meet(top,top),join(zero,complement(join(zero,join(zero,complement(meet(top,top))))))) )],[refute_0_714,refute_0_748]) ).
cnf(refute_0_750,plain,
meet(complement(zero),meet(top,join(top,top))) = meet(complement(zero),meet(top,join(top,top))),
introduced(tautology,[refl,[$fot(meet(complement(zero),meet(top,join(top,top))))]]) ).
cnf(refute_0_751,plain,
( complement(zero) != top
| meet(complement(zero),meet(top,join(top,top))) != meet(complement(zero),meet(top,join(top,top)))
| meet(complement(zero),meet(top,join(top,top))) = meet(top,meet(top,join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(zero),meet(top,join(top,top))),meet(complement(zero),meet(top,join(top,top)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_752,plain,
( complement(zero) != top
| meet(complement(zero),meet(top,join(top,top))) = meet(top,meet(top,join(top,top))) ),
inference(resolve,[$cnf( $equal(meet(complement(zero),meet(top,join(top,top))),meet(complement(zero),meet(top,join(top,top)))) )],[refute_0_750,refute_0_751]) ).
cnf(refute_0_753,plain,
meet(complement(zero),meet(top,join(top,top))) = meet(top,meet(top,join(top,top))),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_749,refute_0_752]) ).
cnf(refute_0_754,plain,
meet(meet(top,join(top,top)),complement(zero)) = meet(complement(zero),meet(top,join(top,top))),
inference(subst,[],[refute_0_511:[bind(X_22,$fot(complement(zero))),bind(X_23,$fot(meet(top,join(top,top))))]]) ).
cnf(refute_0_755,plain,
( meet(complement(zero),meet(top,join(top,top))) != meet(top,meet(top,join(top,top)))
| meet(meet(top,join(top,top)),complement(zero)) != meet(complement(zero),meet(top,join(top,top)))
| meet(meet(top,join(top,top)),complement(zero)) = meet(top,meet(top,join(top,top))) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(meet(meet(top,join(top,top)),complement(zero)))),bind(Y,$fot(meet(complement(zero),meet(top,join(top,top))))),bind(Z,$fot(meet(top,meet(top,join(top,top)))))]]) ).
cnf(refute_0_756,plain,
( meet(complement(zero),meet(top,join(top,top))) != meet(top,meet(top,join(top,top)))
| meet(meet(top,join(top,top)),complement(zero)) = meet(top,meet(top,join(top,top))) ),
inference(resolve,[$cnf( $equal(meet(meet(top,join(top,top)),complement(zero)),meet(complement(zero),meet(top,join(top,top)))) )],[refute_0_754,refute_0_755]) ).
cnf(refute_0_757,plain,
meet(meet(top,join(top,top)),complement(zero)) = meet(top,meet(top,join(top,top))),
inference(resolve,[$cnf( $equal(meet(complement(zero),meet(top,join(top,top))),meet(top,meet(top,join(top,top)))) )],[refute_0_753,refute_0_756]) ).
cnf(refute_0_758,plain,
join(zero,meet(meet(top,join(top,top)),complement(zero))) = join(zero,meet(meet(top,join(top,top)),complement(zero))),
introduced(tautology,[refl,[$fot(join(zero,meet(meet(top,join(top,top)),complement(zero))))]]) ).
cnf(refute_0_759,plain,
( join(zero,meet(meet(top,join(top,top)),complement(zero))) != join(zero,meet(meet(top,join(top,top)),complement(zero)))
| meet(meet(top,join(top,top)),complement(zero)) != meet(top,meet(top,join(top,top)))
| join(zero,meet(meet(top,join(top,top)),complement(zero))) = join(zero,meet(top,meet(top,join(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(meet(top,join(top,top)),complement(zero))),join(zero,meet(meet(top,join(top,top)),complement(zero)))) ),[1,1],$fot(meet(top,meet(top,join(top,top))))]]) ).
cnf(refute_0_760,plain,
( meet(meet(top,join(top,top)),complement(zero)) != meet(top,meet(top,join(top,top)))
| join(zero,meet(meet(top,join(top,top)),complement(zero))) = join(zero,meet(top,meet(top,join(top,top)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(meet(top,join(top,top)),complement(zero))),join(zero,meet(meet(top,join(top,top)),complement(zero)))) )],[refute_0_758,refute_0_759]) ).
cnf(refute_0_761,plain,
join(zero,meet(meet(top,join(top,top)),complement(zero))) = join(zero,meet(top,meet(top,join(top,top)))),
inference(resolve,[$cnf( $equal(meet(meet(top,join(top,top)),complement(zero)),meet(top,meet(top,join(top,top)))) )],[refute_0_757,refute_0_760]) ).
cnf(refute_0_762,plain,
( join(zero,meet(meet(top,join(top,top)),complement(zero))) != join(zero,meet(top,meet(top,join(top,top))))
| join(zero,meet(top,meet(top,join(top,top)))) != top
| join(zero,meet(meet(top,join(top,top)),complement(zero))) = top ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(zero,meet(meet(top,join(top,top)),complement(zero))))),bind(Y,$fot(join(zero,meet(top,meet(top,join(top,top)))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_763,plain,
( join(zero,meet(top,meet(top,join(top,top)))) != top
| join(zero,meet(meet(top,join(top,top)),complement(zero))) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(meet(top,join(top,top)),complement(zero))),join(zero,meet(top,meet(top,join(top,top))))) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
join(zero,meet(meet(top,join(top,top)),complement(zero))) = top,
inference(resolve,[$cnf( $equal(join(zero,meet(top,meet(top,join(top,top)))),top) )],[refute_0_688,refute_0_763]) ).
