TSTP Solution File: SEU553^1 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU553^1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 13:53:14 EDT 2022

% Result   : Theorem 0.18s 0.40s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   73
%            Number of leaves      :  222
% Syntax   : Number of formulae    :  305 ( 171 unt;  14 typ;  69 def)
%            Number of atoms       : 6785 (2130 equ;   0 cnn)
%            Maximal formula atoms :  162 (  23 avg)
%            Number of connectives : 23011 (2593   ~;   4   |;   0   &;12840   @)
%                                         (   0 <=>;7573  =>;   1  <=;   0 <~>)
%            Maximal formula depth :   77 (  13 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  : 1141 (1141   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   90 (  88 usr;  79 con; 0-2 aty)
%            Number of variables   : 7677 (  38   ^7639   !;   0   ?;7677   :)

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

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

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

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

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

thf(ty_nonempty,type,
    nonempty: $i > $o ).

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

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

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

thf(ty_exu,type,
    exu: ( $i > $o ) > $o ).

thf(ty_prop2set,type,
    prop2set: $o > $i ).

thf(ty_set2prop,type,
    set2prop: $i > $o ).

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

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

thf(def_setextAx,definition,
    ( setextAx
    = ( ! [X1: $i,X2: $i] :
          ( ! [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] :
                ( ( 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] :
          ( ( in @ X1 @ omega )
         => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ) ) ).

thf(def_omegaIndAx,definition,
    ( omegaIndAx
    = ( ! [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 ) ) ) ) ) ).

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

thf(def_foundationAx,definition,
    ( foundationAx
    = ( ! [X1: $i] :
          ( ~ ! [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] :
                          ( ( 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 ) ) ) ) ) ) ) ) ).

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

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

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

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

thf(def_exuE1,definition,
    ( exuE1
    = ( ! [X1: $i > $o] :
          ( ( exu @ X1 )
         => ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) ) ) ) ).

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

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

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

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

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

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

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

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

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

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

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

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

thf(def_setadjoinIL,definition,
    ( setadjoinIL
    = ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) ) ) ).

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

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

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

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

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

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

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

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

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

thf(def_exuE2,definition,
    ( exuE2
    = ( ! [X1: $i > $o] :
          ( ( exu @ X1 )
         => ~ ! [X2: $i] :
                ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                    = ( X3 = X2 ) ) ) ) ) ).

thf(def_nonemptyImpWitness,definition,
    ( nonemptyImpWitness
    = ( ! [X1: $i] :
          ( ( nonempty @ X1 )
         => ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 ) ) ) ) ).

thf(def_uniqinunit,definition,
    ( uniqinunit
    = ( ! [X1: $i,X2: $i] :
          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
         => ( X1 = X2 ) ) ) ) ).

thf(def_notinsingleton,definition,
    ( notinsingleton
    = ( ! [X1: $i,X2: $i] :
          ( ( X1 != X2 )
         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ).

thf(def_eqinunit,definition,
    ( eqinunit
    = ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).

thf(def_singletonsswitch,definition,
    ( singletonsswitch
    = ( ! [X1: $i,X2: $i] :
          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ).

thf(def_upairsetE,definition,
    ( upairsetE
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ( X3 != X1 )
           => ( X3 = X2 ) ) ) ) ) ).

thf(def_upairsetIL,definition,
    ( upairsetIL
    = ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).

thf(def_upairsetIR,definition,
    ( upairsetIR
    = ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ) ).

thf(def_emptyE1,definition,
    ( emptyE1
    = ( ! [X1: $i,X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( X2 @ X3 ) )
         => ( ( dsetconstr @ X1 @ X2 )
           != emptyset ) ) ) ) ).

thf(def_vacuousDall,definition,
    ( vacuousDall
    = ( ! [X1: $i > $o,X2: $i] :
          ( ( in @ X2 @ emptyset )
         => ( X1 @ X2 ) ) ) ) ).

thf(def_quantDeMorgan1,definition,
    ( quantDeMorgan1
    = ( ! [X1: $i,X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) )
         => ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) ) ) ) ) ).

thf(def_quantDeMorgan2,definition,
    ( quantDeMorgan2
    = ( ! [X1: $i,X2: $i > $o] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) ) ) ) ) ).

thf(def_quantDeMorgan3,definition,
    ( quantDeMorgan3
    = ( ! [X1: $i,X2: $i > $o] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) ) ) ) ) ).

thf(def_quantDeMorgan4,definition,
    ( quantDeMorgan4
    = ( ! [X1: $i,X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) )
         => ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) ) ) ) ) ).

thf(def_prop2setI,definition,
    ( prop2setI
    = ( ! [X1: $o] :
          ( X1
         => ( in @ emptyset @ ( prop2set @ X1 ) ) ) ) ) ).

thf(def_prop2set2propI,definition,
    ( prop2set2propI
    = ( ! [X1: $o] :
          ( X1
         => ( set2prop @ ( prop2set @ X1 ) ) ) ) ) ).

thf(def_notdexE,definition,
    ( notdexE
    = ( ! [X1: $i,X2: $i > $o] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) ) ) ) ) ).

thf(def_notdallE,definition,
    ( notdallE
    = ( ! [X1: $i,X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) )
         => ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) ) ) ) ) ).

thf(def_exuI1,definition,
    ( exuI1
    = ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
         => ( exu @ X1 ) ) ) ) ).

thf(def_exuI3,definition,
    ( exuI3
    = ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ~ ( X1 @ X2 )
         => ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
           => ( exu @ X1 ) ) ) ) ) ).

thf(def_exuI2,definition,
    ( exuI2
    = ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                    = ( X3 = X2 ) )
         => ( exu @ X1 ) ) ) ) ).

thf(def_inCongP,definition,
    ( inCongP
    = ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( in @ X3 @ X1 )
               => ( in @ X4 @ X2 ) ) ) ) ) ) ).

thf(def_in__Cong,definition,
    ( in__Cong
    = ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( in @ X3 @ X1 )
                = ( in @ X4 @ X2 ) ) ) ) ) ) ).

thf(def_exuE3u,definition,
    ( exuE3u
    = ( ! [X1: $i > $o] :
          ( ( exu @ X1 )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) ) ) ) ).

thf(def_exu__Cong,definition,
    ( exu__Cong
    = ( ! [X1: $i > $o,X2: $i > $o] :
          ( ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( X1 @ X3 )
                = ( X2 @ X4 ) ) )
         => ( ( exu @ X1 )
            = ( exu @ X2 ) ) ) ) ) ).

thf(def_emptyset__Cong,definition,
    ( emptyset__Cong
    = ( emptyset = emptyset ) ) ).

thf(def_setadjoin__Cong,definition,
    ( setadjoin__Cong
    = ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( setadjoin @ X1 @ X3 )
                = ( setadjoin @ X2 @ X4 ) ) ) ) ) ) ).

