TSTP Solution File: SEU525^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU525^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n020.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 : Thu Aug 31 17:18:14 EDT 2023

% Result   : Theorem 1.53s 1.70s
% Output   : Proof 1.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   47
%            Number of leaves      :  208
% Syntax   : Number of formulae    :  258 ( 114 unt;  12 typ;  46 def)
%            Number of atoms       : 2760 ( 562 equ;   7 cnn)
%            Maximal formula atoms :   96 (  11 avg)
%            Number of connectives : 8947 (1185   ~;  49   |;  18   &;5013   @)
%                                         (  44 <=>;2638  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   51 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  236 ( 236   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   98 (  94 usr;  90 con; 0-2 aty)
%            Number of variables   : 2675 ( 196   ^;2463   !;  16   ?;2675   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_setunion,type,
    setunion: $i > $i ).

thf(ty_eigen__0,type,
    eigen__0: $i > $o ).

thf(ty_setadjoin,type,
    setadjoin: $i > $i > $i ).

thf(ty_descr,type,
    descr: ( $i > $o ) > $i ).

thf(ty_dsetconstr,type,
    dsetconstr: $i > ( $i > $o ) > $i ).

thf(ty_in,type,
    in: $i > $i > $o ).

thf(ty_eigen__1,type,
    eigen__1: $i ).

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

thf(ty_omega,type,
    omega: $i ).

thf(ty_eigen__3,type,
    eigen__3: $i ).

thf(ty_eigen__92,type,
    eigen__92: $i ).

thf(ty_emptyset,type,
    emptyset: $i ).

thf(h0,assumption,
    ! [X1: $i > $o,X2: $i] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: $i] :
          ( ( eigen__0 @ X1 )
         != ( X1 = eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(eigendef_eigen__92,definition,
    ( eigen__92
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( in @ X1 @ eigen__3 )
           => ( in @ X1 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__92])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i] :
        ( ( eigen__0 @ X1 )
       => ( eigen__1 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( in @ eigen__1 @ ( powerset @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( in @ eigen__3 @ ( powerset @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP2
      = ( ! [X1: $i] :
            ( ( in @ X1 @ eigen__1 )
           => ( in @ X1 @ eigen__3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
        = ( ! [X3: $i] :
              ( ( in @ X3 @ X2 )
             => ( in @ X3 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__0 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( in @ eigen__92 @ eigen__3 )
     => ( in @ eigen__92 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP6
      = ( eigen__3 = eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ! [X1: $i] :
          ( ( in @ X1 @ eigen__3 )
         => ( in @ X1 @ eigen__1 ) )
     => ( eigen__1 = eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( eigen__3 != eigen__1 )
     => ( in @ eigen__3 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i] : ( in @ eigen__1 @ ( setadjoin @ eigen__1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( powerset @ eigen__3 ) )
        = ( ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( in @ X2 @ eigen__3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( eigen__1 = eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( setadjoin @ eigen__1 @ X1 ) )
       => ( ( X2 != eigen__1 )
         => ( in @ X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ! [X1: $i] :
          ( ( in @ X1 @ eigen__1 )
         => ( in @ X1 @ eigen__3 ) )
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__3 )
       => ( in @ X1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X2 )
           => ( in @ X3 @ X1 ) )
       => ( in @ X2 @ ( powerset @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X1 )
           => ( in @ X2 @ eigen__3 ) )
       => ( in @ X1 @ ( powerset @ eigen__3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( in @ eigen__1 @ ( setadjoin @ eigen__1 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
       => ( ( X3 != X1 )
         => ( in @ X3 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( eigen__3 = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( in @ X3 @ X2 ) )
       => ( ! [X3: $i] :
              ( ( in @ X3 @ X2 )
             => ( in @ X3 @ X1 ) )
         => ( X1 = X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( eigen__0 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( sP6
     => sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ! [X1: $i] :
        ~ ( in @ X1 @ emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: $i] :
        ~ ! [X2: $i] :
            ( ( eigen__0 @ X2 )
            = ( X2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( in @ eigen__3 @ ( setadjoin @ eigen__1 @ emptyset ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( sP28
     => sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( in @ eigen__92 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( in @ eigen__3 @ emptyset ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ! [X1: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ eigen__1 )
           => ( in @ X2 @ X1 ) )
       => ( ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( in @ X2 @ eigen__1 ) )
         => ( eigen__1 = X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: $i] :
        ( ( in @ X1 @ ( setadjoin @ eigen__1 @ emptyset ) )
       => ( ( X1 != eigen__1 )
         => ( in @ X1 @ emptyset ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ! [X1: $i] :
        ( ( eigen__0 @ X1 )
        = ( X1 = eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__1 )
       => ( in @ X1 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( in @ eigen__92 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(def_exu,definition,
    ( exu
    = ( ^ [X1: $i > $o] :
        ? [X2: $i] :
          ( ( X1 @ X2 )
          & ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( X1 @ X3 )
              @ ( X2 = X3 ) ) ) ) ) ).

thf(def_setextAx,definition,
    ( setextAx
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ( in @ X3 @ X1 )
            <=> ( in @ X3 @ X2 ) )
          @ ( X1 = X2 ) ) ) ) ).

thf(def_emptysetAx,definition,
    ( emptysetAx
    = ( ! [X1: $i] : ( (~) @ ( in @ X1 @ emptyset ) ) ) ) ).

thf(def_setadjoinAx,definition,
    ( setadjoinAx
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
        <=> ( ( X3 = X1 )
            | ( in @ X3 @ X2 ) ) ) ) ) ).

thf(def_powersetAx,definition,
    ( powersetAx
    = ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
        <=> ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X2 )
              @ ( in @ X3 @ X1 ) ) ) ) ) ).

thf(def_setunionAx,definition,
    ( setunionAx
    = ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( setunion @ X1 ) )
        <=> ? [X3: $i] :
              ( ( in @ X2 @ X3 )
              & ( in @ X3 @ X1 ) ) ) ) ) ).

thf(def_omega0Ax,definition,
    ( omega0Ax
    = ( in @ emptyset @ omega ) ) ).

thf(def_omegaSAx,definition,
    ( omegaSAx
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( in @ X1 @ omega )
          @ ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ) ) ).

thf(def_omegaIndAx,definition,
    ( omegaIndAx
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( ( in @ emptyset @ X1 )
            & ! [X2: $i] :
                ( ^ [X3: $o,X4: $o] :
                    ( X3
                   => X4 )
                @ ( ( in @ X2 @ omega )
                  & ( in @ X2 @ X1 ) )
                @ ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
          @ ! [X2: $i] :
              ( ^ [X3: $o,X4: $o] :
                  ( X3
                 => X4 )
              @ ( in @ X2 @ omega )
              @ ( in @ X2 @ X1 ) ) ) ) ) ).

thf(def_replAx,definition,
    ( replAx
    = ( ! [X1: $i > $i > $o,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X2 )
              @ ( exu
                @ ^ [X4: $i] : ( X1 @ X3 @ X4 ) ) )
          @ ? [X3: $i] :
            ! [X4: $i] :
              ( ( in @ X4 @ X3 )
            <=> ? [X5: $i] :
                  ( ( in @ X5 @ X2 )
                  & ( X1 @ X5 @ X4 ) ) ) ) ) ) ).

thf(def_foundationAx,definition,
    ( foundationAx
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ? [X2: $i] : ( in @ X2 @ X1 )
          @ ? [X2: $i] :
              ( ( in @ X2 @ X1 )
              & ( (~)
                @ ? [X3: $i] :
                    ( ( in @ X3 @ X2 )
                    & ( in @ X3 @ X1 ) ) ) ) ) ) ) ).

thf(def_wellorderingAx,definition,
    ( wellorderingAx
    = ( ! [X1: $i] :
        ? [X2: $i] :
          ( ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X2 )
              @ ! [X4: $i] :
                  ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( in @ X4 @ X3 )
                  @ ( in @ X4 @ X1 ) ) )
          & ! [X3: $i,X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( ( in @ X3 @ X1 )
                & ( in @ X4 @ X1 ) )
              @ ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ! [X5: $i] :
                    ( ^ [X6: $o,X7: $o] :
                        ( X6
                       => X7 )
                    @ ( in @ X5 @ X2 )
                    @ ( ( in @ X3 @ X5 )
                    <=> ( in @ X4 @ X5 ) ) )
                @ ( X3 = X4 ) ) )
          & ! [X3: $i,X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( ( in @ X3 @ X2 )
                & ( in @ X4 @ X2 ) )
              @ ( ! [X5: $i] :
                    ( ^ [X6: $o,X7: $o] :
                        ( X6
                       => X7 )
                    @ ( in @ X5 @ X3 )
                    @ ( in @ X5 @ X4 ) )
                | ! [X5: $i] :
                    ( ^ [X6: $o,X7: $o] :
                        ( X6
                       => X7 )
                    @ ( in @ X5 @ X4 )
                    @ ( in @ X5 @ X3 ) ) ) )
          & ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( ! [X4: $i] :
                    ( ^ [X5: $o,X6: $o] :
                        ( X5
                       => X6 )
                    @ ( in @ X4 @ X3 )
                    @ ( in @ X4 @ X1 ) )
                & ? [X4: $i] : ( in @ X4 @ X3 ) )
              @ ? [X4: $i,X5: $i] :
                  ( ( in @ X4 @ X2 )
                  & ( in @ X5 @ X3 )
                  & ( (~)
                    @ ? [X6: $i] :
                        ( ( in @ X6 @ X4 )
                        & ( in @ X6 @ X3 ) ) )
                  & ! [X6: $i] :
                      ( ^ [X7: $o,X8: $o] :
                          ( X7
                         => X8 )
                      @ ( in @ X6 @ X2 )
                      @ ( ! [X7: $i] :
                            ( ^ [X8: $o,X9: $o] :
                                ( X8
                               => X9 )
                            @ ( in @ X7 @ X6 )
                            @ ( in @ X7 @ X4 ) )
                        | ( in @ X5 @ X6 ) ) ) ) ) ) ) ) ).

thf(def_descrp,definition,
    ( descrp
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
          @ ( X1
            @ ( descr
              @ ^ [X2: $i] : ( X1 @ X2 ) ) ) ) ) ) ).

thf(def_dsetconstrI,definition,
    ( dsetconstrI
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( X2 @ X3 )
            @ ( in @ X3
              @ ( dsetconstr @ X1
                @ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ).

thf(def_dsetconstrEL,definition,
    ( dsetconstrEL
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3
            @ ( dsetconstr @ X1
              @ ^ [X4: $i] : ( X2 @ X4 ) ) )
          @ ( in @ X3 @ X1 ) ) ) ) ).

thf(def_dsetconstrER,definition,
    ( dsetconstrER
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3
            @ ( dsetconstr @ X1
              @ ^ [X4: $i] : ( X2 @ X4 ) ) )
          @ ( X2 @ X3 ) ) ) ) ).

thf(def_exuE1,definition,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
          @ ? [X2: $i] :
              ( ( X1 @ X2 )
              & ! [X3: $i] :
                  ( ^ [X4: $o,X5: $o] :
                      ( X4
                     => X5 )
                  @ ( X1 @ X3 )
                  @ ( X2 = X3 ) ) ) ) ) ) ).

thf(def_prop2set,definition,
    ( prop2set
    = ( ^ [X1: $o] :
          ( dsetconstr @ ( powerset @ emptyset )
          @ ^ [X2: $i] : X1 ) ) ) ).

thf(def_prop2setE,definition,
    ( prop2setE
    = ( ! [X1: $o,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ ( prop2set @ X1 ) )
          @ X1 ) ) ) ).

thf(def_emptysetE,definition,
    ( emptysetE
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( in @ X1 @ emptyset )
          @ ! [X2: $o] : X2 ) ) ) ).

thf(def_emptysetimpfalse,definition,
    ( emptysetimpfalse
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( in @ X1 @ emptyset )
          @ sP15 ) ) ) ).

thf(def_notinemptyset,definition,
    ( notinemptyset
    = ( ! [X1: $i] : ( (~) @ ( in @ X1 @ emptyset ) ) ) ) ).

thf(def_exuE3e,definition,
    ( exuE3e
    = ( ! [X1: $i > $o] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( exu
            @ ^ [X2: $i] : ( X1 @ X2 ) )
          @ ? [X2: $i] : ( X1 @ X2 ) ) ) ) ).

thf(def_setext,definition,
    ( setext
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X1 )
              @ ( in @ X3 @ X2 ) )
          @ ( ^ [X3: $o,X4: $o] :
                ( X3
               => X4 )
            @ ! [X3: $i] :
                ( ^ [X4: $o,X5: $o] :
                    ( X4
                   => X5 )
                @ ( in @ X3 @ X2 )
                @ ( in @ X3 @ X1 ) )
            @ ( X1 = X2 ) ) ) ) ) ).

thf(def_emptyI,definition,
    ( emptyI
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ! [X2: $i] : ( (~) @ ( in @ X2 @ X1 ) )
          @ ( X1 = emptyset ) ) ) ) ).

thf(def_noeltsimpempty,definition,
    ( noeltsimpempty
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ! [X2: $i] : ( (~) @ ( in @ X2 @ X1 ) )
          @ ( X1 = emptyset ) ) ) ) ).

thf(def_setbeta,definition,
    ( setbeta
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ( in @ X3
              @ ( dsetconstr @ X1
                @ ^ [X4: $i] : ( X2 @ X4 ) ) )
          <=> ( X2 @ X3 ) ) ) ) ) ).

thf(def_nonempty,definition,
    ( nonempty
    = ( ^ [X1: $i] : ( (~) @ ( X1 = emptyset ) ) ) ) ).

thf(def_nonemptyE1,definition,
    ( nonemptyE1
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ( nonempty @ X1 )
          @ ? [X2: $i] : ( in @ X2 @ X1 ) ) ) ) ).

thf(def_nonemptyI,definition,
    ( nonemptyI
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X1 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( X2 @ X3 )
            @ ( nonempty
              @ ( dsetconstr @ X1
                @ ^ [X4: $i] : ( X2 @ X4 ) ) ) ) ) ) ) ).

thf(def_nonemptyI1,definition,
    ( nonemptyI1
    = ( ! [X1: $i] :
          ( ^ [X2: $o,X3: $o] :
              ( X2
             => X3 )
          @ ? [X2: $i] : ( in @ X2 @ X1 )
          @ ( nonempty @ X1 ) ) ) ) ).

thf(def_setadjoinIL,definition,
    setadjoinIL = sP33 ).

thf(def_emptyinunitempty,definition,
    ( emptyinunitempty
    = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).

thf(def_setadjoinIR,definition,
    ( setadjoinIR
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ X2 )
          @ ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) ) ) ) ).

thf(def_setadjoinE,definition,
    ( setadjoinE
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
          @ ! [X4: $o] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ( X3 = X1 )
                @ X4 )
              @ ( ^ [X5: $o,X6: $o] :
                    ( X5
                   => X6 )
                @ ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( in @ X3 @ X2 )
                  @ X4 )
                @ X4 ) ) ) ) ) ).

thf(def_setadjoinOr,definition,
    ( setadjoinOr
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
          @ ( ( X3 = X1 )
            | ( in @ X3 @ X2 ) ) ) ) ) ).

thf(def_setoftrueEq,definition,
    ( setoftrueEq
    = ( ! [X1: $i] :
          ( ( dsetconstr @ X1
            @ ^ [X2: $i] : $true )
          = X1 ) ) ) ).

thf(def_powersetI,definition,
    ( powersetI
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X2 )
              @ ( in @ X3 @ X1 ) )
          @ ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ).

thf(def_emptyinPowerset,definition,
    ( emptyinPowerset
    = ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) ) ) ) ).

thf(def_emptyInPowerset,definition,
    ( emptyInPowerset
    = ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) ) ) ) ).

thf(def_powersetE,definition,
    ( powersetE
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X2 @ ( powerset @ X1 ) )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( in @ X3 @ X2 )
            @ ( in @ X3 @ X1 ) ) ) ) ) ).

thf(def_setunionI,definition,
    ( setunionI
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( in @ X2 @ X3 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( in @ X3 @ X1 )
            @ ( in @ X2 @ ( setunion @ X1 ) ) ) ) ) ) ).

thf(def_setunionE,definition,
    ( setunionE
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ ( setunion @ X1 ) )
          @ ! [X3: $o] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ! [X4: $i] :
                  ( ^ [X5: $o,X6: $o] :
                      ( X5
                     => X6 )
                  @ ( in @ X2 @ X4 )
                  @ ( ^ [X5: $o,X6: $o] :
                        ( X5
                       => X6 )
                    @ ( in @ X4 @ X1 )
                    @ X3 ) )
              @ X3 ) ) ) ) ).

thf(def_subPowSU,definition,
    ( subPowSU
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ( in @ X2 @ X1 )
          @ ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) ) ) ) ).

