TSTP Solution File: SEU711^2 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SEU711^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.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  : 300s
% DateTime : Tue May 21 03:39:15 EDT 2024

% Result   : Theorem 111.64s 20.16s
% Output   : Refutation 112.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  878 (  62 unt;  10 typ;   3 def)
%            Number of atoms       : 2810 (1195 equ;   0 cnn)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives : 10261 (1483   ~;1376   |;   0   &;7355   @)
%                                         (   0 <=>;  47  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   : 1111 (   0   ^1111   !;   0   ?;1111   :)

% Comments : 
%------------------------------------------------------------------------------
thf(in_type,type,
    in: $i > $i > $o ).

thf(powerset_type,type,
    powerset: $i > $i ).

thf(powersetI_type,type,
    powersetI: $o ).

thf(powersetI_def,definition,
    ( powersetI
    = ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ( in @ C @ A ) )
         => ( in @ B @ ( powerset @ A ) ) ) ) ) ).

thf(powersetE_type,type,
    powersetE: $o ).

thf(powersetE_def,definition,
    ( powersetE
    = ( ! [A: $i,B: $i,C: $i] :
          ( ( in @ B @ ( powerset @ A ) )
         => ( ( in @ C @ B )
           => ( in @ C @ A ) ) ) ) ) ).

thf(binunion_type,type,
    binunion: $i > $i > $i ).

thf(binunionEcases_type,type,
    binunionEcases: $o ).

thf(binunionEcases_def,definition,
    ( binunionEcases
    = ( ! [A: $i,B: $i,C: $i,D: $o] :
          ( ( in @ C @ ( binunion @ A @ B ) )
         => ( ( ( in @ C @ A )
             => D )
           => ( ( ( in @ C @ B )
               => D )
             => D ) ) ) ) ) ).

thf(sk1_type,type,
    sk1: $i > $i > $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(1,conjecture,
    ( powersetI
   => ( powersetE
     => ( binunionEcases
       => ! [A: $i,B: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ! [C: $i] :
                ( ( in @ C @ ( powerset @ A ) )
               => ( in @ ( binunion @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).

thf(2,negated_conjecture,
    ~ ( powersetI
     => ( powersetE
       => ( binunionEcases
         => ! [A: $i,B: $i] :
              ( ( in @ B @ ( powerset @ A ) )
             => ! [C: $i] :
                  ( ( in @ C @ ( powerset @ A ) )
                 => ( in @ ( binunion @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ( in @ C @ A ) )
         => ( in @ B @ ( powerset @ A ) ) )
     => ( ! [A: $i,B: $i,C: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ( ( in @ C @ B )
             => ( in @ C @ A ) ) )
       => ( ! [A: $i,B: $i,C: $i,D: $o] :
              ( ( in @ C @ ( binunion @ A @ B ) )
             => ( ( ( in @ C @ A )
                 => D )
               => ( ( ( in @ C @ B )
                   => D )
                 => D ) ) )
         => ! [A: $i,B: $i] :
              ( ( in @ B @ ( powerset @ A ) )
             => ! [C: $i] :
                  ( ( in @ C @ ( powerset @ A ) )
                 => ( in @ ( binunion @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ( ! [A: $i,B: $i] :
          ( ! [C: $i] :
              ( ( in @ C @ B )
             => ( in @ C @ A ) )
         => ( in @ B @ ( powerset @ A ) ) )
     => ( ! [A: $i,B: $i] :
            ( ( in @ B @ ( powerset @ A ) )
           => ! [C: $i] :
                ( ( in @ C @ B )
               => ( in @ C @ A ) ) )
       => ( ! [A: $i,B: $i,C: $i] :
              ( ( in @ C @ ( binunion @ A @ B ) )
             => ! [D: $o] :
                  ( ( ( in @ C @ A )
                   => D )
                 => ( ( ( in @ C @ B )
                     => D )
                   => D ) ) )
         => ! [A: $i,B: $i] :
              ( ( in @ B @ ( powerset @ A ) )
             => ! [C: $i] :
                  ( ( in @ C @ ( powerset @ A ) )
                 => ( in @ ( binunion @ B @ C ) @ ( powerset @ A ) ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(14,plain,
    in @ sk3 @ ( powerset @ sk2 ),
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    in @ sk4 @ ( powerset @ sk2 ),
    inference(cnf,[status(esa)],[4]) ).

thf(7,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ B )
      | ( in @ C @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(19,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ B )
      | ( in @ C @ A ) ),
    inference(simp,[status(thm)],[7]) ).

thf(32,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ B )
      | ( in @ C @ A )
      | ( ( in @ sk4 @ ( powerset @ sk2 ) )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,19]) ).

thf(33,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk4 )
      | ( in @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).

thf(42,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk4 )
      | ( in @ A @ sk2 ) ),
    inference(simp,[status(thm)],[33]) ).

thf(60,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ sk3 @ ( powerset @ sk2 ) )
       != ( in @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[14,42]) ).

thf(66,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( sk3 != A )
      | ( ( powerset @ sk2 )
       != sk4 ) ),
    inference(simp,[status(thm)],[60]) ).

thf(69,plain,
    ( ( in @ sk3 @ sk2 )
    | ( ( powerset @ sk2 )
     != sk4 ) ),
    inference(simp,[status(thm)],[66]) ).

thf(8,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( sk1 @ B @ A ) @ B )
      | ( in @ B @ ( powerset @ A ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(12,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ ( sk1 @ B @ A ) @ A )
      | ( in @ B @ ( powerset @ A ) ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(85,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( in @ D @ ( powerset @ C ) )
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ ( sk1 @ D @ C ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[8,12]) ).

thf(86,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ A ) )
      | ( in @ A @ ( powerset @ A ) ) ),
    inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( B ))]]) ).

thf(92,plain,
    ! [A: $i] : ( in @ A @ ( powerset @ A ) ),
    inference(simp,[status(thm)],[86]) ).

thf(98,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ ( powerset @ B ) )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( sk1 @ C @ B ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[92,12]) ).

thf(105,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ ( powerset @ B ) )
      | ( A
       != ( sk1 @ C @ B ) )
      | ( ( powerset @ A )
       != B ) ),
    inference(simp,[status(thm)],[98]) ).

thf(109,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( powerset @ ( sk1 @ B @ A ) )
       != A ) ),
    inference(simp,[status(thm)],[105]) ).

thf(26,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ B )
      | ( in @ C @ A )
      | ( ( in @ sk3 @ ( powerset @ sk2 ) )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14,19]) ).

thf(27,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk3 )
      | ( in @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(45,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ sk3 )
      | ( in @ A @ sk2 ) ),
    inference(simp,[status(thm)],[27]) ).

thf(145,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ B @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[92,45]) ).

thf(154,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( A != B )
      | ( ( powerset @ A )
       != sk3 ) ),
    inference(simp,[status(thm)],[145]) ).

thf(162,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ A )
       != sk3 ) ),
    inference(simp,[status(thm)],[154]) ).

thf(13,plain,
    ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(30,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ B )
      | ( ( in @ C @ A )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[19,13]) ).

thf(31,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A ) ),
    inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( B )),bind(C,$thf( binunion @ sk3 @ sk4 ))]]) ).

thf(46,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A ) ),
    inference(simp,[status(thm)],[31]) ).

thf(1288,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[162,46]) ).

thf(1289,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1288:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( sk2 ))]]) ).

thf(8929,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
       != sk3 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,1289]) ).

thf(8930,plain,
    ( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk2 ) ) )
     != ( powerset @ sk2 ) )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 ) ),
    inference(pattern_uni,[status(thm)],[8929:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(50,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ D @ ( powerset @ C ) )
      | ( in @ E @ C )
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ E @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[8,19]) ).

thf(51,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ C ) )
      | ~ ( in @ B @ ( powerset @ A ) )
      | ( in @ ( sk1 @ B @ C ) @ A ) ),
    inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( sk1 @ F @ G ))]]) ).

thf(57,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ C ) )
      | ~ ( in @ B @ ( powerset @ A ) )
      | ( in @ ( sk1 @ B @ C ) @ A ) ),
    inference(simp,[status(thm)],[51]) ).

thf(87,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ B )
      | ( in @ E @ ( powerset @ D ) )
      | ( ( in @ C @ A )
       != ( in @ ( sk1 @ E @ D ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[19,12]) ).

thf(88,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ ( sk1 @ C @ A ) @ B )
      | ( in @ C @ ( powerset @ A ) ) ),
    inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 @ F @ A )),bind(D,$thf( A )),bind(E,$thf( F ))]]) ).

thf(93,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ ( sk1 @ C @ A ) @ B )
      | ( in @ C @ ( powerset @ A ) ) ),
    inference(simp,[status(thm)],[88]) ).

thf(6013,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ ( sk1 @ C @ A ) @ B )
      | ( in @ C @ ( powerset @ A ) )
      | ( ( in @ sk4 @ ( powerset @ sk2 ) )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,93]) ).

thf(6014,plain,
    ! [A: $i] :
      ( ~ ( in @ ( sk1 @ A @ sk2 ) @ sk4 )
      | ( in @ A @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[6013:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).

thf(6160,plain,
    ! [A: $i] :
      ( ~ ( in @ ( sk1 @ A @ sk2 ) @ sk4 )
      | ( in @ A @ ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[6014]) ).

thf(29448,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ C ) )
      | ~ ( in @ B @ ( powerset @ A ) )
      | ( in @ D @ ( powerset @ sk2 ) )
      | ( ( in @ ( sk1 @ B @ C ) @ A )
       != ( in @ ( sk1 @ D @ sk2 ) @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[57,6160]) ).

thf(29449,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ~ ( in @ A @ ( powerset @ sk4 ) )
      | ( in @ A @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[29448:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( B ))]]) ).

thf(29675,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ~ ( in @ A @ ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[29449]) ).

thf(40288,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( in @ C @ ( powerset @ sk2 ) )
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ C @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,29675]) ).

thf(40289,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk4 ) @ ( powerset @ A ) )
      | ( in @ ( sk1 @ ( powerset @ sk4 ) @ A ) @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[40288:[bind(A,$thf( E )),bind(B,$thf( powerset @ sk4 )),bind(C,$thf( sk1 @ ( powerset @ sk4 ) @ E ))]]) ).

thf(40459,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk4 ) @ ( powerset @ A ) )
      | ( in @ ( sk1 @ ( powerset @ sk4 ) @ A ) @ ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[40289]) ).

thf(46819,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ ( powerset @ sk4 ) @ ( powerset @ A ) )
      | ( in @ C @ ( powerset @ B ) )
      | ( ( in @ ( sk1 @ ( powerset @ sk4 ) @ A ) @ ( powerset @ sk2 ) )
       != ( in @ ( sk1 @ C @ B ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[40459,12]) ).

thf(46820,plain,
    ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
    | ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[46819:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( powerset @ sk2 )),bind(C,$thf( powerset @ sk4 ))]]) ).

thf(47023,plain,
    in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ),
    inference(simp,[status(thm)],[46820]) ).

thf(47042,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,42]) ).

thf(47205,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ sk4 )
       != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk4 ) ),
    inference(simp,[status(thm)],[47042]) ).

thf(47281,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk4 ) ),
    inference(simp,[status(thm)],[47205]) ).

thf(1297,plain,
    ! [A: $i] :
      ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( in @ sk3 @ ( powerset @ sk2 ) )
       != ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14,46]) ).

thf(1365,plain,
    ! [A: $i] :
      ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( sk3 != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[1297]) ).

thf(1411,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[1365]) ).

thf(9,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binunion @ A @ B ) )
      | ( in @ C @ A )
      | ( in @ C @ B )
      | D ),
    inference(cnf,[status(esa)],[4]) ).

thf(18,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binunion @ A @ B ) )
      | ( in @ C @ A )
      | ( in @ C @ B )
      | D ),
    inference(simp,[status(thm)],[9]) ).

thf(193,plain,
    ! [F: $o,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( in @ E @ C )
      | ( in @ E @ D )
      | F
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ E @ ( binunion @ C @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,18]) ).

thf(194,plain,
    ! [D: $i,C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ C @ D ) @ ( powerset @ B ) )
      | ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ C )
      | ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ D )
      | A ),
    inference(pattern_uni,[status(thm)],[193:[bind(A,$thf( H )),bind(B,$thf( binunion @ I @ J )),bind(C,$thf( I )),bind(D,$thf( J )),bind(E,$thf( sk1 @ ( binunion @ I @ J ) @ H )),bind(F,$thf( F ))]]) ).

thf(226,plain,
    ! [D: $i,C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ C @ D ) @ ( powerset @ B ) )
      | ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ C )
      | ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ D )
      | A ),
    inference(simp,[status(thm)],[194]) ).

thf(496,plain,
    ! [D: $i,C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ C @ D ) @ ( powerset @ B ) )
      | ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ C )
      | A
      | ( ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ D )
       != ( in @ ( sk1 @ ( binunion @ C @ D ) @ B ) @ C ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[226]) ).

thf(518,plain,
    ! [C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ C @ C ) @ ( powerset @ B ) )
      | ( in @ ( sk1 @ ( binunion @ C @ C ) @ B ) @ C )
      | A ),
    inference(pattern_uni,[status(thm)],[496:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).

thf(526,plain,
    ! [C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ C @ C ) @ ( powerset @ B ) )
      | ( in @ ( sk1 @ ( binunion @ C @ C ) @ B ) @ C )
      | A ),
    inference(simp,[status(thm)],[518]) ).

thf(874,plain,
    ! [D: $i,C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ C @ C ) @ ( powerset @ B ) )
      | A
      | ( in @ D @ sk2 )
      | ( ( in @ ( sk1 @ ( binunion @ C @ C ) @ B ) @ C )
       != ( in @ D @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[526,45]) ).

thf(875,plain,
    ! [B: $i,A: $o] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ B ) )
      | A
      | ( in @ ( sk1 @ ( binunion @ sk3 @ sk3 ) @ B ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[874:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( sk3 )),bind(D,$thf( sk1 @ ( binunion @ sk3 @ sk3 ) @ F ))]]) ).

thf(946,plain,
    ! [B: $i,A: $o] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ B ) )
      | A
      | ( in @ ( sk1 @ ( binunion @ sk3 @ sk3 ) @ B ) @ sk2 ) ),
    inference(simp,[status(thm)],[875]) ).

thf(13247,plain,
    ! [D: $i,C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ B ) )
      | A
      | ( in @ D @ ( powerset @ C ) )
      | ( ( in @ ( sk1 @ ( binunion @ sk3 @ sk3 ) @ B ) @ sk2 )
       != ( in @ ( sk1 @ D @ C ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[946,12]) ).

thf(13248,plain,
    ! [A: $o] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
      | A
      | ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[13247:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk2 )),bind(D,$thf( binunion @ sk3 @ sk3 ))]]) ).

thf(13470,plain,
    ! [A: $o] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
      | A ),
    inference(simp,[status(thm)],[13248]) ).

thf(878,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ C @ C ) @ ( powerset @ B ) )
      | A
      | ( in @ E @ ( powerset @ D ) )
      | ( ( in @ ( sk1 @ ( binunion @ C @ C ) @ B ) @ C )
       != ( in @ ( sk1 @ E @ D ) @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[526,12]) ).