cnf(refute_0_765,plain,
( join(zero,meet(meet(top,join(top,top)),complement(zero))) != top
| meet(top,join(top,top)) != join(zero,meet(meet(top,join(top,top)),complement(zero)))
| meet(top,join(top,top)) = top ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(top,top)),join(zero,meet(meet(top,join(top,top)),complement(zero)))) ),[1],$fot(top)]]) ).
cnf(refute_0_766,plain,
( meet(top,join(top,top)) != join(zero,meet(meet(top,join(top,top)),complement(zero)))
| meet(top,join(top,top)) = top ),
inference(resolve,[$cnf( $equal(join(zero,meet(meet(top,join(top,top)),complement(zero))),top) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
meet(top,join(top,top)) = top,
inference(resolve,[$cnf( $equal(meet(top,join(top,top)),join(zero,meet(meet(top,join(top,top)),complement(zero)))) )],[refute_0_614,refute_0_766]) ).
cnf(refute_0_768,plain,
( join(top,top) != join(meet(top,join(top,top)),complement(join(complement(join(top,top)),top)))
| meet(top,join(top,top)) != top
| join(top,top) = join(top,complement(join(complement(join(top,top)),top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,top),join(meet(top,join(top,top)),complement(join(complement(join(top,top)),top)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_769,plain,
( join(top,top) != join(meet(top,join(top,top)),complement(join(complement(join(top,top)),top)))
| join(top,top) = join(top,complement(join(complement(join(top,top)),top))) ),
inference(resolve,[$cnf( $equal(meet(top,join(top,top)),top) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
join(top,top) = join(top,complement(join(complement(join(top,top)),top))),
inference(resolve,[$cnf( $equal(join(top,top),join(meet(top,join(top,top)),complement(join(complement(join(top,top)),top)))) )],[refute_0_292,refute_0_769]) ).
cnf(refute_0_771,plain,
join(complement(join(top,top)),top) = join(top,complement(join(top,top))),
inference(subst,[],[refute_0_247:[bind(A,$fot(complement(join(top,top))))]]) ).
cnf(refute_0_772,plain,
complement(join(complement(join(top,top)),top)) = complement(join(complement(join(top,top)),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(join(top,top)),top)))]]) ).
cnf(refute_0_773,plain,
( complement(join(complement(join(top,top)),top)) != complement(join(complement(join(top,top)),top))
| join(complement(join(top,top)),top) != join(top,complement(join(top,top)))
| complement(join(complement(join(top,top)),top)) = complement(join(top,complement(join(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(join(top,top)),top)),complement(join(complement(join(top,top)),top))) ),[1,0],$fot(join(top,complement(join(top,top))))]]) ).
cnf(refute_0_774,plain,
( join(complement(join(top,top)),top) != join(top,complement(join(top,top)))
| complement(join(complement(join(top,top)),top)) = complement(join(top,complement(join(top,top)))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(join(top,top)),top)),complement(join(complement(join(top,top)),top))) )],[refute_0_772,refute_0_773]) ).
cnf(refute_0_775,plain,
complement(join(complement(join(top,top)),top)) = complement(join(top,complement(join(top,top)))),
inference(resolve,[$cnf( $equal(join(complement(join(top,top)),top),join(top,complement(join(top,top)))) )],[refute_0_771,refute_0_774]) ).
cnf(refute_0_776,plain,
join(top,complement(join(complement(join(top,top)),top))) = join(top,complement(join(complement(join(top,top)),top))),
introduced(tautology,[refl,[$fot(join(top,complement(join(complement(join(top,top)),top))))]]) ).
cnf(refute_0_777,plain,
( complement(join(complement(join(top,top)),top)) != complement(join(top,complement(join(top,top))))
| join(top,complement(join(complement(join(top,top)),top))) != join(top,complement(join(complement(join(top,top)),top)))
| join(top,complement(join(complement(join(top,top)),top))) = join(top,complement(join(top,complement(join(top,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,complement(join(complement(join(top,top)),top))),join(top,complement(join(complement(join(top,top)),top)))) ),[1,1],$fot(complement(join(top,complement(join(top,top)))))]]) ).
cnf(refute_0_778,plain,
( complement(join(complement(join(top,top)),top)) != complement(join(top,complement(join(top,top))))
| join(top,complement(join(complement(join(top,top)),top))) = join(top,complement(join(top,complement(join(top,top))))) ),
inference(resolve,[$cnf( $equal(join(top,complement(join(complement(join(top,top)),top))),join(top,complement(join(complement(join(top,top)),top)))) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
join(top,complement(join(complement(join(top,top)),top))) = join(top,complement(join(top,complement(join(top,top))))),
inference(resolve,[$cnf( $equal(complement(join(complement(join(top,top)),top)),complement(join(top,complement(join(top,top))))) )],[refute_0_775,refute_0_778]) ).
cnf(refute_0_780,plain,
( join(top,complement(join(complement(join(top,top)),top))) != join(top,complement(join(top,complement(join(top,top)))))
| join(top,top) != join(top,complement(join(complement(join(top,top)),top)))
| join(top,top) = join(top,complement(join(top,complement(join(top,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,top),join(top,complement(join(complement(join(top,top)),top)))) ),[1],$fot(join(top,complement(join(top,complement(join(top,top))))))]]) ).