thf(exuE2,conjecture,
    ( ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
            = ( in @ X3 @ X2 ) )
       => ( X1 = X2 ) )
   => ( sP26
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
            = ( ( X3 != X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( sP5
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( setunion @ X1 ) )
                = ( ~ ! [X3: $i] :
                        ( ( in @ X2 @ X3 )
                       => ~ ( in @ X3 @ X1 ) ) ) )
           => ( ( in @ emptyset @ omega )
             => ( ! [X1: $i] :
                    ( ( in @ X1 @ omega )
                   => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
               => ( ! [X1: $i] :
                      ( ~ ( ( in @ emptyset @ X1 )
                         => ~ ! [X2: $i] :
                                ( ~ ( ( in @ X2 @ omega )
                                   => ~ ( in @ X2 @ X1 ) )
                               => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                     => ! [X2: $i] :
                          ( ( in @ X2 @ omega )
                         => ( in @ X2 @ X1 ) ) )
                 => ( ! [X1: $i > $i > $o,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ~ ! [X4: $i] :
                                  ( ( X1 @ X3 @ X4 )
                                 => ~ ! [X5: $i] :
                                        ( ( X1 @ X3 @ X5 )
                                       => ( X4 = X5 ) ) ) )
                       => ~ ! [X3: $i] :
                              ~ ! [X4: $i] :
                                  ( ( in @ X4 @ X3 )
                                  = ( ~ ! [X5: $i] :
                                          ( ( in @ X5 @ X2 )
                                         => ~ ( X1 @ X5 @ X4 ) ) ) ) )
                   => ( ! [X1: $i] :
                          ( ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                         => ~ ! [X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ~ ( in @ X3 @ X1 ) ) ) )
                     => ( ! [X1: $i] :
                            ~ ! [X2: $i] :
                                ( ~ ( ~ ( ! [X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X3 )
                                               => ( in @ X4 @ X1 ) ) )
                                       => ~ ! [X3: $i,X4: $i] :
                                              ( ~ ( ( in @ X3 @ X1 )
                                                 => ~ ( in @ X4 @ X1 ) )
                                             => ( ! [X5: $i] :
                                                    ( ( in @ X5 @ X2 )
                                                   => ( ( in @ X3 @ X5 )
                                                      = ( in @ X4 @ X5 ) ) )
                                               => ( X3 = X4 ) ) ) )
                                   => ~ ! [X3: $i,X4: $i] :
                                          ( ~ ( ( in @ X3 @ X2 )
                                             => ~ ( in @ X4 @ X2 ) )
                                         => ( ~ ! [X5: $i] :
                                                  ( ( in @ X5 @ X3 )
                                                 => ( in @ X5 @ X4 ) )
                                           => ! [X5: $i] :
                                                ( ( in @ X5 @ X4 )
                                               => ( in @ X5 @ X3 ) ) ) ) )
                               => ~ ! [X3: $i] :
                                      ( ~ ( ! [X4: $i] :
                                              ( ( in @ X4 @ X3 )
                                             => ( in @ X4 @ X1 ) )
                                         => ! [X4: $i] :
                                              ~ ( in @ X4 @ X3 ) )
                                     => ~ ! [X4: $i,X5: $i] :
                                            ( ~ ( ~ ( ( in @ X4 @ X2 )
                                                   => ~ ( in @ X5 @ X3 ) )
                                               => ~ ! [X6: $i] :
                                                      ( ( in @ X6 @ X4 )
                                                     => ~ ( in @ X6 @ X3 ) ) )
                                           => ~ ! [X6: $i] :
                                                  ( ( in @ X6 @ X2 )
                                                 => ( ~ ! [X7: $i] :
                                                          ( ( in @ X7 @ X6 )
                                                         => ( in @ X7 @ X4 ) )
                                                   => ( in @ X5 @ X6 ) ) ) ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ( X1 @ ( descr @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( in @ X3 @ X1 ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( X2 @ X3 ) )
                               => ( ! [X1: $o,X2: $i] :
                                      ( ( in @ X2
                                        @ ( dsetconstr @ ( powerset @ emptyset )
                                          @ ^ [X3: $i] : X1 ) )
                                     => X1 )
                                 => ( ! [X1: $i] :
                                        ( ( in @ X1 @ emptyset )
                                       => ! [X2: $o] : X2 )
                                   => ( sP26
                                     => ( sP26
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                             => ~ ! [X2: $i] :
                                                    ~ ( X1 @ X2 ) )
                                         => ( sP23
                                           => ( ! [X1: $i] :
                                                  ( ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 )
                                                 => ( X1 = emptyset ) )
                                             => ( ! [X1: $i] :
                                                    ( ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 )
                                                   => ( X1 = emptyset ) )
                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                        = ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( X1 != emptyset )
                                                       => ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ( X2 @ X3 )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != emptyset ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ~ ! [X2: $i] :
                                                                  ~ ( in @ X2 @ X1 )
                                                           => ( X1 != emptyset ) )
                                                       => ( sP33
                                                         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                   => ! [X4: $o] :
                                                                        ( ( ( X3 = X1 )
                                                                         => X4 )
                                                                       => ( ( ( in @ X3 @ X2 )
                                                                           => X4 )
                                                                         => X4 ) ) )
                                                               => ( sP21
                                                                 => ( ! [X1: $i] :
                                                                        ( ( dsetconstr @ X1
                                                                          @ ^ [X2: $i] : ~ sP15 )
                                                                        = X1 )
                                                                   => ( sP18
                                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                               => ( ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ X1 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X2 @ X3 )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                   => ! [X3: $o] :
                                                                                        ( ! [X4: $i] :
                                                                                            ( ( in @ X2 @ X4 )
                                                                                           => ( ( in @ X4 @ X1 )
                                                                                             => X3 ) )
                                                                                       => X3 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ X1 )
                                                                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                                 => ! [X1: $i > $o] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) )
                                                                                     => ~ ! [X2: $i] :
                                                                                            ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                                = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(h1,negated_conjecture,
    ~ ( ! [X1: $i,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
              = ( in @ X3 @ X2 ) )
         => ( X1 = X2 ) )
     => ( sP26
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
              = ( ( X3 != X1 )
               => ( in @ X3 @ X2 ) ) )
         => ( sP5
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X2 @ ( setunion @ X1 ) )
                  = ( ~ ! [X3: $i] :
                          ( ( in @ X2 @ X3 )
                         => ~ ( in @ X3 @ X1 ) ) ) )
             => ( ( in @ emptyset @ omega )
               => ( ! [X1: $i] :
                      ( ( in @ X1 @ omega )
                     => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
                 => ( ! [X1: $i] :
                        ( ~ ( ( in @ emptyset @ X1 )
                           => ~ ! [X2: $i] :
                                  ( ~ ( ( in @ X2 @ omega )
                                     => ~ ( in @ X2 @ X1 ) )
                                 => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                       => ! [X2: $i] :
                            ( ( in @ X2 @ omega )
                           => ( in @ X2 @ X1 ) ) )
                   => ( ! [X1: $i > $i > $o,X2: $i] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ~ ! [X4: $i] :
                                    ( ( X1 @ X3 @ X4 )
                                   => ~ ! [X5: $i] :
                                          ( ( X1 @ X3 @ X5 )
                                         => ( X4 = X5 ) ) ) )
                         => ~ ! [X3: $i] :
                                ~ ! [X4: $i] :
                                    ( ( in @ X4 @ X3 )
                                    = ( ~ ! [X5: $i] :
                                            ( ( in @ X5 @ X2 )
                                           => ~ ( X1 @ X5 @ X4 ) ) ) ) )
                     => ( ! [X1: $i] :
                            ( ~ ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 )
                           => ~ ! [X2: $i] :
                                  ( ( in @ X2 @ X1 )
                                 => ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ~ ( in @ X3 @ X1 ) ) ) )
                       => ( ! [X1: $i] :
                              ~ ! [X2: $i] :
                                  ( ~ ( ~ ( ! [X3: $i] :
                                              ( ( in @ X3 @ X2 )
                                             => ! [X4: $i] :
                                                  ( ( in @ X4 @ X3 )
                                                 => ( in @ X4 @ X1 ) ) )
                                         => ~ ! [X3: $i,X4: $i] :
                                                ( ~ ( ( in @ X3 @ X1 )
                                                   => ~ ( in @ X4 @ X1 ) )
                                               => ( ! [X5: $i] :
                                                      ( ( in @ X5 @ X2 )
                                                     => ( ( in @ X3 @ X5 )
                                                        = ( in @ X4 @ X5 ) ) )
                                                 => ( X3 = X4 ) ) ) )
                                     => ~ ! [X3: $i,X4: $i] :
                                            ( ~ ( ( in @ X3 @ X2 )
                                               => ~ ( in @ X4 @ X2 ) )
                                           => ( ~ ! [X5: $i] :
                                                    ( ( in @ X5 @ X3 )
                                                   => ( in @ X5 @ X4 ) )
                                             => ! [X5: $i] :
                                                  ( ( in @ X5 @ X4 )
                                                 => ( in @ X5 @ X3 ) ) ) ) )
                                 => ~ ! [X3: $i] :
                                        ( ~ ( ! [X4: $i] :
                                                ( ( in @ X4 @ X3 )
                                               => ( in @ X4 @ X1 ) )
                                           => ! [X4: $i] :
                                                ~ ( in @ X4 @ X3 ) )
                                       => ~ ! [X4: $i,X5: $i] :
                                              ( ~ ( ~ ( ( in @ X4 @ X2 )
                                                     => ~ ( in @ X5 @ X3 ) )
                                                 => ~ ! [X6: $i] :
                                                        ( ( in @ X6 @ X4 )
                                                       => ~ ( in @ X6 @ X3 ) ) )
                                             => ~ ! [X6: $i] :
                                                    ( ( in @ X6 @ X2 )
                                                   => ( ~ ! [X7: $i] :
                                                            ( ( in @ X7 @ X6 )
                                                           => ( in @ X7 @ X4 ) )
                                                     => ( in @ X5 @ X6 ) ) ) ) ) )
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) )
                               => ( X1 @ ( descr @ X1 ) ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ( X2 @ X3 )
                                   => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( in @ X3 @ X1 ) )
                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                     => ( X2 @ X3 ) )
                                 => ( ! [X1: $o,X2: $i] :
                                        ( ( in @ X2
                                          @ ( dsetconstr @ ( powerset @ emptyset )
                                            @ ^ [X3: $i] : X1 ) )
                                       => X1 )
                                   => ( ! [X1: $i] :
                                          ( ( in @ X1 @ emptyset )
                                         => ! [X2: $o] : X2 )
                                     => ( sP26
                                       => ( sP26
                                         => ( ! [X1: $i > $o] :
                                                ( ~ ! [X2: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) )
                                               => ~ ! [X2: $i] :
                                                      ~ ( X1 @ X2 ) )
                                           => ( sP23
                                             => ( ! [X1: $i] :
                                                    ( ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 )
                                                   => ( X1 = emptyset ) )
                                               => ( ! [X1: $i] :
                                                      ( ! [X2: $i] :
                                                          ~ ( in @ X2 @ X1 )
                                                     => ( X1 = emptyset ) )
                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                          = ( X2 @ X3 ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ( X1 != emptyset )
                                                         => ~ ! [X2: $i] :
                                                                ~ ( in @ X2 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ( X2 @ X3 )
                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                               != emptyset ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ~ ! [X2: $i] :
                                                                    ~ ( in @ X2 @ X1 )
                                                             => ( X1 != emptyset ) )
                                                         => ( sP33
                                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ X2 )
                                                                   => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                     => ! [X4: $o] :
                                                                          ( ( ( X3 = X1 )
                                                                           => X4 )
                                                                         => ( ( ( in @ X3 @ X2 )
                                                                             => X4 )
                                                                           => X4 ) ) )
                                                                 => ( sP21
                                                                   => ( ! [X1: $i] :
                                                                          ( ( dsetconstr @ X1
                                                                            @ ^ [X2: $i] : ~ sP15 )
                                                                          = X1 )
                                                                     => ( sP18
                                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                                 => ( ( in @ X3 @ X2 )
                                                                                   => ( in @ X3 @ X1 ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X2 @ X3 )
                                                                                   => ( ( in @ X3 @ X1 )
                                                                                     => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                     => ! [X3: $o] :
                                                                                          ( ! [X4: $i] :
                                                                                              ( ( in @ X2 @ X4 )
                                                                                             => ( ( in @ X4 @ X1 )
                                                                                               => X3 ) )
                                                                                         => X3 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( in @ X2 @ X1 )
                                                                                       => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                                   => ! [X1: $i > $o] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) )
                                                                                       => ~ ! [X2: $i] :
                                                                                              ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                  = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[exuE2]) ).