thf(879,plain,
    ! [B: $i,A: $o] :
      ( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
      | A
      | ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) ) ),
    inference(pattern_uni,[status(thm)],[878:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G )),bind(E,$thf( binunion @ G @ G ))]]) ).

thf(948,plain,
    ! [B: $i,A: $o] :
      ( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
      | A ),
    inference(simp,[status(thm)],[879]) ).

thf(1617,plain,
    ! [B: $i,A: $o] :
      ( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
      | ( A
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[948,13]) ).

thf(1618,plain,
    ! [A: $i] : ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) ),
    inference(pattern_uni,[status(thm)],[1617:[bind(A,$thf( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )),bind(B,$thf( B ))]]) ).

thf(1710,plain,
    ! [A: $i] : ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) ),
    inference(simp,[status(thm)],[1618]) ).

thf(1814,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ B )
      | ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
       != ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1710,46]) ).

thf(1815,plain,
    ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[1814:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ))]]) ).

thf(13530,plain,
    ! [A: $o] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
      | ( A
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13470,1815]) ).

thf(13531,plain,
    in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ),
    inference(pattern_uni,[status(thm)],[13530:[bind(A,$thf( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ))]]) ).

thf(13873,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ B )
      | ( in @ C @ A )
      | ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13531,19]) ).

thf(13874,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( binunion @ sk3 @ sk3 ) )
      | ( in @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[13873:[bind(A,$thf( sk2 )),bind(B,$thf( binunion @ sk3 @ sk3 )),bind(C,$thf( C ))]]) ).

thf(13955,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( binunion @ sk3 @ sk3 ) )
      | ( in @ A @ sk2 ) ),
    inference(simp,[status(thm)],[13874]) ).

thf(143,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ sk3 @ ( powerset @ sk2 ) )
       != ( in @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[14,45]) ).

thf(155,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( sk3 != A )
      | ( ( powerset @ sk2 )
       != sk3 ) ),
    inference(simp,[status(thm)],[143]) ).

thf(163,plain,
    ( ( in @ sk3 @ sk2 )
    | ( ( powerset @ sk2 )
     != sk3 ) ),
    inference(simp,[status(thm)],[155]) ).

thf(1276,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[92,46]) ).

thf(1277,plain,
    ~ ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[1276:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( powerset @ ( binunion @ sk3 @ sk4 ) ))]]) ).

thf(1436,plain,
    ( ( ( powerset @ sk2 )
     != sk3 )
    | ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk3 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[163,1277]) ).

thf(1469,plain,
    ( ( ( powerset @ sk2 )
     != sk3 )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1436]) ).

thf(62,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( in @ C @ sk2 )
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ C @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[8,42]) ).

thf(63,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( in @ ( sk1 @ sk4 @ A ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( E )),bind(B,$thf( sk4 )),bind(C,$thf( sk1 @ sk4 @ E ))]]) ).

thf(71,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( in @ ( sk1 @ sk4 @ A ) @ sk2 ) ),
    inference(simp,[status(thm)],[63]) ).

thf(127,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ B ) )
      | ( in @ D @ B )
      | ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
       != ( in @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[71,19]) ).

thf(128,plain,
    ! [B: $i,A: $i] :
      ( ( in @ sk4 @ ( powerset @ B ) )
      | ~ ( in @ sk2 @ ( powerset @ A ) )
      | ( in @ ( sk1 @ sk4 @ B ) @ A ) ),
    inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( sk1 @ sk4 @ F ))]]) ).

thf(138,plain,
    ! [B: $i,A: $i] :
      ( ( in @ sk4 @ ( powerset @ B ) )
      | ~ ( in @ sk2 @ ( powerset @ A ) )
      | ( in @ ( sk1 @ sk4 @ B ) @ A ) ),
    inference(simp,[status(thm)],[128]) ).

thf(867,plain,
    ! [D: $i,C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ C @ C ) @ ( powerset @ B ) )
      | A
      | ( in @ D @ sk2 )
      | ( ( in @ ( sk1 @ ( binunion @ C @ C ) @ B ) @ C )
       != ( in @ D @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[526,42]) ).

thf(868,plain,
    ! [B: $i,A: $o] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ B ) )
      | A
      | ( in @ ( sk1 @ ( binunion @ sk4 @ sk4 ) @ B ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[867:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( sk4 )),bind(D,$thf( sk1 @ ( binunion @ sk4 @ sk4 ) @ F ))]]) ).

thf(943,plain,
    ! [B: $i,A: $o] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ B ) )
      | A
      | ( in @ ( sk1 @ ( binunion @ sk4 @ sk4 ) @ B ) @ sk2 ) ),
    inference(simp,[status(thm)],[868]) ).

thf(3436,plain,
    ! [D: $i,C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ B ) )
      | A
      | ( in @ D @ ( powerset @ C ) )
      | ( ( in @ ( sk1 @ ( binunion @ sk4 @ sk4 ) @ B ) @ sk2 )
       != ( in @ ( sk1 @ D @ C ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[943,12]) ).

thf(3437,plain,
    ! [A: $o] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
      | A
      | ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[3436:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk2 )),bind(D,$thf( binunion @ sk4 @ sk4 ))]]) ).

thf(3558,plain,
    ! [A: $o] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
      | A ),
    inference(simp,[status(thm)],[3437]) ).

thf(3586,plain,
    ! [A: $o] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
      | ( A
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3558,1815]) ).

thf(3587,plain,
    in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ),
    inference(pattern_uni,[status(thm)],[3586:[bind(A,$thf( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ))]]) ).

thf(64,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ B )
      | ( in @ D @ sk2 )
      | ( ( in @ C @ A )
       != ( in @ D @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[19,42]) ).

thf(65,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk4 ) )
      | ~ ( in @ B @ A )
      | ( in @ B @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( sk4 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).

thf(68,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk4 ) )
      | ~ ( in @ B @ A )
      | ( in @ B @ sk2 ) ),
    inference(simp,[status(thm)],[65]) ).

thf(3883,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk4 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3587,68]) ).

thf(3884,plain,
    ( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) )
    | ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[3883:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( binunion @ sk4 @ sk4 ))]]) ).

thf(5696,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,3884]) ).

thf(5779,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ A )
       != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[5696]) ).

thf(5857,plain,
    ( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[5779]) ).

thf(13859,plain,
    ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
   != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13531,1277]) ).

thf(13896,plain,
    ( ( ( binunion @ sk3 @ sk3 )
     != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[13859]) ).

thf(22012,plain,
    ( ( ( binunion @ sk3 @ sk3 )
     != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[13896]) ).

thf(5907,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ ( sk1 @ C @ A ) @ B )
      | ( in @ C @ ( powerset @ A ) )
      | ( ( in @ sk3 @ ( powerset @ sk2 ) )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14,93]) ).

thf(5908,plain,
    ! [A: $i] :
      ( ~ ( in @ ( sk1 @ A @ sk2 ) @ sk3 )
      | ( in @ A @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[5907:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(6124,plain,
    ! [A: $i] :
      ( ~ ( in @ ( sk1 @ A @ sk2 ) @ sk3 )
      | ( in @ A @ ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[5908]) ).

thf(28178,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ C ) )
      | ~ ( in @ B @ ( powerset @ A ) )
      | ( in @ D @ ( powerset @ sk2 ) )
      | ( ( in @ ( sk1 @ B @ C ) @ A )
       != ( in @ ( sk1 @ D @ sk2 ) @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[57,6124]) ).

thf(28179,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ~ ( in @ A @ ( powerset @ sk3 ) )
      | ( in @ A @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[28178:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( B ))]]) ).

thf(28398,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ~ ( in @ A @ ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[28179]) ).

thf(28769,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( in @ C @ ( powerset @ sk2 ) )
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ C @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,28398]) ).

thf(28770,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk3 ) @ ( powerset @ A ) )
      | ( in @ ( sk1 @ ( powerset @ sk3 ) @ A ) @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[28769:[bind(A,$thf( E )),bind(B,$thf( powerset @ sk3 )),bind(C,$thf( sk1 @ ( powerset @ sk3 ) @ E ))]]) ).

thf(28903,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk3 ) @ ( powerset @ A ) )
      | ( in @ ( sk1 @ ( powerset @ sk3 ) @ A ) @ ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[28770]) ).

thf(29773,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ ( powerset @ sk3 ) @ ( powerset @ A ) )
      | ( in @ C @ ( powerset @ B ) )
      | ( ( in @ ( sk1 @ ( powerset @ sk3 ) @ A ) @ ( powerset @ sk2 ) )
       != ( in @ ( sk1 @ C @ B ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[28903,12]) ).

thf(29774,plain,
    ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
    | ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[29773:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( powerset @ sk2 )),bind(C,$thf( powerset @ sk3 ))]]) ).

thf(29915,plain,
    in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ),
    inference(simp,[status(thm)],[29774]) ).

thf(149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ B )
      | ( in @ D @ sk2 )
      | ( ( in @ C @ A )
       != ( in @ D @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[19,45]) ).

thf(150,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk3 ) )
      | ~ ( in @ B @ A )
      | ( in @ B @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).

thf(159,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk3 ) )
      | ~ ( in @ B @ A )
      | ( in @ B @ sk2 ) ),
    inference(simp,[status(thm)],[150]) ).

thf(30002,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk3 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,159]) ).

thf(30003,plain,
    ( ~ ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) )
    | ( in @ ( powerset @ sk3 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[30002:[bind(A,$thf( powerset @ ( powerset @ sk2 ) )),bind(B,$thf( powerset @ sk3 ))]]) ).

thf(147,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( in @ C @ sk2 )
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ C @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[8,45]) ).

thf(148,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( in @ ( sk1 @ sk3 @ A ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( E )),bind(B,$thf( sk3 )),bind(C,$thf( sk1 @ sk3 @ E ))]]) ).

thf(158,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( in @ ( sk1 @ sk3 @ A ) @ sk2 ) ),
    inference(simp,[status(thm)],[148]) ).

thf(5900,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ B ) )
      | ( in @ D @ ( powerset @ B ) )
      | ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
       != ( in @ ( sk1 @ D @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[158,93]) ).

thf(5901,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ~ ( in @ sk2 @ ( powerset @ A ) )
      | ( in @ sk3 @ ( powerset @ A ) ) ),
    inference(pattern_uni,[status(thm)],[5900:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 )),bind(D,$thf( sk3 ))]]) ).

thf(6122,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ~ ( in @ sk2 @ ( powerset @ A ) ) ),
    inference(simp,[status(thm)],[5901]) ).

thf(7525,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ A ) )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ B )
      | ( ( in @ sk3 @ ( powerset @ A ) )
       != ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6122,46]) ).

thf(7526,plain,
    ( ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) )
    | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[7525:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(8911,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,7526]) ).

thf(8912,plain,
    ( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk2 ) ) )
     != ( powerset @ sk2 ) )
    | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[8911:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(10901,plain,
    ( ( ( sk1 @ sk2 @ ( powerset @ sk2 ) )
     != sk2 )
    | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 ) ),
    inference(simp,[status(thm)],[8912]) ).

thf(47092,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk3 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,159]) ).

thf(47093,plain,
    ( ~ ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) )
    | ( in @ ( powerset @ sk4 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[47092:[bind(A,$thf( powerset @ ( powerset @ sk2 ) )),bind(B,$thf( powerset @ sk4 ))]]) ).

thf(52139,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) )
     != ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,47093]) ).

thf(52247,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[52139]) ).

thf(52350,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[52247]) ).

thf(52387,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ sk2 )
     != sk3 ) ),
    inference(simp,[status(thm)],[52350]) ).

thf(3756,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ B )
      | ( in @ C @ A )
      | ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3587,19]) ).

thf(3757,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( binunion @ sk4 @ sk4 ) )
      | ( in @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[3756:[bind(A,$thf( sk2 )),bind(B,$thf( binunion @ sk4 @ sk4 )),bind(C,$thf( C ))]]) ).

thf(3794,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( binunion @ sk4 @ sk4 ) )
      | ( in @ A @ sk2 ) ),
    inference(simp,[status(thm)],[3757]) ).

thf(6958,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ B @ ( binunion @ sk4 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,3794]) ).

thf(7037,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( A != B )
      | ( ( powerset @ A )
       != ( binunion @ sk4 @ sk4 ) ) ),
    inference(simp,[status(thm)],[6958]) ).

thf(7109,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ A )
       != ( binunion @ sk4 @ sk4 ) ) ),
    inference(simp,[status(thm)],[7037]) ).

thf(11380,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk4 @ sk4 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7109,1277]) ).

thf(11447,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk4 @ sk4 ) )
      | ( A
       != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[11380]) ).

thf(11504,plain,
    ( ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[11447]) ).

thf(14962,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk3 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3587,159]) ).

thf(14963,plain,
    ( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) )
    | ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[14962:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( binunion @ sk4 @ sk4 ))]]) ).

thf(18392,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,14963]) ).

thf(18552,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ A )
       != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[18392]) ).

thf(18691,plain,
    ( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[18552]) ).

thf(169,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ B @ ( powerset @ A ) )
      | ( in @ C @ A )
      | ( ( in @ sk3 @ sk2 )
       != ( in @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[163,19]) ).

thf(170,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ sk2 @ ( powerset @ A ) )
      | ( in @ sk3 @ A ) ),
    inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).

thf(13880,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk4 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[13531,68]) ).

thf(13881,plain,
    ( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) )
    | ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[13880:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( binunion @ sk3 @ sk3 ))]]) ).

thf(18017,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,13881]) ).

thf(18018,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk4 ) )
     != sk4 )
    | ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[18017:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ sk2 ))]]) ).

thf(61,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ sk4 @ ( powerset @ sk2 ) )
       != ( in @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,42]) ).

thf(67,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( sk4 != A )
      | ( ( powerset @ sk2 )
       != sk4 ) ),
    inference(simp,[status(thm)],[61]) ).

thf(70,plain,
    ( ( in @ sk4 @ sk2 )
    | ( ( powerset @ sk2 )
     != sk4 ) ),
    inference(simp,[status(thm)],[67]) ).

thf(1305,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( in @ sk4 @ sk2 )
       != ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[70,46]) ).

thf(1355,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( sk4 != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[1305]) ).

thf(1401,plain,
    ( ( ( powerset @ sk2 )
     != sk4 )
    | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1355]) ).

thf(1430,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ A ) )
     != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,1277]) ).

thf(1462,plain,
    ! [A: $i] :
      ( ( A
       != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
      | ( ( powerset @ A )
       != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[1430]) ).

thf(1486,plain,
    ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
   != ( powerset @ ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[1462]) ).

thf(1348,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( in @ ( binunion @ sk3 @ sk4 ) @ A )
       != ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[46]) ).

thf(1381,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( binunion @ sk3 @ sk4 )
       != A )
      | ( A
       != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[1348]) ).

thf(1426,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[1381]) ).

thf(48,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ E @ D )
      | ( in @ E @ C )
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ D @ ( powerset @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,19]) ).