cnf(refute_0_781,plain,
( join(top,top) != join(top,complement(join(complement(join(top,top)),top)))
| join(top,top) = join(top,complement(join(top,complement(join(top,top))))) ),
inference(resolve,[$cnf( $equal(join(top,complement(join(complement(join(top,top)),top))),join(top,complement(join(top,complement(join(top,top)))))) )],[refute_0_779,refute_0_780]) ).
cnf(refute_0_782,plain,
join(top,top) = join(top,complement(join(top,complement(join(top,top))))),
inference(resolve,[$cnf( $equal(join(top,top),join(top,complement(join(complement(join(top,top)),top)))) )],[refute_0_770,refute_0_781]) ).
cnf(refute_0_783,plain,
top = join(top,complement(top)),
inference(subst,[],[def_top_12:[bind(A,$fot(top))]]) ).
cnf(refute_0_784,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_785,plain,
( top != join(top,complement(top))
| top = join(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_784]) ).
cnf(refute_0_786,plain,
top = join(top,zero),
inference(resolve,[$cnf( $equal(top,join(top,complement(top))) )],[refute_0_783,refute_0_785]) ).
cnf(refute_0_787,plain,
( top != join(top,zero)
| join(top,zero) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(top,zero)))]]) ).
cnf(refute_0_788,plain,
join(top,zero) = top,
inference(resolve,[$cnf( $equal(top,join(top,zero)) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
top = join(meet(top,join(top,top)),complement(join(complement(top),join(top,top)))),
inference(subst,[],[refute_0_43:[bind(A,$fot(top)),bind(B,$fot(join(top,top)))]]) ).
cnf(refute_0_790,plain,
( meet(top,join(top,top)) != top
| top != join(meet(top,join(top,top)),complement(join(complement(top),join(top,top))))
| top = join(top,complement(join(complement(top),join(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(meet(top,join(top,top)),complement(join(complement(top),join(top,top))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_791,plain,
( top != join(meet(top,join(top,top)),complement(join(complement(top),join(top,top))))
| top = join(top,complement(join(complement(top),join(top,top)))) ),
inference(resolve,[$cnf( $equal(meet(top,join(top,top)),top) )],[refute_0_767,refute_0_790]) ).
cnf(refute_0_792,plain,
top = join(top,complement(join(complement(top),join(top,top)))),
inference(resolve,[$cnf( $equal(top,join(meet(top,join(top,top)),complement(join(complement(top),join(top,top))))) )],[refute_0_789,refute_0_791]) ).
cnf(refute_0_793,plain,
join(top,join(top,complement(top))) = join(top,top),
inference(subst,[],[refute_0_21:[bind(X_18,$fot(top)),bind(X_19,$fot(top))]]) ).
cnf(refute_0_794,plain,
join(X_18,join(complement(X_18),complement(complement(X_18)))) = join(top,complement(complement(X_18))),
inference(subst,[],[refute_0_9:[bind(X_15,$fot(X_18)),bind(X_17,$fot(complement(complement(X_18))))]]) ).
cnf(refute_0_795,plain,
top = join(complement(X_18),complement(complement(X_18))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_18)))]]) ).
cnf(refute_0_796,plain,
( top != join(complement(X_18),complement(complement(X_18)))
| join(complement(X_18),complement(complement(X_18))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_18),complement(complement(X_18)))))]]) ).
cnf(refute_0_797,plain,
join(complement(X_18),complement(complement(X_18))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_18),complement(complement(X_18)))) )],[refute_0_795,refute_0_796]) ).
cnf(refute_0_798,plain,
( join(X_18,join(complement(X_18),complement(complement(X_18)))) != join(top,complement(complement(X_18)))
| join(complement(X_18),complement(complement(X_18))) != top
| join(X_18,top) = join(top,complement(complement(X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_18,join(complement(X_18),complement(complement(X_18)))),join(top,complement(complement(X_18)))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_799,plain,
( join(X_18,join(complement(X_18),complement(complement(X_18)))) != join(top,complement(complement(X_18)))
| join(X_18,top) = join(top,complement(complement(X_18))) ),
inference(resolve,[$cnf( $equal(join(complement(X_18),complement(complement(X_18))),top) )],[refute_0_797,refute_0_798]) ).
cnf(refute_0_800,plain,
join(X_18,top) = join(top,complement(complement(X_18))),
inference(resolve,[$cnf( $equal(join(X_18,join(complement(X_18),complement(complement(X_18)))),join(top,complement(complement(X_18)))) )],[refute_0_794,refute_0_799]) ).
cnf(refute_0_801,plain,
join(join(A,B),top) = join(top,complement(complement(join(A,B)))),
inference(subst,[],[refute_0_800:[bind(X_18,$fot(join(A,B)))]]) ).
cnf(refute_0_802,plain,
join(A,join(B,top)) = join(join(A,B),top),
inference(subst,[],[maddux2_join_associativity_2:[bind(C,$fot(top))]]) ).
cnf(refute_0_803,plain,
( join(A,join(B,top)) != join(join(A,B),top)
| join(join(A,B),top) = join(A,join(B,top)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(A,join(B,top)))),bind(Y,$fot(join(join(A,B),top)))]]) ).
cnf(refute_0_804,plain,
join(join(A,B),top) = join(A,join(B,top)),
inference(resolve,[$cnf( $equal(join(A,join(B,top)),join(join(A,B),top)) )],[refute_0_802,refute_0_803]) ).