thf(h2,assumption,
    ! [X1: $i,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X1 )
          = ( in @ X3 @ X2 ) )
     => ( X1 = X2 ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP26
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
            = ( ( X3 != X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( sP5
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( setunion @ X1 ) )
                = ( ~ ! [X3: $i] :
                        ( ( in @ X2 @ X3 )
                       => ~ ( in @ X3 @ X1 ) ) ) )
           => ( ( in @ emptyset @ omega )
             => ( ! [X1: $i] :
                    ( ( in @ X1 @ omega )
                   => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
               => ( ! [X1: $i] :
                      ( ~ ( ( in @ emptyset @ X1 )
                         => ~ ! [X2: $i] :
                                ( ~ ( ( in @ X2 @ omega )
                                   => ~ ( in @ X2 @ X1 ) )
                               => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                     => ! [X2: $i] :
                          ( ( in @ X2 @ omega )
                         => ( in @ X2 @ X1 ) ) )
                 => ( ! [X1: $i > $i > $o,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ~ ! [X4: $i] :
                                  ( ( X1 @ X3 @ X4 )
                                 => ~ ! [X5: $i] :
                                        ( ( X1 @ X3 @ X5 )
                                       => ( X4 = X5 ) ) ) )
                       => ~ ! [X3: $i] :
                              ~ ! [X4: $i] :
                                  ( ( in @ X4 @ X3 )
                                  = ( ~ ! [X5: $i] :
                                          ( ( in @ X5 @ X2 )
                                         => ~ ( X1 @ X5 @ X4 ) ) ) ) )
                   => ( ! [X1: $i] :
                          ( ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                         => ~ ! [X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ~ ( in @ X3 @ X1 ) ) ) )
                     => ( ! [X1: $i] :
                            ~ ! [X2: $i] :
                                ( ~ ( ~ ( ! [X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X3 )
                                               => ( in @ X4 @ X1 ) ) )
                                       => ~ ! [X3: $i,X4: $i] :
                                              ( ~ ( ( in @ X3 @ X1 )
                                                 => ~ ( in @ X4 @ X1 ) )
                                             => ( ! [X5: $i] :
                                                    ( ( in @ X5 @ X2 )
                                                   => ( ( in @ X3 @ X5 )
                                                      = ( in @ X4 @ X5 ) ) )
                                               => ( X3 = X4 ) ) ) )
                                   => ~ ! [X3: $i,X4: $i] :
                                          ( ~ ( ( in @ X3 @ X2 )
                                             => ~ ( in @ X4 @ X2 ) )
                                         => ( ~ ! [X5: $i] :
                                                  ( ( in @ X5 @ X3 )
                                                 => ( in @ X5 @ X4 ) )
                                           => ! [X5: $i] :
                                                ( ( in @ X5 @ X4 )
                                               => ( in @ X5 @ X3 ) ) ) ) )
                               => ~ ! [X3: $i] :
                                      ( ~ ( ! [X4: $i] :
                                              ( ( in @ X4 @ X3 )
                                             => ( in @ X4 @ X1 ) )
                                         => ! [X4: $i] :
                                              ~ ( in @ X4 @ X3 ) )
                                     => ~ ! [X4: $i,X5: $i] :
                                            ( ~ ( ~ ( ( in @ X4 @ X2 )
                                                   => ~ ( in @ X5 @ X3 ) )
                                               => ~ ! [X6: $i] :
                                                      ( ( in @ X6 @ X4 )
                                                     => ~ ( in @ X6 @ X3 ) ) )
                                           => ~ ! [X6: $i] :
                                                  ( ( in @ X6 @ X2 )
                                                 => ( ~ ! [X7: $i] :
                                                          ( ( in @ X7 @ X6 )
                                                         => ( in @ X7 @ X4 ) )
                                                   => ( in @ X5 @ X6 ) ) ) ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ( X1 @ ( descr @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( in @ X3 @ X1 ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( X2 @ X3 ) )
                               => ( ! [X1: $o,X2: $i] :
                                      ( ( in @ X2
                                        @ ( dsetconstr @ ( powerset @ emptyset )
                                          @ ^ [X3: $i] : X1 ) )
                                     => X1 )
                                 => ( ! [X1: $i] :
                                        ( ( in @ X1 @ emptyset )
                                       => ! [X2: $o] : X2 )
                                   => ( sP26
                                     => ( sP26
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                             => ~ ! [X2: $i] :
                                                    ~ ( X1 @ X2 ) )
                                         => ( sP23
                                           => ( ! [X1: $i] :
                                                  ( ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 )
                                                 => ( X1 = emptyset ) )
                                             => ( ! [X1: $i] :
                                                    ( ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 )
                                                   => ( X1 = emptyset ) )
                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                        = ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( X1 != emptyset )
                                                       => ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ( X2 @ X3 )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != emptyset ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ~ ! [X2: $i] :
                                                                  ~ ( in @ X2 @ X1 )
                                                           => ( X1 != emptyset ) )
                                                       => ( sP33
                                                         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                   => ! [X4: $o] :
                                                                        ( ( ( X3 = X1 )
                                                                         => X4 )
                                                                       => ( ( ( in @ X3 @ X2 )
                                                                           => X4 )
                                                                         => X4 ) ) )
                                                               => ( sP21
                                                                 => ( ! [X1: $i] :
                                                                        ( ( dsetconstr @ X1
                                                                          @ ^ [X2: $i] : ~ sP15 )
                                                                        = X1 )
                                                                   => ( sP18
                                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                               => ( ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ X1 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X2 @ X3 )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                   => ! [X3: $o] :
                                                                                        ( ! [X4: $i] :
                                                                                            ( ( in @ X2 @ X4 )
                                                                                           => ( ( in @ X4 @ X1 )
                                                                                             => X3 ) )
                                                                                       => X3 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ X1 )
                                                                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                                 => ! [X1: $i > $o] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) )
                                                                                     => ~ ! [X2: $i] :
                                                                                            ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                                = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP26,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
          = ( ( X3 != X1 )
           => ( in @ X3 @ X2 ) ) )
     => ( sP5
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( setunion @ X1 ) )
              = ( ~ ! [X3: $i] :
                      ( ( in @ X2 @ X3 )
                     => ~ ( in @ X3 @ X1 ) ) ) )
         => ( ( in @ emptyset @ omega )
           => ( ! [X1: $i] :
                  ( ( in @ X1 @ omega )
                 => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
             => ( ! [X1: $i] :
                    ( ~ ( ( in @ emptyset @ X1 )
                       => ~ ! [X2: $i] :
                              ( ~ ( ( in @ X2 @ omega )
                                 => ~ ( in @ X2 @ X1 ) )
                             => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                   => ! [X2: $i] :
                        ( ( in @ X2 @ omega )
                       => ( in @ X2 @ X1 ) ) )
               => ( ! [X1: $i > $i > $o,X2: $i] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ~ ! [X4: $i] :
                                ( ( X1 @ X3 @ X4 )
                               => ~ ! [X5: $i] :
                                      ( ( X1 @ X3 @ X5 )
                                     => ( X4 = X5 ) ) ) )
                     => ~ ! [X3: $i] :
                            ~ ! [X4: $i] :
                                ( ( in @ X4 @ X3 )
                                = ( ~ ! [X5: $i] :
                                        ( ( in @ X5 @ X2 )
                                       => ~ ( X1 @ X5 @ X4 ) ) ) ) )
                 => ( ! [X1: $i] :
                        ( ~ ! [X2: $i] :
                              ~ ( in @ X2 @ X1 )
                       => ~ ! [X2: $i] :
                              ( ( in @ X2 @ X1 )
                             => ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ~ ( in @ X3 @ X1 ) ) ) )
                   => ( ! [X1: $i] :
                          ~ ! [X2: $i] :
                              ( ~ ( ~ ( ! [X3: $i] :
                                          ( ( in @ X3 @ X2 )
                                         => ! [X4: $i] :
                                              ( ( in @ X4 @ X3 )
                                             => ( in @ X4 @ X1 ) ) )
                                     => ~ ! [X3: $i,X4: $i] :
                                            ( ~ ( ( in @ X3 @ X1 )
                                               => ~ ( in @ X4 @ X1 ) )
                                           => ( ! [X5: $i] :
                                                  ( ( in @ X5 @ X2 )
                                                 => ( ( in @ X3 @ X5 )
                                                    = ( in @ X4 @ X5 ) ) )
                                             => ( X3 = X4 ) ) ) )
                                 => ~ ! [X3: $i,X4: $i] :
                                        ( ~ ( ( in @ X3 @ X2 )
                                           => ~ ( in @ X4 @ X2 ) )
                                       => ( ~ ! [X5: $i] :
                                                ( ( in @ X5 @ X3 )
                                               => ( in @ X5 @ X4 ) )
                                         => ! [X5: $i] :
                                              ( ( in @ X5 @ X4 )
                                             => ( in @ X5 @ X3 ) ) ) ) )
                             => ~ ! [X3: $i] :
                                    ( ~ ( ! [X4: $i] :
                                            ( ( in @ X4 @ X3 )
                                           => ( in @ X4 @ X1 ) )
                                       => ! [X4: $i] :
                                            ~ ( in @ X4 @ X3 ) )
                                   => ~ ! [X4: $i,X5: $i] :
                                          ( ~ ( ~ ( ( in @ X4 @ X2 )
                                                 => ~ ( in @ X5 @ X3 ) )
                                             => ~ ! [X6: $i] :
                                                    ( ( in @ X6 @ X4 )
                                                   => ~ ( in @ X6 @ X3 ) ) )
                                         => ~ ! [X6: $i] :
                                                ( ( in @ X6 @ X2 )
                                               => ( ~ ! [X7: $i] :
                                                        ( ( in @ X7 @ X6 )
                                                       => ( in @ X7 @ X4 ) )
                                                 => ( in @ X5 @ X6 ) ) ) ) ) )
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) )
                           => ( X1 @ ( descr @ X1 ) ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ( X2 @ X3 )
                               => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                               => ( in @ X3 @ X1 ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( X2 @ X3 ) )
                             => ( ! [X1: $o,X2: $i] :
                                    ( ( in @ X2
                                      @ ( dsetconstr @ ( powerset @ emptyset )
                                        @ ^ [X3: $i] : X1 ) )
                                   => X1 )
                               => ( ! [X1: $i] :
                                      ( ( in @ X1 @ emptyset )
                                     => ! [X2: $o] : X2 )
                                 => ( sP26
                                   => ( sP26
                                     => ( ! [X1: $i > $o] :
                                            ( ~ ! [X2: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) )
                                           => ~ ! [X2: $i] :
                                                  ~ ( X1 @ X2 ) )
                                       => ( sP23
                                         => ( ! [X1: $i] :
                                                ( ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 )
                                               => ( X1 = emptyset ) )
                                           => ( ! [X1: $i] :
                                                  ( ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 )
                                                 => ( X1 = emptyset ) )
                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                      = ( X2 @ X3 ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ( X1 != emptyset )
                                                     => ~ ! [X2: $i] :
                                                            ~ ( in @ X2 @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ( X2 @ X3 )
                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                           != emptyset ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ~ ! [X2: $i] :
                                                                ~ ( in @ X2 @ X1 )
                                                         => ( X1 != emptyset ) )
                                                     => ( sP33
                                                       => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ X2 )
                                                               => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                 => ! [X4: $o] :
                                                                      ( ( ( X3 = X1 )
                                                                       => X4 )
                                                                     => ( ( ( in @ X3 @ X2 )
                                                                         => X4 )
                                                                       => X4 ) ) )
                                                             => ( sP21
                                                               => ( ! [X1: $i] :
                                                                      ( ( dsetconstr @ X1
                                                                        @ ^ [X2: $i] : ~ sP15 )
                                                                      = X1 )
                                                                 => ( sP18
                                                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                             => ( ( in @ X3 @ X2 )
                                                                               => ( in @ X3 @ X1 ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X2 @ X3 )
                                                                               => ( ( in @ X3 @ X1 )
                                                                                 => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                 => ! [X3: $o] :
                                                                                      ( ! [X4: $i] :
                                                                                          ( ( in @ X2 @ X4 )
                                                                                         => ( ( in @ X4 @ X1 )
                                                                                           => X3 ) )
                                                                                     => X3 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ X1 )
                                                                                   => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                               => ! [X1: $i > $o] :
                                                                                    ( ~ ! [X2: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) )
                                                                                   => ~ ! [X2: $i] :
                                                                                          ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                              = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
      = ( ( X3 != X1 )
       => ( in @ X3 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ( sP5
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( setunion @ X1 ) )
            = ( ~ ! [X3: $i] :
                    ( ( in @ X2 @ X3 )
                   => ~ ( in @ X3 @ X1 ) ) ) )
       => ( ( in @ emptyset @ omega )
         => ( ! [X1: $i] :
                ( ( in @ X1 @ omega )
               => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
           => ( ! [X1: $i] :
                  ( ~ ( ( in @ emptyset @ X1 )
                     => ~ ! [X2: $i] :
                            ( ~ ( ( in @ X2 @ omega )
                               => ~ ( in @ X2 @ X1 ) )
                           => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                 => ! [X2: $i] :
                      ( ( in @ X2 @ omega )
                     => ( in @ X2 @ X1 ) ) )
             => ( ! [X1: $i > $i > $o,X2: $i] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ~ ! [X4: $i] :
                              ( ( X1 @ X3 @ X4 )
                             => ~ ! [X5: $i] :
                                    ( ( X1 @ X3 @ X5 )
                                   => ( X4 = X5 ) ) ) )
                   => ~ ! [X3: $i] :
                          ~ ! [X4: $i] :
                              ( ( in @ X4 @ X3 )
                              = ( ~ ! [X5: $i] :
                                      ( ( in @ X5 @ X2 )
                                     => ~ ( X1 @ X5 @ X4 ) ) ) ) )
               => ( ! [X1: $i] :
                      ( ~ ! [X2: $i] :
                            ~ ( in @ X2 @ X1 )
                     => ~ ! [X2: $i] :
                            ( ( in @ X2 @ X1 )
                           => ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ~ ( in @ X3 @ X1 ) ) ) )
                 => ( ! [X1: $i] :
                        ~ ! [X2: $i] :
                            ( ~ ( ~ ( ! [X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ! [X4: $i] :
                                            ( ( in @ X4 @ X3 )
                                           => ( in @ X4 @ X1 ) ) )
                                   => ~ ! [X3: $i,X4: $i] :
                                          ( ~ ( ( in @ X3 @ X1 )
                                             => ~ ( in @ X4 @ X1 ) )
                                         => ( ! [X5: $i] :
                                                ( ( in @ X5 @ X2 )
                                               => ( ( in @ X3 @ X5 )
                                                  = ( in @ X4 @ X5 ) ) )
                                           => ( X3 = X4 ) ) ) )
                               => ~ ! [X3: $i,X4: $i] :
                                      ( ~ ( ( in @ X3 @ X2 )
                                         => ~ ( in @ X4 @ X2 ) )
                                     => ( ~ ! [X5: $i] :
                                              ( ( in @ X5 @ X3 )
                                             => ( in @ X5 @ X4 ) )
                                       => ! [X5: $i] :
                                            ( ( in @ X5 @ X4 )
                                           => ( in @ X5 @ X3 ) ) ) ) )
                           => ~ ! [X3: $i] :
                                  ( ~ ( ! [X4: $i] :
                                          ( ( in @ X4 @ X3 )
                                         => ( in @ X4 @ X1 ) )
                                     => ! [X4: $i] :
                                          ~ ( in @ X4 @ X3 ) )
                                 => ~ ! [X4: $i,X5: $i] :
                                        ( ~ ( ~ ( ( in @ X4 @ X2 )
                                               => ~ ( in @ X5 @ X3 ) )
                                           => ~ ! [X6: $i] :
                                                  ( ( in @ X6 @ X4 )
                                                 => ~ ( in @ X6 @ X3 ) ) )
                                       => ~ ! [X6: $i] :
                                              ( ( in @ X6 @ X2 )
                                             => ( ~ ! [X7: $i] :
                                                      ( ( in @ X7 @ X6 )
                                                     => ( in @ X7 @ X4 ) )
                                               => ( in @ X5 @ X6 ) ) ) ) ) )
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) )
                         => ( X1 @ ( descr @ X1 ) ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ( X2 @ X3 )
                             => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                             => ( in @ X3 @ X1 ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                               => ( X2 @ X3 ) )
                           => ( ! [X1: $o,X2: $i] :
                                  ( ( in @ X2
                                    @ ( dsetconstr @ ( powerset @ emptyset )
                                      @ ^ [X3: $i] : X1 ) )
                                 => X1 )
                             => ( ! [X1: $i] :
                                    ( ( in @ X1 @ emptyset )
                                   => ! [X2: $o] : X2 )
                               => ( sP26
                                 => ( sP26
                                   => ( ! [X1: $i > $o] :
                                          ( ~ ! [X2: $i] :
                                                ( ( X1 @ X2 )
                                               => ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) )
                                         => ~ ! [X2: $i] :
                                                ~ ( X1 @ X2 ) )
                                     => ( sP23
                                       => ( ! [X1: $i] :
                                              ( ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 )
                                             => ( X1 = emptyset ) )
                                         => ( ! [X1: $i] :
                                                ( ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 )
                                               => ( X1 = emptyset ) )
                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                    = ( X2 @ X3 ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ( X1 != emptyset )
                                                   => ~ ! [X2: $i] :
                                                          ~ ( in @ X2 @ X1 ) )
                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( X2 @ X3 )
                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                         != emptyset ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 )
                                                       => ( X1 != emptyset ) )
                                                   => ( sP33
                                                     => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ X2 )
                                                             => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                               => ! [X4: $o] :
                                                                    ( ( ( X3 = X1 )
                                                                     => X4 )
                                                                   => ( ( ( in @ X3 @ X2 )
                                                                       => X4 )
                                                                     => X4 ) ) )
                                                           => ( sP21
                                                             => ( ! [X1: $i] :
                                                                    ( ( dsetconstr @ X1
                                                                      @ ^ [X2: $i] : ~ sP15 )
                                                                    = X1 )
                                                               => ( sP18
                                                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                           => ( ( in @ X3 @ X2 )
                                                                             => ( in @ X3 @ X1 ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X2 @ X3 )
                                                                             => ( ( in @ X3 @ X1 )
                                                                               => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                               => ! [X3: $o] :
                                                                                    ( ! [X4: $i] :
                                                                                        ( ( in @ X2 @ X4 )
                                                                                       => ( ( in @ X4 @ X1 )
                                                                                         => X3 ) )
                                                                                   => X3 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X2 @ X1 )
                                                                                 => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                             => ! [X1: $i > $o] :
                                                                                  ( ~ ! [X2: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) )
                                                                                 => ~ ! [X2: $i] :
                                                                                        ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                            = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( setunion @ X1 ) )
          = ( ~ ! [X3: $i] :
                  ( ( in @ X2 @ X3 )
                 => ~ ( in @ X3 @ X1 ) ) ) )
     => ( ( in @ emptyset @ omega )
       => ( ! [X1: $i] :
              ( ( in @ X1 @ omega )
             => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
         => ( ! [X1: $i] :
                ( ~ ( ( in @ emptyset @ X1 )
                   => ~ ! [X2: $i] :
                          ( ~ ( ( in @ X2 @ omega )
                             => ~ ( in @ X2 @ X1 ) )
                         => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
               => ! [X2: $i] :
                    ( ( in @ X2 @ omega )
                   => ( in @ X2 @ X1 ) ) )
           => ( ! [X1: $i > $i > $o,X2: $i] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ~ ! [X4: $i] :
                            ( ( X1 @ X3 @ X4 )
                           => ~ ! [X5: $i] :
                                  ( ( X1 @ X3 @ X5 )
                                 => ( X4 = X5 ) ) ) )
                 => ~ ! [X3: $i] :
                        ~ ! [X4: $i] :
                            ( ( in @ X4 @ X3 )
                            = ( ~ ! [X5: $i] :
                                    ( ( in @ X5 @ X2 )
                                   => ~ ( X1 @ X5 @ X4 ) ) ) ) )
             => ( ! [X1: $i] :
                    ( ~ ! [X2: $i] :
                          ~ ( in @ X2 @ X1 )
                   => ~ ! [X2: $i] :
                          ( ( in @ X2 @ X1 )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ~ ( in @ X3 @ X1 ) ) ) )
               => ( ! [X1: $i] :
                      ~ ! [X2: $i] :
                          ( ~ ( ~ ( ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ! [X4: $i] :
                                          ( ( in @ X4 @ X3 )
                                         => ( in @ X4 @ X1 ) ) )
                                 => ~ ! [X3: $i,X4: $i] :
                                        ( ~ ( ( in @ X3 @ X1 )
                                           => ~ ( in @ X4 @ X1 ) )
                                       => ( ! [X5: $i] :
                                              ( ( in @ X5 @ X2 )
                                             => ( ( in @ X3 @ X5 )
                                                = ( in @ X4 @ X5 ) ) )
                                         => ( X3 = X4 ) ) ) )
                             => ~ ! [X3: $i,X4: $i] :
                                    ( ~ ( ( in @ X3 @ X2 )
                                       => ~ ( in @ X4 @ X2 ) )
                                   => ( ~ ! [X5: $i] :
                                            ( ( in @ X5 @ X3 )
                                           => ( in @ X5 @ X4 ) )
                                     => ! [X5: $i] :
                                          ( ( in @ X5 @ X4 )
                                         => ( in @ X5 @ X3 ) ) ) ) )
                         => ~ ! [X3: $i] :
                                ( ~ ( ! [X4: $i] :
                                        ( ( in @ X4 @ X3 )
                                       => ( in @ X4 @ X1 ) )
                                   => ! [X4: $i] :
                                        ~ ( in @ X4 @ X3 ) )
                               => ~ ! [X4: $i,X5: $i] :
                                      ( ~ ( ~ ( ( in @ X4 @ X2 )
                                             => ~ ( in @ X5 @ X3 ) )
                                         => ~ ! [X6: $i] :
                                                ( ( in @ X6 @ X4 )
                                               => ~ ( in @ X6 @ X3 ) ) )
                                     => ~ ! [X6: $i] :
                                            ( ( in @ X6 @ X2 )
                                           => ( ~ ! [X7: $i] :
                                                    ( ( in @ X7 @ X6 )
                                                   => ( in @ X7 @ X4 ) )
                                             => ( in @ X5 @ X6 ) ) ) ) ) )
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) )
                       => ( X1 @ ( descr @ X1 ) ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ( X2 @ X3 )
                           => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                           => ( in @ X3 @ X1 ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                             => ( X2 @ X3 ) )
                         => ( ! [X1: $o,X2: $i] :
                                ( ( in @ X2
                                  @ ( dsetconstr @ ( powerset @ emptyset )
                                    @ ^ [X3: $i] : X1 ) )
                               => X1 )
                           => ( ! [X1: $i] :
                                  ( ( in @ X1 @ emptyset )
                                 => ! [X2: $o] : X2 )
                             => ( sP26
                               => ( sP26
                                 => ( ! [X1: $i > $o] :
                                        ( ~ ! [X2: $i] :
                                              ( ( X1 @ X2 )
                                             => ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) )
                                       => ~ ! [X2: $i] :
                                              ~ ( X1 @ X2 ) )
                                   => ( sP23
                                     => ( ! [X1: $i] :
                                            ( ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 )
                                           => ( X1 = emptyset ) )
                                       => ( ! [X1: $i] :
                                              ( ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 )
                                             => ( X1 = emptyset ) )
                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                  = ( X2 @ X3 ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ( X1 != emptyset )
                                                 => ~ ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 ) )
                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ( X2 @ X3 )
                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                       != emptyset ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ~ ! [X2: $i] :
                                                            ~ ( in @ X2 @ X1 )
                                                     => ( X1 != emptyset ) )
                                                 => ( sP33
                                                   => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ X2 )
                                                           => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                             => ! [X4: $o] :
                                                                  ( ( ( X3 = X1 )
                                                                   => X4 )
                                                                 => ( ( ( in @ X3 @ X2 )
                                                                     => X4 )
                                                                   => X4 ) ) )
                                                         => ( sP21
                                                           => ( ! [X1: $i] :
                                                                  ( ( dsetconstr @ X1
                                                                    @ ^ [X2: $i] : ~ sP15 )
                                                                  = X1 )
                                                             => ( sP18
                                                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                         => ( ( in @ X3 @ X2 )
                                                                           => ( in @ X3 @ X1 ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X2 @ X3 )
                                                                           => ( ( in @ X3 @ X1 )
                                                                             => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                             => ! [X3: $o] :
                                                                                  ( ! [X4: $i] :
                                                                                      ( ( in @ X2 @ X4 )
                                                                                     => ( ( in @ X4 @ X1 )
                                                                                       => X3 ) )
                                                                                 => X3 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X2 @ X1 )
                                                                               => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                           => ! [X1: $i > $o] :
                                                                                ( ~ ! [X2: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) )
                                                                               => ~ ! [X2: $i] :
                                                                                      ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                          = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ ( setunion @ X1 ) )
      = ( ~ ! [X3: $i] :
              ( ( in @ X2 @ X3 )
             => ~ ( in @ X3 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ ( ( in @ emptyset @ omega )
     => ( ! [X1: $i] :
            ( ( in @ X1 @ omega )
           => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
       => ( ! [X1: $i] :
              ( ~ ( ( in @ emptyset @ X1 )
                 => ~ ! [X2: $i] :
                        ( ~ ( ( in @ X2 @ omega )
                           => ~ ( in @ X2 @ X1 ) )
                       => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
             => ! [X2: $i] :
                  ( ( in @ X2 @ omega )
                 => ( in @ X2 @ X1 ) ) )
         => ( ! [X1: $i > $i > $o,X2: $i] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ~ ! [X4: $i] :
                          ( ( X1 @ X3 @ X4 )
                         => ~ ! [X5: $i] :
                                ( ( X1 @ X3 @ X5 )
                               => ( X4 = X5 ) ) ) )
               => ~ ! [X3: $i] :
                      ~ ! [X4: $i] :
                          ( ( in @ X4 @ X3 )
                          = ( ~ ! [X5: $i] :
                                  ( ( in @ X5 @ X2 )
                                 => ~ ( X1 @ X5 @ X4 ) ) ) ) )
           => ( ! [X1: $i] :
                  ( ~ ! [X2: $i] :
                        ~ ( in @ X2 @ X1 )
                 => ~ ! [X2: $i] :
                        ( ( in @ X2 @ X1 )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ~ ( in @ X3 @ X1 ) ) ) )
             => ( ! [X1: $i] :
                    ~ ! [X2: $i] :
                        ( ~ ( ~ ( ! [X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ! [X4: $i] :
                                        ( ( in @ X4 @ X3 )
                                       => ( in @ X4 @ X1 ) ) )
                               => ~ ! [X3: $i,X4: $i] :
                                      ( ~ ( ( in @ X3 @ X1 )
                                         => ~ ( in @ X4 @ X1 ) )
                                     => ( ! [X5: $i] :
                                            ( ( in @ X5 @ X2 )
                                           => ( ( in @ X3 @ X5 )
                                              = ( in @ X4 @ X5 ) ) )
                                       => ( X3 = X4 ) ) ) )
                           => ~ ! [X3: $i,X4: $i] :
                                  ( ~ ( ( in @ X3 @ X2 )
                                     => ~ ( in @ X4 @ X2 ) )
                                 => ( ~ ! [X5: $i] :
                                          ( ( in @ X5 @ X3 )
                                         => ( in @ X5 @ X4 ) )
                                   => ! [X5: $i] :
                                        ( ( in @ X5 @ X4 )
                                       => ( in @ X5 @ X3 ) ) ) ) )
                       => ~ ! [X3: $i] :
                              ( ~ ( ! [X4: $i] :
                                      ( ( in @ X4 @ X3 )
                                     => ( in @ X4 @ X1 ) )
                                 => ! [X4: $i] :
                                      ~ ( in @ X4 @ X3 ) )
                             => ~ ! [X4: $i,X5: $i] :
                                    ( ~ ( ~ ( ( in @ X4 @ X2 )
                                           => ~ ( in @ X5 @ X3 ) )
                                       => ~ ! [X6: $i] :
                                              ( ( in @ X6 @ X4 )
                                             => ~ ( in @ X6 @ X3 ) ) )
                                   => ~ ! [X6: $i] :
                                          ( ( in @ X6 @ X2 )
                                         => ( ~ ! [X7: $i] :
                                                  ( ( in @ X7 @ X6 )
                                                 => ( in @ X7 @ X4 ) )
                                           => ( in @ X5 @ X6 ) ) ) ) ) )
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) )
                     => ( X1 @ ( descr @ X1 ) ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ( X2 @ X3 )
                         => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                         => ( in @ X3 @ X1 ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                           => ( X2 @ X3 ) )
                       => ( ! [X1: $o,X2: $i] :
                              ( ( in @ X2
                                @ ( dsetconstr @ ( powerset @ emptyset )
                                  @ ^ [X3: $i] : X1 ) )
                             => X1 )
                         => ( ! [X1: $i] :
                                ( ( in @ X1 @ emptyset )
                               => ! [X2: $o] : X2 )
                           => ( sP26
                             => ( sP26
                               => ( ! [X1: $i > $o] :
                                      ( ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) )
                                     => ~ ! [X2: $i] :
                                            ~ ( X1 @ X2 ) )
                                 => ( sP23
                                   => ( ! [X1: $i] :
                                          ( ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 )
                                         => ( X1 = emptyset ) )
                                     => ( ! [X1: $i] :
                                            ( ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 )
                                           => ( X1 = emptyset ) )
                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                = ( X2 @ X3 ) ) )
                                         => ( ! [X1: $i] :
                                                ( ( X1 != emptyset )
                                               => ~ ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 ) )
                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ( X2 @ X3 )
                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                     != emptyset ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ~ ! [X2: $i] :
                                                          ~ ( in @ X2 @ X1 )
                                                   => ( X1 != emptyset ) )
                                               => ( sP33
                                                 => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                           => ! [X4: $o] :
                                                                ( ( ( X3 = X1 )
                                                                 => X4 )
                                                               => ( ( ( in @ X3 @ X2 )
                                                                   => X4 )
                                                                 => X4 ) ) )
                                                       => ( sP21
                                                         => ( ! [X1: $i] :
                                                                ( ( dsetconstr @ X1
                                                                  @ ^ [X2: $i] : ~ sP15 )
                                                                = X1 )
                                                           => ( sP18
                                                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                       => ( ( in @ X3 @ X2 )
                                                                         => ( in @ X3 @ X1 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X2 @ X3 )
                                                                         => ( ( in @ X3 @ X1 )
                                                                           => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                           => ! [X3: $o] :
                                                                                ( ! [X4: $i] :
                                                                                    ( ( in @ X2 @ X4 )
                                                                                   => ( ( in @ X4 @ X1 )
                                                                                     => X3 ) )
                                                                               => X3 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X2 @ X1 )
                                                                             => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                         => ! [X1: $i > $o] :
                                                                              ( ~ ! [X2: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) )
                                                                             => ~ ! [X2: $i] :
                                                                                    ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                        = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    in @ emptyset @ omega,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ( ! [X1: $i] :
          ( ( in @ X1 @ omega )
         => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
     => ( ! [X1: $i] :
            ( ~ ( ( in @ emptyset @ X1 )
               => ~ ! [X2: $i] :
                      ( ~ ( ( in @ X2 @ omega )
                         => ~ ( in @ X2 @ X1 ) )
                     => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
           => ! [X2: $i] :
                ( ( in @ X2 @ omega )
               => ( in @ X2 @ X1 ) ) )
       => ( ! [X1: $i > $i > $o,X2: $i] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ~ ! [X4: $i] :
                        ( ( X1 @ X3 @ X4 )
                       => ~ ! [X5: $i] :
                              ( ( X1 @ X3 @ X5 )
                             => ( X4 = X5 ) ) ) )
             => ~ ! [X3: $i] :
                    ~ ! [X4: $i] :
                        ( ( in @ X4 @ X3 )
                        = ( ~ ! [X5: $i] :
                                ( ( in @ X5 @ X2 )
                               => ~ ( X1 @ X5 @ X4 ) ) ) ) )
         => ( ! [X1: $i] :
                ( ~ ! [X2: $i] :
                      ~ ( in @ X2 @ X1 )
               => ~ ! [X2: $i] :
                      ( ( in @ X2 @ X1 )
                     => ~ ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ~ ( in @ X3 @ X1 ) ) ) )
           => ( ! [X1: $i] :
                  ~ ! [X2: $i] :
                      ( ~ ( ~ ( ! [X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ! [X4: $i] :
                                      ( ( in @ X4 @ X3 )
                                     => ( in @ X4 @ X1 ) ) )
                             => ~ ! [X3: $i,X4: $i] :
                                    ( ~ ( ( in @ X3 @ X1 )
                                       => ~ ( in @ X4 @ X1 ) )
                                   => ( ! [X5: $i] :
                                          ( ( in @ X5 @ X2 )
                                         => ( ( in @ X3 @ X5 )
                                            = ( in @ X4 @ X5 ) ) )
                                     => ( X3 = X4 ) ) ) )
                         => ~ ! [X3: $i,X4: $i] :
                                ( ~ ( ( in @ X3 @ X2 )
                                   => ~ ( in @ X4 @ X2 ) )
                               => ( ~ ! [X5: $i] :
                                        ( ( in @ X5 @ X3 )
                                       => ( in @ X5 @ X4 ) )
                                 => ! [X5: $i] :
                                      ( ( in @ X5 @ X4 )
                                     => ( in @ X5 @ X3 ) ) ) ) )
                     => ~ ! [X3: $i] :
                            ( ~ ( ! [X4: $i] :
                                    ( ( in @ X4 @ X3 )
                                   => ( in @ X4 @ X1 ) )
                               => ! [X4: $i] :
                                    ~ ( in @ X4 @ X3 ) )
                           => ~ ! [X4: $i,X5: $i] :
                                  ( ~ ( ~ ( ( in @ X4 @ X2 )
                                         => ~ ( in @ X5 @ X3 ) )
                                     => ~ ! [X6: $i] :
                                            ( ( in @ X6 @ X4 )
                                           => ~ ( in @ X6 @ X3 ) ) )
                                 => ~ ! [X6: $i] :
                                        ( ( in @ X6 @ X2 )
                                       => ( ~ ! [X7: $i] :
                                                ( ( in @ X7 @ X6 )
                                               => ( in @ X7 @ X4 ) )
                                         => ( in @ X5 @ X6 ) ) ) ) ) )
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) )
                   => ( X1 @ ( descr @ X1 ) ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ( X2 @ X3 )
                       => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                       => ( in @ X3 @ X1 ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                         => ( X2 @ X3 ) )
                     => ( ! [X1: $o,X2: $i] :
                            ( ( in @ X2
                              @ ( dsetconstr @ ( powerset @ emptyset )
                                @ ^ [X3: $i] : X1 ) )
                           => X1 )
                       => ( ! [X1: $i] :
                              ( ( in @ X1 @ emptyset )
                             => ! [X2: $o] : X2 )
                         => ( sP26
                           => ( sP26
                             => ( ! [X1: $i > $o] :
                                    ( ~ ! [X2: $i] :
                                          ( ( X1 @ X2 )
                                         => ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) )
                                   => ~ ! [X2: $i] :
                                          ~ ( X1 @ X2 ) )
                               => ( sP23
                                 => ( ! [X1: $i] :
                                        ( ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 )
                                       => ( X1 = emptyset ) )
                                   => ( ! [X1: $i] :
                                          ( ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 )
                                         => ( X1 = emptyset ) )
                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                              = ( X2 @ X3 ) ) )
                                       => ( ! [X1: $i] :
                                              ( ( X1 != emptyset )
                                             => ~ ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 ) )
                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ( X2 @ X3 )
                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                   != emptyset ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ~ ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 )
                                                 => ( X1 != emptyset ) )
                                             => ( sP33
                                               => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                         => ! [X4: $o] :
                                                              ( ( ( X3 = X1 )
                                                               => X4 )
                                                             => ( ( ( in @ X3 @ X2 )
                                                                 => X4 )
                                                               => X4 ) ) )
                                                     => ( sP21
                                                       => ( ! [X1: $i] :
                                                              ( ( dsetconstr @ X1
                                                                @ ^ [X2: $i] : ~ sP15 )
                                                              = X1 )
                                                         => ( sP18
                                                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                     => ( ( in @ X3 @ X2 )
                                                                       => ( in @ X3 @ X1 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X2 @ X3 )
                                                                       => ( ( in @ X3 @ X1 )
                                                                         => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                         => ! [X3: $o] :
                                                                              ( ! [X4: $i] :
                                                                                  ( ( in @ X2 @ X4 )
                                                                                 => ( ( in @ X4 @ X1 )
                                                                                   => X3 ) )
                                                                             => X3 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X2 @ X1 )
                                                                           => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                       => ! [X1: $i > $o] :
                                                                            ( ~ ! [X2: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) )
                                                                           => ~ ! [X2: $i] :
                                                                                  ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                      = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ omega )
     => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ ( ! [X1: $i] :
          ( ~ ( ( in @ emptyset @ X1 )
             => ~ ! [X2: $i] :
                    ( ~ ( ( in @ X2 @ omega )
                       => ~ ( in @ X2 @ X1 ) )
                   => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
         => ! [X2: $i] :
              ( ( in @ X2 @ omega )
             => ( in @ X2 @ X1 ) ) )
     => ( ! [X1: $i > $i > $o,X2: $i] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X2 )
               => ~ ! [X4: $i] :
                      ( ( X1 @ X3 @ X4 )
                     => ~ ! [X5: $i] :
                            ( ( X1 @ X3 @ X5 )
                           => ( X4 = X5 ) ) ) )
           => ~ ! [X3: $i] :
                  ~ ! [X4: $i] :
                      ( ( in @ X4 @ X3 )
                      = ( ~ ! [X5: $i] :
                              ( ( in @ X5 @ X2 )
                             => ~ ( X1 @ X5 @ X4 ) ) ) ) )
       => ( ! [X1: $i] :
              ( ~ ! [X2: $i] :
                    ~ ( in @ X2 @ X1 )
             => ~ ! [X2: $i] :
                    ( ( in @ X2 @ X1 )
                   => ~ ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ~ ( in @ X3 @ X1 ) ) ) )
         => ( ! [X1: $i] :
                ~ ! [X2: $i] :
                    ( ~ ( ~ ( ! [X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ! [X4: $i] :
                                    ( ( in @ X4 @ X3 )
                                   => ( in @ X4 @ X1 ) ) )
                           => ~ ! [X3: $i,X4: $i] :
                                  ( ~ ( ( in @ X3 @ X1 )
                                     => ~ ( in @ X4 @ X1 ) )
                                 => ( ! [X5: $i] :
                                        ( ( in @ X5 @ X2 )
                                       => ( ( in @ X3 @ X5 )
                                          = ( in @ X4 @ X5 ) ) )
                                   => ( X3 = X4 ) ) ) )
                       => ~ ! [X3: $i,X4: $i] :
                              ( ~ ( ( in @ X3 @ X2 )
                                 => ~ ( in @ X4 @ X2 ) )
                             => ( ~ ! [X5: $i] :
                                      ( ( in @ X5 @ X3 )
                                     => ( in @ X5 @ X4 ) )
                               => ! [X5: $i] :
                                    ( ( in @ X5 @ X4 )
                                   => ( in @ X5 @ X3 ) ) ) ) )
                   => ~ ! [X3: $i] :
                          ( ~ ( ! [X4: $i] :
                                  ( ( in @ X4 @ X3 )
                                 => ( in @ X4 @ X1 ) )
                             => ! [X4: $i] :
                                  ~ ( in @ X4 @ X3 ) )
                         => ~ ! [X4: $i,X5: $i] :
                                ( ~ ( ~ ( ( in @ X4 @ X2 )
                                       => ~ ( in @ X5 @ X3 ) )
                                   => ~ ! [X6: $i] :
                                          ( ( in @ X6 @ X4 )
                                         => ~ ( in @ X6 @ X3 ) ) )
                               => ~ ! [X6: $i] :
                                      ( ( in @ X6 @ X2 )
                                     => ( ~ ! [X7: $i] :
                                              ( ( in @ X7 @ X6 )
                                             => ( in @ X7 @ X4 ) )
                                       => ( in @ X5 @ X6 ) ) ) ) ) )
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) )
                 => ( X1 @ ( descr @ X1 ) ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( X2 @ X3 )
                     => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                     => ( in @ X3 @ X1 ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                       => ( X2 @ X3 ) )
                   => ( ! [X1: $o,X2: $i] :
                          ( ( in @ X2
                            @ ( dsetconstr @ ( powerset @ emptyset )
                              @ ^ [X3: $i] : X1 ) )
                         => X1 )
                     => ( ! [X1: $i] :
                            ( ( in @ X1 @ emptyset )
                           => ! [X2: $o] : X2 )
                       => ( sP26
                         => ( sP26
                           => ( ! [X1: $i > $o] :
                                  ( ~ ! [X2: $i] :
                                        ( ( X1 @ X2 )
                                       => ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) )
                                 => ~ ! [X2: $i] :
                                        ~ ( X1 @ X2 ) )
                             => ( sP23
                               => ( ! [X1: $i] :
                                      ( ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 )
                                     => ( X1 = emptyset ) )
                                 => ( ! [X1: $i] :
                                        ( ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 )
                                       => ( X1 = emptyset ) )
                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                            = ( X2 @ X3 ) ) )
                                     => ( ! [X1: $i] :
                                            ( ( X1 != emptyset )
                                           => ~ ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 ) )
                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ( X2 @ X3 )
                                               => ( ( dsetconstr @ X1 @ X2 )
                                                 != emptyset ) ) )
                                         => ( ! [X1: $i] :
                                                ( ~ ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 )
                                               => ( X1 != emptyset ) )
                                           => ( sP33
                                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                       => ! [X4: $o] :
                                                            ( ( ( X3 = X1 )
                                                             => X4 )
                                                           => ( ( ( in @ X3 @ X2 )
                                                               => X4 )
                                                             => X4 ) ) )
                                                   => ( sP21
                                                     => ( ! [X1: $i] :
                                                            ( ( dsetconstr @ X1
                                                              @ ^ [X2: $i] : ~ sP15 )
                                                            = X1 )
                                                       => ( sP18
                                                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                   => ( ( in @ X3 @ X2 )
                                                                     => ( in @ X3 @ X1 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X2 @ X3 )
                                                                     => ( ( in @ X3 @ X1 )
                                                                       => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                       => ! [X3: $o] :
                                                                            ( ! [X4: $i] :
                                                                                ( ( in @ X2 @ X4 )
                                                                               => ( ( in @ X4 @ X1 )
                                                                                 => X3 ) )
                                                                           => X3 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X2 @ X1 )
                                                                         => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                     => ! [X1: $i > $o] :
                                                                          ( ~ ! [X2: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) )
                                                                         => ~ ! [X2: $i] :
                                                                                ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                    = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    ! [X1: $i] :
      ( ~ ( ( in @ emptyset @ X1 )
         => ~ ! [X2: $i] :
                ( ~ ( ( in @ X2 @ omega )
                   => ~ ( in @ X2 @ X1 ) )
               => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
     => ! [X2: $i] :
          ( ( in @ X2 @ omega )
         => ( in @ X2 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h17,assumption,
    ~ ( ! [X1: $i > $i > $o,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X2 )
             => ~ ! [X4: $i] :
                    ( ( X1 @ X3 @ X4 )
                   => ~ ! [X5: $i] :
                          ( ( X1 @ X3 @ X5 )
                         => ( X4 = X5 ) ) ) )
         => ~ ! [X3: $i] :
                ~ ! [X4: $i] :
                    ( ( in @ X4 @ X3 )
                    = ( ~ ! [X5: $i] :
                            ( ( in @ X5 @ X2 )
                           => ~ ( X1 @ X5 @ X4 ) ) ) ) )
     => ( ! [X1: $i] :
            ( ~ ! [X2: $i] :
                  ~ ( in @ X2 @ X1 )
           => ~ ! [X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ~ ! [X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ~ ( in @ X3 @ X1 ) ) ) )
       => ( ! [X1: $i] :
              ~ ! [X2: $i] :
                  ( ~ ( ~ ( ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ! [X4: $i] :
                                  ( ( in @ X4 @ X3 )
                                 => ( in @ X4 @ X1 ) ) )
                         => ~ ! [X3: $i,X4: $i] :
                                ( ~ ( ( in @ X3 @ X1 )
                                   => ~ ( in @ X4 @ X1 ) )
                               => ( ! [X5: $i] :
                                      ( ( in @ X5 @ X2 )
                                     => ( ( in @ X3 @ X5 )
                                        = ( in @ X4 @ X5 ) ) )
                                 => ( X3 = X4 ) ) ) )
                     => ~ ! [X3: $i,X4: $i] :
                            ( ~ ( ( in @ X3 @ X2 )
                               => ~ ( in @ X4 @ X2 ) )
                           => ( ~ ! [X5: $i] :
                                    ( ( in @ X5 @ X3 )
                                   => ( in @ X5 @ X4 ) )
                             => ! [X5: $i] :
                                  ( ( in @ X5 @ X4 )
                                 => ( in @ X5 @ X3 ) ) ) ) )
                 => ~ ! [X3: $i] :
                        ( ~ ( ! [X4: $i] :
                                ( ( in @ X4 @ X3 )
                               => ( in @ X4 @ X1 ) )
                           => ! [X4: $i] :
                                ~ ( in @ X4 @ X3 ) )
                       => ~ ! [X4: $i,X5: $i] :
                              ( ~ ( ~ ( ( in @ X4 @ X2 )
                                     => ~ ( in @ X5 @ X3 ) )
                                 => ~ ! [X6: $i] :
                                        ( ( in @ X6 @ X4 )
                                       => ~ ( in @ X6 @ X3 ) ) )
                             => ~ ! [X6: $i] :
                                    ( ( in @ X6 @ X2 )
                                   => ( ~ ! [X7: $i] :
                                            ( ( in @ X7 @ X6 )
                                           => ( in @ X7 @ X4 ) )
                                     => ( in @ X5 @ X6 ) ) ) ) ) )
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) )
               => ( X1 @ ( descr @ X1 ) ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ( X2 @ X3 )
                   => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                   => ( in @ X3 @ X1 ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                     => ( X2 @ X3 ) )
                 => ( ! [X1: $o,X2: $i] :
                        ( ( in @ X2
                          @ ( dsetconstr @ ( powerset @ emptyset )
                            @ ^ [X3: $i] : X1 ) )
                       => X1 )
                   => ( ! [X1: $i] :
                          ( ( in @ X1 @ emptyset )
                         => ! [X2: $o] : X2 )
                     => ( sP26
                       => ( sP26
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) )
                               => ~ ! [X2: $i] :
                                      ~ ( X1 @ X2 ) )
                           => ( sP23
                             => ( ! [X1: $i] :
                                    ( ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 )
                                   => ( X1 = emptyset ) )
                               => ( ! [X1: $i] :
                                      ( ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 )
                                     => ( X1 = emptyset ) )
                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                          = ( X2 @ X3 ) ) )
                                   => ( ! [X1: $i] :
                                          ( ( X1 != emptyset )
                                         => ~ ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 ) )
                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ( X2 @ X3 )
                                             => ( ( dsetconstr @ X1 @ X2 )
                                               != emptyset ) ) )
                                       => ( ! [X1: $i] :
                                              ( ~ ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 )
                                             => ( X1 != emptyset ) )
                                         => ( sP33
                                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                     => ! [X4: $o] :
                                                          ( ( ( X3 = X1 )
                                                           => X4 )
                                                         => ( ( ( in @ X3 @ X2 )
                                                             => X4 )
                                                           => X4 ) ) )
                                                 => ( sP21
                                                   => ( ! [X1: $i] :
                                                          ( ( dsetconstr @ X1
                                                            @ ^ [X2: $i] : ~ sP15 )
                                                          = X1 )
                                                     => ( sP18
                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                 => ( ( in @ X3 @ X2 )
                                                                   => ( in @ X3 @ X1 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X2 @ X3 )
                                                                   => ( ( in @ X3 @ X1 )
                                                                     => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                     => ! [X3: $o] :
                                                                          ( ! [X4: $i] :
                                                                              ( ( in @ X2 @ X4 )
                                                                             => ( ( in @ X4 @ X1 )
                                                                               => X3 ) )
                                                                         => X3 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X2 @ X1 )
                                                                       => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                   => ! [X1: $i > $o] :
                                                                        ( ~ ! [X2: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) )
                                                                       => ~ ! [X2: $i] :
                                                                              ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                  = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h18,assumption,
    ! [X1: $i > $i > $o,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X2 )
         => ~ ! [X4: $i] :
                ( ( X1 @ X3 @ X4 )
               => ~ ! [X5: $i] :
                      ( ( X1 @ X3 @ X5 )
                     => ( X4 = X5 ) ) ) )
     => ~ ! [X3: $i] :
            ~ ! [X4: $i] :
                ( ( in @ X4 @ X3 )
                = ( ~ ! [X5: $i] :
                        ( ( in @ X5 @ X2 )
                       => ~ ( X1 @ X5 @ X4 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ ( ! [X1: $i] :
          ( ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 )
         => ~ ! [X2: $i] :
                ( ( in @ X2 @ X1 )
               => ~ ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ~ ( in @ X3 @ X1 ) ) ) )
     => ( ! [X1: $i] :
            ~ ! [X2: $i] :
                ( ~ ( ~ ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ! [X4: $i] :
                                ( ( in @ X4 @ X3 )
                               => ( in @ X4 @ X1 ) ) )
                       => ~ ! [X3: $i,X4: $i] :
                              ( ~ ( ( in @ X3 @ X1 )
                                 => ~ ( in @ X4 @ X1 ) )
                             => ( ! [X5: $i] :
                                    ( ( in @ X5 @ X2 )
                                   => ( ( in @ X3 @ X5 )
                                      = ( in @ X4 @ X5 ) ) )
                               => ( X3 = X4 ) ) ) )
                   => ~ ! [X3: $i,X4: $i] :
                          ( ~ ( ( in @ X3 @ X2 )
                             => ~ ( in @ X4 @ X2 ) )
                         => ( ~ ! [X5: $i] :
                                  ( ( in @ X5 @ X3 )
                                 => ( in @ X5 @ X4 ) )
                           => ! [X5: $i] :
                                ( ( in @ X5 @ X4 )
                               => ( in @ X5 @ X3 ) ) ) ) )
               => ~ ! [X3: $i] :
                      ( ~ ( ! [X4: $i] :
                              ( ( in @ X4 @ X3 )
                             => ( in @ X4 @ X1 ) )
                         => ! [X4: $i] :
                              ~ ( in @ X4 @ X3 ) )
                     => ~ ! [X4: $i,X5: $i] :
                            ( ~ ( ~ ( ( in @ X4 @ X2 )
                                   => ~ ( in @ X5 @ X3 ) )
                               => ~ ! [X6: $i] :
                                      ( ( in @ X6 @ X4 )
                                     => ~ ( in @ X6 @ X3 ) ) )
                           => ~ ! [X6: $i] :
                                  ( ( in @ X6 @ X2 )
                                 => ( ~ ! [X7: $i] :
                                          ( ( in @ X7 @ X6 )
                                         => ( in @ X7 @ X4 ) )
                                   => ( in @ X5 @ X6 ) ) ) ) ) )
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) )
             => ( X1 @ ( descr @ X1 ) ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( X2 @ X3 )
                 => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                 => ( in @ X3 @ X1 ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                   => ( X2 @ X3 ) )
               => ( ! [X1: $o,X2: $i] :
                      ( ( in @ X2
                        @ ( dsetconstr @ ( powerset @ emptyset )
                          @ ^ [X3: $i] : X1 ) )
                     => X1 )
                 => ( ! [X1: $i] :
                        ( ( in @ X1 @ emptyset )
                       => ! [X2: $o] : X2 )
                   => ( sP26
                     => ( sP26
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ~ ! [X2: $i] :
                                    ~ ( X1 @ X2 ) )
                         => ( sP23
                           => ( ! [X1: $i] :
                                  ( ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 )
                                 => ( X1 = emptyset ) )
                             => ( ! [X1: $i] :
                                    ( ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 )
                                   => ( X1 = emptyset ) )
                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                        = ( X2 @ X3 ) ) )
                                 => ( ! [X1: $i] :
                                        ( ( X1 != emptyset )
                                       => ~ ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 ) )
                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ( X2 @ X3 )
                                           => ( ( dsetconstr @ X1 @ X2 )
                                             != emptyset ) ) )
                                     => ( ! [X1: $i] :
                                            ( ~ ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 )
                                           => ( X1 != emptyset ) )
                                       => ( sP33
                                         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                   => ! [X4: $o] :
                                                        ( ( ( X3 = X1 )
                                                         => X4 )
                                                       => ( ( ( in @ X3 @ X2 )
                                                           => X4 )
                                                         => X4 ) ) )
                                               => ( sP21
                                                 => ( ! [X1: $i] :
                                                        ( ( dsetconstr @ X1
                                                          @ ^ [X2: $i] : ~ sP15 )
                                                        = X1 )
                                                   => ( sP18
                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                               => ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ X1 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X2 @ X3 )
                                                                 => ( ( in @ X3 @ X1 )
                                                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                   => ! [X3: $o] :
                                                                        ( ! [X4: $i] :
                                                                            ( ( in @ X2 @ X4 )
                                                                           => ( ( in @ X4 @ X1 )
                                                                             => X3 ) )
                                                                       => X3 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X2 @ X1 )
                                                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                 => ! [X1: $i > $o] :
                                                                      ( ~ ! [X2: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) )
                                                                     => ~ ! [X2: $i] :
                                                                            ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                                = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h20,assumption,
    ! [X1: $i] :
      ( ~ ! [X2: $i] :
            ~ ( in @ X2 @ X1 )
     => ~ ! [X2: $i] :
            ( ( in @ X2 @ X1 )
           => ~ ! [X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ~ ( in @ X3 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h21,assumption,
    ~ ( ! [X1: $i] :
          ~ ! [X2: $i] :
              ( ~ ( ~ ( ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ! [X4: $i] :
                              ( ( in @ X4 @ X3 )
                             => ( in @ X4 @ X1 ) ) )
                     => ~ ! [X3: $i,X4: $i] :
                            ( ~ ( ( in @ X3 @ X1 )
                               => ~ ( in @ X4 @ X1 ) )
                           => ( ! [X5: $i] :
                                  ( ( in @ X5 @ X2 )
                                 => ( ( in @ X3 @ X5 )
                                    = ( in @ X4 @ X5 ) ) )
                             => ( X3 = X4 ) ) ) )
                 => ~ ! [X3: $i,X4: $i] :
                        ( ~ ( ( in @ X3 @ X2 )
                           => ~ ( in @ X4 @ X2 ) )
                       => ( ~ ! [X5: $i] :
                                ( ( in @ X5 @ X3 )
                               => ( in @ X5 @ X4 ) )
                         => ! [X5: $i] :
                              ( ( in @ X5 @ X4 )
                             => ( in @ X5 @ X3 ) ) ) ) )
             => ~ ! [X3: $i] :
                    ( ~ ( ! [X4: $i] :
                            ( ( in @ X4 @ X3 )
                           => ( in @ X4 @ X1 ) )
                       => ! [X4: $i] :
                            ~ ( in @ X4 @ X3 ) )
                   => ~ ! [X4: $i,X5: $i] :
                          ( ~ ( ~ ( ( in @ X4 @ X2 )
                                 => ~ ( in @ X5 @ X3 ) )
                             => ~ ! [X6: $i] :
                                    ( ( in @ X6 @ X4 )
                                   => ~ ( in @ X6 @ X3 ) ) )
                         => ~ ! [X6: $i] :
                                ( ( in @ X6 @ X2 )
                               => ( ~ ! [X7: $i] :
                                        ( ( in @ X7 @ X6 )
                                       => ( in @ X7 @ X4 ) )
                                 => ( in @ X5 @ X6 ) ) ) ) ) )
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
           => ( X1 @ ( descr @ X1 ) ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( X2 @ X3 )
               => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
               => ( in @ X3 @ X1 ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                 => ( X2 @ X3 ) )
             => ( ! [X1: $o,X2: $i] :
                    ( ( in @ X2
                      @ ( dsetconstr @ ( powerset @ emptyset )
                        @ ^ [X3: $i] : X1 ) )
                   => X1 )
               => ( ! [X1: $i] :
                      ( ( in @ X1 @ emptyset )
                     => ! [X2: $o] : X2 )
                 => ( sP26
                   => ( sP26
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) )
                           => ~ ! [X2: $i] :
                                  ~ ( X1 @ X2 ) )
                       => ( sP23
                         => ( ! [X1: $i] :
                                ( ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 )
                               => ( X1 = emptyset ) )
                           => ( ! [X1: $i] :
                                  ( ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 )
                                 => ( X1 = emptyset ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                      = ( X2 @ X3 ) ) )
                               => ( ! [X1: $i] :
                                      ( ( X1 != emptyset )
                                     => ~ ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 ) )
                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ( X2 @ X3 )
                                         => ( ( dsetconstr @ X1 @ X2 )
                                           != emptyset ) ) )
                                   => ( ! [X1: $i] :
                                          ( ~ ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 )
                                         => ( X1 != emptyset ) )
                                     => ( sP33
                                       => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ X2 )
                                               => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                 => ! [X4: $o] :
                                                      ( ( ( X3 = X1 )
                                                       => X4 )
                                                     => ( ( ( in @ X3 @ X2 )
                                                         => X4 )
                                                       => X4 ) ) )
                                             => ( sP21
                                               => ( ! [X1: $i] :
                                                      ( ( dsetconstr @ X1
                                                        @ ^ [X2: $i] : ~ sP15 )
                                                      = X1 )
                                                 => ( sP18
                                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                                             => ( ( in @ X3 @ X2 )
                                                               => ( in @ X3 @ X1 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X2 @ X3 )
                                                               => ( ( in @ X3 @ X1 )
                                                                 => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                 => ! [X3: $o] :
                                                                      ( ! [X4: $i] :
                                                                          ( ( in @ X2 @ X4 )
                                                                         => ( ( in @ X4 @ X1 )
                                                                           => X3 ) )
                                                                     => X3 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X2 @ X1 )
                                                                   => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                               => ! [X1: $i > $o] :
                                                                    ( ~ ! [X2: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) )
                                                                   => ~ ! [X2: $i] :
                                                                          ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                              = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h22,assumption,
    ! [X1: $i] :
      ~ ! [X2: $i] :
          ( ~ ( ~ ( ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ! [X4: $i] :
                          ( ( in @ X4 @ X3 )
                         => ( in @ X4 @ X1 ) ) )
                 => ~ ! [X3: $i,X4: $i] :
                        ( ~ ( ( in @ X3 @ X1 )
                           => ~ ( in @ X4 @ X1 ) )
                       => ( ! [X5: $i] :
                              ( ( in @ X5 @ X2 )
                             => ( ( in @ X3 @ X5 )
                                = ( in @ X4 @ X5 ) ) )
                         => ( X3 = X4 ) ) ) )
             => ~ ! [X3: $i,X4: $i] :
                    ( ~ ( ( in @ X3 @ X2 )
                       => ~ ( in @ X4 @ X2 ) )
                   => ( ~ ! [X5: $i] :
                            ( ( in @ X5 @ X3 )
                           => ( in @ X5 @ X4 ) )
                     => ! [X5: $i] :
                          ( ( in @ X5 @ X4 )
                         => ( in @ X5 @ X3 ) ) ) ) )
         => ~ ! [X3: $i] :
                ( ~ ( ! [X4: $i] :
                        ( ( in @ X4 @ X3 )
                       => ( in @ X4 @ X1 ) )
                   => ! [X4: $i] :
                        ~ ( in @ X4 @ X3 ) )
               => ~ ! [X4: $i,X5: $i] :
                      ( ~ ( ~ ( ( in @ X4 @ X2 )
                             => ~ ( in @ X5 @ X3 ) )
                         => ~ ! [X6: $i] :
                                ( ( in @ X6 @ X4 )
                               => ~ ( in @ X6 @ X3 ) ) )
                     => ~ ! [X6: $i] :
                            ( ( in @ X6 @ X2 )
                           => ( ~ ! [X7: $i] :
                                    ( ( in @ X7 @ X6 )
                                   => ( in @ X7 @ X4 ) )
                             => ( in @ X5 @ X6 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h23,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
         => ( X1 @ ( descr @ X1 ) ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ( X2 @ X3 )
             => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
             => ( in @ X3 @ X1 ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
               => ( X2 @ X3 ) )
           => ( ! [X1: $o,X2: $i] :
                  ( ( in @ X2
                    @ ( dsetconstr @ ( powerset @ emptyset )
                      @ ^ [X3: $i] : X1 ) )
                 => X1 )
             => ( ! [X1: $i] :
                    ( ( in @ X1 @ emptyset )
                   => ! [X2: $o] : X2 )
               => ( sP26
                 => ( sP26
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) )
                         => ~ ! [X2: $i] :
                                ~ ( X1 @ X2 ) )
                     => ( sP23
                       => ( ! [X1: $i] :
                              ( ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 )
                             => ( X1 = emptyset ) )
                         => ( ! [X1: $i] :
                                ( ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 )
                               => ( X1 = emptyset ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                    = ( X2 @ X3 ) ) )
                             => ( ! [X1: $i] :
                                    ( ( X1 != emptyset )
                                   => ~ ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 ) )
                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ( X2 @ X3 )
                                       => ( ( dsetconstr @ X1 @ X2 )
                                         != emptyset ) ) )
                                 => ( ! [X1: $i] :
                                        ( ~ ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 )
                                       => ( X1 != emptyset ) )
                                   => ( sP33
                                     => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ X2 )
                                             => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                               => ! [X4: $o] :
                                                    ( ( ( X3 = X1 )
                                                     => X4 )
                                                   => ( ( ( in @ X3 @ X2 )
                                                       => X4 )
                                                     => X4 ) ) )
                                           => ( sP21
                                             => ( ! [X1: $i] :
                                                    ( ( dsetconstr @ X1
                                                      @ ^ [X2: $i] : ~ sP15 )
                                                    = X1 )
                                               => ( sP18
                                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                                           => ( ( in @ X3 @ X2 )
                                                             => ( in @ X3 @ X1 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X2 @ X3 )
                                                             => ( ( in @ X3 @ X1 )
                                                               => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                                               => ! [X3: $o] :
                                                                    ( ! [X4: $i] :
                                                                        ( ( in @ X2 @ X4 )
                                                                       => ( ( in @ X4 @ X1 )
                                                                         => X3 ) )
                                                                   => X3 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X2 @ X1 )
                                                                 => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                             => ! [X1: $i > $o] :
                                                                  ( ~ ! [X2: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) )
                                                                 => ~ ! [X2: $i] :
                                                                        ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                            = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h24,assumption,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ( ( X1 @ X2 )
           => ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
     => ( X1 @ ( descr @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h25,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( X2 @ X3 )
           => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
           => ( in @ X3 @ X1 ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
             => ( X2 @ X3 ) )
         => ( ! [X1: $o,X2: $i] :
                ( ( in @ X2
                  @ ( dsetconstr @ ( powerset @ emptyset )
                    @ ^ [X3: $i] : X1 ) )
               => X1 )
           => ( ! [X1: $i] :
                  ( ( in @ X1 @ emptyset )
                 => ! [X2: $o] : X2 )
             => ( sP26
               => ( sP26
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) )
                       => ~ ! [X2: $i] :
                              ~ ( X1 @ X2 ) )
                   => ( sP23
                     => ( ! [X1: $i] :
                            ( ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                           => ( X1 = emptyset ) )
                       => ( ! [X1: $i] :
                              ( ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 )
                             => ( X1 = emptyset ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                  = ( X2 @ X3 ) ) )
                           => ( ! [X1: $i] :
                                  ( ( X1 != emptyset )
                                 => ~ ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ( X2 @ X3 )
                                     => ( ( dsetconstr @ X1 @ X2 )
                                       != emptyset ) ) )
                               => ( ! [X1: $i] :
                                      ( ~ ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 )
                                     => ( X1 != emptyset ) )
                                 => ( sP33
                                   => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                             => ! [X4: $o] :
                                                  ( ( ( X3 = X1 )
                                                   => X4 )
                                                 => ( ( ( in @ X3 @ X2 )
                                                     => X4 )
                                                   => X4 ) ) )
                                         => ( sP21
                                           => ( ! [X1: $i] :
                                                  ( ( dsetconstr @ X1
                                                    @ ^ [X2: $i] : ~ sP15 )
                                                  = X1 )
                                             => ( sP18
                                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                                         => ( ( in @ X3 @ X2 )
                                                           => ( in @ X3 @ X1 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X2 @ X3 )
                                                           => ( ( in @ X3 @ X1 )
                                                             => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                                             => ! [X3: $o] :
                                                                  ( ! [X4: $i] :
                                                                      ( ( in @ X2 @ X4 )
                                                                     => ( ( in @ X4 @ X1 )
                                                                       => X3 ) )
                                                                 => X3 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X2 @ X1 )
                                                               => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                           => ! [X1: $i > $o] :
                                                                ( ~ ! [X2: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) )
                                                               => ~ ! [X2: $i] :
                                                                      ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                          = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h26,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( X2 @ X3 )
       => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h27,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
         => ( in @ X3 @ X1 ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
           => ( X2 @ X3 ) )
       => ( ! [X1: $o,X2: $i] :
              ( ( in @ X2
                @ ( dsetconstr @ ( powerset @ emptyset )
                  @ ^ [X3: $i] : X1 ) )
             => X1 )
         => ( ! [X1: $i] :
                ( ( in @ X1 @ emptyset )
               => ! [X2: $o] : X2 )
           => ( sP26
             => ( sP26
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) )
                     => ~ ! [X2: $i] :
                            ~ ( X1 @ X2 ) )
                 => ( sP23
                   => ( ! [X1: $i] :
                          ( ! [X2: $i] :
                              ~ ( in @ X2 @ X1 )
                         => ( X1 = emptyset ) )
                     => ( ! [X1: $i] :
                            ( ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                           => ( X1 = emptyset ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                = ( X2 @ X3 ) ) )
                         => ( ! [X1: $i] :
                                ( ( X1 != emptyset )
                               => ~ ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ( X2 @ X3 )
                                   => ( ( dsetconstr @ X1 @ X2 )
                                     != emptyset ) ) )
                             => ( ! [X1: $i] :
                                    ( ~ ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 )
                                   => ( X1 != emptyset ) )
                               => ( sP33
                                 => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ X2 )
                                         => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                           => ! [X4: $o] :
                                                ( ( ( X3 = X1 )
                                                 => X4 )
                                               => ( ( ( in @ X3 @ X2 )
                                                   => X4 )
                                                 => X4 ) ) )
                                       => ( sP21
                                         => ( ! [X1: $i] :
                                                ( ( dsetconstr @ X1
                                                  @ ^ [X2: $i] : ~ sP15 )
                                                = X1 )
                                           => ( sP18
                                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                                       => ( ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ X1 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X2 @ X3 )
                                                         => ( ( in @ X3 @ X1 )
                                                           => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                                           => ! [X3: $o] :
                                                                ( ! [X4: $i] :
                                                                    ( ( in @ X2 @ X4 )
                                                                   => ( ( in @ X4 @ X1 )
                                                                     => X3 ) )
                                                               => X3 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X2 @ X1 )
                                                             => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                         => ! [X1: $i > $o] :
                                                              ( ~ ! [X2: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) )
                                                             => ~ ! [X2: $i] :
                                                                    ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                        = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h28,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
     => ( in @ X3 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h29,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
         => ( X2 @ X3 ) )
     => ( ! [X1: $o,X2: $i] :
            ( ( in @ X2
              @ ( dsetconstr @ ( powerset @ emptyset )
                @ ^ [X3: $i] : X1 ) )
           => X1 )
       => ( ! [X1: $i] :
              ( ( in @ X1 @ emptyset )
             => ! [X2: $o] : X2 )
         => ( sP26
           => ( sP26
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) )
                   => ~ ! [X2: $i] :
                          ~ ( X1 @ X2 ) )
               => ( sP23
                 => ( ! [X1: $i] :
                        ( ! [X2: $i] :
                            ~ ( in @ X2 @ X1 )
                       => ( X1 = emptyset ) )
                   => ( ! [X1: $i] :
                          ( ! [X2: $i] :
                              ~ ( in @ X2 @ X1 )
                         => ( X1 = emptyset ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                              = ( X2 @ X3 ) ) )
                       => ( ! [X1: $i] :
                              ( ( X1 != emptyset )
                             => ~ ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( ( dsetconstr @ X1 @ X2 )
                                   != emptyset ) ) )
                           => ( ! [X1: $i] :
                                  ( ~ ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 )
                                 => ( X1 != emptyset ) )
                             => ( sP33
                               => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                         => ! [X4: $o] :
                                              ( ( ( X3 = X1 )
                                               => X4 )
                                             => ( ( ( in @ X3 @ X2 )
                                                 => X4 )
                                               => X4 ) ) )
                                     => ( sP21
                                       => ( ! [X1: $i] :
                                              ( ( dsetconstr @ X1
                                                @ ^ [X2: $i] : ~ sP15 )
                                              = X1 )
                                         => ( sP18
                                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                                     => ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ X1 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X2 @ X3 )
                                                       => ( ( in @ X3 @ X1 )
                                                         => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                                         => ! [X3: $o] :
                                                              ( ! [X4: $i] :
                                                                  ( ( in @ X2 @ X4 )
                                                                 => ( ( in @ X4 @ X1 )
                                                                   => X3 ) )
                                                             => X3 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X2 @ X1 )
                                                           => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                       => ! [X1: $i > $o] :
                                                            ( ~ ! [X2: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) )
                                                           => ~ ! [X2: $i] :
                                                                  ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                      = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h30,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
     => ( X2 @ X3 ) ),
    introduced(assumption,[]) ).