thf(powerset__Cong,conjecture,
    ( ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
            = ( in @ X3 @ X2 ) )
       => ( X1 = X2 ) )
   => ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
            = ( ( X3 != X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
              = ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) ) ) )
         => ( ! [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 )
                           => ( exu @ ( X1 @ X3 ) ) )
                       => ~ ! [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] :
                              ( ( exu @ X1 )
                             => ( 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: $i > $o] :
                                      ( ( exu @ X1 )
                                     => ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) ) )
                                 => ( ! [X1: $o,X2: $i] :
                                        ( ( in @ X2 @ ( prop2set @ X1 ) )
                                       => X1 )
                                   => ( ! [X1: $i] :
                                          ( ( in @ X1 @ emptyset )
                                         => ! [X2: $o] : X2 )
                                     => ( ! [X1: $i] :
                                            ~ ( in @ X1 @ emptyset )
                                       => ( ! [X1: $i] :
                                              ~ ( in @ X1 @ emptyset )
                                         => ( ! [X1: $i > $o] :
                                                ( ( exu @ X1 )
                                               => ~ ! [X2: $i] :
                                                      ~ ( X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( in @ X3 @ X2 ) )
                                                 => ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ X1 ) )
                                                   => ( X1 = X2 ) ) )
                                             => ( ! [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] :
                                                          ( ( nonempty @ X1 )
                                                         => ~ ! [X2: $i] :
                                                                ~ ( in @ X2 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ( X2 @ X3 )
                                                             => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ~ ! [X2: $i] :
                                                                    ~ ( in @ X2 @ X1 )
                                                             => ( nonempty @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                           => ( ( 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 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                       => ( ( X3 != X1 )
                                                                         => ( in @ X3 @ X2 ) ) )
                                                                   => ( ! [X1: $i] :
                                                                          ( ( dsetconstr @ X1
                                                                            @ ^ [X2: $i] : ~ $false )
                                                                          = X1 )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X2 )
                                                                               => ( in @ X3 @ X1 ) )
                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                       => ( ! [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] :
                                                                                          ( ( exu @ X1 )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                    = ( X3 = X2 ) ) )
                                                                                     => ( ! [X1: $i] :
                                                                                            ( ( nonempty @ X1 )
                                                                                           => ~ ! [X2: $i] :
                                                                                                  ~ ( in @ X2 @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                             => ( X1 = X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 != X2 )
                                                                                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ( X3 != X1 )
                                                                                                       => ( X3 = X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                             != emptyset ) )
                                                                                                       => ( ! [X1: $i > $o,X2: $i] :
                                                                                                              ( ( in @ X2 @ emptyset )
                                                                                                             => ( X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( X2 @ X3 ) )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( X2 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                  ( ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                 => ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                    ( ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                   => ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( X2 @ X3 ) )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( X2 @ X3 ) ) )
                                                                                                                 => ( ! [X1: $o] :
                                                                                                                        ( X1
                                                                                                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                                   => ( ! [X1: $o] :
                                                                                                                          ( X1
                                                                                                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                            ( ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                           => ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( X2 @ X3 ) )
                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( X2 @ X3 ) ) )
                                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                      ( ( X1 @ X2 )
                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                            ( ( X1 @ X3 )
                                                                                                                                           => ( X2 = X3 ) ) )
                                                                                                                               => ( exu @ X1 ) )
                                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                        ~ ( X1 @ X2 )
                                                                                                                                 => ( ! [X2: $i,X3: $i] :
                                                                                                                                        ( ( X1 @ X2 )
                                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                                                   => ( exu @ X1 ) ) )
                                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                          ~ ! [X3: $i] :
                                                                                                                                              ( ( X1 @ X3 )
                                                                                                                                              = ( X3 = X2 ) )
                                                                                                                                   => ( exu @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                                          ( ( X3 = X4 )
                                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                                            ( ( X3 = X4 )
                                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                                                          ( ( exu @ X1 )
                                                                                                                                         => ! [X2: $i,X3: $i] :
                                                                                                                                              ( ( X1 @ X2 )
                                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                                                                ( ( X3 = X4 )
                                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                                  = ( X2 @ X4 ) ) )
                                                                                                                                           => ( ( exu @ X1 )
                                                                                                                                              = ( exu @ X2 ) ) )
                                                                                                                                       => ( ( emptyset = emptyset )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                                                    ( ( X3 = X4 )
                                                                                                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                                           => ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                               => ( ( powerset @ X1 )
                                                                                                                                                  = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ( ! [X1: $i,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
              = ( in @ X3 @ X2 ) )
         => ( X1 = X2 ) )
     => ( ! [X1: $i] :
            ~ ( in @ X1 @ emptyset )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
              = ( ( X3 != X1 )
               => ( in @ X3 @ X2 ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X2 @ ( powerset @ X1 ) )
                = ( ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ X1 ) ) ) )
           => ( ! [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 )
                             => ( exu @ ( X1 @ X3 ) ) )
                         => ~ ! [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] :
                                ( ( exu @ X1 )
                               => ( 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: $i > $o] :
                                        ( ( exu @ X1 )
                                       => ~ ! [X2: $i] :
                                              ( ( X1 @ X2 )
                                             => ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) ) )
                                   => ( ! [X1: $o,X2: $i] :
                                          ( ( in @ X2 @ ( prop2set @ X1 ) )
                                         => X1 )
                                     => ( ! [X1: $i] :
                                            ( ( in @ X1 @ emptyset )
                                           => ! [X2: $o] : X2 )
                                       => ( ! [X1: $i] :
                                              ~ ( in @ X1 @ emptyset )
                                         => ( ! [X1: $i] :
                                                ~ ( in @ X1 @ emptyset )
                                           => ( ! [X1: $i > $o] :
                                                  ( ( exu @ X1 )
                                                 => ~ ! [X2: $i] :
                                                        ~ ( X1 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( in @ X3 @ X2 ) )
                                                   => ( ! [X3: $i] :
                                                          ( ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ X1 ) )
                                                     => ( X1 = X2 ) ) )
                                               => ( ! [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] :
                                                            ( ( nonempty @ X1 )
                                                           => ~ ! [X2: $i] :
                                                                  ~ ( in @ X2 @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( ( X2 @ X3 )
                                                               => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                                         => ( ! [X1: $i] :
                                                                ( ~ ! [X2: $i] :
                                                                      ~ ( in @ X2 @ X1 )
                                                               => ( nonempty @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                             => ( ( 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 ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                         => ( ( X3 != X1 )
                                                                           => ( in @ X3 @ X2 ) ) )
                                                                     => ( ! [X1: $i] :
                                                                            ( ( dsetconstr @ X1
                                                                              @ ^ [X2: $i] : ~ $false )
                                                                            = X1 )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X2 )
                                                                                 => ( in @ X3 @ X1 ) )
                                                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                         => ( ! [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] :
                                                                                            ( ( exu @ X1 )
                                                                                           => ~ ! [X2: $i] :
                                                                                                  ~ ! [X3: $i] :
                                                                                                      ( ( X1 @ X3 )
                                                                                                      = ( X3 = X2 ) ) )
                                                                                       => ( ! [X1: $i] :
                                                                                              ( ( nonempty @ X1 )
                                                                                             => ~ ! [X2: $i] :
                                                                                                    ~ ( in @ X2 @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                               => ( X1 = X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 != X2 )
                                                                                                 => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                       => ( ( X3 != X1 )
                                                                                                         => ( X3 = X2 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                                               != emptyset ) )
                                                                                                         => ( ! [X1: $i > $o,X2: $i] :
                                                                                                                ( ( in @ X2 @ emptyset )
                                                                                                               => ( X1 @ X2 ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( X2 @ X3 ) )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( X2 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                    ( ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                   => ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                      ( ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                     => ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( X2 @ X3 ) )
                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( X2 @ X3 ) ) )
                                                                                                                   => ( ! [X1: $o] :
                                                                                                                          ( X1
                                                                                                                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                                     => ( ! [X1: $o] :
                                                                                                                            ( X1
                                                                                                                           => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                              ( ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                                             => ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( X2 @ X3 ) )
                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                                     => ( X2 @ X3 ) ) )
                                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                        ( ( X1 @ X2 )
                                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                                              ( ( X1 @ X3 )
                                                                                                                                             => ( X2 = X3 ) ) )
                                                                                                                                 => ( exu @ X1 ) )
                                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                          ~ ( X1 @ X2 )
                                                                                                                                   => ( ! [X2: $i,X3: $i] :
                                                                                                                                          ( ( X1 @ X2 )
                                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                                           => ( X2 = X3 ) ) )
                                                                                                                                     => ( exu @ X1 ) ) )
                                                                                                                               => ( ! [X1: $i > $o] :
                                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                                            ~ ! [X3: $i] :
                                                                                                                                                ( ( X1 @ X3 )
                                                                                                                                                = ( X3 = X2 ) )
                                                                                                                                     => ( exu @ X1 ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                                            ( ( X3 = X4 )
                                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                                             => ( in @ X4 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                                                              ( ( X3 = X4 )
                                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                                                = ( in @ X4 @ X2 ) ) ) )
                                                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                                                            ( ( exu @ X1 )
                                                                                                                                           => ! [X2: $i,X3: $i] :
                                                                                                                                                ( ( X1 @ X2 )
                                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                              ( ! [X3: $i,X4: $i] :
                                                                                                                                                  ( ( X3 = X4 )
                                                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                                                    = ( X2 @ X4 ) ) )
                                                                                                                                             => ( ( exu @ X1 )
                                                                                                                                                = ( exu @ X2 ) ) )
                                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                                                                      ( ( X3 = X4 )
                                                                                                                                                     => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                                             => ! [X1: $i,X2: $i] :
                                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                                 => ( ( powerset @ X1 )
                                                                                                                                                    = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[powerset__Cong]) ).