cnf(refute_0_805,plain,
( join(join(A,B),top) != join(A,join(B,top))
| join(join(A,B),top) != join(top,complement(complement(join(A,B))))
| join(A,join(B,top)) = join(top,complement(complement(join(A,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(A,B),top),join(top,complement(complement(join(A,B))))) ),[0],$fot(join(A,join(B,top)))]]) ).
cnf(refute_0_806,plain,
( join(join(A,B),top) != join(top,complement(complement(join(A,B))))
| join(A,join(B,top)) = join(top,complement(complement(join(A,B)))) ),
inference(resolve,[$cnf( $equal(join(join(A,B),top),join(A,join(B,top))) )],[refute_0_804,refute_0_805]) ).
cnf(refute_0_807,plain,
join(A,join(B,top)) = join(top,complement(complement(join(A,B)))),
inference(resolve,[$cnf( $equal(join(join(A,B),top),join(top,complement(complement(join(A,B))))) )],[refute_0_801,refute_0_806]) ).
cnf(refute_0_808,plain,
join(join(A,B),top) = join(top,join(A,B)),
inference(subst,[],[refute_0_247:[bind(A,$fot(join(A,B)))]]) ).
cnf(refute_0_809,plain,
( join(X_18,top) != join(top,complement(complement(X_18)))
| join(top,complement(complement(X_18))) = join(X_18,top) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X_18,top))),bind(Y,$fot(join(top,complement(complement(X_18)))))]]) ).
cnf(refute_0_810,plain,
join(top,complement(complement(X_18))) = join(X_18,top),
inference(resolve,[$cnf( $equal(join(X_18,top),join(top,complement(complement(X_18)))) )],[refute_0_800,refute_0_809]) ).
cnf(refute_0_811,plain,
join(top,complement(complement(join(A,B)))) = join(join(A,B),top),
inference(subst,[],[refute_0_810:[bind(X_18,$fot(join(A,B)))]]) ).
cnf(refute_0_812,plain,
( join(join(A,B),top) != join(top,join(A,B))
| join(top,complement(complement(join(A,B)))) != join(join(A,B),top)
| join(top,complement(complement(join(A,B)))) = join(top,join(A,B)) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(top,complement(complement(join(A,B)))))),bind(Y,$fot(join(join(A,B),top))),bind(Z,$fot(join(top,join(A,B))))]]) ).
cnf(refute_0_813,plain,
( join(join(A,B),top) != join(top,join(A,B))
| join(top,complement(complement(join(A,B)))) = join(top,join(A,B)) ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(join(A,B)))),join(join(A,B),top)) )],[refute_0_811,refute_0_812]) ).
cnf(refute_0_814,plain,
join(top,complement(complement(join(A,B)))) = join(top,join(A,B)),
inference(resolve,[$cnf( $equal(join(join(A,B),top),join(top,join(A,B))) )],[refute_0_808,refute_0_813]) ).
cnf(refute_0_815,plain,
( join(A,join(B,top)) != join(top,complement(complement(join(A,B))))
| join(top,complement(complement(join(A,B)))) != join(top,join(A,B))
| join(A,join(B,top)) = join(top,join(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(B,top)),join(top,join(A,B))) ),[0],$fot(join(top,complement(complement(join(A,B)))))]]) ).
cnf(refute_0_816,plain,
( join(A,join(B,top)) != join(top,complement(complement(join(A,B))))
| join(A,join(B,top)) = join(top,join(A,B)) ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(join(A,B)))),join(top,join(A,B))) )],[refute_0_814,refute_0_815]) ).
cnf(refute_0_817,plain,
join(A,join(B,top)) = join(top,join(A,B)),
inference(resolve,[$cnf( $equal(join(A,join(B,top)),join(top,complement(complement(join(A,B))))) )],[refute_0_807,refute_0_816]) ).
cnf(refute_0_818,plain,
join(top,join(complement(top),top)) = join(top,join(top,complement(top))),
inference(subst,[],[refute_0_817:[bind(A,$fot(top)),bind(B,$fot(complement(top)))]]) ).
cnf(refute_0_819,plain,
( join(top,join(complement(top),top)) != join(top,join(top,complement(top)))
| join(top,join(top,complement(top))) != join(top,top)
| join(top,join(complement(top),top)) = join(top,top) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(top,join(complement(top),top)))),bind(Y,$fot(join(top,join(top,complement(top))))),bind(Z,$fot(join(top,top)))]]) ).
cnf(refute_0_820,plain,
( join(top,join(top,complement(top))) != join(top,top)
| join(top,join(complement(top),top)) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(top,join(complement(top),top)),join(top,join(top,complement(top)))) )],[refute_0_818,refute_0_819]) ).
cnf(refute_0_821,plain,
join(top,join(complement(top),top)) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,join(top,complement(top))),join(top,top)) )],[refute_0_793,refute_0_820]) ).
cnf(refute_0_822,plain,
join(complement(top),join(top,top)) = join(top,join(complement(top),top)),
inference(subst,[],[refute_0_817:[bind(A,$fot(complement(top))),bind(B,$fot(top))]]) ).
cnf(refute_0_823,plain,
( join(complement(top),join(top,top)) != join(top,join(complement(top),top))
| join(top,join(complement(top),top)) != join(top,top)
| join(complement(top),join(top,top)) = join(top,top) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(complement(top),join(top,top)))),bind(Y,$fot(join(top,join(complement(top),top)))),bind(Z,$fot(join(top,top)))]]) ).