thf(h31,assumption,
    ~ ( ! [X1: $o,X2: $i] :
          ( ( in @ X2
            @ ( dsetconstr @ ( powerset @ emptyset )
              @ ^ [X3: $i] : X1 ) )
         => X1 )
     => ( ! [X1: $i] :
            ( ( in @ X1 @ emptyset )
           => ! [X2: $o] : X2 )
       => ( sP26
         => ( sP26
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) )
                 => ~ ! [X2: $i] :
                        ~ ( X1 @ X2 ) )
             => ( sP23
               => ( ! [X1: $i] :
                      ( ! [X2: $i] :
                          ~ ( in @ X2 @ X1 )
                     => ( X1 = emptyset ) )
                 => ( ! [X1: $i] :
                        ( ! [X2: $i] :
                            ~ ( in @ X2 @ X1 )
                       => ( X1 = emptyset ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                            = ( X2 @ X3 ) ) )
                     => ( ! [X1: $i] :
                            ( ( X1 != emptyset )
                           => ~ ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ( X2 @ X3 )
                               => ( ( dsetconstr @ X1 @ X2 )
                                 != emptyset ) ) )
                         => ( ! [X1: $i] :
                                ( ~ ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 )
                               => ( X1 != emptyset ) )
                           => ( sP33
                             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                       => ! [X4: $o] :
                                            ( ( ( X3 = X1 )
                                             => X4 )
                                           => ( ( ( in @ X3 @ X2 )
                                               => X4 )
                                             => X4 ) ) )
                                   => ( sP21
                                     => ( ! [X1: $i] :
                                            ( ( dsetconstr @ X1
                                              @ ^ [X2: $i] : ~ sP15 )
                                            = X1 )
                                       => ( sP18
                                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                                   => ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ X1 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X2 @ X3 )
                                                     => ( ( in @ X3 @ X1 )
                                                       => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                                       => ! [X3: $o] :
                                                            ( ! [X4: $i] :
                                                                ( ( in @ X2 @ X4 )
                                                               => ( ( in @ X4 @ X1 )
                                                                 => X3 ) )
                                                           => X3 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X2 @ X1 )
                                                         => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                     => ! [X1: $i > $o] :
                                                          ( ~ ! [X2: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) )
                                                         => ~ ! [X2: $i] :
                                                                ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                    = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h32,assumption,
    ! [X1: $o,X2: $i] :
      ( ( in @ X2
        @ ( dsetconstr @ ( powerset @ emptyset )
          @ ^ [X3: $i] : X1 ) )
     => X1 ),
    introduced(assumption,[]) ).