thf(49,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ ( powerset @ C ) @ ( powerset @ B ) )
      | ~ ( in @ A @ ( sk1 @ ( powerset @ C ) @ B ) )
      | ( in @ A @ C ) ),
    inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( G )),bind(B,$thf( powerset @ H )),bind(C,$thf( H )),bind(D,$thf( sk1 @ ( powerset @ H ) @ G )),bind(E,$thf( E ))]]) ).

thf(56,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ ( powerset @ C ) @ ( powerset @ B ) )
      | ~ ( in @ A @ ( sk1 @ ( powerset @ C ) @ B ) )
      | ( in @ A @ C ) ),
    inference(simp,[status(thm)],[49]) ).

thf(22743,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
       != ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3587,13955]) ).

thf(22884,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( binunion @ sk4 @ sk4 )
       != A )
      | ( ( binunion @ sk3 @ sk3 )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[22743]) ).

thf(22970,plain,
    ( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
    | ( ( binunion @ sk3 @ sk3 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[22884]) ).

thf(1336,plain,
    ! [A: $i] :
      ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( in @ sk4 @ ( powerset @ sk2 ) )
       != ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,46]) ).

thf(1374,plain,
    ! [A: $i] :
      ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( sk4 != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[1336]) ).

thf(1420,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[1374]) ).

thf(2184,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[1420]) ).

thf(22725,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ B @ ( binunion @ sk3 @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,13955]) ).

thf(22873,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( A != B )
      | ( ( powerset @ A )
       != ( binunion @ sk3 @ sk3 ) ) ),
    inference(simp,[status(thm)],[22725]) ).

thf(22961,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ A )
       != ( binunion @ sk3 @ sk3 ) ) ),
    inference(simp,[status(thm)],[22873]) ).

thf(25020,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk3 @ sk3 ) )
      | ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[22961,46]) ).

thf(25021,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != ( binunion @ sk3 @ sk3 ) )
    | ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[25020:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( sk2 ))]]) ).

thf(47071,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != ( binunion @ sk3 @ sk3 ) )
    | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,25021]) ).

thf(47164,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != ( binunion @ sk3 @ sk3 ) )
    | ( ( powerset @ sk4 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47071]) ).

thf(47261,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != ( binunion @ sk3 @ sk3 ) )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[47164]) ).

thf(292,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ~ ( in @ C @ ( powerset @ B ) )
      | ( in @ D @ B )
      | ( ( in @ A @ sk2 )
       != ( in @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[162,19]) ).

thf(293,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ~ ( in @ sk2 @ ( powerset @ B ) )
      | ( in @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( A ))]]) ).

thf(47048,plain,
    ! [A: $i] :
      ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,46]) ).

thf(47049,plain,
    ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[47048:[bind(A,$thf( powerset @ sk4 ))]]) ).

thf(47325,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ~ ( in @ sk2 @ ( powerset @ B ) )
      | ( ( in @ A @ B )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[293,47049]) ).

thf(47326,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk4 ) ) ) ),
    inference(pattern_uni,[status(thm)],[47325:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( powerset @ sk4 ))]]) ).

thf(56832,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
       != sk3 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ sk4 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,47326]) ).

thf(57075,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
       != sk3 )
      | ( A != sk2 )
      | ( ( powerset @ A )
       != ( powerset @ ( powerset @ sk4 ) ) ) ),
    inference(simp,[status(thm)],[56832]) ).

thf(57185,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( powerset @ ( powerset @ sk4 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[57075]) ).

thf(13820,plain,
    ! [A: $i] :
      ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
       != ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13531,46]) ).

thf(13908,plain,
    ! [A: $i] :
      ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( binunion @ sk3 @ sk3 )
       != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[13820]) ).

thf(13960,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ sk3 @ sk3 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[13908]) ).

thf(22016,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ sk3 @ sk3 ) )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[13960]) ).

thf(33890,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk3 ) @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,30003]) ).

thf(34011,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk3 ) @ sk2 )
      | ( A
       != ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( powerset @ A )
       != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[33890]) ).

thf(34139,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[34011]) ).

thf(22777,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ sk4 @ ( powerset @ sk2 ) )
       != ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,13955]) ).

thf(22834,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( sk4 != A )
      | ( ( binunion @ sk3 @ sk3 )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[22777]) ).

thf(22925,plain,
    ( ( in @ sk4 @ sk2 )
    | ( ( binunion @ sk3 @ sk3 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[22834]) ).

thf(1429,plain,
    ( ( ( powerset @ sk2 )
     != sk4 )
    | ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk3 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[69,1277]) ).

thf(1475,plain,
    ( ( ( powerset @ sk2 )
     != sk4 )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1429]) ).

thf(317,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
       != ( in @ sk3 @ ( powerset @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[158]) ).

thf(320,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( ( sk1 @ sk3 @ A )
       != sk3 )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[317]) ).

thf(21,plain,
    ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
   != ( in @ sk3 @ ( powerset @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[14,13]) ).

thf(23,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != sk3 )
    | ( ( powerset @ sk2 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[21]) ).

thf(25,plain,
    ( ( binunion @ sk3 @ sk4 )
   != sk3 ),
    inference(simp,[status(thm)],[23]) ).

thf(20,plain,
    ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
   != ( in @ sk4 @ ( powerset @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,13]) ).

thf(22,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != sk4 )
    | ( ( powerset @ sk2 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[20]) ).

thf(24,plain,
    ( ( binunion @ sk3 @ sk4 )
   != sk4 ),
    inference(simp,[status(thm)],[22]) ).

thf(29956,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,28398]) ).

thf(30103,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( powerset @ sk3 )
       != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[29956]) ).

thf(30162,plain,
    ( ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[30103]) ).

thf(3809,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ sk4 ) )
      | ( in @ C @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[92,68]) ).

thf(3810,plain,
    ! [A: $i] :
      ( ~ ( in @ ( powerset @ A ) @ ( powerset @ sk4 ) )
      | ( in @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[3809:[bind(A,$thf( D )),bind(B,$thf( powerset @ D )),bind(C,$thf( D ))]]) ).

thf(4118,plain,
    ! [A: $i] :
      ( ~ ( in @ ( powerset @ A ) @ ( powerset @ sk4 ) )
      | ( in @ A @ sk2 ) ),
    inference(simp,[status(thm)],[3810]) ).

thf(7384,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ B ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,4118]) ).

thf(7441,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( A
       != ( powerset @ B ) )
      | ( ( powerset @ A )
       != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[7384]) ).

thf(7492,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[7441]) ).

thf(11774,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk4 ) )
      | ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[7492,46]) ).

thf(11775,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk4 ) )
    | ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[11774:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( sk2 ))]]) ).

thf(30013,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk4 ) )
    | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,11775]) ).

thf(30069,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ sk3 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[30013]) ).

thf(30149,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ sk3 )
     != sk2 ) ),
    inference(simp,[status(thm)],[30069]) ).

thf(3950,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk4 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ sk4 @ ( powerset @ sk2 ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[11,68]) ).

thf(3951,plain,
    ( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) )
    | ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[3950:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk4 ))]]) ).

thf(8874,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ sk4 @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,3951]) ).

thf(8875,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk4 ) )
     != sk4 )
    | ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[8874:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ sk2 ))]]) ).

thf(103,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ B @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[92,42]) ).

thf(106,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( A != B )
      | ( ( powerset @ A )
       != sk4 ) ),
    inference(simp,[status(thm)],[103]) ).

thf(110,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ A )
       != sk4 ) ),
    inference(simp,[status(thm)],[106]) ).

thf(295,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ( in @ C @ ( powerset @ B ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( sk1 @ C @ B ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[162,12]) ).

thf(296,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk3 )
      | ( in @ A @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( sk1 @ D @ sk2 )),bind(B,$thf( sk2 )),bind(C,$thf( D ))]]) ).

thf(302,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk3 )
      | ( in @ A @ ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[296]) ).

thf(801,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk3 )
      | ( ( in @ A @ ( powerset @ sk2 ) )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[302,13]) ).

thf(802,plain,
    ( ( powerset @ ( sk1 @ ( binunion @ sk3 @ sk4 ) @ sk2 ) )
   != sk3 ),
    inference(pattern_uni,[status(thm)],[801:[bind(A,$thf( binunion @ sk3 @ sk4 ))]]) ).

thf(47109,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
    | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,7526]) ).

thf(47158,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
    | ( ( powerset @ sk4 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47109]) ).

thf(47259,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[47158]) ).

thf(14846,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk3 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ sk3 @ ( powerset @ sk2 ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[14,159]) ).

thf(14847,plain,
    ( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) )
    | ( in @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[14846:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(15476,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ sk3 @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,14847]) ).

thf(15477,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk3 ) )
     != sk3 )
    | ( in @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[15476:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ sk2 ))]]) ).

thf(11351,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk4 @ sk4 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7109,1815]) ).

thf(11453,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk4 @ sk4 ) )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[11351]) ).

thf(11510,plain,
    ( ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
    | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[11453]) ).

thf(268,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[110,13]) ).

thf(278,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ sk2 )
       != sk2 ) ),
    inference(simp,[status(thm)],[268]) ).

thf(284,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[278]) ).

thf(311,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ~ ( in @ D @ C )
      | ( in @ D @ B )
      | ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
       != ( in @ C @ ( powerset @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[158,19]) ).

thf(321,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( in @ D @ B )
      | ~ ( in @ D @ C )
      | ( ( sk1 @ sk3 @ A )
       != C )
      | ( ( powerset @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[311]) ).

thf(325,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( in @ C @ B )
      | ~ ( in @ C @ ( sk1 @ sk3 @ A ) )
      | ( ( powerset @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[321]) ).

thf(15072,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk3 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ sk4 @ ( powerset @ sk2 ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[11,159]) ).

thf(15073,plain,
    ( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) )
    | ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[15072:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk4 ))]]) ).

thf(1440,plain,
    ( ( ( powerset @ sk2 )
     != sk4 )
    | ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk4 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[70,1277]) ).

thf(1479,plain,
    ( ( ( powerset @ sk2 )
     != sk4 )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1440]) ).

thf(28,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ( in @ C @ A )
      | ( ( in @ sk3 @ ( powerset @ sk2 ) )
       != ( in @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[14,19]) ).

thf(29,plain,
    ! [A: $i] :
      ( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ A ) )
      | ( in @ sk3 @ A ) ),
    inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( A )),bind(B,$thf( powerset @ sk2 )),bind(C,$thf( sk3 ))]]) ).

thf(3846,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk4 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ sk3 @ ( powerset @ sk2 ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[14,68]) ).

thf(3847,plain,
    ( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) )
    | ( in @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[3846:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(4535,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ( in @ sk3 @ sk2 )
      | ( ( in @ A @ sk2 )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[162,3847]) ).

thf(4558,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ sk2 )
      | ( ( powerset @ A )
       != sk3 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ sk4 )
       != sk2 ) ),
    inference(simp,[status(thm)],[4535]) ).

thf(4595,plain,
    ( ( in @ sk3 @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk3 )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[4558]) ).

thf(1439,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk3 )
      | ( ( in @ A @ ( powerset @ sk2 ) )
       != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[302,1277]) ).

thf(1468,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk3 )
      | ( A
       != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[1439]) ).

thf(1489,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ sk2 ) )
     != sk3 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[1468]) ).

thf(168,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ C @ B )
      | ( in @ C @ A )
      | ( ( in @ sk3 @ sk2 )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[163,19]) ).

thf(177,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ C @ B )
      | ( sk3 != B )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[168]) ).

thf(179,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ A )
      | ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ B @ sk3 )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[177]) ).

thf(29984,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != ( binunion @ sk3 @ sk3 ) )
    | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,25021]) ).

thf(30052,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != ( binunion @ sk3 @ sk3 ) )
    | ( ( powerset @ sk3 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[29984]) ).

thf(30144,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != ( binunion @ sk3 @ sk3 ) )
    | ( ( powerset @ sk3 )
     != sk2 ) ),
    inference(simp,[status(thm)],[30052]) ).

thf(6996,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ sk4 @ ( powerset @ sk2 ) )
       != ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,3794]) ).

thf(7032,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( sk4 != A )
      | ( ( binunion @ sk4 @ sk4 )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[6996]) ).

thf(7104,plain,
    ( ( in @ sk4 @ sk2 )
    | ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[7032]) ).

thf(185,plain,
    ! [E: $o,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ D @ B )
      | ( in @ D @ C )
      | E
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ D @ ( binunion @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,18]) ).

thf(215,plain,
    ! [E: $o,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ D @ B )
      | ( in @ D @ C )
      | E
      | ( A != D )
      | ( ( powerset @ A )
       != ( binunion @ B @ C ) ) ),
    inference(simp,[status(thm)],[185]) ).

thf(238,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( powerset @ C )
       != ( binunion @ A @ B ) ) ),
    inference(simp,[status(thm)],[215]) ).

thf(25068,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk3 @ sk3 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[22961,1277]) ).

thf(25161,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk3 @ sk3 ) )
      | ( A
       != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[25068]) ).

thf(25240,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( binunion @ sk3 @ sk3 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[25161]) ).

thf(11812,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk4 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7492,1277]) ).

thf(11878,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk4 ) )
      | ( A
       != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[11812]) ).

thf(12041,plain,
    ( ( ( powerset @ ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) ) )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[11878]) ).

thf(14913,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ sk3 ) )
      | ( in @ C @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[92,159]) ).

thf(14914,plain,
    ! [A: $i] :
      ( ~ ( in @ ( powerset @ A ) @ ( powerset @ sk3 ) )
      | ( in @ A @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[14913:[bind(A,$thf( D )),bind(B,$thf( powerset @ D )),bind(C,$thf( D ))]]) ).

thf(15290,plain,
    ! [A: $i] :
      ( ~ ( in @ ( powerset @ A ) @ ( powerset @ sk3 ) )
      | ( in @ A @ sk2 ) ),
    inference(simp,[status(thm)],[14914]) ).

thf(24772,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ B ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,15290]) ).

thf(24872,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ sk2 )
      | ( A
       != ( powerset @ B ) )
      | ( ( powerset @ A )
       != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[24772]) ).

thf(24965,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[24872]) ).

thf(25524,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk3 ) )
      | ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[24965,46]) ).

thf(25525,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk3 ) )
    | ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[25524:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( sk2 ))]]) ).

thf(26457,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
       != ( powerset @ sk3 ) )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,25525]) ).

thf(26629,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
       != ( powerset @ sk3 ) )
      | ( A != sk2 )
      | ( ( powerset @ A )
       != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[26457]) ).

thf(26853,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[26629]) ).

thf(26909,plain,
    ( ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) )
    | ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk2 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(eqfactor_ordered,[status(thm)],[26853]) ).

thf(26916,plain,
    ( ( ( powerset @ sk2 )
     != sk2 )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk2 )
    | ( ( powerset @ sk2 )
     != sk3 ) ),
    inference(simp,[status(thm)],[26909]) ).

thf(29965,plain,
    ! [A: $i] :
      ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,46]) ).

thf(29966,plain,
    ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[29965:[bind(A,$thf( powerset @ sk3 ))]]) ).

thf(44243,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ~ ( in @ sk2 @ ( powerset @ B ) )
      | ( ( in @ A @ B )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[293,29966]) ).