cnf(refute_0_824,plain,
( join(top,join(complement(top),top)) != join(top,top)
| join(complement(top),join(top,top)) = join(top,top) ),
inference(resolve,[$cnf( $equal(join(complement(top),join(top,top)),join(top,join(complement(top),top))) )],[refute_0_822,refute_0_823]) ).
cnf(refute_0_825,plain,
join(complement(top),join(top,top)) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,join(complement(top),top)),join(top,top)) )],[refute_0_821,refute_0_824]) ).
cnf(refute_0_826,plain,
complement(join(complement(top),join(top,top))) = complement(join(complement(top),join(top,top))),
introduced(tautology,[refl,[$fot(complement(join(complement(top),join(top,top))))]]) ).
cnf(refute_0_827,plain,
( complement(join(complement(top),join(top,top))) != complement(join(complement(top),join(top,top)))
| join(complement(top),join(top,top)) != join(top,top)
| complement(join(complement(top),join(top,top))) = complement(join(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(top),join(top,top))),complement(join(complement(top),join(top,top)))) ),[1,0],$fot(join(top,top))]]) ).
cnf(refute_0_828,plain,
( join(complement(top),join(top,top)) != join(top,top)
| complement(join(complement(top),join(top,top))) = complement(join(top,top)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(top),join(top,top))),complement(join(complement(top),join(top,top)))) )],[refute_0_826,refute_0_827]) ).
cnf(refute_0_829,plain,
complement(join(complement(top),join(top,top))) = complement(join(top,top)),
inference(resolve,[$cnf( $equal(join(complement(top),join(top,top)),join(top,top)) )],[refute_0_825,refute_0_828]) ).
cnf(refute_0_830,plain,
join(top,complement(join(complement(top),join(top,top)))) = join(top,complement(join(complement(top),join(top,top)))),
introduced(tautology,[refl,[$fot(join(top,complement(join(complement(top),join(top,top)))))]]) ).
cnf(refute_0_831,plain,
( complement(join(complement(top),join(top,top))) != complement(join(top,top))
| join(top,complement(join(complement(top),join(top,top)))) != join(top,complement(join(complement(top),join(top,top))))
| join(top,complement(join(complement(top),join(top,top)))) = join(top,complement(join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,complement(join(complement(top),join(top,top)))),join(top,complement(join(complement(top),join(top,top))))) ),[1,1],$fot(complement(join(top,top)))]]) ).
cnf(refute_0_832,plain,
( complement(join(complement(top),join(top,top))) != complement(join(top,top))
| join(top,complement(join(complement(top),join(top,top)))) = join(top,complement(join(top,top))) ),
inference(resolve,[$cnf( $equal(join(top,complement(join(complement(top),join(top,top)))),join(top,complement(join(complement(top),join(top,top))))) )],[refute_0_830,refute_0_831]) ).
cnf(refute_0_833,plain,
join(top,complement(join(complement(top),join(top,top)))) = join(top,complement(join(top,top))),
inference(resolve,[$cnf( $equal(complement(join(complement(top),join(top,top))),complement(join(top,top))) )],[refute_0_829,refute_0_832]) ).
cnf(refute_0_834,plain,
( join(top,complement(join(complement(top),join(top,top)))) != join(top,complement(join(top,top)))
| top != join(top,complement(join(complement(top),join(top,top))))
| top = join(top,complement(join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(join(complement(top),join(top,top))))) ),[1],$fot(join(top,complement(join(top,top))))]]) ).
cnf(refute_0_835,plain,
( top != join(top,complement(join(complement(top),join(top,top))))
| top = join(top,complement(join(top,top))) ),
inference(resolve,[$cnf( $equal(join(top,complement(join(complement(top),join(top,top)))),join(top,complement(join(top,top)))) )],[refute_0_833,refute_0_834]) ).
cnf(refute_0_836,plain,
top = join(top,complement(join(top,top))),
inference(resolve,[$cnf( $equal(top,join(top,complement(join(complement(top),join(top,top))))) )],[refute_0_792,refute_0_835]) ).
cnf(refute_0_837,plain,
( top != join(top,complement(join(top,top)))
| join(top,complement(join(top,top))) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(join(top,top)))))]]) ).
cnf(refute_0_838,plain,
join(top,complement(join(top,top))) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(join(top,top)))) )],[refute_0_836,refute_0_837]) ).
cnf(refute_0_839,plain,
complement(join(top,complement(join(top,top)))) = complement(join(top,complement(join(top,top)))),
introduced(tautology,[refl,[$fot(complement(join(top,complement(join(top,top)))))]]) ).
cnf(refute_0_840,plain,
( complement(join(top,complement(join(top,top)))) != complement(join(top,complement(join(top,top))))
| join(top,complement(join(top,top))) != top
| complement(join(top,complement(join(top,top)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(top,complement(join(top,top)))),complement(join(top,complement(join(top,top))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_841,plain,
( join(top,complement(join(top,top))) != top
| complement(join(top,complement(join(top,top)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(join(top,top)))),complement(join(top,complement(join(top,top))))) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
complement(join(top,complement(join(top,top)))) = complement(top),
inference(resolve,[$cnf( $equal(join(top,complement(join(top,top))),top) )],[refute_0_838,refute_0_841]) ).
cnf(refute_0_843,plain,
( complement(join(top,complement(join(top,top)))) != complement(top)
| complement(top) != zero
| complement(join(top,complement(join(top,top)))) = zero ),
inference(subst,[],[refute_0_37:[bind(X,$fot(complement(join(top,complement(join(top,top)))))),bind(Y,$fot(complement(top))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_844,plain,
( complement(top) != zero
| complement(join(top,complement(join(top,top)))) = zero ),
inference(resolve,[$cnf( $equal(complement(join(top,complement(join(top,top)))),complement(top)) )],[refute_0_842,refute_0_843]) ).