thf(h1,assumption,
    ! [X1: $i,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X1 )
          = ( in @ X3 @ X2 ) )
     => ( X1 = X2 ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
            = ( ( X3 != X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
              = ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) ) ) )
         => ( ! [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 )
                           => ( exu @ ( X1 @ X3 ) ) )
                       => ~ ! [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] :
                              ( ( exu @ X1 )
                             => ( 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: $i > $o] :
                                      ( ( exu @ X1 )
                                     => ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) ) )
                                 => ( ! [X1: $o,X2: $i] :
                                        ( ( in @ X2 @ ( prop2set @ X1 ) )
                                       => X1 )
                                   => ( ! [X1: $i] :
                                          ( ( in @ X1 @ emptyset )
                                         => ! [X2: $o] : X2 )
                                     => ( ! [X1: $i] :
                                            ~ ( in @ X1 @ emptyset )
                                       => ( ! [X1: $i] :
                                              ~ ( in @ X1 @ emptyset )
                                         => ( ! [X1: $i > $o] :
                                                ( ( exu @ X1 )
                                               => ~ ! [X2: $i] :
                                                      ~ ( X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( in @ X3 @ X2 ) )
                                                 => ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ X1 ) )
                                                   => ( X1 = X2 ) ) )
                                             => ( ! [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] :
                                                          ( ( nonempty @ X1 )
                                                         => ~ ! [X2: $i] :
                                                                ~ ( in @ X2 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ( X2 @ X3 )
                                                             => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ~ ! [X2: $i] :
                                                                    ~ ( in @ X2 @ X1 )
                                                             => ( nonempty @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                           => ( ( 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 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                       => ( ( X3 != X1 )
                                                                         => ( in @ X3 @ X2 ) ) )
                                                                   => ( ! [X1: $i] :
                                                                          ( ( dsetconstr @ X1
                                                                            @ ^ [X2: $i] : ~ $false )
                                                                          = X1 )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X2 )
                                                                               => ( in @ X3 @ X1 ) )
                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                       => ( ! [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] :
                                                                                          ( ( exu @ X1 )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                    = ( X3 = X2 ) ) )
                                                                                     => ( ! [X1: $i] :
                                                                                            ( ( nonempty @ X1 )
                                                                                           => ~ ! [X2: $i] :
                                                                                                  ~ ( in @ X2 @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                             => ( X1 = X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 != X2 )
                                                                                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ( X3 != X1 )
                                                                                                       => ( X3 = X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                             != emptyset ) )
                                                                                                       => ( ! [X1: $i > $o,X2: $i] :
                                                                                                              ( ( in @ X2 @ emptyset )
                                                                                                             => ( X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( X2 @ X3 ) )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( X2 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                  ( ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                 => ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                    ( ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                   => ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( X2 @ X3 ) )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( X2 @ X3 ) ) )
                                                                                                                 => ( ! [X1: $o] :
                                                                                                                        ( X1
                                                                                                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                                   => ( ! [X1: $o] :
                                                                                                                          ( X1
                                                                                                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                            ( ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                           => ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( X2 @ X3 ) )
                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( X2 @ X3 ) ) )
                                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                      ( ( X1 @ X2 )
                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                            ( ( X1 @ X3 )
                                                                                                                                           => ( X2 = X3 ) ) )
                                                                                                                               => ( exu @ X1 ) )
                                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                        ~ ( X1 @ X2 )
                                                                                                                                 => ( ! [X2: $i,X3: $i] :
                                                                                                                                        ( ( X1 @ X2 )
                                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                                                   => ( exu @ X1 ) ) )
                                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                          ~ ! [X3: $i] :
                                                                                                                                              ( ( X1 @ X3 )
                                                                                                                                              = ( X3 = X2 ) )
                                                                                                                                   => ( exu @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                                          ( ( X3 = X4 )
                                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                                            ( ( X3 = X4 )
                                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                                                          ( ( exu @ X1 )
                                                                                                                                         => ! [X2: $i,X3: $i] :
                                                                                                                                              ( ( X1 @ X2 )
                                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                                                                ( ( X3 = X4 )
                                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                                  = ( X2 @ X4 ) ) )
                                                                                                                                           => ( ( exu @ X1 )
                                                                                                                                              = ( exu @ X2 ) ) )
                                                                                                                                       => ( ( emptyset = emptyset )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                                                    ( ( X3 = X4 )
                                                                                                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                                           => ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                               => ( ( powerset @ X1 )
                                                                                                                                                  = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ! [X1: $i] :
      ~ ( in @ X1 @ emptyset ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
          = ( ( X3 != X1 )
           => ( in @ X3 @ X2 ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ ( powerset @ X1 ) )
            = ( ! [X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ X1 ) ) ) )
       => ( ! [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 )
                         => ( exu @ ( X1 @ X3 ) ) )
                     => ~ ! [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] :
                            ( ( exu @ X1 )
                           => ( 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: $i > $o] :
                                    ( ( exu @ X1 )
                                   => ~ ! [X2: $i] :
                                          ( ( X1 @ X2 )
                                         => ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) ) )
                               => ( ! [X1: $o,X2: $i] :
                                      ( ( in @ X2 @ ( prop2set @ X1 ) )
                                     => X1 )
                                 => ( ! [X1: $i] :
                                        ( ( in @ X1 @ emptyset )
                                       => ! [X2: $o] : X2 )
                                   => ( ! [X1: $i] :
                                          ~ ( in @ X1 @ emptyset )
                                     => ( ! [X1: $i] :
                                            ~ ( in @ X1 @ emptyset )
                                       => ( ! [X1: $i > $o] :
                                              ( ( exu @ X1 )
                                             => ~ ! [X2: $i] :
                                                    ~ ( X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ X2 ) )
                                               => ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ X1 ) )
                                                 => ( X1 = X2 ) ) )
                                           => ( ! [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] :
                                                        ( ( nonempty @ X1 )
                                                       => ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( ( X2 @ X3 )
                                                           => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ~ ! [X2: $i] :
                                                                  ~ ( in @ X2 @ X1 )
                                                           => ( nonempty @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                         => ( ( 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 ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                     => ( ( X3 != X1 )
                                                                       => ( in @ X3 @ X2 ) ) )
                                                                 => ( ! [X1: $i] :
                                                                        ( ( dsetconstr @ X1
                                                                          @ ^ [X2: $i] : ~ $false )
                                                                        = X1 )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X2 )
                                                                             => ( in @ X3 @ X1 ) )
                                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                     => ( ! [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] :
                                                                                        ( ( exu @ X1 )
                                                                                       => ~ ! [X2: $i] :
                                                                                              ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                  = ( X3 = X2 ) ) )
                                                                                   => ( ! [X1: $i] :
                                                                                          ( ( nonempty @ X1 )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ~ ( in @ X2 @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                           => ( X1 = X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 != X2 )
                                                                                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ( X3 != X1 )
                                                                                                     => ( X3 = X2 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                                           != emptyset ) )
                                                                                                     => ( ! [X1: $i > $o,X2: $i] :
                                                                                                            ( ( in @ X2 @ emptyset )
                                                                                                           => ( X1 @ X2 ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( X2 @ X3 ) )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( X2 @ X3 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                ( ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                               => ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                  ( ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                 => ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( X2 @ X3 ) )
                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( X2 @ X3 ) ) )
                                                                                                               => ( ! [X1: $o] :
                                                                                                                      ( X1
                                                                                                                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                                 => ( ! [X1: $o] :
                                                                                                                        ( X1
                                                                                                                       => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                          ( ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                                         => ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( X2 @ X3 ) )
                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                                 => ( X2 @ X3 ) ) )
                                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                    ( ( X1 @ X2 )
                                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                                          ( ( X1 @ X3 )
                                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                                             => ( exu @ X1 ) )
                                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                      ~ ( X1 @ X2 )
                                                                                                                               => ( ! [X2: $i,X3: $i] :
                                                                                                                                      ( ( X1 @ X2 )
                                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                                       => ( X2 = X3 ) ) )
                                                                                                                                 => ( exu @ X1 ) ) )
                                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                        ~ ! [X3: $i] :
                                                                                                                                            ( ( X1 @ X3 )
                                                                                                                                            = ( X3 = X2 ) )