thf(44244,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ),
    inference(pattern_uni,[status(thm)],[44243:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( powerset @ sk3 ))]]) ).

thf(44766,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
       != sk3 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,44244]) ).

thf(44767,plain,
    ( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk3 ) ) )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 ) ),
    inference(pattern_uni,[status(thm)],[44766:[bind(A,$thf( powerset @ sk3 )),bind(B,$thf( sk2 ))]]) ).

thf(46040,plain,
    ( ( ( sk1 @ sk2 @ ( powerset @ sk3 ) )
     != sk3 )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 ) ),
    inference(simp,[status(thm)],[44767]) ).

thf(47309,plain,
    ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) )
   != ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,47049]) ).

thf(47613,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[47309]) ).

thf(29998,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk3 ) )
    | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,25525]) ).

thf(30088,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( powerset @ sk3 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[29998]) ).

thf(30154,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( powerset @ sk3 )
     != sk2 ) ),
    inference(simp,[status(thm)],[30088]) ).

thf(1300,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ~ ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[110,46]) ).

thf(1301,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[1300:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( sk2 ))]]) ).

thf(8891,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
       != sk4 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,1301]) ).

thf(8892,plain,
    ( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk2 ) ) )
     != ( powerset @ sk2 ) )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 ) ),
    inference(pattern_uni,[status(thm)],[8891:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(146,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ sk4 @ ( powerset @ sk2 ) )
       != ( in @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,45]) ).

thf(157,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( sk4 != A )
      | ( ( powerset @ sk2 )
       != sk3 ) ),
    inference(simp,[status(thm)],[146]) ).

thf(165,plain,
    ( ( in @ sk4 @ sk2 )
    | ( ( powerset @ sk2 )
     != sk3 ) ),
    inference(simp,[status(thm)],[157]) ).

thf(251,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( in @ sk4 @ sk2 )
       != ( in @ C @ ( binunion @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[165,18]) ).

thf(260,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( powerset @ sk2 )
       != sk3 )
      | ( sk4 != C )
      | ( ( binunion @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[251]) ).

thf(265,plain,
    ! [C: $o,B: $i,A: $i] :
      ( ( in @ sk4 @ A )
      | ( in @ sk4 @ B )
      | C
      | ( ( powerset @ sk2 )
       != sk3 )
      | ( ( binunion @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[260]) ).

thf(15156,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk3 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ B @ A )
       != ( in @ A @ ( powerset @ sk3 ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[159]) ).

thf(15197,plain,
    ( ~ ( in @ ( powerset @ sk3 ) @ ( powerset @ sk3 ) )
    | ( in @ ( powerset @ sk3 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[15156:[bind(A,$thf( powerset @ sk3 )),bind(B,$thf( powerset @ sk3 ))]]) ).

thf(125,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[71,13]) ).

thf(133,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( ( sk1 @ sk4 @ A )
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ sk2 )
       != sk2 ) ),
    inference(simp,[status(thm)],[125]) ).

thf(115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ B @ ( powerset @ A ) )
      | ( in @ C @ A )
      | ( ( in @ sk4 @ sk2 )
       != ( in @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[70,19]) ).

thf(116,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ sk2 @ ( powerset @ A ) )
      | ( in @ sk4 @ A ) ),
    inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).

thf(184,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( in @ sk4 @ sk2 )
       != ( in @ C @ ( binunion @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[70,18]) ).

thf(220,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( powerset @ sk2 )
       != sk4 )
      | ( sk4 != C )
      | ( ( binunion @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[184]) ).

thf(243,plain,
    ! [C: $o,B: $i,A: $i] :
      ( ( in @ sk4 @ A )
      | ( in @ sk4 @ B )
      | C
      | ( ( powerset @ sk2 )
       != sk4 )
      | ( ( binunion @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[220]) ).

thf(209,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binunion @ A @ B ) )
      | ( in @ C @ A )
      | ( in @ C @ B )
      | ( D
       != ( in @ C @ B ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[18]) ).

thf(223,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( binunion @ A @ C ) )
      | ( in @ B @ A )
      | ( in @ B @ C ) ),
    inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( in @ E @ F ))]]) ).

thf(248,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( binunion @ A @ C ) )
      | ( in @ B @ A )
      | ( in @ B @ C ) ),
    inference(simp,[status(thm)],[223]) ).

thf(25526,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk3 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24965,1815]) ).

thf(25668,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk3 ) )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[25526]) ).

thf(25884,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk3 ) )
    | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[25668]) ).

thf(5957,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ B ) )
      | ( in @ D @ ( powerset @ B ) )
      | ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
       != ( in @ ( sk1 @ D @ B ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[71,93]) ).

thf(5958,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ~ ( in @ sk2 @ ( powerset @ A ) )
      | ( in @ sk4 @ ( powerset @ A ) ) ),
    inference(pattern_uni,[status(thm)],[5957:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 )),bind(D,$thf( sk4 ))]]) ).

thf(6139,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ~ ( in @ sk2 @ ( powerset @ A ) ) ),
    inference(simp,[status(thm)],[5958]) ).

thf(1632,plain,
    ! [C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
      | ( in @ sk3 @ C )
      | ( A
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[948,29]) ).

thf(1633,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ sk3 @ B ) ),
    inference(pattern_uni,[status(thm)],[1632:[bind(A,$thf( in @ ( powerset @ sk2 ) @ ( powerset @ G ) )),bind(B,$thf( B )),bind(C,$thf( G ))]]) ).

thf(1725,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ sk3 @ B ) ),
    inference(simp,[status(thm)],[1633]) ).

thf(7004,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ C @ sk2 )
      | ( ( in @ sk3 @ B )
       != ( in @ C @ ( binunion @ sk4 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1725,3794]) ).

thf(7005,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[7004:[bind(A,$thf( A )),bind(B,$thf( binunion @ sk4 @ sk4 )),bind(C,$thf( sk3 ))]]) ).

thf(34,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ( in @ C @ A )
      | ( ( in @ sk4 @ ( powerset @ sk2 ) )
       != ( in @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[11,19]) ).

thf(35,plain,
    ! [A: $i] :
      ( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ A ) )
      | ( in @ sk4 @ A ) ),
    inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( A )),bind(B,$thf( powerset @ sk2 )),bind(C,$thf( sk4 ))]]) ).

thf(1655,plain,
    ! [C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
      | ( in @ sk4 @ C )
      | ( A
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[948,35]) ).

thf(1656,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ sk4 @ B ) ),
    inference(pattern_uni,[status(thm)],[1655:[bind(A,$thf( in @ ( powerset @ sk2 ) @ ( powerset @ G ) )),bind(B,$thf( B )),bind(C,$thf( G ))]]) ).

thf(1736,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ sk4 @ B ) ),
    inference(simp,[status(thm)],[1656]) ).

thf(3734,plain,
    ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
   != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[3587,13]) ).

thf(3762,plain,
    ( ( ( binunion @ sk4 @ sk4 )
     != ( binunion @ sk3 @ sk4 ) )
    | ( ( powerset @ sk2 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[3734]) ).

thf(3795,plain,
    ( ( binunion @ sk4 @ sk4 )
   != ( binunion @ sk3 @ sk4 ) ),
    inference(simp,[status(thm)],[3762]) ).

thf(47143,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk4 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,68]) ).

thf(47144,plain,
    ( ~ ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) )
    | ( in @ ( powerset @ sk4 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[47143:[bind(A,$thf( powerset @ ( powerset @ sk2 ) )),bind(B,$thf( powerset @ sk4 ))]]) ).

thf(47083,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,45]) ).

thf(47202,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ sk4 )
       != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk3 ) ),
    inference(simp,[status(thm)],[47083]) ).

thf(47279,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk3 ) ),
    inference(simp,[status(thm)],[47202]) ).

thf(29947,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,13955]) ).

thf(30112,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ sk3 )
       != A )
      | ( ( binunion @ sk3 @ sk3 )
       != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[29947]) ).

thf(30167,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( binunion @ sk3 @ sk3 )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[30112]) ).

thf(4510,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ( in @ sk3 @ sk2 )
      | ( ( in @ A @ sk2 )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[110,3847]) ).

thf(4587,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ sk2 )
      | ( ( powerset @ A )
       != sk4 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ sk4 )
       != sk2 ) ),
    inference(simp,[status(thm)],[4510]) ).

thf(4609,plain,
    ( ( in @ sk3 @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk4 )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[4587]) ).

thf(47103,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk4 ) )
    | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,11775]) ).

thf(47171,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ sk4 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47103]) ).

thf(47264,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[47171]) ).

thf(47088,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk3 ) )
    | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,25525]) ).

thf(47207,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ sk4 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47088]) ).

thf(47282,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[47207]) ).

thf(8197,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ sk2 @ ( powerset @ A ) )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ B )
      | ( ( in @ sk4 @ ( powerset @ A ) )
       != ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[6139,46]) ).

thf(8198,plain,
    ( ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) )
    | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[8197:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk4 ))]]) ).

thf(8905,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,8198]) ).

thf(8906,plain,
    ( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk2 ) ) )
     != ( powerset @ sk2 ) )
    | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[8905:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(9993,plain,
    ( ( ( sk1 @ sk2 @ ( powerset @ sk2 ) )
     != sk2 )
    | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 ) ),
    inference(simp,[status(thm)],[8906]) ).

thf(25544,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk3 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24965,13]) ).

thf(25712,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk3 ) )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ sk2 )
       != sk2 ) ),
    inference(simp,[status(thm)],[25544]) ).

thf(25912,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[25712]) ).

thf(1450,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ( ( in @ A @ sk2 )
       != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[162,1277]) ).

thf(1463,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ( A
       != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[1450]) ).

thf(1487,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != sk3 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1463]) ).

thf(11781,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk4 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7492,1815]) ).

thf(11943,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk4 ) )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[11781]) ).

thf(12083,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk4 ) )
    | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[11943]) ).

thf(199,plain,
    ! [G: $o,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ B )
      | ( in @ F @ D )
      | ( in @ F @ E )
      | G
      | ( ( in @ C @ A )
       != ( in @ F @ ( binunion @ D @ E ) ) ) ),
    inference(paramod_ordered,[status(thm)],[19,18]) ).

thf(200,plain,
    ! [E: $i,D: $i,C: $o,B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ ( binunion @ D @ E ) ) )
      | ~ ( in @ B @ A )
      | ( in @ B @ D )
      | ( in @ B @ E )
      | C ),
    inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( binunion @ H @ I )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H )),bind(E,$thf( I )),bind(F,$thf( C ))]]) ).

thf(229,plain,
    ! [E: $i,D: $i,C: $o,B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ ( binunion @ D @ E ) ) )
      | ~ ( in @ B @ A )
      | ( in @ B @ D )
      | ( in @ B @ E )
      | C ),
    inference(simp,[status(thm)],[200]) ).

thf(8919,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ sk3 @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,3847]) ).

thf(8920,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk4 ) )
     != sk4 )
    | ( in @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[8919:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ sk2 ))]]) ).

thf(3727,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
       != ( in @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[3587,42]) ).

thf(3773,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( binunion @ sk4 @ sk4 )
       != A )
      | ( ( powerset @ sk2 )
       != sk4 ) ),
    inference(simp,[status(thm)],[3727]) ).

thf(3799,plain,
    ( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
    | ( ( powerset @ sk2 )
     != sk4 ) ),
    inference(simp,[status(thm)],[3773]) ).

thf(312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ~ ( in @ C @ ( powerset @ B ) )
      | ( in @ D @ B )
      | ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
       != ( in @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[158,19]) ).

thf(313,plain,
    ! [B: $i,A: $i] :
      ( ( in @ sk3 @ ( powerset @ B ) )
      | ~ ( in @ sk2 @ ( powerset @ A ) )
      | ( in @ ( sk1 @ sk3 @ B ) @ A ) ),
    inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( sk1 @ sk3 @ F ))]]) ).

thf(329,plain,
    ! [B: $i,A: $i] :
      ( ( in @ sk3 @ ( powerset @ B ) )
      | ~ ( in @ sk2 @ ( powerset @ A ) )
      | ( in @ ( sk1 @ sk3 @ B ) @ A ) ),
    inference(simp,[status(thm)],[313]) ).

thf(8915,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,1277]) ).

thf(8916,plain,
    ( ( powerset @ ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ sk2 ) ) )
   != ( powerset @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[8915:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( powerset @ ( binunion @ sk3 @ sk4 ) ))]]) ).

thf(29989,plain,
    ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
   != ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,13]) ).

thf(30099,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[29989]) ).

thf(3728,plain,
    ! [A: $i] :
      ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
       != ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3587,46]) ).

thf(3776,plain,
    ! [A: $i] :
      ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( binunion @ sk4 @ sk4 )
       != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[3728]) ).

thf(3784,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ sk4 @ sk4 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[3776]) ).

thf(30011,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
    | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,8198]) ).

thf(30105,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
    | ( ( powerset @ sk3 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[30011]) ).

thf(30163,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
    | ( ( powerset @ sk3 )
     != sk2 ) ),
    inference(simp,[status(thm)],[30105]) ).

thf(47039,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,28398]) ).

thf(47243,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( powerset @ sk4 )
       != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[47039]) ).

thf(47289,plain,
    ( ( in @ ( powerset @ sk4 ) @ ( powerset @ sk2 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[47243]) ).

thf(56249,plain,
    ( ( in @ ( powerset @ sk4 ) @ ( powerset @ sk2 ) )
    | ( ( powerset @ sk2 )
     != sk3 ) ),
    inference(simp,[status(thm)],[47289]) ).

thf(18401,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,14963]) ).

thf(18402,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk3 ) )
     != sk3 )
    | ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[18401:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ sk2 ))]]) ).

thf(47372,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk4 @ sk4 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7109,47049]) ).

thf(47494,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk4 @ sk4 ) )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ sk4 )
       != sk2 ) ),
    inference(simp,[status(thm)],[47372]) ).

thf(47636,plain,
    ( ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[47494]) ).

thf(126,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ~ ( in @ D @ C )
      | ( in @ D @ B )
      | ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
       != ( in @ C @ ( powerset @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[71,19]) ).

thf(137,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( in @ D @ B )
      | ~ ( in @ D @ C )
      | ( ( sk1 @ sk4 @ A )
       != C )
      | ( ( powerset @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[126]) ).

thf(141,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( in @ C @ B )
      | ~ ( in @ C @ ( sk1 @ sk4 @ A ) )
      | ( ( powerset @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[137]) ).

thf(272,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ~ ( in @ C @ ( powerset @ B ) )
      | ( in @ D @ B )
      | ( ( in @ A @ sk2 )
       != ( in @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[110,19]) ).

thf(273,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ~ ( in @ sk2 @ ( powerset @ B ) )
      | ( in @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( A ))]]) ).

thf(47449,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ~ ( in @ sk2 @ ( powerset @ B ) )
      | ( ( in @ A @ B )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[273,47049]) ).

thf(47450,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk4 ) ) ) ),
    inference(pattern_uni,[status(thm)],[47449:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( powerset @ sk4 ))]]) ).

thf(40692,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ~ ( in @ sk2 @ ( powerset @ B ) )
      | ( ( in @ A @ B )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[273,29966]) ).