cnf(refute_0_845,plain,
complement(join(top,complement(join(top,top)))) = zero,
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_71,refute_0_844]) ).
cnf(refute_0_846,plain,
join(top,complement(join(top,complement(join(top,top))))) = join(top,complement(join(top,complement(join(top,top))))),
introduced(tautology,[refl,[$fot(join(top,complement(join(top,complement(join(top,top))))))]]) ).
cnf(refute_0_847,plain,
( complement(join(top,complement(join(top,top)))) != zero
| join(top,complement(join(top,complement(join(top,top))))) != join(top,complement(join(top,complement(join(top,top)))))
| join(top,complement(join(top,complement(join(top,top))))) = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,complement(join(top,complement(join(top,top))))),join(top,complement(join(top,complement(join(top,top)))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_848,plain,
( complement(join(top,complement(join(top,top)))) != zero
| join(top,complement(join(top,complement(join(top,top))))) = join(top,zero) ),
inference(resolve,[$cnf( $equal(join(top,complement(join(top,complement(join(top,top))))),join(top,complement(join(top,complement(join(top,top)))))) )],[refute_0_846,refute_0_847]) ).
cnf(refute_0_849,plain,
join(top,complement(join(top,complement(join(top,top))))) = join(top,zero),
inference(resolve,[$cnf( $equal(complement(join(top,complement(join(top,top)))),zero) )],[refute_0_845,refute_0_848]) ).
cnf(refute_0_850,plain,
( join(top,complement(join(top,complement(join(top,top))))) != join(top,zero)
| join(top,zero) != top
| join(top,complement(join(top,complement(join(top,top))))) = top ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(top,complement(join(top,complement(join(top,top))))))),bind(Y,$fot(join(top,zero))),bind(Z,$fot(top))]]) ).
cnf(refute_0_851,plain,
( join(top,zero) != top
| join(top,complement(join(top,complement(join(top,top))))) = top ),
inference(resolve,[$cnf( $equal(join(top,complement(join(top,complement(join(top,top))))),join(top,zero)) )],[refute_0_849,refute_0_850]) ).
cnf(refute_0_852,plain,
join(top,complement(join(top,complement(join(top,top))))) = top,
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_788,refute_0_851]) ).
cnf(refute_0_853,plain,
( join(top,complement(join(top,complement(join(top,top))))) != top
| join(top,top) != join(top,complement(join(top,complement(join(top,top)))))
| join(top,top) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(top,top),join(top,complement(join(top,complement(join(top,top)))))) ),[1],$fot(top)]]) ).
cnf(refute_0_854,plain,
( join(top,top) != join(top,complement(join(top,complement(join(top,top)))))
| join(top,top) = top ),
inference(resolve,[$cnf( $equal(join(top,complement(join(top,complement(join(top,top))))),top) )],[refute_0_852,refute_0_853]) ).
cnf(refute_0_855,plain,
join(top,top) = top,
inference(resolve,[$cnf( $equal(join(top,top),join(top,complement(join(top,complement(join(top,top)))))) )],[refute_0_782,refute_0_854]) ).
cnf(refute_0_856,plain,
join(join(complement(X_31),X_32),join(meet(X_32,X_31),complement(join(complement(X_31),X_32)))) = join(top,meet(X_32,X_31)),
inference(subst,[],[refute_0_21:[bind(X_18,$fot(join(complement(X_31),X_32))),bind(X_19,$fot(meet(X_32,X_31)))]]) ).
cnf(refute_0_857,plain,
( X_31 != join(meet(X_32,X_31),complement(join(complement(X_31),X_32)))
| join(meet(X_32,X_31),complement(join(complement(X_31),X_32))) = X_31 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_31)),bind(Y,$fot(join(meet(X_32,X_31),complement(join(complement(X_31),X_32)))))]]) ).
cnf(refute_0_858,plain,
join(meet(X_32,X_31),complement(join(complement(X_31),X_32))) = X_31,
inference(resolve,[$cnf( $equal(X_31,join(meet(X_32,X_31),complement(join(complement(X_31),X_32)))) )],[refute_0_291,refute_0_857]) ).
cnf(refute_0_859,plain,
( join(join(complement(X_31),X_32),join(meet(X_32,X_31),complement(join(complement(X_31),X_32)))) != join(top,meet(X_32,X_31))
| join(meet(X_32,X_31),complement(join(complement(X_31),X_32))) != X_31
| join(join(complement(X_31),X_32),X_31) = join(top,meet(X_32,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_31),X_32),join(meet(X_32,X_31),complement(join(complement(X_31),X_32)))),join(top,meet(X_32,X_31))) ),[0,1],$fot(X_31)]]) ).
cnf(refute_0_860,plain,
( join(join(complement(X_31),X_32),join(meet(X_32,X_31),complement(join(complement(X_31),X_32)))) != join(top,meet(X_32,X_31))
| join(join(complement(X_31),X_32),X_31) = join(top,meet(X_32,X_31)) ),
inference(resolve,[$cnf( $equal(join(meet(X_32,X_31),complement(join(complement(X_31),X_32))),X_31) )],[refute_0_858,refute_0_859]) ).