thf(h33,assumption,
    ~ ( ! [X1: $i] :
          ( ( in @ X1 @ emptyset )
         => ! [X2: $o] : X2 )
     => ( sP26
       => ( sP26
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) )
               => ~ ! [X2: $i] :
                      ~ ( X1 @ X2 ) )
           => ( sP23
             => ( ! [X1: $i] :
                    ( ! [X2: $i] :
                        ~ ( in @ X2 @ X1 )
                   => ( X1 = emptyset ) )
               => ( ! [X1: $i] :
                      ( ! [X2: $i] :
                          ~ ( in @ X2 @ X1 )
                     => ( X1 = emptyset ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                          = ( X2 @ X3 ) ) )
                   => ( ! [X1: $i] :
                          ( ( X1 != emptyset )
                         => ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ( X2 @ X3 )
                             => ( ( dsetconstr @ X1 @ X2 )
                               != emptyset ) ) )
                       => ( ! [X1: $i] :
                              ( ~ ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 )
                             => ( X1 != emptyset ) )
                         => ( sP33
                           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                     => ! [X4: $o] :
                                          ( ( ( X3 = X1 )
                                           => X4 )
                                         => ( ( ( in @ X3 @ X2 )
                                             => X4 )
                                           => X4 ) ) )
                                 => ( sP21
                                   => ( ! [X1: $i] :
                                          ( ( dsetconstr @ X1
                                            @ ^ [X2: $i] : ~ sP15 )
                                          = X1 )
                                     => ( sP18
                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                                 => ( ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ X1 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X2 @ X3 )
                                                   => ( ( in @ X3 @ X1 )
                                                     => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                                     => ! [X3: $o] :
                                                          ( ! [X4: $i] :
                                                              ( ( in @ X2 @ X4 )
                                                             => ( ( in @ X4 @ X1 )
                                                               => X3 ) )
                                                         => X3 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X2 @ X1 )
                                                       => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                   => ! [X1: $i > $o] :
                                                        ( ~ ! [X2: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) )
                                                       => ~ ! [X2: $i] :
                                                              ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                  = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h34,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ emptyset )
     => ! [X2: $o] : X2 ),
    introduced(assumption,[]) ).