                                                                                                                                 => ( exu @ X1 ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                                                        ( ( X3 = X4 )
                                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                                         => ( in @ X4 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                                          ( ( X3 = X4 )
                                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                                            = ( in @ X4 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                                                        ( ( exu @ X1 )
                                                                                                                                       => ! [X2: $i,X3: $i] :
                                                                                                                                            ( ( X1 @ X2 )
                                                                                                                                           => ( ( X1 @ X3 )
                                                                                                                                             => ( X2 = X3 ) ) ) )
                                                                                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                          ( ! [X3: $i,X4: $i] :
                                                                                                                                              ( ( X3 = X4 )
                                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                                                = ( X2 @ X4 ) ) )
                                                                                                                                         => ( ( exu @ X1 )
                                                                                                                                            = ( exu @ X2 ) ) )
                                                                                                                                     => ( ( emptyset = emptyset )
                                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                                                  ( ( X3 = X4 )
                                                                                                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                                         => ! [X1: $i,X2: $i] :
                                                                                                                                              ( ( X1 = X2 )
                                                                                                                                             => ( ( powerset @ X1 )
                                                                                                                                                = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
      = ( ( X3 != X1 )
       => ( in @ X3 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
          = ( ! [X3: $i] :
                ( ( in @ X3 @ X2 )
               => ( in @ X3 @ X1 ) ) ) )
     => ( ! [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 )
                       => ( exu @ ( X1 @ X3 ) ) )
                   => ~ ! [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] :
                          ( ( exu @ X1 )
                         => ( 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: $i > $o] :
                                  ( ( exu @ X1 )
                                 => ~ ! [X2: $i] :
                                        ( ( X1 @ X2 )
                                       => ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) ) )
                             => ( ! [X1: $o,X2: $i] :
                                    ( ( in @ X2 @ ( prop2set @ X1 ) )
                                   => X1 )
                               => ( ! [X1: $i] :
                                      ( ( in @ X1 @ emptyset )
                                     => ! [X2: $o] : X2 )
                                 => ( ! [X1: $i] :
                                        ~ ( in @ X1 @ emptyset )
                                   => ( ! [X1: $i] :
                                          ~ ( in @ X1 @ emptyset )
                                     => ( ! [X1: $i > $o] :
                                            ( ( exu @ X1 )
                                           => ~ ! [X2: $i] :
                                                  ~ ( X1 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( in @ X3 @ X2 ) )
                                             => ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ X1 ) )
                                               => ( X1 = X2 ) ) )
                                         => ( ! [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] :
                                                      ( ( nonempty @ X1 )
                                                     => ~ ! [X2: $i] :
                                                            ~ ( in @ X2 @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( ( X2 @ X3 )
                                                         => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ~ ! [X2: $i] :
                                                                ~ ( in @ X2 @ X1 )
                                                         => ( nonempty @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                       => ( ( 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 ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                   => ( ( X3 != X1 )
                                                                     => ( in @ X3 @ X2 ) ) )
                                                               => ( ! [X1: $i] :
                                                                      ( ( dsetconstr @ X1
                                                                        @ ^ [X2: $i] : ~ $false )
                                                                      = X1 )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ! [X3: $i] :
                                                                            ( ( in @ X3 @ X2 )
                                                                           => ( in @ X3 @ X1 ) )
                                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                   => ( ! [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] :
                                                                                      ( ( exu @ X1 )
                                                                                     => ~ ! [X2: $i] :
                                                                                            ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                                = ( X3 = X2 ) ) )
                                                                                 => ( ! [X1: $i] :
                                                                                        ( ( nonempty @ X1 )
                                                                                       => ~ ! [X2: $i] :
                                                                                              ~ ( in @ X2 @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                         => ( X1 = X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 != X2 )
                                                                                           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( ( X3 != X1 )
                                                                                                   => ( X3 = X2 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                        ( ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                                         != emptyset ) )
                                                                                                   => ( ! [X1: $i > $o,X2: $i] :
                                                                                                          ( ( in @ X2 @ emptyset )
                                                                                                         => ( X1 @ X2 ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( X2 @ X3 ) )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( X2 @ X3 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                              ( ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                             => ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                ( ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                               => ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( X2 @ X3 ) )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( X2 @ X3 ) ) )
                                                                                                             => ( ! [X1: $o] :
                                                                                                                    ( X1
                                                                                                                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                               => ( ! [X1: $o] :
                                                                                                                      ( X1
                                                                                                                     => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                        ( ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                                       => ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( X2 @ X3 ) )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ( X2 @ X3 ) ) )
                                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                  ( ( X1 @ X2 )
                                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                                        ( ( X1 @ X3 )
                                                                                                                                       => ( X2 = X3 ) ) )
                                                                                                                           => ( exu @ X1 ) )
                                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                    ~ ( X1 @ X2 )
                                                                                                                             => ( ! [X2: $i,X3: $i] :
                                                                                                                                    ( ( X1 @ X2 )
                                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                                     => ( X2 = X3 ) ) )
                                                                                                                               => ( exu @ X1 ) ) )
                                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                      ~ ! [X3: $i] :
                                                                                                                                          ( ( X1 @ X3 )
                                                                                                                                          = ( X3 = X2 ) )
                                                                                                                               => ( exu @ X1 ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                                                      ( ( X3 = X4 )
                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                       => ( in @ X4 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                                                        ( ( X3 = X4 )
                                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                                          = ( in @ X4 @ X2 ) ) ) )
                                                                                                                               => ( ! [X1: $i > $o] :
                                                                                                                                      ( ( exu @ X1 )
                                                                                                                                     => ! [X2: $i,X3: $i] :
                                                                                                                                          ( ( X1 @ X2 )
                                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                                           => ( X2 = X3 ) ) ) )
                                                                                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                        ( ! [X3: $i,X4: $i] :
                                                                                                                                            ( ( X3 = X4 )
                                                                                                                                           => ( ( X1 @ X3 )
                                                                                                                                              = ( X2 @ X4 ) ) )
                                                                                                                                       => ( ( exu @ X1 )
                                                                                                                                          = ( exu @ X2 ) ) )
                                                                                                                                   => ( ( emptyset = emptyset )
                                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                                                                ( ( X3 = X4 )
                                                                                                                                               => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                                       => ! [X1: $i,X2: $i] :
                                                                                                                                            ( ( X1 = X2 )
                                                                                                                                           => ( ( powerset @ X1 )
                                                                                                                                              = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ ( powerset @ X1 ) )
      = ( ! [X3: $i] :
            ( ( in @ X3 @ X2 )
           => ( in @ X3 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h8,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 )
                     => ( exu @ ( X1 @ X3 ) ) )
                 => ~ ! [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] :
                        ( ( exu @ X1 )
                       => ( 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: $i > $o] :
                                ( ( exu @ X1 )
                               => ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) ) )
                           => ( ! [X1: $o,X2: $i] :
                                  ( ( in @ X2 @ ( prop2set @ X1 ) )
                                 => X1 )
                             => ( ! [X1: $i] :
                                    ( ( in @ X1 @ emptyset )
                                   => ! [X2: $o] : X2 )
                               => ( ! [X1: $i] :
                                      ~ ( in @ X1 @ emptyset )
                                 => ( ! [X1: $i] :
                                        ~ ( in @ X1 @ emptyset )
                                   => ( ! [X1: $i > $o] :
                                          ( ( exu @ X1 )
                                         => ~ ! [X2: $i] :
                                                ~ ( X1 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( in @ X3 @ X2 ) )
                                           => ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ X1 ) )
                                             => ( X1 = X2 ) ) )
                                       => ( ! [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] :
                                                    ( ( nonempty @ X1 )
                                                   => ~ ! [X2: $i] :
                                                          ~ ( in @ X2 @ X1 ) )
                                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( ( X2 @ X3 )
                                                       => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 )
                                                       => ( nonempty @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                     => ( ( 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 ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                 => ( ( X3 != X1 )
                                                                   => ( in @ X3 @ X2 ) ) )
                                                             => ( ! [X1: $i] :
                                                                    ( ( dsetconstr @ X1
                                                                      @ ^ [X2: $i] : ~ $false )
                                                                    = X1 )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ! [X3: $i] :
                                                                          ( ( in @ X3 @ X2 )
                                                                         => ( in @ X3 @ X1 ) )
                                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                 => ( ! [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] :
                                                                                    ( ( exu @ X1 )