thf(40693,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ~ ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ),
    inference(pattern_uni,[status(thm)],[40692:[bind(A,$thf( binunion @ sk3 @ sk4 )),bind(B,$thf( powerset @ sk3 ))]]) ).

thf(42872,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
       != sk4 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,40693]) ).

thf(42873,plain,
    ( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk3 ) ) )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 ) ),
    inference(pattern_uni,[status(thm)],[42872:[bind(A,$thf( powerset @ sk3 )),bind(B,$thf( sk2 ))]]) ).

thf(1893,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[162,1815]) ).

thf(1917,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[1893]) ).

thf(1937,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1917]) ).

thf(12146,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
       != ( powerset @ sk4 ) )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,11775]) ).

thf(12314,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
       != ( powerset @ sk4 ) )
      | ( A != sk2 )
      | ( ( powerset @ A )
       != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[12146]) ).

thf(12396,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[12314]) ).

thf(12593,plain,
    ( ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) )
    | ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk2 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(eqfactor_ordered,[status(thm)],[12396]) ).

thf(12600,plain,
    ( ( ( powerset @ sk2 )
     != sk2 )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk2 )
    | ( ( powerset @ sk2 )
     != sk4 ) ),
    inference(simp,[status(thm)],[12593]) ).

thf(83,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ B @ A ) @ A )
       != ( in @ sk3 @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14,12]) ).

thf(91,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( sk1 @ B @ A )
       != sk3 )
      | ( A
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[83]) ).

thf(96,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( sk1 @ A @ ( powerset @ sk2 ) )
       != sk3 ) ),
    inference(simp,[status(thm)],[91]) ).

thf(114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ C @ B )
      | ( in @ C @ A )
      | ( ( in @ sk4 @ sk2 )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[70,19]) ).

thf(121,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ C @ B )
      | ( sk4 != B )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[114]) ).

thf(124,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ A )
      | ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ B @ sk4 )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[121]) ).

thf(47078,plain,
    ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
   != ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,13]) ).

thf(47204,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[47078]) ).

thf(50231,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[47204]) ).

thf(207,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binunion @ A @ B ) )
      | ( in @ C @ A )
      | ( in @ C @ B )
      | ( D
       != ( ~ ( in @ C @ ( binunion @ A @ B ) ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[18]) ).

thf(224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( binunion @ B @ C ) )
      | ( in @ A @ B )
      | ( in @ A @ C ) ),
    inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( F )),bind(D,$thf( ~ ( in @ F @ ( binunion @ H @ I ) ) ))]]) ).

thf(225,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( binunion @ B @ C ) )
      | ( in @ A @ B )
      | ( in @ A @ C ) ),
    inference(simp,[status(thm)],[224]) ).

thf(25573,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk3 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[24965,1277]) ).

thf(25706,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk3 ) )
      | ( A
       != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[25573]) ).

thf(25908,plain,
    ( ( ( powerset @ ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) ) )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[25706]) ).

thf(1441,plain,
    ( ( ( powerset @ sk2 )
     != sk3 )
    | ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk4 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[165,1277]) ).

thf(1461,plain,
    ( ( ( powerset @ sk2 )
     != sk3 )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1441]) ).

thf(13014,plain,
    ! [A: $i] :
      ( ( ( binunion @ sk3 @ sk4 )
       != ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,1426]) ).

thf(13112,plain,
    ! [A: $i] :
      ( ( ( binunion @ sk3 @ sk4 )
       != ( powerset @ ( powerset @ sk2 ) ) )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ A )
       != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[13014]) ).

thf(13154,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ ( powerset @ sk2 ) ) )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[13112]) ).

thf(30070,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ( ( powerset @ sk3 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[30013]) ).

thf(30150,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ( ( powerset @ sk3 )
     != sk2 ) ),
    inference(simp,[status(thm)],[30070]) ).

thf(1867,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ A ) )
     != ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,1815]) ).

thf(1904,plain,
    ! [A: $i] :
      ( ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ A )
       != ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[1867]) ).

thf(1932,plain,
    ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
   != ( powerset @ ( binunion @ sk3 @ sk4 ) ) ),
    inference(simp,[status(thm)],[1904]) ).

thf(30087,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ sk3 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[29998]) ).

thf(30153,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ sk3 )
     != sk2 ) ),
    inference(simp,[status(thm)],[30087]) ).

thf(1686,plain,
    ! [C: $o,B: $o,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | B
      | C ),
    inference(prim_subst,[status(thm)],[948:[bind(A,$thf( C | D ))]]) ).

thf(1714,plain,
    ! [C: $o,B: $o,A: $i] :
      ( B
      | C
      | ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) ) ),
    inference(cnf,[status(esa)],[1686]) ).

thf(1715,plain,
    ! [C: $o,B: $o,A: $i] :
      ( B
      | C
      | ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) ) ),
    inference(simp,[status(thm)],[1714]) ).

thf(14985,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk3 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[13531,159]) ).

thf(14986,plain,
    ( ~ ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) )
    | ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[14985:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( binunion @ sk3 @ sk3 ))]]) ).

thf(40282,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,29675]) ).

thf(40343,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( powerset @ sk3 )
       != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[40282]) ).

thf(40479,plain,
    ( ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[40343]) ).

thf(132,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
       != ( in @ sk4 @ ( powerset @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[71]) ).

thf(134,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
       != ( in @ sk4 @ ( powerset @ A ) ) ) ),
    inference(simp,[status(thm)],[132]) ).

thf(10918,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( sk1 @ sk2 @ ( powerset @ sk2 ) ) )
       != ( powerset @ sk2 ) )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[92,8912]) ).

thf(11043,plain,
    ! [A: $i] :
      ( ( ( sk1 @ sk2 @ ( powerset @ sk2 ) )
       != sk2 )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ A )
       != sk3 ) ),
    inference(simp,[status(thm)],[10918]) ).

thf(11153,plain,
    ( ( ( sk1 @ sk2 @ ( powerset @ sk2 ) )
     != sk2 )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 ) ),
    inference(simp,[status(thm)],[11043]) ).

thf(804,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk3 )
      | ( in @ sk3 @ B )
      | ( ( in @ A @ ( powerset @ sk2 ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[302,29]) ).

thf(805,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
     != sk3 )
    | ( in @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[804:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(9008,plain,
    ( ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ sk2 ) )
   != sk2 ),
    inference(simp,[status(thm)],[8916]) ).

thf(13819,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
       != ( in @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[13531,42]) ).

thf(13942,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( binunion @ sk3 @ sk3 )
       != A )
      | ( ( powerset @ sk2 )
       != sk4 ) ),
    inference(simp,[status(thm)],[13819]) ).

thf(13968,plain,
    ( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
    | ( ( powerset @ sk2 )
     != sk4 ) ),
    inference(simp,[status(thm)],[13942]) ).

thf(3988,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk4 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ B @ A )
       != ( in @ A @ ( powerset @ sk4 ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[68]) ).

thf(4020,plain,
    ( ~ ( in @ ( powerset @ sk4 ) @ ( powerset @ sk4 ) )
    | ( in @ ( powerset @ sk4 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[3988:[bind(A,$thf( powerset @ sk4 )),bind(B,$thf( powerset @ sk4 ))]]) ).

thf(47116,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ ( powerset @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,4020]) ).

thf(47178,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ sk4 )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[47116]) ).

thf(47269,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[47178]) ).

thf(49708,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ sk2 )
     != sk4 ) ),
    inference(simp,[status(thm)],[47269]) ).

thf(29975,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ ( powerset @ sk3 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,15197]) ).

thf(30065,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ sk3 )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[29975]) ).

thf(30148,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[30065]) ).

thf(32391,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ sk2 )
     != sk3 ) ),
    inference(simp,[status(thm)],[30148]) ).

thf(275,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ( in @ C @ ( powerset @ B ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( sk1 @ C @ B ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[110,12]) ).

thf(276,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk4 )
      | ( in @ A @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( sk1 @ D @ sk2 )),bind(B,$thf( sk2 )),bind(C,$thf( D ))]]) ).

thf(282,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk4 )
      | ( in @ A @ ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[276]) ).

thf(411,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk4 )
      | ( in @ sk3 @ B )
      | ( ( in @ A @ ( powerset @ sk2 ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[282,29]) ).

thf(412,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
     != sk4 )
    | ( in @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[411:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(4130,plain,
    ( ( sk4 != sk3 )
    | ( sk4 != sk4 ) ),
    inference(simp,[status(thm)],[3795]) ).

thf(4131,plain,
    sk4 != sk3,
    inference(simp,[status(thm)],[4130]) ).

thf(40,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ( in @ C @ A )
      | ( ( in @ C @ B )
       != ( in @ B @ ( powerset @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[19]) ).

thf(41,plain,
    ! [A: $i] :
      ( ~ ( in @ ( powerset @ A ) @ ( powerset @ A ) )
      | ( in @ ( powerset @ A ) @ A ) ),
    inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( D )),bind(B,$thf( powerset @ D )),bind(C,$thf( powerset @ D ))]]) ).

thf(44,plain,
    ! [A: $i] :
      ( ~ ( in @ ( powerset @ A ) @ ( powerset @ A ) )
      | ( in @ ( powerset @ A ) @ A ) ),
    inference(simp,[status(thm)],[41]) ).

thf(1753,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk3 )
      | ( in @ ( powerset @ B ) @ B )
      | ( ( in @ A @ ( powerset @ sk2 ) )
       != ( in @ ( powerset @ B ) @ ( powerset @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[302,44]) ).

thf(1754,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
     != sk3 )
    | ( in @ ( powerset @ sk2 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[1753:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(172,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ( in @ B @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ B @ A ) @ A )
       != ( in @ sk3 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[163,12]) ).

thf(174,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( powerset @ sk2 )
       != sk3 )
      | ( ( sk1 @ B @ A )
       != sk3 )
      | ( A != sk2 ) ),
    inference(simp,[status(thm)],[172]) ).

thf(180,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( powerset @ sk2 )
       != sk3 )
      | ( ( sk1 @ A @ sk2 )
       != sk3 ) ),
    inference(simp,[status(thm)],[174]) ).

thf(256,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ( in @ B @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ B @ A ) @ A )
       != ( in @ sk4 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[165,12]) ).

thf(259,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( powerset @ sk2 )
       != sk3 )
      | ( ( sk1 @ B @ A )
       != sk4 )
      | ( A != sk2 ) ),
    inference(simp,[status(thm)],[256]) ).

thf(264,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( powerset @ sk2 )
       != sk3 )
      | ( ( sk1 @ A @ sk2 )
       != sk4 ) ),
    inference(simp,[status(thm)],[259]) ).

thf(1880,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[110,1815]) ).

thf(1924,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[1880]) ).

thf(1927,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1924]) ).

thf(3748,plain,
    ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
   != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3587,1277]) ).

thf(3783,plain,
    ( ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[3748]) ).

thf(6422,plain,
    ( ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[3783]) ).

thf(30042,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ sk4 ) )
      | ( in @ B @ sk2 )
      | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,68]) ).

thf(30043,plain,
    ( ~ ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) )
    | ( in @ ( powerset @ sk3 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[30042:[bind(A,$thf( powerset @ ( powerset @ sk2 ) )),bind(B,$thf( powerset @ sk3 ))]]) ).

thf(47087,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) )
     != ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,30043]) ).

thf(47194,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[47087]) ).

thf(47275,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[47194]) ).

thf(401,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk4 )
      | ( ( in @ A @ ( powerset @ sk2 ) )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[282,13]) ).

thf(402,plain,
    ( ( powerset @ ( sk1 @ ( binunion @ sk3 @ sk4 ) @ sk2 ) )
   != sk4 ),
    inference(pattern_uni,[status(thm)],[401:[bind(A,$thf( binunion @ sk3 @ sk4 ))]]) ).

thf(47113,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,29675]) ).

thf(47165,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( powerset @ sk4 )
       != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[47113]) ).

thf(47262,plain,
    ( ( in @ ( powerset @ sk4 ) @ ( powerset @ sk2 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[47165]) ).

thf(54559,plain,
    ( ( in @ ( powerset @ sk4 ) @ ( powerset @ sk2 ) )
    | ( ( powerset @ sk2 )
     != sk4 ) ),
    inference(simp,[status(thm)],[47262]) ).

thf(29953,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,3794]) ).

thf(30078,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ sk3 )
       != A )
      | ( ( binunion @ sk4 @ sk4 )
       != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[29953]) ).

thf(30151,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[30078]) ).

thf(52,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ B @ ( powerset @ A ) ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[8]) ).

thf(55,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( sk1 @ B @ A )
       != B )
      | ( B
       != ( powerset @ A ) ) ),
    inference(simp,[status(thm)],[52]) ).

thf(59,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ A ) @ ( powerset @ A ) )
      | ( ( sk1 @ ( powerset @ A ) @ A )
       != ( powerset @ A ) ) ),
    inference(simp,[status(thm)],[55]) ).

thf(1438,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ( ( in @ A @ sk2 )
       != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[110,1277]) ).

thf(1464,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ( A
       != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[1438]) ).

thf(1488,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != sk4 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1464]) ).

thf(16507,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk3 ) @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk3 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,15197]) ).

thf(16643,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk3 ) @ sk2 )
      | ( A
       != ( powerset @ sk3 ) )
      | ( ( powerset @ A )
       != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[16507]) ).

thf(16653,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk3 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[16643]) ).

thf(17020,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ sk3 )
     != sk3 ) ),
    inference(simp,[status(thm)],[16653]) ).

thf(30276,plain,
    ( ( ( powerset @ sk3 )
     != sk3 )
    | ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) )
     != ( in @ ( powerset @ sk3 ) @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[17020,29966]) ).

thf(30313,plain,
    ( ( ( powerset @ sk3 )
     != sk3 )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ sk3 )
     != sk2 ) ),
    inference(simp,[status(thm)],[30276]) ).

thf(54,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(simp,[status(thm)],[52]) ).

thf(34197,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ ( powerset @ sk3 ) @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,30043]) ).

thf(34198,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ ( powerset @ sk2 ) ) @ sk4 ) )
     != sk4 )
    | ( in @ ( powerset @ sk3 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[34197:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ ( powerset @ sk2 ) ))]]) ).

thf(3735,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
       != ( in @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[3587,45]) ).

thf(3766,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( binunion @ sk4 @ sk4 )
       != A )
      | ( ( powerset @ sk2 )
       != sk3 ) ),
    inference(simp,[status(thm)],[3735]) ).

thf(3796,plain,
    ( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
    | ( ( powerset @ sk2 )
     != sk3 ) ),
    inference(simp,[status(thm)],[3766]) ).

thf(15469,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,14847]) ).

thf(15589,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ sk2 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ A )
       != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[15469]) ).

thf(15630,plain,
    ( ( in @ sk3 @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[15589]) ).

thf(41193,plain,
    ( ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) )
    | ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
     != ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[40479,13]) ).

thf(41526,plain,
    ( ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ sk2 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[41193]) ).

thf(41555,plain,
    ( ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[41526]) ).

thf(25022,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk3 @ sk3 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[22961,1815]) ).