thf(h35,assumption,
    ~ ( sP26
     => ( sP26
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) )
             => ~ ! [X2: $i] :
                    ~ ( X1 @ X2 ) )
         => ( sP23
           => ( ! [X1: $i] :
                  ( ! [X2: $i] :
                      ~ ( in @ X2 @ X1 )
                 => ( X1 = emptyset ) )
             => ( ! [X1: $i] :
                    ( ! [X2: $i] :
                        ~ ( in @ X2 @ X1 )
                   => ( X1 = emptyset ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                        = ( X2 @ X3 ) ) )
                 => ( ! [X1: $i] :
                        ( ( X1 != emptyset )
                       => ~ ! [X2: $i] :
                              ~ ( in @ X2 @ X1 ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ( X2 @ X3 )
                           => ( ( dsetconstr @ X1 @ X2 )
                             != emptyset ) ) )
                     => ( ! [X1: $i] :
                            ( ~ ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 )
                           => ( X1 != emptyset ) )
                       => ( sP33
                         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                   => ! [X4: $o] :
                                        ( ( ( X3 = X1 )
                                         => X4 )
                                       => ( ( ( in @ X3 @ X2 )
                                           => X4 )
                                         => X4 ) ) )
                               => ( sP21
                                 => ( ! [X1: $i] :
                                        ( ( dsetconstr @ X1
                                          @ ^ [X2: $i] : ~ sP15 )
                                        = X1 )
                                   => ( sP18
                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                               => ( ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ X1 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X2 @ X3 )
                                                 => ( ( in @ X3 @ X1 )
                                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                   => ! [X3: $o] :
                                                        ( ! [X4: $i] :
                                                            ( ( in @ X2 @ X4 )
                                                           => ( ( in @ X4 @ X1 )
                                                             => X3 ) )
                                                       => X3 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X2 @ X1 )
                                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                 => ! [X1: $i > $o] :
                                                      ( ~ ! [X2: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) )
                                                     => ~ ! [X2: $i] :
                                                            ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                                = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h36,assumption,
    ~ ( sP26
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
           => ~ ! [X2: $i] :
                  ~ ( X1 @ X2 ) )
       => ( sP23
         => ( ! [X1: $i] :
                ( ! [X2: $i] :
                    ~ ( in @ X2 @ X1 )
               => ( X1 = emptyset ) )
           => ( ! [X1: $i] :
                  ( ! [X2: $i] :
                      ~ ( in @ X2 @ X1 )
                 => ( X1 = emptyset ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                      = ( X2 @ X3 ) ) )
               => ( ! [X1: $i] :
                      ( ( X1 != emptyset )
                     => ~ ! [X2: $i] :
                            ~ ( in @ X2 @ X1 ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ( X2 @ X3 )
                         => ( ( dsetconstr @ X1 @ X2 )
                           != emptyset ) ) )
                   => ( ! [X1: $i] :
                          ( ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                         => ( X1 != emptyset ) )
                     => ( sP33
                       => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                 => ! [X4: $o] :
                                      ( ( ( X3 = X1 )
                                       => X4 )
                                     => ( ( ( in @ X3 @ X2 )
                                         => X4 )
                                       => X4 ) ) )
                             => ( sP21
                               => ( ! [X1: $i] :
                                      ( ( dsetconstr @ X1
                                        @ ^ [X2: $i] : ~ sP15 )
                                      = X1 )
                                 => ( sP18
                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X2 @ ( powerset @ X1 ) )
                                             => ( ( in @ X3 @ X2 )
                                               => ( in @ X3 @ X1 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X2 @ X3 )
                                               => ( ( in @ X3 @ X1 )
                                                 => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                                 => ! [X3: $o] :
                                                      ( ! [X4: $i] :
                                                          ( ( in @ X2 @ X4 )
                                                         => ( ( in @ X4 @ X1 )
                                                           => X3 ) )
                                                     => X3 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X2 @ X1 )
                                                   => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                               => ! [X1: $i > $o] :
                                                    ( ~ ! [X2: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) )
                                                   => ~ ! [X2: $i] :
                                                          ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                              = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h37,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
         => ~ ! [X2: $i] :
                ~ ( X1 @ X2 ) )
     => ( sP23
       => ( ! [X1: $i] :
              ( ! [X2: $i] :
                  ~ ( in @ X2 @ X1 )
             => ( X1 = emptyset ) )
         => ( ! [X1: $i] :
                ( ! [X2: $i] :
                    ~ ( in @ X2 @ X1 )
               => ( X1 = emptyset ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                    = ( X2 @ X3 ) ) )
             => ( ! [X1: $i] :
                    ( ( X1 != emptyset )
                   => ~ ! [X2: $i] :
                          ~ ( in @ X2 @ X1 ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ( X2 @ X3 )
                       => ( ( dsetconstr @ X1 @ X2 )
                         != emptyset ) ) )
                 => ( ! [X1: $i] :
                        ( ~ ! [X2: $i] :
                              ~ ( in @ X2 @ X1 )
                       => ( X1 != emptyset ) )
                   => ( sP33
                     => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                               => ! [X4: $o] :
                                    ( ( ( X3 = X1 )
                                     => X4 )
                                   => ( ( ( in @ X3 @ X2 )
                                       => X4 )
                                     => X4 ) ) )
                           => ( sP21
                             => ( ! [X1: $i] :
                                    ( ( dsetconstr @ X1
                                      @ ^ [X2: $i] : ~ sP15 )
                                    = X1 )
                               => ( sP18
                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X2 @ ( powerset @ X1 ) )
                                           => ( ( in @ X3 @ X2 )
                                             => ( in @ X3 @ X1 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X2 @ X3 )
                                             => ( ( in @ X3 @ X1 )
                                               => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X2 @ ( setunion @ X1 ) )
                                               => ! [X3: $o] :
                                                    ( ! [X4: $i] :
                                                        ( ( in @ X2 @ X4 )
                                                       => ( ( in @ X4 @ X1 )
                                                         => X3 ) )
                                                   => X3 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X2 @ X1 )
                                                 => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                             => ! [X1: $i > $o] :
                                                  ( ~ ! [X2: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) )
                                                 => ~ ! [X2: $i] :
                                                        ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                            = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h38,assumption,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ( ( X1 @ X2 )
           => ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
     => ~ ! [X2: $i] :
            ~ ( X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h39,assumption,
    ~ ( sP23
     => ( ! [X1: $i] :
            ( ! [X2: $i] :
                ~ ( in @ X2 @ X1 )
           => ( X1 = emptyset ) )
       => ( ! [X1: $i] :
              ( ! [X2: $i] :
                  ~ ( in @ X2 @ X1 )
             => ( X1 = emptyset ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                  = ( X2 @ X3 ) ) )
           => ( ! [X1: $i] :
                  ( ( X1 != emptyset )
                 => ~ ! [X2: $i] :
                        ~ ( in @ X2 @ X1 ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( X2 @ X3 )
                     => ( ( dsetconstr @ X1 @ X2 )
                       != emptyset ) ) )
               => ( ! [X1: $i] :
                      ( ~ ! [X2: $i] :
                            ~ ( in @ X2 @ X1 )
                     => ( X1 != emptyset ) )
                 => ( sP33
                   => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                             => ! [X4: $o] :
                                  ( ( ( X3 = X1 )
                                   => X4 )
                                 => ( ( ( in @ X3 @ X2 )
                                     => X4 )
                                   => X4 ) ) )
                         => ( sP21
                           => ( ! [X1: $i] :
                                  ( ( dsetconstr @ X1
                                    @ ^ [X2: $i] : ~ sP15 )
                                  = X1 )
                             => ( sP18
                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X2 @ ( powerset @ X1 ) )
                                         => ( ( in @ X3 @ X2 )
                                           => ( in @ X3 @ X1 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X2 @ X3 )
                                           => ( ( in @ X3 @ X1 )
                                             => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X2 @ ( setunion @ X1 ) )
                                             => ! [X3: $o] :
                                                  ( ! [X4: $i] :
                                                      ( ( in @ X2 @ X4 )
                                                     => ( ( in @ X4 @ X1 )
                                                       => X3 ) )
                                                 => X3 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X2 @ X1 )
                                               => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                           => ! [X1: $i > $o] :
                                                ( ~ ! [X2: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) )
                                               => ~ ! [X2: $i] :
                                                      ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                          = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h40,assumption,
    sP23,
    introduced(assumption,[]) ).