cnf(refute_0_861,plain,
join(join(complement(X_31),X_32),X_31) = join(top,meet(X_32,X_31)),
inference(resolve,[$cnf( $equal(join(join(complement(X_31),X_32),join(meet(X_32,X_31),complement(join(complement(X_31),X_32)))),join(top,meet(X_32,X_31))) )],[refute_0_856,refute_0_860]) ).
cnf(refute_0_862,plain,
join(X_31,join(complement(X_31),X_32)) = join(top,X_32),
inference(subst,[],[refute_0_9:[bind(X_15,$fot(X_31)),bind(X_17,$fot(X_32))]]) ).
cnf(refute_0_863,plain,
join(complement(X_31),join(X_32,X_31)) = join(X_31,join(complement(X_31),X_32)),
inference(subst,[],[refute_0_211:[bind(A,$fot(X_31)),bind(X_15,$fot(complement(X_31))),bind(X_16,$fot(X_32))]]) ).
cnf(refute_0_864,plain,
( join(X_31,join(complement(X_31),X_32)) != join(top,X_32)
| join(complement(X_31),join(X_32,X_31)) != join(X_31,join(complement(X_31),X_32))
| join(complement(X_31),join(X_32,X_31)) = join(top,X_32) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(complement(X_31),join(X_32,X_31)))),bind(Y,$fot(join(X_31,join(complement(X_31),X_32)))),bind(Z,$fot(join(top,X_32)))]]) ).
cnf(refute_0_865,plain,
( join(X_31,join(complement(X_31),X_32)) != join(top,X_32)
| join(complement(X_31),join(X_32,X_31)) = join(top,X_32) ),
inference(resolve,[$cnf( $equal(join(complement(X_31),join(X_32,X_31)),join(X_31,join(complement(X_31),X_32))) )],[refute_0_863,refute_0_864]) ).
cnf(refute_0_866,plain,
join(complement(X_31),join(X_32,X_31)) = join(top,X_32),
inference(resolve,[$cnf( $equal(join(X_31,join(complement(X_31),X_32)),join(top,X_32)) )],[refute_0_862,refute_0_865]) ).
cnf(refute_0_867,plain,
join(join(complement(X_31),X_32),X_31) = join(complement(X_31),join(X_32,X_31)),
inference(subst,[],[refute_0_155:[bind(A,$fot(complement(X_31))),bind(B,$fot(X_32)),bind(C,$fot(X_31))]]) ).
cnf(refute_0_868,plain,
( join(complement(X_31),join(X_32,X_31)) != join(top,X_32)
| join(join(complement(X_31),X_32),X_31) != join(complement(X_31),join(X_32,X_31))
| join(join(complement(X_31),X_32),X_31) = join(top,X_32) ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(join(complement(X_31),X_32),X_31))),bind(Y,$fot(join(complement(X_31),join(X_32,X_31)))),bind(Z,$fot(join(top,X_32)))]]) ).
cnf(refute_0_869,plain,
( join(complement(X_31),join(X_32,X_31)) != join(top,X_32)
| join(join(complement(X_31),X_32),X_31) = join(top,X_32) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_31),X_32),X_31),join(complement(X_31),join(X_32,X_31))) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
join(join(complement(X_31),X_32),X_31) = join(top,X_32),
inference(resolve,[$cnf( $equal(join(complement(X_31),join(X_32,X_31)),join(top,X_32)) )],[refute_0_866,refute_0_869]) ).
cnf(refute_0_871,plain,
( join(join(complement(X_31),X_32),X_31) != join(top,X_32)
| join(join(complement(X_31),X_32),X_31) != join(top,meet(X_32,X_31))
| join(top,X_32) = join(top,meet(X_32,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_31),X_32),X_31),join(top,meet(X_32,X_31))) ),[0],$fot(join(top,X_32))]]) ).
cnf(refute_0_872,plain,
( join(join(complement(X_31),X_32),X_31) != join(top,meet(X_32,X_31))
| join(top,X_32) = join(top,meet(X_32,X_31)) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_31),X_32),X_31),join(top,X_32)) )],[refute_0_870,refute_0_871]) ).
cnf(refute_0_873,plain,
join(top,X_32) = join(top,meet(X_32,X_31)),
inference(resolve,[$cnf( $equal(join(join(complement(X_31),X_32),X_31),join(top,meet(X_32,X_31))) )],[refute_0_861,refute_0_872]) ).
cnf(refute_0_874,plain,
( join(top,X_32) != join(top,meet(X_32,X_31))
| join(top,meet(X_32,X_31)) = join(top,X_32) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(top,X_32))),bind(Y,$fot(join(top,meet(X_32,X_31))))]]) ).
cnf(refute_0_875,plain,
join(top,meet(X_32,X_31)) = join(top,X_32),
inference(resolve,[$cnf( $equal(join(top,X_32),join(top,meet(X_32,X_31))) )],[refute_0_873,refute_0_874]) ).
cnf(refute_0_876,plain,
join(top,meet(top,X_32)) = join(top,top),
inference(subst,[],[refute_0_875:[bind(X_31,$fot(X_32)),bind(X_32,$fot(top))]]) ).
cnf(refute_0_877,plain,
( join(top,meet(top,X_32)) != join(top,top)
| join(top,top) != top
| join(top,meet(top,X_32)) = top ),
inference(subst,[],[refute_0_37:[bind(X,$fot(join(top,meet(top,X_32)))),bind(Y,$fot(join(top,top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_878,plain,
( join(top,top) != top
| join(top,meet(top,X_32)) = top ),
inference(resolve,[$cnf( $equal(join(top,meet(top,X_32)),join(top,top)) )],[refute_0_876,refute_0_877]) ).