                                                                                   => ~ ! [X2: $i] :
                                                                                          ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                              = ( X3 = X2 ) ) )
                                                                               => ( ! [X1: $i] :
                                                                                      ( ( nonempty @ X1 )
                                                                                     => ~ ! [X2: $i] :
                                                                                            ~ ( in @ X2 @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                       => ( X1 = X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 != X2 )
                                                                                         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                               => ( ( X3 != X1 )
                                                                                                 => ( X3 = X2 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                      ( ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                                       != emptyset ) )
                                                                                                 => ( ! [X1: $i > $o,X2: $i] :
                                                                                                        ( ( in @ X2 @ emptyset )
                                                                                                       => ( X1 @ X2 ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( X2 @ X3 ) )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( X2 @ X3 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                           => ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                              ( ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                             => ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( X2 @ X3 ) )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( X2 @ X3 ) ) )
                                                                                                           => ( ! [X1: $o] :
                                                                                                                  ( X1
                                                                                                                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                             => ( ! [X1: $o] :
                                                                                                                    ( X1
                                                                                                                   => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                      ( ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                                     => ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                        ( ~ ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( X2 @ X3 ) )
                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                                             => ( X2 @ X3 ) ) )
                                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                ( ( X1 @ X2 )
                                                                                                                               => ~ ! [X3: $i] :
                                                                                                                                      ( ( X1 @ X3 )
                                                                                                                                     => ( X2 = X3 ) ) )
                                                                                                                         => ( exu @ X1 ) )
                                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                  ~ ( X1 @ X2 )
                                                                                                                           => ( ! [X2: $i,X3: $i] :
                                                                                                                                  ( ( X1 @ X2 )
                                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                                   => ( X2 = X3 ) ) )
                                                                                                                             => ( exu @ X1 ) ) )
                                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                                    ~ ! [X3: $i] :
                                                                                                                                        ( ( X1 @ X3 )
                                                                                                                                        = ( X3 = X2 ) )
                                                                                                                             => ( exu @ X1 ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                                    ( ( X3 = X4 )
                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                     => ( in @ X4 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                                                      ( ( X3 = X4 )
                                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                                        = ( in @ X4 @ X2 ) ) ) )
                                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                                    ( ( exu @ X1 )
                                                                                                                                   => ! [X2: $i,X3: $i] :
                                                                                                                                        ( ( X1 @ X2 )
                                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                                                                          ( ( X3 = X4 )
                                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                                            = ( X2 @ X4 ) ) )
                                                                                                                                     => ( ( exu @ X1 )
                                                                                                                                        = ( exu @ X2 ) ) )
                                                                                                                                 => ( ( emptyset = emptyset )
                                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                                                              ( ( X3 = X4 )
                                                                                                                                             => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                                     => ! [X1: $i,X2: $i] :
                                                                                                                                          ( ( X1 = X2 )
                                                                                                                                         => ( ( powerset @ X1 )
                                                                                                                                            = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ ( setunion @ X1 ) )
      = ( ~ ! [X3: $i] :
              ( ( in @ X2 @ X3 )
             => ~ ( in @ X3 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h10,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 )
                   => ( exu @ ( X1 @ X3 ) ) )
               => ~ ! [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] :
                      ( ( exu @ X1 )
                     => ( 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: $i > $o] :
                              ( ( exu @ X1 )
                             => ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) ) )
                         => ( ! [X1: $o,X2: $i] :
                                ( ( in @ X2 @ ( prop2set @ X1 ) )
                               => X1 )
                           => ( ! [X1: $i] :
                                  ( ( in @ X1 @ emptyset )
                                 => ! [X2: $o] : X2 )
                             => ( ! [X1: $i] :
                                    ~ ( in @ X1 @ emptyset )
                               => ( ! [X1: $i] :
                                      ~ ( in @ X1 @ emptyset )
                                 => ( ! [X1: $i > $o] :
                                        ( ( exu @ X1 )
                                       => ~ ! [X2: $i] :
                                              ~ ( X1 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( in @ X3 @ X2 ) )
                                         => ( ! [X3: $i] :
                                                ( ( in @ X3 @ X2 )
                                               => ( in @ X3 @ X1 ) )
                                           => ( X1 = X2 ) ) )
                                     => ( ! [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] :
                                                  ( ( nonempty @ X1 )
                                                 => ~ ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 ) )
                                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( ( X2 @ X3 )
                                                     => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ~ ! [X2: $i] :
                                                            ~ ( in @ X2 @ X1 )
                                                     => ( nonempty @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                   => ( ( 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 ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                               => ( ( X3 != X1 )
                                                                 => ( in @ X3 @ X2 ) ) )
                                                           => ( ! [X1: $i] :
                                                                  ( ( dsetconstr @ X1
                                                                    @ ^ [X2: $i] : ~ $false )
                                                                  = X1 )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ! [X3: $i] :
                                                                        ( ( in @ X3 @ X2 )
                                                                       => ( in @ X3 @ X1 ) )
                                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                               => ( ! [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] :
                                                                                  ( ( exu @ X1 )
                                                                                 => ~ ! [X2: $i] :
                                                                                        ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                            = ( X3 = X2 ) ) )
                                                                             => ( ! [X1: $i] :
                                                                                    ( ( nonempty @ X1 )
                                                                                   => ~ ! [X2: $i] :
                                                                                          ~ ( in @ X2 @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                     => ( X1 = X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 != X2 )
                                                                                       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ( X3 != X1 )
                                                                                               => ( X3 = X2 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                    ( ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                                     != emptyset ) )
                                                                                               => ( ! [X1: $i > $o,X2: $i] :
                                                                                                      ( ( in @ X2 @ emptyset )
                                                                                                     => ( X1 @ X2 ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                        ( ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( X2 @ X3 ) )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( X2 @ X3 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                         => ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                           => ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( X2 @ X3 ) )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( X2 @ X3 ) ) )
                                                                                                         => ( ! [X1: $o] :
                                                                                                                ( X1
                                                                                                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                           => ( ! [X1: $o] :
                                                                                                                  ( X1
                                                                                                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                    ( ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                   => ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( X2 @ X3 ) )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( X2 @ X3 ) ) )
                                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                              ( ( X1 @ X2 )
                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                    ( ( X1 @ X3 )
                                                                                                                                   => ( X2 = X3 ) ) )
                                                                                                                       => ( exu @ X1 ) )
                                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                ~ ( X1 @ X2 )
                                                                                                                         => ( ! [X2: $i,X3: $i] :
                                                                                                                                ( ( X1 @ X2 )
                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                 => ( X2 = X3 ) ) )
                                                                                                                           => ( exu @ X1 ) ) )
                                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                                  ~ ! [X3: $i] :
                                                                                                                                      ( ( X1 @ X3 )
                                                                                                                                      = ( X3 = X2 ) )
                                                                                                                           => ( exu @ X1 ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                                  ( ( X3 = X4 )
                                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                                   => ( in @ X4 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                                    ( ( X3 = X4 )
                                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                                      = ( in @ X4 @ X2 ) ) ) )
                                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                                  ( ( exu @ X1 )
                                                                                                                                 => ! [X2: $i,X3: $i] :
                                                                                                                                      ( ( X1 @ X2 )
                                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                                       => ( X2 = X3 ) ) ) )
                                                                                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                    ( ! [X3: $i,X4: $i] :
                                                                                                                                        ( ( X3 = X4 )
                                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                                          = ( X2 @ X4 ) ) )
                                                                                                                                   => ( ( exu @ X1 )
                                                                                                                                      = ( exu @ X2 ) ) )
                                                                                                                               => ( ( emptyset = emptyset )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                                            ( ( X3 = X4 )
                                                                                                                                           => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                                   => ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ( ( powerset @ X1 )
                                                                                                                                          = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    in @ emptyset @ omega,
    introduced(assumption,[]) ).