thf(h41,assumption,
    ~ ( ! [X1: $i] :
          ( ! [X2: $i] :
              ~ ( in @ X2 @ X1 )
         => ( X1 = emptyset ) )
     => ( ! [X1: $i] :
            ( ! [X2: $i] :
                ~ ( in @ X2 @ X1 )
           => ( X1 = emptyset ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                = ( X2 @ X3 ) ) )
         => ( ! [X1: $i] :
                ( ( X1 != emptyset )
               => ~ ! [X2: $i] :
                      ~ ( in @ X2 @ X1 ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ( X2 @ X3 )
                   => ( ( dsetconstr @ X1 @ X2 )
                     != emptyset ) ) )
             => ( ! [X1: $i] :
                    ( ~ ! [X2: $i] :
                          ~ ( in @ X2 @ X1 )
                   => ( X1 != emptyset ) )
               => ( sP33
                 => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                           => ! [X4: $o] :
                                ( ( ( X3 = X1 )
                                 => X4 )
                               => ( ( ( in @ X3 @ X2 )
                                   => X4 )
                                 => X4 ) ) )
                       => ( sP21
                         => ( ! [X1: $i] :
                                ( ( dsetconstr @ X1
                                  @ ^ [X2: $i] : ~ sP15 )
                                = X1 )
                           => ( sP18
                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X2 @ ( powerset @ X1 ) )
                                       => ( ( in @ X3 @ X2 )
                                         => ( in @ X3 @ X1 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X2 @ X3 )
                                         => ( ( in @ X3 @ X1 )
                                           => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X2 @ ( setunion @ X1 ) )
                                           => ! [X3: $o] :
                                                ( ! [X4: $i] :
                                                    ( ( in @ X2 @ X4 )
                                                   => ( ( in @ X4 @ X1 )
                                                     => X3 ) )
                                               => X3 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X2 @ X1 )
                                             => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                         => ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                             => ~ ! [X2: $i] :
                                                    ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                        = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h42,assumption,
    ! [X1: $i] :
      ( ! [X2: $i] :
          ~ ( in @ X2 @ X1 )
     => ( X1 = emptyset ) ),
    introduced(assumption,[]) ).

thf(h43,assumption,
    ~ ( ! [X1: $i] :
          ( ! [X2: $i] :
              ~ ( in @ X2 @ X1 )
         => ( X1 = emptyset ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
              = ( X2 @ X3 ) ) )
       => ( ! [X1: $i] :
              ( ( X1 != emptyset )
             => ~ ! [X2: $i] :
                    ~ ( in @ X2 @ X1 ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( X2 @ X3 )
                 => ( ( dsetconstr @ X1 @ X2 )
                   != emptyset ) ) )
           => ( ! [X1: $i] :
                  ( ~ ! [X2: $i] :
                        ~ ( in @ X2 @ X1 )
                 => ( X1 != emptyset ) )
             => ( sP33
               => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                         => ! [X4: $o] :
                              ( ( ( X3 = X1 )
                               => X4 )
                             => ( ( ( in @ X3 @ X2 )
                                 => X4 )
                               => X4 ) ) )
                     => ( sP21
                       => ( ! [X1: $i] :
                              ( ( dsetconstr @ X1
                                @ ^ [X2: $i] : ~ sP15 )
                              = X1 )
                         => ( sP18
                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X2 @ ( powerset @ X1 ) )
                                     => ( ( in @ X3 @ X2 )
                                       => ( in @ X3 @ X1 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X2 @ X3 )
                                       => ( ( in @ X3 @ X1 )
                                         => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X2 @ ( setunion @ X1 ) )
                                         => ! [X3: $o] :
                                              ( ! [X4: $i] :
                                                  ( ( in @ X2 @ X4 )
                                                 => ( ( in @ X4 @ X1 )
                                                   => X3 ) )
                                             => X3 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X2 @ X1 )
                                           => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                       => ! [X1: $i > $o] :
                                            ( ~ ! [X2: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) )
                                           => ~ ! [X2: $i] :
                                                  ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                      = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h44,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
            = ( X2 @ X3 ) ) )
     => ( ! [X1: $i] :
            ( ( X1 != emptyset )
           => ~ ! [X2: $i] :
                  ~ ( in @ X2 @ X1 ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( X2 @ X3 )
               => ( ( dsetconstr @ X1 @ X2 )
                 != emptyset ) ) )
         => ( ! [X1: $i] :
                ( ~ ! [X2: $i] :
                      ~ ( in @ X2 @ X1 )
               => ( X1 != emptyset ) )
           => ( sP33
             => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                       => ! [X4: $o] :
                            ( ( ( X3 = X1 )
                             => X4 )
                           => ( ( ( in @ X3 @ X2 )
                               => X4 )
                             => X4 ) ) )
                   => ( sP21
                     => ( ! [X1: $i] :
                            ( ( dsetconstr @ X1
                              @ ^ [X2: $i] : ~ sP15 )
                            = X1 )
                       => ( sP18
                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X2 @ ( powerset @ X1 ) )
                                   => ( ( in @ X3 @ X2 )
                                     => ( in @ X3 @ X1 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X2 @ X3 )
                                     => ( ( in @ X3 @ X1 )
                                       => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X2 @ ( setunion @ X1 ) )
                                       => ! [X3: $o] :
                                            ( ! [X4: $i] :
                                                ( ( in @ X2 @ X4 )
                                               => ( ( in @ X4 @ X1 )
                                                 => X3 ) )
                                           => X3 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X2 @ X1 )
                                         => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                     => ! [X1: $i > $o] :
                                          ( ~ ! [X2: $i] :
                                                ( ( X1 @ X2 )
                                               => ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) )
                                         => ~ ! [X2: $i] :
                                                ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                    = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h45,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
        = ( X2 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h46,assumption,
    ~ ( ! [X1: $i] :
          ( ( X1 != emptyset )
         => ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ( X2 @ X3 )
             => ( ( dsetconstr @ X1 @ X2 )
               != emptyset ) ) )
       => ( ! [X1: $i] :
              ( ~ ! [X2: $i] :
                    ~ ( in @ X2 @ X1 )
             => ( X1 != emptyset ) )
         => ( sP33
           => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                     => ! [X4: $o] :
                          ( ( ( X3 = X1 )
                           => X4 )
                         => ( ( ( in @ X3 @ X2 )
                             => X4 )
                           => X4 ) ) )
                 => ( sP21
                   => ( ! [X1: $i] :
                          ( ( dsetconstr @ X1
                            @ ^ [X2: $i] : ~ sP15 )
                          = X1 )
                     => ( sP18
                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X2 @ ( powerset @ X1 ) )
                                 => ( ( in @ X3 @ X2 )
                                   => ( in @ X3 @ X1 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X2 @ X3 )
                                   => ( ( in @ X3 @ X1 )
                                     => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X2 @ ( setunion @ X1 ) )
                                     => ! [X3: $o] :
                                          ( ! [X4: $i] :
                                              ( ( in @ X2 @ X4 )
                                             => ( ( in @ X4 @ X1 )
                                               => X3 ) )
                                         => X3 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X2 @ X1 )
                                       => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                   => ! [X1: $i > $o] :
                                        ( ~ ! [X2: $i] :
                                              ( ( X1 @ X2 )
                                             => ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) )
                                       => ~ ! [X2: $i] :
                                              ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                  = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h47,assumption,
    ! [X1: $i] :
      ( ( X1 != emptyset )
     => ~ ! [X2: $i] :
            ~ ( in @ X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h48,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( X2 @ X3 )
           => ( ( dsetconstr @ X1 @ X2 )
             != emptyset ) ) )
     => ( ! [X1: $i] :
            ( ~ ! [X2: $i] :
                  ~ ( in @ X2 @ X1 )
           => ( X1 != emptyset ) )
       => ( sP33
         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                   => ! [X4: $o] :
                        ( ( ( X3 = X1 )
                         => X4 )
                       => ( ( ( in @ X3 @ X2 )
                           => X4 )
                         => X4 ) ) )
               => ( sP21
                 => ( ! [X1: $i] :
                        ( ( dsetconstr @ X1
                          @ ^ [X2: $i] : ~ sP15 )
                        = X1 )
                   => ( sP18
                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X2 @ ( powerset @ X1 ) )
                               => ( ( in @ X3 @ X2 )
                                 => ( in @ X3 @ X1 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X2 @ X3 )
                                 => ( ( in @ X3 @ X1 )
                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                   => ! [X3: $o] :
                                        ( ! [X4: $i] :
                                            ( ( in @ X2 @ X4 )
                                           => ( ( in @ X4 @ X1 )
                                             => X3 ) )
                                       => X3 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X2 @ X1 )
                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                 => ! [X1: $i > $o] :
                                      ( ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) )
                                     => ~ ! [X2: $i] :
                                            ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                                = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h49,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( X2 @ X3 )
       => ( ( dsetconstr @ X1 @ X2 )
         != emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h50,assumption,
    ~ ( ! [X1: $i] :
          ( ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 )
         => ( X1 != emptyset ) )
     => ( sP33
       => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ X2 )
               => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                 => ! [X4: $o] :
                      ( ( ( X3 = X1 )
                       => X4 )
                     => ( ( ( in @ X3 @ X2 )
                         => X4 )
                       => X4 ) ) )
             => ( sP21
               => ( ! [X1: $i] :
                      ( ( dsetconstr @ X1
                        @ ^ [X2: $i] : ~ sP15 )
                      = X1 )
                 => ( sP18
                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X2 @ ( powerset @ X1 ) )
                             => ( ( in @ X3 @ X2 )
                               => ( in @ X3 @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X2 @ X3 )
                               => ( ( in @ X3 @ X1 )
                                 => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X2 @ ( setunion @ X1 ) )
                                 => ! [X3: $o] :
                                      ( ! [X4: $i] :
                                          ( ( in @ X2 @ X4 )
                                         => ( ( in @ X4 @ X1 )
                                           => X3 ) )
                                     => X3 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X2 @ X1 )
                                   => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                               => ! [X1: $i > $o] :
                                    ( ~ ! [X2: $i] :
                                          ( ( X1 @ X2 )
                                         => ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) )
                                   => ~ ! [X2: $i] :
                                          ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                              = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h51,assumption,
    ! [X1: $i] :
      ( ~ ! [X2: $i] :
            ~ ( in @ X2 @ X1 )
     => ( X1 != emptyset ) ),
    introduced(assumption,[]) ).

thf(h52,assumption,
    ~ ( sP33
     => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ X2 )
             => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
               => ! [X4: $o] :
                    ( ( ( X3 = X1 )
                     => X4 )
                   => ( ( ( in @ X3 @ X2 )
                       => X4 )
                     => X4 ) ) )
           => ( sP21
             => ( ! [X1: $i] :
                    ( ( dsetconstr @ X1
                      @ ^ [X2: $i] : ~ sP15 )
                    = X1 )
               => ( sP18
                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                   => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X2 @ ( powerset @ X1 ) )
                           => ( ( in @ X3 @ X2 )
                             => ( in @ X3 @ X1 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X2 @ X3 )
                             => ( ( in @ X3 @ X1 )
                               => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X2 @ ( setunion @ X1 ) )
                               => ! [X3: $o] :
                                    ( ! [X4: $i] :
                                        ( ( in @ X2 @ X4 )
                                       => ( ( in @ X4 @ X1 )
                                         => X3 ) )
                                   => X3 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X2 @ X1 )
                                 => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                             => ! [X1: $i > $o] :
                                  ( ~ ! [X2: $i] :
                                        ( ( X1 @ X2 )
                                       => ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) )
                                 => ~ ! [X2: $i] :
                                        ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                            = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h53,assumption,
    sP33,
    introduced(assumption,[]) ).

thf(h54,assumption,
    ~ ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ X2 )
           => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
             => ! [X4: $o] :
                  ( ( ( X3 = X1 )
                   => X4 )
                 => ( ( ( in @ X3 @ X2 )
                     => X4 )
                   => X4 ) ) )
         => ( sP21
           => ( ! [X1: $i] :
                  ( ( dsetconstr @ X1
                    @ ^ [X2: $i] : ~ sP15 )
                  = X1 )
             => ( sP18
               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                 => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X2 @ ( powerset @ X1 ) )
                         => ( ( in @ X3 @ X2 )
                           => ( in @ X3 @ X1 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X2 @ X3 )
                           => ( ( in @ X3 @ X1 )
                             => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X2 @ ( setunion @ X1 ) )
                             => ! [X3: $o] :
                                  ( ! [X4: $i] :
                                      ( ( in @ X2 @ X4 )
                                     => ( ( in @ X4 @ X1 )
                                       => X3 ) )
                                 => X3 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                           => ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) )
                               => ~ ! [X2: $i] :
                                      ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                          = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h55,assumption,
    in @ emptyset @ ( setadjoin @ emptyset @ emptyset ),
    introduced(assumption,[]) ).

thf(h56,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ X2 )
         => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
           => ! [X4: $o] :
                ( ( ( X3 = X1 )
                 => X4 )
               => ( ( ( in @ X3 @ X2 )
                   => X4 )
                 => X4 ) ) )
       => ( sP21
         => ( ! [X1: $i] :
                ( ( dsetconstr @ X1
                  @ ^ [X2: $i] : ~ sP15 )
                = X1 )
           => ( sP18
             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
               => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X2 @ ( powerset @ X1 ) )
                       => ( ( in @ X3 @ X2 )
                         => ( in @ X3 @ X1 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X2 @ X3 )
                         => ( ( in @ X3 @ X1 )
                           => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X2 @ ( setunion @ X1 ) )
                           => ! [X3: $o] :
                                ( ! [X4: $i] :
                                    ( ( in @ X2 @ X4 )
                                   => ( ( in @ X4 @ X1 )
                                     => X3 ) )
                               => X3 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X2 @ X1 )
                             => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                         => ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ~ ! [X2: $i] :
                                    ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                        = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h57,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X2 )
     => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h58,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
         => ! [X4: $o] :
              ( ( ( X3 = X1 )
               => X4 )
             => ( ( ( in @ X3 @ X2 )
                 => X4 )
               => X4 ) ) )
     => ( sP21
       => ( ! [X1: $i] :
              ( ( dsetconstr @ X1
                @ ^ [X2: $i] : ~ sP15 )
              = X1 )
         => ( sP18
           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
             => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X2 @ ( powerset @ X1 ) )
                     => ( ( in @ X3 @ X2 )
                       => ( in @ X3 @ X1 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X2 @ X3 )
                       => ( ( in @ X3 @ X1 )
                         => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X2 @ ( setunion @ X1 ) )
                         => ! [X3: $o] :
                              ( ! [X4: $i] :
                                  ( ( in @ X2 @ X4 )
                                 => ( ( in @ X4 @ X1 )
                                   => X3 ) )
                             => X3 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X2 @ X1 )
                           => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                       => ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) )
                           => ~ ! [X2: $i] :
                                  ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                      = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h59,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
     => ! [X4: $o] :
          ( ( ( X3 = X1 )
           => X4 )
         => ( ( ( in @ X3 @ X2 )
             => X4 )
           => X4 ) ) ),
    introduced(assumption,[]) ).

thf(h60,assumption,
    ~ ( sP21
     => ( ! [X1: $i] :
            ( ( dsetconstr @ X1
              @ ^ [X2: $i] : ~ sP15 )
            = X1 )
       => ( sP18
         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
           => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X2 @ ( powerset @ X1 ) )
                   => ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ X1 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X2 @ X3 )
                     => ( ( in @ X3 @ X1 )
                       => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X2 @ ( setunion @ X1 ) )
                       => ! [X3: $o] :
                            ( ! [X4: $i] :
                                ( ( in @ X2 @ X4 )
                               => ( ( in @ X4 @ X1 )
                                 => X3 ) )
                           => X3 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X2 @ X1 )
                         => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                     => ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) )
                         => ~ ! [X2: $i] :
                                ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                    = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h61,assumption,
    sP21,
    introduced(assumption,[]) ).