cnf(refute_0_879,plain,
join(top,meet(top,X_32)) = top,
inference(resolve,[$cnf( $equal(join(top,top),top) )],[refute_0_855,refute_0_878]) ).
cnf(refute_0_880,plain,
( join(top,X_32) != join(top,meet(top,X_32))
| join(top,meet(top,X_32)) != top
| join(top,X_32) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(top,X_32),top) ),[0],$fot(join(top,meet(top,X_32)))]]) ).
cnf(refute_0_881,plain,
( join(top,X_32) != join(top,meet(top,X_32))
| join(top,X_32) = top ),
inference(resolve,[$cnf( $equal(join(top,meet(top,X_32)),top) )],[refute_0_879,refute_0_880]) ).
cnf(refute_0_882,plain,
join(top,X_32) = top,
inference(resolve,[$cnf( $equal(join(top,X_32),join(top,meet(top,X_32))) )],[refute_0_274,refute_0_881]) ).
cnf(refute_0_883,plain,
join(top,X_19) = top,
inference(subst,[],[refute_0_882:[bind(X_32,$fot(X_19))]]) ).
cnf(refute_0_884,plain,
join(X_15,join(top,X_19)) = join(X_15,join(top,X_19)),
introduced(tautology,[refl,[$fot(join(X_15,join(top,X_19)))]]) ).
cnf(refute_0_885,plain,
( join(X_15,join(top,X_19)) != join(X_15,join(top,X_19))
| join(top,X_19) != top
| join(X_15,join(top,X_19)) = join(X_15,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_15,join(top,X_19)),join(X_15,join(top,X_19))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_886,plain,
( join(top,X_19) != top
| join(X_15,join(top,X_19)) = join(X_15,top) ),
inference(resolve,[$cnf( $equal(join(X_15,join(top,X_19)),join(X_15,join(top,X_19))) )],[refute_0_884,refute_0_885]) ).
cnf(refute_0_887,plain,
join(X_15,join(top,X_19)) = join(X_15,top),
inference(resolve,[$cnf( $equal(join(top,X_19),top) )],[refute_0_883,refute_0_886]) ).
cnf(refute_0_888,plain,
( join(X_15,join(top,X_19)) != join(X_15,top)
| join(X_15,join(top,X_19)) != join(top,join(complement(complement(X_15)),X_19))
| join(X_15,top) = join(top,join(complement(complement(X_15)),X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_15,join(top,X_19)),join(top,join(complement(complement(X_15)),X_19))) ),[0],$fot(join(X_15,top))]]) ).
cnf(refute_0_889,plain,
( join(X_15,join(top,X_19)) != join(top,join(complement(complement(X_15)),X_19))
| join(X_15,top) = join(top,join(complement(complement(X_15)),X_19)) ),
inference(resolve,[$cnf( $equal(join(X_15,join(top,X_19)),join(X_15,top)) )],[refute_0_887,refute_0_888]) ).
cnf(refute_0_890,plain,
join(top,join(complement(complement(X_15)),X_19)) = top,
inference(subst,[],[refute_0_882:[bind(X_32,$fot(join(complement(complement(X_15)),X_19)))]]) ).
cnf(refute_0_891,plain,
( join(X_15,top) != join(top,join(complement(complement(X_15)),X_19))
| join(top,join(complement(complement(X_15)),X_19)) != top
| join(X_15,top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_15,top),top) ),[0],$fot(join(top,join(complement(complement(X_15)),X_19)))]]) ).
cnf(refute_0_892,plain,
( join(X_15,top) != join(top,join(complement(complement(X_15)),X_19))
| join(X_15,top) = top ),
inference(resolve,[$cnf( $equal(join(top,join(complement(complement(X_15)),X_19)),top) )],[refute_0_890,refute_0_891]) ).
cnf(refute_0_893,plain,
( join(X_15,join(top,X_19)) != join(top,join(complement(complement(X_15)),X_19))
| join(X_15,top) = top ),
inference(resolve,[$cnf( $equal(join(X_15,top),join(top,join(complement(complement(X_15)),X_19))) )],[refute_0_889,refute_0_892]) ).
cnf(refute_0_894,plain,
join(X_15,top) = top,
inference(resolve,[$cnf( $equal(join(X_15,join(top,X_19)),join(top,join(complement(complement(X_15)),X_19))) )],[refute_0_14,refute_0_893]) ).
cnf(refute_0_895,plain,
join(sk1,top) = top,
inference(subst,[],[refute_0_894:[bind(X_15,$fot(sk1))]]) ).
cnf(refute_0_896,plain,
( join(sk1,top) != top
| top != top
| join(sk1,top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(sk1,top),top) ),[0],$fot(top)]]) ).
cnf(refute_0_897,plain,
( top != top
| join(sk1,top) = top ),
inference(resolve,[$cnf( $equal(join(sk1,top),top) )],[refute_0_895,refute_0_896]) ).
cnf(refute_0_898,plain,
top != top,
inference(resolve,[$cnf( $equal(join(sk1,top),top) )],[refute_0_897,goals_14]) ).
cnf(refute_0_899,plain,
top = top,
introduced(tautology,[refl,[$fot(top)]]) ).
cnf(refute_0_900,plain,
$false,
inference(resolve,[$cnf( $equal(top,top) )],[refute_0_899,refute_0_898]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL002-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 8 11:23:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.60/0.75
% 0.60/0.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.69/0.86
%------------------------------------------------------------------------------