thf(h12,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 )
                 => ( exu @ ( X1 @ X3 ) ) )
             => ~ ! [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] :
                    ( ( exu @ X1 )
                   => ( 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: $i > $o] :
                            ( ( exu @ X1 )
                           => ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) ) )
                       => ( ! [X1: $o,X2: $i] :
                              ( ( in @ X2 @ ( prop2set @ X1 ) )
                             => X1 )
                         => ( ! [X1: $i] :
                                ( ( in @ X1 @ emptyset )
                               => ! [X2: $o] : X2 )
                           => ( ! [X1: $i] :
                                  ~ ( in @ X1 @ emptyset )
                             => ( ! [X1: $i] :
                                    ~ ( in @ X1 @ emptyset )
                               => ( ! [X1: $i > $o] :
                                      ( ( exu @ X1 )
                                     => ~ ! [X2: $i] :
                                            ~ ( X1 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( in @ X3 @ X2 ) )
                                       => ( ! [X3: $i] :
                                              ( ( in @ X3 @ X2 )
                                             => ( in @ X3 @ X1 ) )
                                         => ( X1 = X2 ) ) )
                                   => ( ! [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] :
                                                ( ( nonempty @ X1 )
                                               => ~ ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 ) )
                                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( ( X2 @ X3 )
                                                   => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ~ ! [X2: $i] :
                                                          ~ ( in @ X2 @ X1 )
                                                   => ( nonempty @ X1 ) )
                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                 => ( ( 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 ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                             => ( ( X3 != X1 )
                                                               => ( in @ X3 @ X2 ) ) )
                                                         => ( ! [X1: $i] :
                                                                ( ( dsetconstr @ X1
                                                                  @ ^ [X2: $i] : ~ $false )
                                                                = X1 )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ! [X3: $i] :
                                                                      ( ( in @ X3 @ X2 )
                                                                     => ( in @ X3 @ X1 ) )
                                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                             => ( ! [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] :
                                                                                ( ( exu @ X1 )
                                                                               => ~ ! [X2: $i] :
                                                                                      ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                          = ( X3 = X2 ) ) )
                                                                           => ( ! [X1: $i] :
                                                                                  ( ( nonempty @ X1 )
                                                                                 => ~ ! [X2: $i] :
                                                                                        ~ ( in @ X2 @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                   => ( X1 = X2 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 != X2 )
                                                                                     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ( X3 != X1 )
                                                                                             => ( X3 = X2 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                  ( ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                                   != emptyset ) )
                                                                                             => ( ! [X1: $i > $o,X2: $i] :
                                                                                                    ( ( in @ X2 @ emptyset )
                                                                                                   => ( X1 @ X2 ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                      ( ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( X2 @ X3 ) )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( X2 @ X3 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                        ( ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                       => ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                         => ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( X2 @ X3 ) )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( X2 @ X3 ) ) )
                                                                                                       => ( ! [X1: $o] :
                                                                                                              ( X1
                                                                                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                         => ( ! [X1: $o] :
                                                                                                                ( X1
                                                                                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                  ( ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                 => ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                    ( ~ ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( X2 @ X3 ) )
                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                                         => ( X2 @ X3 ) ) )
                                                                                                               => ( ! [X1: $i > $o] :
                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                            ( ( X1 @ X2 )
                                                                                                                           => ~ ! [X3: $i] :
                                                                                                                                  ( ( X1 @ X3 )
                                                                                                                                 => ( X2 = X3 ) ) )
                                                                                                                     => ( exu @ X1 ) )
                                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                              ~ ( X1 @ X2 )
                                                                                                                       => ( ! [X2: $i,X3: $i] :
                                                                                                                              ( ( X1 @ X2 )
                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) )
                                                                                                                         => ( exu @ X1 ) ) )
                                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                                ~ ! [X3: $i] :
                                                                                                                                    ( ( X1 @ X3 )
                                                                                                                                    = ( X3 = X2 ) )
                                                                                                                         => ( exu @ X1 ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                                                ( ( X3 = X4 )
                                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                                 => ( in @ X4 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                                  ( ( X3 = X4 )
                                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                                    = ( in @ X4 @ X2 ) ) ) )
                                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                                ( ( exu @ X1 )
                                                                                                                               => ! [X2: $i,X3: $i] :
                                                                                                                                    ( ( X1 @ X2 )
                                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                                     => ( X2 = X3 ) ) ) )
                                                                                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                  ( ! [X3: $i,X4: $i] :
                                                                                                                                      ( ( X3 = X4 )
                                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                                        = ( X2 @ X4 ) ) )
                                                                                                                                 => ( ( exu @ X1 )
                                                                                                                                    = ( exu @ X2 ) ) )
                                                                                                                             => ( ( emptyset = emptyset )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                                          ( ( X3 = X4 )
                                                                                                                                         => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                                 => ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                     => ( ( powerset @ X1 )
                                                                                                                                        = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ omega )
     => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ),
    introduced(assumption,[]) ).