thf(h62,assumption,
    ~ ( ! [X1: $i] :
          ( ( dsetconstr @ X1
            @ ^ [X2: $i] : ~ sP15 )
          = X1 )
     => ( sP18
       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
         => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X2 @ ( powerset @ X1 ) )
                 => ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X2 @ X3 )
                   => ( ( in @ X3 @ X1 )
                     => ( in @ X2 @ ( setunion @ X1 ) ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X2 @ ( setunion @ X1 ) )
                     => ! [X3: $o] :
                          ( ! [X4: $i] :
                              ( ( in @ X2 @ X4 )
                             => ( ( in @ X4 @ X1 )
                               => X3 ) )
                         => X3 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X2 @ X1 )
                       => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                   => ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) )
                       => ~ ! [X2: $i] :
                              ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                  = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h63,assumption,
    ! [X1: $i] :
      ( ( dsetconstr @ X1
        @ ^ [X2: $i] : ~ sP15 )
      = X1 ),
    introduced(assumption,[]) ).

thf(h64,assumption,
    ~ ( sP18
     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X2 @ ( powerset @ X1 ) )
               => ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ X1 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X2 @ X3 )
                 => ( ( in @ X3 @ X1 )
                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X2 @ ( setunion @ X1 ) )
                   => ! [X3: $o] :
                        ( ! [X4: $i] :
                            ( ( in @ X2 @ X4 )
                           => ( ( in @ X4 @ X1 )
                             => X3 ) )
                       => X3 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X2 @ X1 )
                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                 => ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) )
                     => ~ ! [X2: $i] :
                            ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                                = ( X3 = X2 ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h65,assumption,
    sP18,
    introduced(assumption,[]) ).

thf(h66,assumption,
    ~ ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
             => ( ( in @ X3 @ X2 )
               => ( in @ X3 @ X1 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X2 @ X3 )
               => ( ( in @ X3 @ X1 )
                 => ( in @ X2 @ ( setunion @ X1 ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X2 @ ( setunion @ X1 ) )
                 => ! [X3: $o] :
                      ( ! [X4: $i] :
                          ( ( in @ X2 @ X4 )
                         => ( ( in @ X4 @ X1 )
                           => X3 ) )
                     => X3 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X2 @ X1 )
                   => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
               => ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) )
                   => ~ ! [X2: $i] :
                          ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                              = ( X3 = X2 ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h67,assumption,
    ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) ),
    introduced(assumption,[]) ).

thf(h68,assumption,
    ~ ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X2 @ ( powerset @ X1 ) )
           => ( ( in @ X3 @ X2 )
             => ( in @ X3 @ X1 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X2 @ X3 )
             => ( ( in @ X3 @ X1 )
               => ( in @ X2 @ ( setunion @ X1 ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( setunion @ X1 ) )
               => ! [X3: $o] :
                    ( ! [X4: $i] :
                        ( ( in @ X2 @ X4 )
                       => ( ( in @ X4 @ X1 )
                         => X3 ) )
                   => X3 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X2 @ X1 )
                 => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
             => ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) )
                 => ~ ! [X2: $i] :
                        ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                            = ( X3 = X2 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h69,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
         => ( ( in @ X3 @ X2 )
           => ( in @ X3 @ X1 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X2 @ X3 )
           => ( ( in @ X3 @ X1 )
             => ( in @ X2 @ ( setunion @ X1 ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( setunion @ X1 ) )
             => ! [X3: $o] :
                  ( ! [X4: $i] :
                      ( ( in @ X2 @ X4 )
                     => ( ( in @ X4 @ X1 )
                       => X3 ) )
                 => X3 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ X1 )
               => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
           => ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) )
               => ~ ! [X2: $i] :
                      ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                          = ( X3 = X2 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h70,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X2 @ ( powerset @ X1 ) )
     => ( ( in @ X3 @ X2 )
       => ( in @ X3 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h71,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X2 @ X3 )
         => ( ( in @ X3 @ X1 )
           => ( in @ X2 @ ( setunion @ X1 ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( setunion @ X1 ) )
           => ! [X3: $o] :
                ( ! [X4: $i] :
                    ( ( in @ X2 @ X4 )
                   => ( ( in @ X4 @ X1 )
                     => X3 ) )
               => X3 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
         => ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) )
             => ~ ! [X2: $i] :
                    ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                        = ( X3 = X2 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h72,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X2 @ X3 )
     => ( ( in @ X3 @ X1 )
       => ( in @ X2 @ ( setunion @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h73,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( setunion @ X1 ) )
         => ! [X3: $o] :
              ( ! [X4: $i] :
                  ( ( in @ X2 @ X4 )
                 => ( ( in @ X4 @ X1 )
                   => X3 ) )
             => X3 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ X1 )
           => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
       => ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
           => ~ ! [X2: $i] :
                  ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                      = ( X3 = X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h74,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ ( setunion @ X1 ) )
     => ! [X3: $o] :
          ( ! [X4: $i] :
              ( ( in @ X2 @ X4 )
             => ( ( in @ X4 @ X1 )
               => X3 ) )
         => X3 ) ),
    introduced(assumption,[]) ).

thf(h75,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ X1 )
         => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
     => ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
         => ~ ! [X2: $i] :
                ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                    = ( X3 = X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h76,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ X1 )
     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h77,assumption,
    ~ ! [X1: $i > $o] :
        ( ~ ! [X2: $i] :
              ( ( X1 @ X2 )
             => ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) )
       => ~ ! [X2: $i] :
              ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                  = ( X3 = X2 ) ) ),
    introduced(assumption,[]) ).

thf(h78,assumption,
    ~ ( ~ ! [X1: $i] :
            ( ( eigen__0 @ X1 )
           => ~ ! [X2: $i] :
                  ( ( eigen__0 @ X2 )
                 => ( X1 = X2 ) ) )
     => ~ sP27 ),
    introduced(assumption,[]) ).

thf(h79,assumption,
    ~ ! [X1: $i] :
        ( ( eigen__0 @ X1 )
       => ~ ! [X2: $i] :
              ( ( eigen__0 @ X2 )
             => ( X1 = X2 ) ) ),
    introduced(assumption,[]) ).

thf(h80,assumption,
    sP27,
    introduced(assumption,[]) ).

thf(h81,assumption,
    ~ ( sP24
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h82,assumption,
    sP24,
    introduced(assumption,[]) ).

thf(h83,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP3
    | sP2
    | sP15
    | ~ sP22 ),
    inference(mating_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP37
    | sP30
    | ~ sP22
    | sP15 ),
    inference(mating_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP20
    | sP28
    | sP15
    | ~ sP13 ),
    inference(mating_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP4
    | ~ sP2
    | sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP19
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP12
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP9
    | ~ sP17
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP16
    | ~ sP36
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP7
    | ~ sP30 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP7
    | sP37 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP17
    | ~ sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__92]) ).

thf(12,plain,
    ( ~ sP29
    | ~ sP28
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP10
    | sP22
    | sP31 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP25
    | ~ sP6
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP1
    | sP25 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP26
    | ~ sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP18
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP5
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP32
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP34
    | sP29 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP11
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP14
    | sP34 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP24
    | sP6
    | ~ sP13 ),
    inference(mating_rule,[status(thm)],]) ).

thf(24,plain,
    ( sP8
    | ~ sP6
    | ~ sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( sP8
    | sP6
    | sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( sP35
    | ~ sP8 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(27,plain,
    ~ sP15,
    inference(prop_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP27
    | ~ sP35 ),
    inference(all_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP33
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP21
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP23
    | sP32 ),
    inference(all_rule,[status(thm)],]) ).

thf(32,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h82,h83,h81,h79,h80,h78,h76,h77,h74,h75,h72,h73,h70,h71,h67,h69,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,h4,h8,h40,h53,h61,h65,h82,h83,h80]) ).

thf(33,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h81,h79,h80,h78,h76,h77,h74,h75,h72,h73,h70,h71,h67,h69,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h82,h83])],[h81,32,h82,h83]) ).

thf(34,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h79,h80,h78,h76,h77,h74,h75,h72,h73,h70,h71,h67,h69,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h81]),tab_negall(eigenvar,eigen__1)],[h79,33,h81]) ).

thf(35,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h78,h76,h77,h74,h75,h72,h73,h70,h71,h67,h69,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h79,h80])],[h78,34,h79,h80]) ).

thf(36,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h76,h77,h74,h75,h72,h73,h70,h71,h67,h69,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h78]),tab_negall(eigenvar,eigen__0)],[h77,35,h78]) ).

thf(37,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h74,h75,h72,h73,h70,h71,h67,h69,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h76,h77])],[h75,36,h76,h77]) ).

thf(38,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h72,h73,h70,h71,h67,h69,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h74,h75])],[h73,37,h74,h75]) ).

thf(39,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h70,h71,h67,h69,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h72,h73])],[h71,38,h72,h73]) ).

thf(40,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h67,h69,h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h70,h71])],[h69,39,h70,h71]) ).

thf(41,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h67,h68,h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h67,h69])],[h68,40,h67,h69]) ).

thf(42,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h65,h66,h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h67,h68])],[h66,41,h67,h68]) ).

thf(43,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h63,h64,h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h65,h66])],[h64,42,h65,h66]) ).

thf(44,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h61,h62,h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h63,h64])],[h62,43,h63,h64]) ).

thf(45,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h59,h60,h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h61,h62])],[h60,44,h61,h62]) ).

thf(46,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h57,h58,h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h59,h60])],[h58,45,h59,h60]) ).

thf(47,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h55,h56,h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h57,h58])],[h56,46,h57,h58]) ).

thf(48,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h53,h54,h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h55,h56])],[h54,47,h55,h56]) ).

thf(49,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h51,h52,h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h53,h54])],[h52,48,h53,h54]) ).

thf(50,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h49,h50,h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h51,h52])],[h50,49,h51,h52]) ).

thf(51,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h47,h48,h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h49,h50])],[h48,50,h49,h50]) ).

thf(52,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h45,h46,h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h47,h48])],[h46,51,h47,h48]) ).

thf(53,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h42,h44,h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h45,h46])],[h44,52,h45,h46]) ).

thf(54,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h42,h43,h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h42,h44])],[h43,53,h42,h44]) ).

thf(55,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h40,h41,h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h42,h43])],[h41,54,h42,h43]) ).

thf(56,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h38,h39,h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h40,h41])],[h39,55,h40,h41]) ).

thf(57,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h37,h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h38,h39])],[h37,56,h38,h39]) ).

thf(58,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h36,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h4,h37])],[h36,57,h4,h37]) ).

thf(59,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h4,h36])],[h35,58,h4,h36]) ).

thf(60,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h34,h35])],[h33,59,h34,h35]) ).

thf(61,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h32,h33])],[h31,60,h32,h33]) ).

thf(62,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h30,h31])],[h29,61,h30,h31]) ).

thf(63,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,62,h28,h29]) ).

thf(64,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h26,h27])],[h25,63,h26,h27]) ).

thf(65,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,64,h24,h25]) ).

thf(66,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,65,h22,h23]) ).

thf(67,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,66,h20,h21]) ).

thf(68,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,67,h18,h19]) ).

thf(69,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,68,h16,h17]) ).

thf(70,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,69,h14,h15]) ).

thf(71,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,70,h12,h13]) ).

thf(72,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,71,h10,h11]) ).

thf(73,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,72,h8,h9]) ).

thf(74,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,73,h6,h7]) ).

thf(75,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,74,h4,h5]) ).

thf(76,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,75,h2,h3]) ).

thf(77,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[76,h0]) ).

thf(0,theorem,
    ( ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
            = ( in @ X3 @ X2 ) )
       => ( X1 = X2 ) )
   => ( sP26
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
            = ( ( X3 != X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( sP5
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( setunion @ X1 ) )
                = ( ~ ! [X3: $i] :
                        ( ( in @ X2 @ X3 )
                       => ~ ( in @ X3 @ X1 ) ) ) )
           => ( ( in @ emptyset @ omega )
             => ( ! [X1: $i] :
                    ( ( in @ X1 @ omega )
                   => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) )
               => ( ! [X1: $i] :
                      ( ~ ( ( in @ emptyset @ X1 )
                         => ~ ! [X2: $i] :
                                ( ~ ( ( in @ X2 @ omega )
                                   => ~ ( in @ X2 @ X1 ) )
                               => ( in @ ( setadjoin @ X2 @ X2 ) @ X1 ) ) )
                     => ! [X2: $i] :
                          ( ( in @ X2 @ omega )
                         => ( in @ X2 @ X1 ) ) )
                 => ( ! [X1: $i > $i > $o,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ~ ! [X4: $i] :
                                  ( ( X1 @ X3 @ X4 )
                                 => ~ ! [X5: $i] :
                                        ( ( X1 @ X3 @ X5 )
                                       => ( X4 = X5 ) ) ) )
                       => ~ ! [X3: $i] :
                              ~ ! [X4: $i] :
                                  ( ( in @ X4 @ X3 )
                                  = ( ~ ! [X5: $i] :
                                          ( ( in @ X5 @ X2 )
                                         => ~ ( X1 @ X5 @ X4 ) ) ) ) )
                   => ( ! [X1: $i] :
                          ( ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                         => ~ ! [X2: $i] :
                                ( ( in @ X2 @ X1 )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ~ ( in @ X3 @ X1 ) ) ) )
                     => ( ! [X1: $i] :
                            ~ ! [X2: $i] :
                                ( ~ ( ~ ( ! [X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ! [X4: $i] :
                                                ( ( in @ X4 @ X3 )
                                               => ( in @ X4 @ X1 ) ) )
                                       => ~ ! [X3: $i,X4: $i] :
                                              ( ~ ( ( in @ X3 @ X1 )
                                                 => ~ ( in @ X4 @ X1 ) )
                                             => ( ! [X5: $i] :
                                                    ( ( in @ X5 @ X2 )
                                                   => ( ( in @ X3 @ X5 )
                                                      = ( in @ X4 @ X5 ) ) )
                                               => ( X3 = X4 ) ) ) )
                                   => ~ ! [X3: $i,X4: $i] :
                                          ( ~ ( ( in @ X3 @ X2 )
                                             => ~ ( in @ X4 @ X2 ) )
                                         => ( ~ ! [X5: $i] :
                                                  ( ( in @ X5 @ X3 )
                                                 => ( in @ X5 @ X4 ) )
                                           => ! [X5: $i] :
                                                ( ( in @ X5 @ X4 )
                                               => ( in @ X5 @ X3 ) ) ) ) )
                               => ~ ! [X3: $i] :
                                      ( ~ ( ! [X4: $i] :
                                              ( ( in @ X4 @ X3 )
                                             => ( in @ X4 @ X1 ) )
                                         => ! [X4: $i] :
                                              ~ ( in @ X4 @ X3 ) )
                                     => ~ ! [X4: $i,X5: $i] :
                                            ( ~ ( ~ ( ( in @ X4 @ X2 )
                                                   => ~ ( in @ X5 @ X3 ) )
                                               => ~ ! [X6: $i] :
                                                      ( ( in @ X6 @ X4 )
                                                     => ~ ( in @ X6 @ X3 ) ) )
                                           => ~ ! [X6: $i] :
                                                  ( ( in @ X6 @ X2 )
                                                 => ( ~ ! [X7: $i] :
                                                          ( ( in @ X7 @ X6 )
                                                         => ( in @ X7 @ X4 ) )
                                                   => ( in @ X5 @ X6 ) ) ) ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ( X1 @ ( descr @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                 => ( in @ X3 @ X1 ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                   => ( X2 @ X3 ) )
                               => ( ! [X1: $o,X2: $i] :
                                      ( ( in @ X2
                                        @ ( dsetconstr @ ( powerset @ emptyset )
                                          @ ^ [X3: $i] : X1 ) )
                                     => X1 )
                                 => ( ! [X1: $i] :
                                        ( ( in @ X1 @ emptyset )
                                       => ! [X2: $o] : X2 )
                                   => ( sP26
                                     => ( sP26
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                             => ~ ! [X2: $i] :
                                                    ~ ( X1 @ X2 ) )
                                         => ( sP23
                                           => ( ! [X1: $i] :
                                                  ( ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 )
                                                 => ( X1 = emptyset ) )
                                             => ( ! [X1: $i] :
                                                    ( ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 )
                                                   => ( X1 = emptyset ) )
                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
                                                        = ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( X1 != emptyset )
                                                       => ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ( X2 @ X3 )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != emptyset ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ~ ! [X2: $i] :
                                                                  ~ ( in @ X2 @ X1 )
                                                           => ( X1 != emptyset ) )
                                                       => ( sP33
                                                         => ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ ( setadjoin @ X1 @ X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                   => ! [X4: $o] :
                                                                        ( ( ( X3 = X1 )
                                                                         => X4 )
                                                                       => ( ( ( in @ X3 @ X2 )
                                                                           => X4 )
                                                                         => X4 ) ) )
                                                               => ( sP21
                                                                 => ( ! [X1: $i] :
                                                                        ( ( dsetconstr @ X1
                                                                          @ ^ [X2: $i] : ~ sP15 )
                                                                        = X1 )
                                                                   => ( sP18
                                                                     => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                       => ( ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X2 @ ( powerset @ X1 ) )
                                                                               => ( ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ X1 ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X2 @ X3 )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X2 @ ( setunion @ X1 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X2 @ ( setunion @ X1 ) )
                                                                                   => ! [X3: $o] :
                                                                                        ( ! [X4: $i] :
                                                                                            ( ( in @ X2 @ X4 )
                                                                                           => ( ( in @ X4 @ X1 )
                                                                                             => X3 ) )
                                                                                       => X3 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X2 @ X1 )
                                                                                     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
                                                                                 => ! [X1: $i > $o] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) )
                                                                                     => ~ ! [X2: $i] :
                                                                                            ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                                = ( X3 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[76,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU525^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Wed Aug 23 20:44:15 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 1.53/1.70  % SZS status Theorem
% 1.53/1.70  % Mode: cade22grackle2xfee4
% 1.53/1.70  % Steps: 23201
% 1.53/1.70  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------