thf(25114,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk3 @ sk3 ) )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[25022]) ).

thf(25194,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != ( binunion @ sk3 @ sk3 ) )
    | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[25114]) ).

thf(16514,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ ( powerset @ sk3 ) @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk3 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,15197]) ).

thf(16515,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk3 ) @ sk3 ) )
     != sk3 )
    | ( in @ ( powerset @ sk3 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[16514:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ sk3 ))]]) ).

thf(3487,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ A ) )
      | $false
      | ( in @ ( sk1 @ ( binunion @ sk4 @ sk4 ) @ A ) @ sk2 ) ),
    inference(prim_subst,[status(thm)],[943:[bind(A,$thf( $false ))]]) ).

thf(3532,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ A ) )
      | ( in @ ( sk1 @ ( binunion @ sk4 @ sk4 ) @ A ) @ sk2 ) ),
    inference(simp,[status(thm)],[3487]) ).

thf(47124,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,1289]) ).

thf(47167,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( powerset @ sk4 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47124]) ).

thf(47263,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[47167]) ).

thf(4627,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,3951]) ).

thf(4701,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ sk2 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ A )
       != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[4627]) ).

thf(4716,plain,
    ( ( in @ sk4 @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[4701]) ).

thf(186,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binunion @ A @ B ) )
      | ( in @ C @ A )
      | ( in @ C @ B )
      | ( D
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[18,13]) ).

thf(187,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binunion @ A @ B ) )
      | ( in @ C @ A )
      | ( in @ C @ B ) ),
    inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ))]]) ).

thf(26924,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ sk2 ) )
     != sk3 )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[1489]) ).

thf(29968,plain,
    ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) )
   != ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,1815]) ).

thf(30115,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) )
    | ( ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[29968]) ).

thf(29952,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ ( powerset @ sk2 ) ) )
    | ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,1426]) ).

thf(30060,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ ( powerset @ sk2 ) ) )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[29952]) ).

thf(30147,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ ( powerset @ sk2 ) ) )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[30060]) ).

thf(204,plain,
    ! [E: $o,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( in @ D @ B )
      | ( in @ D @ C )
      | E
      | ( ( in @ ( sk1 @ sk4 @ A ) @ sk2 )
       != ( in @ D @ ( binunion @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[71,18]) ).

thf(221,plain,
    ! [E: $o,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( in @ D @ B )
      | ( in @ D @ C )
      | E
      | ( ( sk1 @ sk4 @ A )
       != D )
      | ( ( binunion @ B @ C )
       != sk2 ) ),
    inference(simp,[status(thm)],[204]) ).

thf(245,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( in @ ( sk1 @ sk4 @ A ) @ B )
      | ( in @ ( sk1 @ sk4 @ A ) @ C )
      | D
      | ( ( binunion @ B @ C )
       != sk2 ) ),
    inference(simp,[status(thm)],[221]) ).

thf(308,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[158,13]) ).

thf(318,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( ( sk1 @ sk3 @ A )
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ sk2 )
       != sk2 ) ),
    inference(simp,[status(thm)],[308]) ).

thf(38,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ B )
      | ~ ( in @ E @ ( powerset @ D ) )
      | ( in @ F @ D )
      | ( ( in @ C @ A )
       != ( in @ F @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[19,19]) ).

thf(39,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ B )
      | ~ ( in @ A @ ( powerset @ D ) )
      | ( in @ C @ D ) ),
    inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).

thf(288,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[162,13]) ).

thf(297,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ sk2 )
       != sk2 ) ),
    inference(simp,[status(thm)],[288]) ).

thf(303,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[297]) ).

thf(30236,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk4 @ sk4 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7109,29966]) ).

thf(30314,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != ( binunion @ sk4 @ sk4 ) )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ sk3 )
       != sk2 ) ),
    inference(simp,[status(thm)],[30236]) ).

thf(30423,plain,
    ( ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
    | ( ( powerset @ sk3 )
     != sk2 ) ),
    inference(simp,[status(thm)],[30314]) ).

thf(11790,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk4 ) )
      | ( ( in @ A @ sk2 )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[7492,13]) ).

thf(11838,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ A ) )
       != ( powerset @ sk4 ) )
      | ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ sk2 )
       != sk2 ) ),
    inference(simp,[status(thm)],[11790]) ).

thf(12015,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[11838]) ).

thf(18789,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,14986]) ).

thf(18790,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk3 ) )
     != sk3 )
    | ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[18789:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ sk2 ))]]) ).

thf(55512,plain,
    ! [C: $o,B: $o,A: $i] :
      ( B
      | ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( C
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1715,1815]) ).

thf(55513,plain,
    ! [B: $o,A: $i] :
      ( B
      | ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) ) ),
    inference(pattern_uni,[status(thm)],[55512:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ ( powerset @ sk2 ) @ ( powerset @ sk2 ) ) ))]]) ).

thf(815,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk3 )
      | ( in @ sk4 @ B )
      | ( ( in @ A @ ( powerset @ sk2 ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[302,35]) ).

thf(816,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
     != sk3 )
    | ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[815:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(53234,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk4 ) @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,47144]) ).

thf(53514,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk4 ) @ sk2 )
      | ( A
       != ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( powerset @ A )
       != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[53234]) ).

thf(53533,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[53514]) ).

thf(47029,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,13955]) ).

thf(47201,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ sk4 )
       != A )
      | ( ( binunion @ sk3 @ sk3 )
       != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47029]) ).

thf(47278,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( binunion @ sk3 @ sk3 )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47201]) ).

thf(192,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( in @ sk4 @ ( powerset @ sk2 ) )
       != ( in @ C @ ( binunion @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,18]) ).

thf(217,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( sk4 != C )
      | ( ( binunion @ A @ B )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[192]) ).

thf(240,plain,
    ! [C: $o,B: $i,A: $i] :
      ( ( in @ sk4 @ A )
      | ( in @ sk4 @ B )
      | C
      | ( ( binunion @ A @ B )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[217]) ).

thf(33904,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ ( powerset @ sk3 ) @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,30003]) ).

thf(33905,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ ( powerset @ sk2 ) ) @ sk3 ) )
     != sk3 )
    | ( in @ ( powerset @ sk3 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[33904:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ ( powerset @ sk2 ) ))]]) ).

thf(1454,plain,
    ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
   != ( in @ sk4 @ ( powerset @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[11,1277]) ).

thf(1460,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[1454]) ).

thf(42858,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
       != sk4 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,40693]) ).

thf(43119,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
       != sk4 )
      | ( A != sk2 )
      | ( ( powerset @ A )
       != ( powerset @ ( powerset @ sk3 ) ) ) ),
    inference(simp,[status(thm)],[42858]) ).

thf(43141,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ( ( powerset @ ( powerset @ sk3 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[43119]) ).

thf(97,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ A ) )
     != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[92,13]) ).

thf(104,plain,
    ! [A: $i] :
      ( ( A
       != ( binunion @ sk3 @ sk4 ) )
      | ( ( powerset @ A )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[97]) ).

thf(108,plain,
    ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
   != ( powerset @ sk2 ) ),
    inference(simp,[status(thm)],[104]) ).

thf(35312,plain,
    ( ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) )
    | ( ( powerset @ sk2 )
     != sk3 ) ),
    inference(simp,[status(thm)],[30162]) ).

thf(47036,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,3794]) ).

thf(47176,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ sk4 )
       != A )
      | ( ( binunion @ sk4 @ sk4 )
       != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47036]) ).

thf(47268,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47176]) ).

thf(4645,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ( in @ sk4 @ sk2 )
      | ( ( in @ A @ sk2 )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[162,3951]) ).

thf(4668,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ sk2 )
      | ( ( powerset @ A )
       != sk3 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ sk4 )
       != sk2 ) ),
    inference(simp,[status(thm)],[4645]) ).

thf(4720,plain,
    ( ( in @ sk4 @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk3 )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[4668]) ).

thf(290,plain,
    ! [E: $o,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ( in @ D @ B )
      | ( in @ D @ C )
      | E
      | ( ( in @ A @ sk2 )
       != ( in @ D @ ( binunion @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[162,18]) ).

thf(300,plain,
    ! [E: $o,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ D @ B )
      | ( in @ D @ C )
      | E
      | ( ( powerset @ A )
       != sk3 )
      | ( A != D )
      | ( ( binunion @ B @ C )
       != sk2 ) ),
    inference(simp,[status(thm)],[290]) ).

thf(306,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( powerset @ C )
       != sk3 )
      | ( ( binunion @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[300]) ).

thf(135,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ ( powerset @ A ) )
      | ( ( sk1 @ sk4 @ A )
       != sk4 )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[132]) ).

thf(30016,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
    | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,7526]) ).

thf(30098,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
    | ( ( powerset @ sk3 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[30016]) ).

thf(30159,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
    | ( ( powerset @ sk3 )
     != sk2 ) ),
    inference(simp,[status(thm)],[30098]) ).

thf(8921,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ ( powerset @ sk4 ) @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,4020]) ).

thf(8922,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk4 ) @ sk4 ) )
     != sk4 )
    | ( in @ ( powerset @ sk4 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[8921:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ sk4 ))]]) ).

thf(182,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( in @ sk3 @ sk2 )
       != ( in @ C @ ( binunion @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[69,18]) ).

thf(218,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( powerset @ sk2 )
       != sk4 )
      | ( sk3 != C )
      | ( ( binunion @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[182]) ).

thf(241,plain,
    ! [C: $o,B: $i,A: $i] :
      ( ( in @ sk3 @ A )
      | ( in @ sk3 @ B )
      | C
      | ( ( powerset @ sk2 )
       != sk4 )
      | ( ( binunion @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[218]) ).

thf(73,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ C @ B )
      | ( in @ C @ A )
      | ( ( in @ sk3 @ sk2 )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[69,19]) ).

thf(78,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ C @ B )
      | ( sk3 != B )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[73]) ).

thf(80,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ A )
      | ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ B @ sk3 )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[78]) ).

thf(27578,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ ( powerset @ sk2 ) ) )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[13154]) ).

thf(1990,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[1411]) ).

thf(13345,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ A ) )
      | $false
      | ( in @ ( sk1 @ ( binunion @ sk3 @ sk3 ) @ A ) @ sk2 ) ),
    inference(prim_subst,[status(thm)],[946:[bind(A,$thf( $false ))]]) ).

thf(13431,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ A ) )
      | ( in @ ( sk1 @ ( binunion @ sk3 @ sk3 ) @ A ) @ sk2 ) ),
    inference(simp,[status(thm)],[13345]) ).

thf(22750,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
       != ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13531,13955]) ).

thf(22877,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( binunion @ sk3 @ sk3 )
       != A )
      | ( ( binunion @ sk3 @ sk3 )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[22750]) ).

thf(22964,plain,
    ( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
    | ( ( binunion @ sk3 @ sk3 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[22877]) ).

thf(44369,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ~ ( in @ sk2 @ ( powerset @ B ) )
      | ( ( in @ A @ B )
       != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[293,1277]) ).

thf(44370,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != sk3 )
    | ~ ( in @ sk2 @ ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[44369:[bind(A,$thf( powerset @ ( binunion @ sk3 @ sk4 ) )),bind(B,$thf( powerset @ ( powerset @ sk2 ) ))]]) ).

thf(30222,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,29966]) ).

thf(30223,plain,
    ( ( powerset @ ( sk1 @ ( binunion @ sk3 @ sk4 ) @ sk3 ) )
   != sk3 ),
    inference(pattern_uni,[status(thm)],[30222:[bind(A,$thf( sk3 )),bind(B,$thf( binunion @ sk3 @ sk4 ))]]) ).

thf(113,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ( in @ B @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ B @ A ) @ A )
       != ( in @ sk4 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[70,12]) ).

thf(119,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( powerset @ sk2 )
       != sk4 )
      | ( ( sk1 @ B @ A )
       != sk4 )
      | ( A != sk2 ) ),
    inference(simp,[status(thm)],[113]) ).

thf(123,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( powerset @ sk2 )
       != sk4 )
      | ( ( sk1 @ A @ sk2 )
       != sk4 ) ),
    inference(simp,[status(thm)],[119]) ).

thf(1437,plain,
    ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
   != ( in @ sk3 @ ( powerset @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[14,1277]) ).

thf(1472,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[1437]) ).

thf(1769,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk4 )
      | ( in @ ( powerset @ B ) @ B )
      | ( ( in @ A @ ( powerset @ sk2 ) )
       != ( in @ ( powerset @ B ) @ ( powerset @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[282,44]) ).

thf(1770,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
     != sk4 )
    | ( in @ ( powerset @ sk2 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[1769:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(13816,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
       != ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13531,3794]) ).

thf(13940,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( binunion @ sk3 @ sk3 )
       != A )
      | ( ( binunion @ sk4 @ sk4 )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[13816]) ).

thf(13967,plain,
    ( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
    | ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[13940]) ).

thf(29994,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,45]) ).

thf(30091,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ sk3 )
       != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk3 ) ),
    inference(simp,[status(thm)],[29994]) ).

thf(30156,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk3 ) ),
    inference(simp,[status(thm)],[30091]) ).

thf(44125,plain,
    ( ( ( sk1 @ sk2 @ ( powerset @ sk3 ) )
     != sk3 )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 ) ),
    inference(simp,[status(thm)],[42873]) ).

thf(82,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ( in @ B @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ B @ A ) @ A )
       != ( in @ sk3 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[69,12]) ).

thf(90,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( powerset @ sk2 )
       != sk4 )
      | ( ( sk1 @ B @ A )
       != sk3 )
      | ( A != sk2 ) ),
    inference(simp,[status(thm)],[82]) ).

thf(95,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ sk2 ) )
      | ( ( powerset @ sk2 )
       != sk4 )
      | ( ( sk1 @ A @ sk2 )
       != sk3 ) ),
    inference(simp,[status(thm)],[90]) ).

thf(47070,plain,
    ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) )
   != ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,29966]) ).

thf(47240,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[47070]) ).

thf(1453,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk4 )
      | ( ( in @ A @ ( powerset @ sk2 ) )
       != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[282,1277]) ).

thf(1478,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk4 )
      | ( A
       != ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[1453]) ).

thf(1484,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ sk2 ) )
     != sk4 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[1478]) ).

thf(252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ C @ B )
      | ( in @ C @ A )
      | ( ( in @ sk4 @ sk2 )
       != ( in @ B @ ( powerset @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[165,19]) ).

thf(258,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ C @ B )
      | ( sk4 != B )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[252]) ).

thf(263,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ A )
      | ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ B @ sk4 )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[258]) ).

thf(5303,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk4 ) @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,4020]) ).

thf(5377,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk4 ) @ sk2 )
      | ( A
       != ( powerset @ sk4 ) )
      | ( ( powerset @ A )
       != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[5303]) ).

thf(5388,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk4 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[5377]) ).

thf(1622,plain,
    ! [C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
      | ( in @ C @ sk2 )
      | ( A
       != ( in @ C @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[948,42]) ).

thf(1623,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ B @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[1622:[bind(A,$thf( in @ D @ sk4 )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).

thf(1716,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ B @ sk2 ) ),
    inference(simp,[status(thm)],[1623]) ).