thf(h14,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 )
               => ( exu @ ( X1 @ X3 ) ) )
           => ~ ! [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] :
                  ( ( exu @ X1 )
                 => ( 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: $i > $o] :
                          ( ( exu @ X1 )
                         => ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) ) )
                     => ( ! [X1: $o,X2: $i] :
                            ( ( in @ X2 @ ( prop2set @ X1 ) )
                           => X1 )
                       => ( ! [X1: $i] :
                              ( ( in @ X1 @ emptyset )
                             => ! [X2: $o] : X2 )
                         => ( ! [X1: $i] :
                                ~ ( in @ X1 @ emptyset )
                           => ( ! [X1: $i] :
                                  ~ ( in @ X1 @ emptyset )
                             => ( ! [X1: $i > $o] :
                                    ( ( exu @ X1 )
                                   => ~ ! [X2: $i] :
                                          ~ ( X1 @ X2 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( in @ X3 @ X2 ) )
                                     => ( ! [X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ( in @ X3 @ X1 ) )
                                       => ( X1 = X2 ) ) )
                                 => ( ! [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] :
                                              ( ( nonempty @ X1 )
                                             => ~ ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 ) )
                                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( ( X2 @ X3 )
                                                 => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ~ ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 )
                                                 => ( nonempty @ X1 ) )
                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                               => ( ( 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 ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                           => ( ( X3 != X1 )
                                                             => ( in @ X3 @ X2 ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ( dsetconstr @ X1
                                                                @ ^ [X2: $i] : ~ $false )
                                                              = X1 )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ! [X3: $i] :
                                                                    ( ( in @ X3 @ X2 )
                                                                   => ( in @ X3 @ X1 ) )
                                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                           => ( ! [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] :
                                                                              ( ( exu @ X1 )
                                                                             => ~ ! [X2: $i] :
                                                                                    ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                        = ( X3 = X2 ) ) )
                                                                         => ( ! [X1: $i] :
                                                                                ( ( nonempty @ X1 )
                                                                               => ~ ! [X2: $i] :
                                                                                      ~ ( in @ X2 @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                 => ( X1 = X2 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 != X2 )
                                                                                   => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                       => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( ( X3 != X1 )
                                                                                           => ( X3 = X2 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                ( ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                                 != emptyset ) )
                                                                                           => ( ! [X1: $i > $o,X2: $i] :
                                                                                                  ( ( in @ X2 @ emptyset )
                                                                                                 => ( X1 @ X2 ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                    ( ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( X2 @ X3 ) )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( X2 @ X3 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                      ( ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                     => ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                        ( ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                       => ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( X2 @ X3 ) )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( X2 @ X3 ) ) )
                                                                                                     => ( ! [X1: $o] :
                                                                                                            ( X1
                                                                                                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                       => ( ! [X1: $o] :
                                                                                                              ( X1
                                                                                                             => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                ( ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                                               => ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                  ( ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( X2 @ X3 ) )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ( X2 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) )
                                                                                                                   => ( exu @ X1 ) )
                                                                                                               => ( ! [X1: $i > $o] :
                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                            ~ ( X1 @ X2 )
                                                                                                                     => ( ! [X2: $i,X3: $i] :
                                                                                                                            ( ( X1 @ X2 )
                                                                                                                           => ( ( X1 @ X3 )
                                                                                                                             => ( X2 = X3 ) ) )
                                                                                                                       => ( exu @ X1 ) ) )
                                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                                        ( ~ ! [X2: $i] :
                                                                                                                              ~ ! [X3: $i] :
                                                                                                                                  ( ( X1 @ X3 )
                                                                                                                                  = ( X3 = X2 ) )
                                                                                                                       => ( exu @ X1 ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                                              ( ( X3 = X4 )
                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                               => ( in @ X4 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                                                ( ( X3 = X4 )
                                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                                  = ( in @ X4 @ X2 ) ) ) )
                                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                                              ( ( exu @ X1 )
                                                                                                                             => ! [X2: $i,X3: $i] :
                                                                                                                                  ( ( X1 @ X2 )
                                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                                   => ( X2 = X3 ) ) ) )
                                                                                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                ( ! [X3: $i,X4: $i] :
                                                                                                                                    ( ( X3 = X4 )
                                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                                      = ( X2 @ X4 ) ) )
                                                                                                                               => ( ( exu @ X1 )
                                                                                                                                  = ( exu @ X2 ) ) )
                                                                                                                           => ( ( emptyset = emptyset )
                                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                                                        ( ( X3 = X4 )
                                                                                                                                       => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                               => ! [X1: $i,X2: $i] :
                                                                                                                                    ( ( X1 = X2 )
                                                                                                                                   => ( ( powerset @ X1 )
                                                                                                                                      = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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 ) ) ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ ( ! [X1: $i > $i > $o,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X2 )
             => ( exu @ ( X1 @ X3 ) ) )
         => ~ ! [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] :
                ( ( exu @ X1 )
               => ( 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: $i > $o] :
                        ( ( exu @ X1 )
                       => ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) ) )
                   => ( ! [X1: $o,X2: $i] :
                          ( ( in @ X2 @ ( prop2set @ X1 ) )
                         => X1 )
                     => ( ! [X1: $i] :
                            ( ( in @ X1 @ emptyset )
                           => ! [X2: $o] : X2 )
                       => ( ! [X1: $i] :
                              ~ ( in @ X1 @ emptyset )
                         => ( ! [X1: $i] :
                                ~ ( in @ X1 @ emptyset )
                           => ( ! [X1: $i > $o] :
                                  ( ( exu @ X1 )
                                 => ~ ! [X2: $i] :
                                        ~ ( X1 @ X2 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( in @ X3 @ X2 ) )
                                   => ( ! [X3: $i] :
                                          ( ( in @ X3 @ X2 )
                                         => ( in @ X3 @ X1 ) )
                                     => ( X1 = X2 ) ) )
                               => ( ! [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] :
                                            ( ( nonempty @ X1 )
                                           => ~ ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 ) )
                                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( ( X2 @ X3 )
                                               => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                         => ( ! [X1: $i] :
                                                ( ~ ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 )
                                               => ( nonempty @ X1 ) )
                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                             => ( ( 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 ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                         => ( ( X3 != X1 )
                                                           => ( in @ X3 @ X2 ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ( dsetconstr @ X1
                                                              @ ^ [X2: $i] : ~ $false )
                                                            = X1 )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ! [X3: $i] :
                                                                  ( ( in @ X3 @ X2 )
                                                                 => ( in @ X3 @ X1 ) )
                                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                         => ( ! [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] :
                                                                            ( ( exu @ X1 )
                                                                           => ~ ! [X2: $i] :
                                                                                  ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                      = ( X3 = X2 ) ) )
                                                                       => ( ! [X1: $i] :
                                                                              ( ( nonempty @ X1 )
                                                                             => ~ ! [X2: $i] :
                                                                                    ~ ( in @ X2 @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                               => ( X1 = X2 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 != X2 )
                                                                                 => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( ( X3 != X1 )
                                                                                         => ( X3 = X2 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                              ( ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                                               != emptyset ) )
                                                                                         => ( ! [X1: $i > $o,X2: $i] :
                                                                                                ( ( in @ X2 @ emptyset )
                                                                                               => ( X1 @ X2 ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                  ( ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( X2 @ X3 ) )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( X2 @ X3 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                    ( ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                   => ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                      ( ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                     => ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                        ( ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( X2 @ X3 ) )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( X2 @ X3 ) ) )
                                                                                                   => ( ! [X1: $o] :
                                                                                                          ( X1
                                                                                                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                     => ( ! [X1: $o] :
                                                                                                            ( X1
                                                                                                           => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                              ( ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                             => ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( X2 @ X3 ) )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( X2 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ~ ! [X3: $i] :
                                                                                                                              ( ( X1 @ X3 )
                                                                                                                             => ( X2 = X3 ) ) )
                                                                                                                 => ( exu @ X1 ) )
                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                          ~ ( X1 @ X2 )
                                                                                                                   => ( ! [X2: $i,X3: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                           => ( X2 = X3 ) ) )
                                                                                                                     => ( exu @ X1 ) ) )
                                                                                                               => ( ! [X1: $i > $o] :
                                                                                                                      ( ~ ! [X2: $i] :
                                                                                                                            ~ ! [X3: $i] :
                                                                                                                                ( ( X1 @ X3 )
                                                                                                                                = ( X3 = X2 ) )
                                                                                                                     => ( exu @ X1 ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                            ( ( X3 = X4 )
                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                             => ( in @ X4 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                                              ( ( X3 = X4 )
                                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                                = ( in @ X4 @ X2 ) ) ) )
                                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                                            ( ( exu @ X1 )
                                                                                                                           => ! [X2: $i,X3: $i] :
                                                                                                                                ( ( X1 @ X2 )
                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                              ( ! [X3: $i,X4: $i] :
                                                                                                                                  ( ( X3 = X4 )
                                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                                    = ( X2 @ X4 ) ) )
                                                                                                                             => ( ( exu @ X1 )
                                                                                                                                = ( exu @ X2 ) ) )
                                                                                                                         => ( ( emptyset = emptyset )
                                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                                                      ( ( X3 = X4 )
                                                                                                                                     => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                             => ! [X1: $i,X2: $i] :
                                                                                                                                  ( ( X1 = X2 )
                                                                                                                                 => ( ( powerset @ X1 )
                                                                                                                                    = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h17,assumption,
    ! [X1: $i > $i > $o,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X2 )
         => ( exu @ ( X1 @ X3 ) ) )
     => ~ ! [X3: $i] :
            ~ ! [X4: $i] :
                ( ( in @ X4 @ X3 )
                = ( ~ ! [X5: $i] :
                        ( ( in @ X5 @ X2 )
                       => ~ ( X1 @ X5 @ X4 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h18,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] :
              ( ( exu @ X1 )
             => ( 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: $i > $o] :
                      ( ( exu @ X1 )
                     => ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) ) )
                 => ( ! [X1: $o,X2: $i] :
                        ( ( in @ X2 @ ( prop2set @ X1 ) )
                       => X1 )
                   => ( ! [X1: $i] :
                          ( ( in @ X1 @ emptyset )
                         => ! [X2: $o] : X2 )
                     => ( ! [X1: $i] :
                            ~ ( in @ X1 @ emptyset )
                       => ( ! [X1: $i] :
                              ~ ( in @ X1 @ emptyset )
                         => ( ! [X1: $i > $o] :
                                ( ( exu @ X1 )
                               => ~ ! [X2: $i] :
                                      ~ ( X1 @ X2 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( in @ X3 @ X2 ) )
                                 => ( ! [X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ( in @ X3 @ X1 ) )
                                   => ( X1 = X2 ) ) )
                             => ( ! [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] :
                                          ( ( nonempty @ X1 )
                                         => ~ ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 ) )
                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( ( X2 @ X3 )
                                             => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                       => ( ! [X1: $i] :
                                              ( ~ ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 )
                                             => ( nonempty @ X1 ) )
                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                           => ( ( 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 ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                       => ( ( X3 != X1 )
                                                         => ( in @ X3 @ X2 ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ( dsetconstr @ X1
                                                            @ ^ [X2: $i] : ~ $false )
                                                          = X1 )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ! [X3: $i] :
                                                                ( ( in @ X3 @ X2 )
                                                               => ( in @ X3 @ X1 ) )
                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                       => ( ! [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] :
                                                                          ( ( exu @ X1 )
                                                                         => ~ ! [X2: $i] :
                                                                                ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                    = ( X3 = X2 ) ) )
                                                                     => ( ! [X1: $i] :
                                                                            ( ( nonempty @ X1 )
                                                                           => ~ ! [X2: $i] :
                                                                                  ~ ( in @ X2 @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                             => ( X1 = X2 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 != X2 )
                                                                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( ( X3 != X1 )
                                                                                       => ( X3 = X2 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                            ( ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                             != emptyset ) )
                                                                                       => ( ! [X1: $i > $o,X2: $i] :
                                                                                              ( ( in @ X2 @ emptyset )
                                                                                             => ( X1 @ X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                ( ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( X2 @ X3 ) )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( X2 @ X3 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                  ( ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                 => ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                    ( ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                   => ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                      ( ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( X2 @ X3 ) )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( X2 @ X3 ) ) )
                                                                                                 => ( ! [X1: $o] :
                                                                                                        ( X1
                                                                                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                   => ( ! [X1: $o] :
                                                                                                          ( X1
                                                                                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                           => ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( X2 @ X3 ) )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                   => ( X2 @ X3 ) ) )
                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                      ( ( X1 @ X2 )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( X1 @ X3 )
                                                                                                                           => ( X2 = X3 ) ) )
                                                                                                               => ( exu @ X1 ) )
                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                        ~ ( X1 @ X2 )
                                                                                                                 => ( ! [X2: $i,X3: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                                   => ( exu @ X1 ) ) )
                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                          ~ ! [X3: $i] :
                                                                                                                              ( ( X1 @ X3 )
                                                                                                                              = ( X3 = X2 ) )
                                                                                                                   => ( exu @ X1 ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                          ( ( X3 = X4 )
                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                            ( ( X3 = X4 )
                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                                          ( ( exu @ X1 )
                                                                                                                         => ! [X2: $i,X3: $i] :
                                                                                                                              ( ( X1 @ X2 )
                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                                                ( ( X3 = X4 )
                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                  = ( X2 @ X4 ) ) )
                                                                                                                           => ( ( exu @ X1 )
                                                                                                                              = ( exu @ X2 ) ) )
                                                                                                                       => ( ( emptyset = emptyset )
                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                                    ( ( X3 = X4 )
                                                                                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                           => ! [X1: $i,X2: $i] :
                                                                                                                                ( ( X1 = X2 )
                                                                                                                               => ( ( powerset @ X1 )
                                                                                                                                  = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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 ) ) ) ),
    introduced(assumption,[]) ).