thf(29959,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) )
       != ( in @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,42]) ).

thf(30119,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ sk3 )
       != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk4 ) ),
    inference(simp,[status(thm)],[29959]) ).

thf(30171,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk4 ) ),
    inference(simp,[status(thm)],[30119]) ).

thf(30273,plain,
    ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) )
   != ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,29966]) ).

thf(30402,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[30273]) ).

thf(6968,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( binunion @ sk4 @ sk4 ) @ ( powerset @ sk2 ) )
       != ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3587,3794]) ).

thf(7033,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( binunion @ sk4 @ sk4 )
       != A )
      | ( ( binunion @ sk4 @ sk4 )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[6968]) ).

thf(7105,plain,
    ( ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
    | ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[7033]) ).

thf(53575,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ sk2 )
     != sk3 ) ),
    inference(simp,[status(thm)],[47240]) ).

thf(47112,plain,
    ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
   != ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,1277]) ).

thf(47184,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47112]) ).

thf(47270,plain,
    ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
   != ( powerset @ sk4 ) ),
    inference(simp,[status(thm)],[47184]) ).

thf(27579,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk2 ) )
    | ( ( binunion @ sk3 @ sk4 )
     != ( binunion @ sk3 @ sk4 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(eqfactor_ordered,[status(thm)],[27578]) ).

thf(27581,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk2 ) )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[27579]) ).

thf(45736,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
       != sk3 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,44370]) ).

thf(45869,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
       != sk3 )
      | ( A != sk2 )
      | ( ( powerset @ A )
       != ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(simp,[status(thm)],[45736]) ).

thf(46012,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != sk3 )
    | ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[45869]) ).

thf(47172,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ( ( powerset @ sk4 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47103]) ).

thf(47265,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[47172]) ).

thf(36,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( powerset @ A ) )
      | ~ ( in @ C @ B )
      | ~ ( in @ F @ E )
      | ( in @ F @ D )
      | ( ( in @ C @ A )
       != ( in @ E @ ( powerset @ D ) ) ) ),
    inference(paramod_ordered,[status(thm)],[19,19]) ).

thf(37,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ ( powerset @ D ) ) )
      | ~ ( in @ B @ A )
      | ~ ( in @ C @ B )
      | ( in @ C @ D ) ),
    inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( powerset @ G )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( C ))]]) ).

thf(43,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ A @ ( powerset @ ( powerset @ D ) ) )
      | ~ ( in @ B @ A )
      | ~ ( in @ C @ B )
      | ( in @ C @ D ) ),
    inference(simp,[status(thm)],[37]) ).

thf(27580,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk2 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[27579]) ).

thf(52053,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk4 ) @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,47093]) ).

thf(52220,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk4 ) @ sk2 )
      | ( A
       != ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( powerset @ A )
       != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[52053]) ).

thf(52383,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[52220]) ).

thf(41161,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ sk2 ) )
       != ( powerset @ sk4 ) )
      | ( in @ A @ sk2 )
      | ( ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) )
       != ( in @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[40479,42]) ).

thf(41500,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( powerset @ sk2 )
       != sk4 )
      | ( ( powerset @ sk3 )
       != A )
      | ( ( powerset @ sk2 )
       != sk4 ) ),
    inference(simp,[status(thm)],[41161]) ).

thf(41546,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ sk2 )
     != sk4 ) ),
    inference(simp,[status(thm)],[41500]) ).

thf(1272,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( in @ sk3 @ sk2 )
       != ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[69,46]) ).

thf(1375,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( sk3 != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[1272]) ).

thf(1421,plain,
    ( ( ( powerset @ sk2 )
     != sk4 )
    | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1375]) ).

thf(6947,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ sk3 @ ( powerset @ sk2 ) )
       != ( in @ A @ ( binunion @ sk4 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14,3794]) ).

thf(7015,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( sk3 != A )
      | ( ( binunion @ sk4 @ sk4 )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[6947]) ).

thf(7089,plain,
    ( ( in @ sk3 @ sk2 )
    | ( ( binunion @ sk4 @ sk4 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[7015]) ).

thf(44752,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
       != sk3 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ sk3 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,44244]) ).

thf(44999,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
       != sk3 )
      | ( A != sk2 )
      | ( ( powerset @ A )
       != ( powerset @ ( powerset @ sk3 ) ) ) ),
    inference(simp,[status(thm)],[44752]) ).

thf(45047,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk3 )
    | ( ( powerset @ ( powerset @ sk3 ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[44999]) ).

thf(6952,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ C @ sk2 )
      | ( ( in @ sk4 @ B )
       != ( in @ C @ ( binunion @ sk4 @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1736,3794]) ).

thf(6953,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[6952:[bind(A,$thf( A )),bind(B,$thf( binunion @ sk4 @ sk4 )),bind(C,$thf( sk4 ))]]) ).

thf(47101,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
    | ( ( in @ ( powerset @ sk4 ) @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( in @ sk2 @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47023,8198]) ).

thf(47209,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
    | ( ( powerset @ sk4 )
     != sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[47101]) ).

thf(47284,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[47209]) ).

thf(13837,plain,
    ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
   != ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[13531,13]) ).

thf(13945,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( binunion @ sk3 @ sk3 ) )
    | ( ( powerset @ sk2 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[13837]) ).

thf(13969,plain,
    ( ( binunion @ sk3 @ sk4 )
   != ( binunion @ sk3 @ sk3 ) ),
    inference(simp,[status(thm)],[13945]) ).

thf(2407,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ D @ ( powerset @ C ) )
      | ( ( in @ B @ sk2 )
       != ( in @ ( sk1 @ D @ C ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1716,12]) ).

thf(2408,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ B @ ( powerset @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[2407:[bind(A,$thf( A )),bind(B,$thf( sk1 @ E @ sk2 )),bind(C,$thf( sk2 )),bind(D,$thf( E ))]]) ).

thf(2534,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ B @ ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[2408]) ).

thf(32009,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ D @ ( powerset @ C ) )
      | ( ( in @ B @ ( powerset @ sk2 ) )
       != ( in @ ( sk1 @ D @ C ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[2534,12]) ).

thf(32010,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(pattern_uni,[status(thm)],[32009:[bind(A,$thf( A )),bind(B,$thf( sk1 @ E @ ( powerset @ sk2 ) )),bind(C,$thf( powerset @ sk2 )),bind(D,$thf( E ))]]) ).

thf(32296,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ B @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[32010]) ).

thf(319,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
       != ( in @ sk3 @ ( powerset @ A ) ) ) ),
    inference(simp,[status(thm)],[317]) ).

thf(343,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ A )
      | ( ( in @ ( powerset @ sk2 ) @ ( powerset @ A ) )
       != ( in @ sk3 @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14,29]) ).

thf(351,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ A )
      | ( ( powerset @ sk2 )
       != sk3 )
      | ( ( powerset @ A )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[343]) ).

thf(18780,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,14986]) ).

thf(19012,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ A )
       != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[18780]) ).

thf(19087,plain,
    ( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[19012]) ).

thf(41146,plain,
    ( ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) )
    | ( ( powerset @ sk2 )
     != sk4 ) ),
    inference(simp,[status(thm)],[40479]) ).

thf(74,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ B @ ( powerset @ A ) )
      | ( in @ C @ A )
      | ( ( in @ sk3 @ sk2 )
       != ( in @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[69,19]) ).

thf(75,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk4 )
      | ~ ( in @ sk2 @ ( powerset @ A ) )
      | ( in @ sk3 @ A ) ),
    inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).

thf(47,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ B @ A ) @ B )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[8,13]) ).

thf(53,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( sk1 @ B @ A )
       != ( binunion @ sk3 @ sk4 ) )
      | ( B
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[47]) ).

thf(58,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk2 ) @ ( powerset @ A ) )
      | ( ( sk1 @ ( powerset @ sk2 ) @ A )
       != ( binunion @ sk3 @ sk4 ) ) ),
    inference(simp,[status(thm)],[53]) ).

thf(208,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( binunion @ A @ B ) )
      | ( in @ C @ A )
      | ( in @ C @ B )
      | ( D
       != ( in @ C @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[18]) ).

thf(222,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( binunion @ C @ A ) )
      | ( in @ B @ C )
      | ( in @ B @ A ) ),
    inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( in @ E @ F ))]]) ).

thf(246,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( in @ B @ ( binunion @ C @ A ) )
      | ( in @ B @ C )
      | ( in @ B @ A ) ),
    inference(simp,[status(thm)],[222]) ).

thf(29967,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( in @ ( binunion @ sk3 @ sk4 ) @ A )
       != ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,46]) ).

thf(30131,plain,
    ! [A: $i] :
      ( ~ ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( binunion @ sk3 @ sk4 )
       != ( powerset @ sk3 ) )
      | ( A
       != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[29967]) ).

thf(30173,plain,
    ( ~ ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[30131]) ).

thf(39607,plain,
    ! [A: $i] :
      ( ( ( binunion @ sk3 @ sk4 )
       != ( powerset @ sk3 ) )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,30173]) ).

thf(39781,plain,
    ! [A: $i] :
      ( ( ( binunion @ sk3 @ sk4 )
       != ( powerset @ sk3 ) )
      | ( A
       != ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( powerset @ A )
       != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[39607]) ).

thf(39874,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[39781]) ).

thf(47357,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,47049]) ).

thf(47358,plain,
    ( ( powerset @ ( sk1 @ ( binunion @ sk3 @ sk4 ) @ sk4 ) )
   != sk4 ),
    inference(pattern_uni,[status(thm)],[47357:[bind(A,$thf( sk4 )),bind(B,$thf( binunion @ sk3 @ sk4 ))]]) ).

thf(271,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ~ ( in @ D @ C )
      | ( in @ D @ B )
      | ( ( in @ A @ sk2 )
       != ( in @ C @ ( powerset @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[110,19]) ).

thf(281,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ D @ B )
      | ( ( powerset @ A )
       != sk4 )
      | ~ ( in @ D @ C )
      | ( A != C )
      | ( ( powerset @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[271]) ).

thf(287,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( ( powerset @ B )
       != sk4 )
      | ~ ( in @ C @ B )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[281]) ).

thf(34183,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk3 ) @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ ( powerset @ sk2 ) ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,30043]) ).

thf(34377,plain,
    ! [A: $i] :
      ( ( in @ ( powerset @ sk3 ) @ sk2 )
      | ( A
       != ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( powerset @ A )
       != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[34183]) ).

thf(34424,plain,
    ( ( in @ ( powerset @ sk3 ) @ sk2 )
    | ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[34377]) ).

thf(54613,plain,
    ( ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) )
    | ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
     != ( in @ ( powerset @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[47262,13]) ).

thf(54824,plain,
    ( ( ( powerset @ sk2 )
     != sk4 )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ sk2 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[54613]) ).

thf(55013,plain,
    ( ( ( powerset @ sk2 )
     != sk4 )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[54824]) ).

thf(7551,plain,
    ! [C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
      | ( in @ sk3 @ ( powerset @ C ) )
      | ( A
       != ( in @ sk2 @ ( powerset @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[948,6122]) ).

thf(7552,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ sk3 @ ( powerset @ B ) ) ),
    inference(pattern_uni,[status(thm)],[7551:[bind(A,$thf( in @ sk2 @ ( powerset @ F ) )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).

thf(7744,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ sk3 @ ( powerset @ B ) ) ),
    inference(simp,[status(thm)],[7552]) ).

thf(8225,plain,
    ! [C: $i,B: $i,A: $o] :
      ( ( in @ ( binunion @ B @ B ) @ ( powerset @ B ) )
      | ( in @ sk4 @ ( powerset @ C ) )
      | ( A
       != ( in @ sk2 @ ( powerset @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[948,6139]) ).

thf(8226,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ sk4 @ ( powerset @ B ) ) ),
    inference(pattern_uni,[status(thm)],[8225:[bind(A,$thf( in @ sk2 @ ( powerset @ F ) )),bind(B,$thf( B )),bind(C,$thf( F ))]]) ).

thf(8412,plain,
    ! [B: $i,A: $i] :
      ( ( in @ ( binunion @ A @ A ) @ ( powerset @ A ) )
      | ( in @ sk4 @ ( powerset @ B ) ) ),
    inference(simp,[status(thm)],[8226]) ).

thf(404,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ A @ sk2 ) )
       != sk4 )
      | ( in @ sk4 @ B )
      | ( ( in @ A @ ( powerset @ sk2 ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[282,35]) ).

thf(405,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk2 ) )
     != sk4 )
    | ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[404:[bind(A,$thf( powerset @ sk2 )),bind(B,$thf( sk2 ))]]) ).

thf(4517,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,3847]) ).

thf(4565,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ sk2 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ A )
       != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[4517]) ).

thf(4597,plain,
    ( ( in @ sk3 @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[4565]) ).

thf(33051,plain,
    ( ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[30099]) ).

thf(4620,plain,
    ! [A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ( in @ sk4 @ sk2 )
      | ( ( in @ A @ sk2 )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[110,3951]) ).

thf(4685,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ sk2 )
      | ( ( powerset @ A )
       != sk4 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ sk4 )
       != sk2 ) ),
    inference(simp,[status(thm)],[4620]) ).

thf(4706,plain,
    ( ( in @ sk4 @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk4 )
    | ( ( powerset @ sk4 )
     != sk2 ) ),
    inference(simp,[status(thm)],[4685]) ).

thf(8885,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,3884]) ).

thf(8886,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk4 ) )
     != sk4 )
    | ( in @ ( binunion @ sk4 @ sk4 ) @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[8885:[bind(A,$thf( sk4 )),bind(B,$thf( powerset @ sk2 ))]]) ).

thf(30019,plain,
    ( ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) )
   != ( in @ ( powerset @ sk3 ) @ ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[29915,1277]) ).

thf(30107,plain,
    ( ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ ( powerset @ sk2 ) ) ) ),
    inference(simp,[status(thm)],[30019]) ).

thf(30165,plain,
    ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
   != ( powerset @ sk3 ) ),
    inference(simp,[status(thm)],[30107]) ).

thf(291,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk3 )
      | ~ ( in @ D @ C )
      | ( in @ D @ B )
      | ( ( in @ A @ sk2 )
       != ( in @ C @ ( powerset @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[162,19]) ).

thf(299,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ D @ B )
      | ( ( powerset @ A )
       != sk3 )
      | ~ ( in @ D @ C )
      | ( A != C )
      | ( ( powerset @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[291]) ).

thf(305,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( ( powerset @ B )
       != sk3 )
      | ~ ( in @ C @ B )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[299]) ).

thf(5404,plain,
    ( ( in @ ( powerset @ sk4 ) @ sk2 )
    | ( ( powerset @ sk4 )
     != sk4 ) ),
    inference(simp,[status(thm)],[5388]) ).

thf(84,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( in @ ( sk1 @ B @ A ) @ A )
       != ( in @ sk4 @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[11,12]) ).

thf(89,plain,
    ! [B: $i,A: $i] :
      ( ( in @ B @ ( powerset @ A ) )
      | ( ( sk1 @ B @ A )
       != sk4 )
      | ( A
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[84]) ).

thf(94,plain,
    ! [A: $i] :
      ( ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) )
      | ( ( sk1 @ A @ ( powerset @ sk2 ) )
       != sk4 ) ),
    inference(simp,[status(thm)],[89]) ).

thf(270,plain,
    ! [E: $o,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ( in @ D @ B )
      | ( in @ D @ C )
      | E
      | ( ( in @ A @ sk2 )
       != ( in @ D @ ( binunion @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[110,18]) ).

thf(277,plain,
    ! [E: $o,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ D @ B )
      | ( in @ D @ C )
      | E
      | ( ( powerset @ A )
       != sk4 )
      | ( A != D )
      | ( ( binunion @ B @ C )
       != sk2 ) ),
    inference(simp,[status(thm)],[270]) ).

thf(283,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( powerset @ C )
       != sk4 )
      | ( ( binunion @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[277]) ).

thf(40816,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ A )
       != sk4 )
      | ~ ( in @ sk2 @ ( powerset @ B ) )
      | ( ( in @ A @ B )
       != ( in @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[273,1277]) ).

thf(40817,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != sk4 )
    | ~ ( in @ sk2 @ ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[40816:[bind(A,$thf( powerset @ ( binunion @ sk3 @ sk4 ) )),bind(B,$thf( powerset @ ( powerset @ sk2 ) ))]]) ).

thf(310,plain,
    ! [E: $o,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( in @ D @ B )
      | ( in @ D @ C )
      | E
      | ( ( in @ ( sk1 @ sk3 @ A ) @ sk2 )
       != ( in @ D @ ( binunion @ B @ C ) ) ) ),
    inference(paramod_ordered,[status(thm)],[158,18]) ).

thf(322,plain,
    ! [E: $o,D: $i,C: $i,B: $i,A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( in @ D @ B )
      | ( in @ D @ C )
      | E
      | ( ( sk1 @ sk3 @ A )
       != D )
      | ( ( binunion @ B @ C )
       != sk2 ) ),
    inference(simp,[status(thm)],[310]) ).

thf(326,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ sk3 @ ( powerset @ A ) )
      | ( in @ ( sk1 @ sk3 @ A ) @ B )
      | ( in @ ( sk1 @ sk3 @ A ) @ C )
      | D
      | ( ( binunion @ B @ C )
       != sk2 ) ),
    inference(simp,[status(thm)],[322]) ).

thf(101,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ C @ ( powerset @ B ) )
      | ( in @ D @ B )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ D @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[92,19]) ).

thf(102,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ ( powerset @ B ) @ ( powerset @ A ) )
      | ( in @ B @ A ) ),
    inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( powerset @ E )),bind(D,$thf( E ))]]) ).

thf(107,plain,
    ! [B: $i,A: $i] :
      ( ~ ( in @ ( powerset @ B ) @ ( powerset @ A ) )
      | ( in @ B @ A ) ),
    inference(simp,[status(thm)],[102]) ).

thf(201,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( in @ sk3 @ sk2 )
       != ( in @ C @ ( binunion @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[163,18]) ).

thf(216,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( powerset @ sk2 )
       != sk3 )
      | ( sk3 != C )
      | ( ( binunion @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[201]) ).

thf(239,plain,
    ! [C: $o,B: $i,A: $i] :
      ( ( in @ sk3 @ A )
      | ( in @ sk3 @ B )
      | C
      | ( ( powerset @ sk2 )
       != sk3 )
      | ( ( binunion @ A @ B )
       != sk2 ) ),
    inference(simp,[status(thm)],[216]) ).

thf(183,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( ( in @ sk3 @ ( powerset @ sk2 ) )
       != ( in @ C @ ( binunion @ A @ B ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14,18]) ).

thf(219,plain,
    ! [D: $o,C: $i,B: $i,A: $i] :
      ( ( in @ C @ A )
      | ( in @ C @ B )
      | D
      | ( sk3 != C )
      | ( ( binunion @ A @ B )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[183]) ).

thf(242,plain,
    ! [C: $o,B: $i,A: $i] :
      ( ( in @ sk3 @ A )
      | ( in @ sk3 @ B )
      | C
      | ( ( binunion @ A @ B )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[219]) ).

thf(15661,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( in @ sk4 @ sk2 )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,15073]) ).

thf(15662,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ sk2 ) @ sk3 ) )
     != sk3 )
    | ( in @ sk4 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[15661:[bind(A,$thf( sk3 )),bind(B,$thf( powerset @ sk2 ))]]) ).

thf(8888,plain,
    ! [B: $i,A: $i] :
      ( ( ( powerset @ ( sk1 @ B @ A ) )
       != A )
      | ( ( in @ B @ ( powerset @ A ) )
       != ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[109,13]) ).

thf(8889,plain,
    ( ( powerset @ ( sk1 @ ( binunion @ sk3 @ sk4 ) @ sk2 ) )
   != sk2 ),
    inference(pattern_uni,[status(thm)],[8888:[bind(A,$thf( sk2 )),bind(B,$thf( binunion @ sk3 @ sk4 ))]]) ).

thf(22704,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ sk3 @ ( powerset @ sk2 ) )
       != ( in @ A @ ( binunion @ sk3 @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[14,13955]) ).

thf(22825,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( sk3 != A )
      | ( ( binunion @ sk3 @ sk3 )
       != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[22704]) ).

thf(22918,plain,
    ( ( in @ sk3 @ sk2 )
    | ( ( binunion @ sk3 @ sk3 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[22825]) ).

thf(13161,plain,
    ( ( ( powerset @ ( sk1 @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) @ sk2 ) )
     != sk4 )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[1484]) ).

thf(1295,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( in @ sk3 @ sk2 )
       != ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[163,46]) ).

thf(1353,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( sk3 != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[1295]) ).

thf(1399,plain,
    ( ( ( powerset @ sk2 )
     != sk3 )
    | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk3 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1353]) ).

thf(6424,plain,
    ( ~ ( in @ ( binunion @ sk3 @ sk4 ) @ ( binunion @ sk4 @ sk4 ) )
    | ( ( powerset @ sk2 )
     != sk2 ) ),
    inference(simp,[status(thm)],[3784]) ).

thf(9992,plain,
    ( ( ( sk1 @ sk2 @ ( powerset @ sk2 ) )
     != sk2 )
    | ( ( powerset @ ( binunion @ sk3 @ sk4 ) )
     != sk4 ) ),
    inference(simp,[status(thm)],[8892]) ).

thf(253,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ B @ ( powerset @ A ) )
      | ( in @ C @ A )
      | ( ( in @ sk4 @ sk2 )
       != ( in @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[165,19]) ).

thf(254,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ sk2 @ ( powerset @ A ) )
      | ( in @ sk4 @ A ) ),
    inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk4 ))]]) ).

thf(35358,plain,
    ( ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) )
    | ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk2 ) )
     != ( in @ ( powerset @ sk3 ) @ ( powerset @ sk2 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[30162,13]) ).

thf(35511,plain,
    ( ( ( powerset @ sk2 )
     != sk3 )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ sk2 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[35358]) ).

thf(35722,plain,
    ( ( ( powerset @ sk2 )
     != sk3 )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[35511]) ).

thf(41527,plain,
    ( ( ( powerset @ sk2 )
     != sk4 )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) )
    | ( ( powerset @ sk2 )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[41193]) ).

thf(41556,plain,
    ( ( ( powerset @ sk2 )
     != sk4 )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[41527]) ).

thf(13839,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( in @ ( binunion @ sk3 @ sk3 ) @ ( powerset @ sk2 ) )
       != ( in @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[13531,45]) ).

thf(13923,plain,
    ! [A: $i] :
      ( ( in @ A @ sk2 )
      | ( ( binunion @ sk3 @ sk3 )
       != A )
      | ( ( powerset @ sk2 )
       != sk3 ) ),
    inference(simp,[status(thm)],[13839]) ).

thf(13962,plain,
    ( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
    | ( ( powerset @ sk2 )
     != sk3 ) ),
    inference(simp,[status(thm)],[13923]) ).

thf(1307,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( ( in @ sk4 @ sk2 )
       != ( in @ A @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[165,46]) ).

thf(1371,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ A )
      | ( sk4 != A )
      | ( ( powerset @ ( powerset @ sk2 ) )
       != sk2 ) ),
    inference(simp,[status(thm)],[1307]) ).

thf(1417,plain,
    ( ( ( powerset @ sk2 )
     != sk3 )
    | ~ ( in @ ( binunion @ sk3 @ sk4 ) @ sk4 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != sk2 ) ),
    inference(simp,[status(thm)],[1371]) ).

thf(111,plain,
    ( ( binunion @ sk3 @ sk4 )
   != sk2 ),
    inference(simp,[status(thm)],[108]) ).

thf(43824,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
       != sk4 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ sk2 @ ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,40817]) ).

thf(44039,plain,
    ! [A: $i] :
      ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
       != sk4 )
      | ( A != sk2 )
      | ( ( powerset @ A )
       != ( powerset @ ( powerset @ ( powerset @ sk2 ) ) ) ) ),
    inference(simp,[status(thm)],[43824]) ).

thf(44091,plain,
    ( ( ( powerset @ ( powerset @ ( binunion @ sk3 @ sk4 ) ) )
     != sk4 )
    | ( ( powerset @ ( powerset @ ( powerset @ sk2 ) ) )
     != ( powerset @ sk2 ) ) ),
    inference(simp,[status(thm)],[44039]) ).

thf(30291,plain,
    ( ( ( powerset @ sk4 )
     != sk4 )
    | ( ( in @ ( binunion @ sk3 @ sk4 ) @ ( powerset @ sk3 ) )
     != ( in @ ( powerset @ sk4 ) @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[5404,29966]) ).

thf(30373,plain,
    ( ( ( powerset @ sk4 )
     != sk4 )
    | ( ( binunion @ sk3 @ sk4 )
     != ( powerset @ sk4 ) )
    | ( ( powerset @ sk3 )
     != sk2 ) ),
    inference(simp,[status(thm)],[30291]) ).

thf(346,plain,
    ! [A: $i] :
      ( ( ( powerset @ sk2 )
       != sk3 )
      | ( in @ sk3 @ A )
      | ( ( in @ ( powerset @ sk2 ) @ ( powerset @ A ) )
       != ( in @ sk4 @ sk2 ) ) ),
    inference(paramod_ordered,[status(thm)],[165,29]) ).

thf(354,plain,
    ! [A: $i] :
      ( ( in @ sk3 @ A )
      | ( ( powerset @ sk2 )
       != sk3 )
      | ( ( powerset @ sk2 )
       != sk4 )
      | ( ( powerset @ A )
       != sk2 ) ),
    inference(simp,[status(thm)],[346]) ).

thf(15654,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk3 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,15073]) ).

thf(15770,plain,
    ! [A: $i] :
      ( ( in @ sk4 @ sk2 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ A )
       != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[15654]) ).

thf(15800,plain,
    ( ( in @ sk4 @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk3 ) ) ),
    inference(simp,[status(thm)],[15770]) ).

thf(18008,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
      | ( ( in @ A @ ( powerset @ A ) )
       != ( in @ ( powerset @ sk2 ) @ ( powerset @ sk4 ) ) ) ),
    inference(paramod_ordered,[status(thm)],[92,13881]) ).

thf(18130,plain,
    ! [A: $i] :
      ( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
      | ( A
       != ( powerset @ sk2 ) )
      | ( ( powerset @ A )
       != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[18008]) ).

thf(18334,plain,
    ( ( in @ ( binunion @ sk3 @ sk3 ) @ sk2 )
    | ( ( powerset @ ( powerset @ sk2 ) )
     != ( powerset @ sk4 ) ) ),
    inference(simp,[status(thm)],[18130]) ).

thf(72875,plain,
    $false,
    inference(e,[status(thm)],[69,8930,47281,1411,13955,1469,138,5857,22012,30003,10901,52387,11504,18691,170,18018,1401,1486,1426,3794,56,22970,2184,28398,47261,57185,13960,22016,34139,22925,42,1475,320,25,47023,24,30162,30149,14,8875,110,802,47259,15477,11510,93,284,325,3951,15073,1479,46,1815,57,29,4595,1489,7492,179,30144,7104,238,25240,12041,14847,26916,46040,47613,30154,293,8892,265,15197,133,44244,116,243,248,25884,6139,7005,1736,3795,47144,47279,6124,6122,30167,302,4609,47264,47282,3884,165,9993,25912,1487,70,12083,92,229,8920,3799,29966,329,25021,8916,30099,3784,948,30163,56249,47093,18402,47636,141,109,47450,42873,526,1937,12600,96,124,50231,225,25908,1461,13154,30150,1932,30153,1715,14986,40479,13,40693,134,11153,6160,805,3587,9008,13968,49708,32391,44767,15290,28903,412,4131,1754,13896,45,1301,180,264,1927,8906,6422,47275,402,54559,52350,30151,59,47204,1488,30313,44,30043,25525,12,54,7109,3783,34198,40459,13531,71,3796,15630,41555,25194,16515,3532,47263,159,4716,187,26924,30115,30147,245,318,39,303,30423,12015,18790,55513,816,53533,47278,240,33905,1460,43141,108,8198,35312,47268,4720,11775,306,135,47289,30159,8922,35,226,3,241,80,162,1420,27578,1990,13431,22964,7526,44370,1277,30223,123,1472,1770,16653,13967,30156,44125,95,47240,29675,1484,263,282,5388,1716,12396,30171,3847,30402,4020,7105,53575,47270,27581,11,46012,47265,43,27580,24965,52383,41546,1421,7089,1289,45047,47049,6953,47284,13969,30148,32296,319,29915,158,17020,351,19087,8912,41146,8,75,58,246,39874,47326,47358,287,34424,14963,55013,26853,1725,47262,7744,8412,405,19,273,4597,33051,4706,8886,30165,2534,305,5404,1710,94,283,40817,326,107,239,242,15662,8889,4118,22918,163,68,13161,47269,1399,6424,9992,30173,254,13881,35722,41556,13962,1417,111,44091,30373,354,22961,15800,18334]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU711^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n017.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Sun May 19 15:25:24 EDT 2024
% 0.15/0.36  % CPUTime  : 
% 0.98/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.18/0.96  % [INFO] 	 Parsing done (101ms). 
% 1.29/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.59/1.17  % [INFO] 	 eprover registered as external prover. 
% 1.59/1.17  % [INFO] 	 cvc4 registered as external prover. 
% 1.59/1.18  % [INFO] 	 Scanning for conjecture ... 
% 1.88/1.24  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.92/1.26  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.92/1.26  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.92/1.27  % [INFO] 	 Type checking passed. 
% 1.92/1.27  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 111.64/20.16  % External prover 'e' found a proof!
% 111.64/20.16  % [INFO] 	 Killing All external provers ... 
% 111.64/20.16  % Time passed: 19642ms (effective reasoning time: 19184ms)
% 111.64/20.16  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 111.64/20.16  % Axioms used in derivation (0): 
% 111.64/20.16  % No. of inferences in proof: 865
% 111.64/20.16  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19642 ms resp. 19184 ms w/o parsing
% 112.51/20.40  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 112.51/20.41  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------