thf(h20,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] :
            ( ( exu @ X1 )
           => ( 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: $i > $o] :
                    ( ( exu @ X1 )
                   => ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) ) )
               => ( ! [X1: $o,X2: $i] :
                      ( ( in @ X2 @ ( prop2set @ X1 ) )
                     => X1 )
                 => ( ! [X1: $i] :
                        ( ( in @ X1 @ emptyset )
                       => ! [X2: $o] : X2 )
                   => ( ! [X1: $i] :
                          ~ ( in @ X1 @ emptyset )
                     => ( ! [X1: $i] :
                            ~ ( in @ X1 @ emptyset )
                       => ( ! [X1: $i > $o] :
                              ( ( exu @ X1 )
                             => ~ ! [X2: $i] :
                                    ~ ( X1 @ X2 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( in @ X3 @ X2 ) )
                               => ( ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ( in @ X3 @ X1 ) )
                                 => ( X1 = X2 ) ) )
                           => ( ! [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] :
                                        ( ( nonempty @ X1 )
                                       => ~ ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 ) )
                                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( ( X2 @ X3 )
                                           => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                     => ( ! [X1: $i] :
                                            ( ~ ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 )
                                           => ( nonempty @ X1 ) )
                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                         => ( ( 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 ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                     => ( ( X3 != X1 )
                                                       => ( in @ X3 @ X2 ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( dsetconstr @ X1
                                                          @ ^ [X2: $i] : ~ $false )
                                                        = X1 )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ! [X3: $i] :
                                                              ( ( in @ X3 @ X2 )
                                                             => ( in @ X3 @ X1 ) )
                                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                     => ( ! [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] :
                                                                        ( ( exu @ X1 )
                                                                       => ~ ! [X2: $i] :
                                                                              ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                  = ( X3 = X2 ) ) )
                                                                   => ( ! [X1: $i] :
                                                                          ( ( nonempty @ X1 )
                                                                         => ~ ! [X2: $i] :
                                                                                ~ ( in @ X2 @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                           => ( X1 = X2 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 != X2 )
                                                                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( ( X3 != X1 )
                                                                                     => ( X3 = X2 ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                          ( ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( X2 @ X3 ) )
                                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                                           != emptyset ) )
                                                                                     => ( ! [X1: $i > $o,X2: $i] :
                                                                                            ( ( in @ X2 @ emptyset )
                                                                                           => ( X1 @ X2 ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                              ( ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( X2 @ X3 ) )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( X2 @ X3 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                ( ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                               => ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                  ( ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                 => ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                    ( ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( X2 @ X3 ) )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( X2 @ X3 ) ) )
                                                                                               => ( ! [X1: $o] :
                                                                                                      ( X1
                                                                                                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                 => ( ! [X1: $o] :
                                                                                                        ( X1
                                                                                                       => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( X2 @ X3 ) )
                                                                                                         => ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( X2 @ X3 ) )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ( X2 @ X3 ) ) )
                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                    ( ( X1 @ X2 )
                                                                                                                   => ~ ! [X3: $i] :
                                                                                                                          ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                             => ( exu @ X1 ) )
                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                      ~ ( X1 @ X2 )
                                                                                                               => ( ! [X2: $i,X3: $i] :
                                                                                                                      ( ( X1 @ X2 )
                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                       => ( X2 = X3 ) ) )
                                                                                                                 => ( exu @ X1 ) ) )
                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                        ~ ! [X3: $i] :
                                                                                                                            ( ( X1 @ X3 )
                                                                                                                            = ( X3 = X2 ) )
                                                                                                                 => ( exu @ X1 ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                                        ( ( X3 = X4 )
                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                         => ( in @ X4 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                          ( ( X3 = X4 )
                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                            = ( in @ X4 @ X2 ) ) ) )
                                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                                        ( ( exu @ X1 )
                                                                                                                       => ! [X2: $i,X3: $i] :
                                                                                                                            ( ( X1 @ X2 )
                                                                                                                           => ( ( X1 @ X3 )
                                                                                                                             => ( X2 = X3 ) ) ) )
                                                                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                          ( ! [X3: $i,X4: $i] :
                                                                                                                              ( ( X3 = X4 )
                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                                = ( X2 @ X4 ) ) )
                                                                                                                         => ( ( exu @ X1 )
                                                                                                                            = ( exu @ X2 ) ) )
                                                                                                                     => ( ( emptyset = emptyset )
                                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                                  ( ( X3 = X4 )
                                                                                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                         => ! [X1: $i,X2: $i] :
                                                                                                                              ( ( X1 = X2 )
                                                                                                                             => ( ( powerset @ X1 )
                                                                                                                                = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    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 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h22,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ( exu @ X1 )
         => ( 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: $i > $o] :
                  ( ( exu @ X1 )
                 => ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) ) )
             => ( ! [X1: $o,X2: $i] :
                    ( ( in @ X2 @ ( prop2set @ X1 ) )
                   => X1 )
               => ( ! [X1: $i] :
                      ( ( in @ X1 @ emptyset )
                     => ! [X2: $o] : X2 )
                 => ( ! [X1: $i] :
                        ~ ( in @ X1 @ emptyset )
                   => ( ! [X1: $i] :
                          ~ ( in @ X1 @ emptyset )
                     => ( ! [X1: $i > $o] :
                            ( ( exu @ X1 )
                           => ~ ! [X2: $i] :
                                  ~ ( X1 @ X2 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( in @ X3 @ X2 ) )
                             => ( ! [X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ( in @ X3 @ X1 ) )
                               => ( X1 = X2 ) ) )
                         => ( ! [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] :
                                      ( ( nonempty @ X1 )
                                     => ~ ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 ) )
                                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( ( X2 @ X3 )
                                         => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                   => ( ! [X1: $i] :
                                          ( ~ ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 )
                                         => ( nonempty @ X1 ) )
                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                       => ( ( 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 ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                   => ( ( X3 != X1 )
                                                     => ( in @ X3 @ X2 ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ( dsetconstr @ X1
                                                        @ ^ [X2: $i] : ~ $false )
                                                      = X1 )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ! [X3: $i] :
                                                            ( ( in @ X3 @ X2 )
                                                           => ( in @ X3 @ X1 ) )
                                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                   => ( ! [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] :
                                                                      ( ( exu @ X1 )
                                                                     => ~ ! [X2: $i] :
                                                                            ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                                = ( X3 = X2 ) ) )
                                                                 => ( ! [X1: $i] :
                                                                        ( ( nonempty @ X1 )
                                                                       => ~ ! [X2: $i] :
                                                                              ~ ( in @ X2 @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                         => ( X1 = X2 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 != X2 )
                                                                           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( ( X3 != X1 )
                                                                                   => ( X3 = X2 ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                        ( ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( X2 @ X3 ) )
                                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                                         != emptyset ) )
                                                                                   => ( ! [X1: $i > $o,X2: $i] :
                                                                                          ( ( in @ X2 @ emptyset )
                                                                                         => ( X1 @ X2 ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                            ( ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( X2 @ X3 ) )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( X2 @ X3 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                              ( ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                             => ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                ( ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                               => ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                  ( ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( X2 @ X3 ) )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( X2 @ X3 ) ) )
                                                                                             => ( ! [X1: $o] :
                                                                                                    ( X1
                                                                                                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                               => ( ! [X1: $o] :
                                                                                                      ( X1
                                                                                                     => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                        ( ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( X2 @ X3 ) )
                                                                                                       => ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                                          ( ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( X2 @ X3 ) )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                               => ( X2 @ X3 ) ) )
                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                  ( ( X1 @ X2 )
                                                                                                                 => ~ ! [X3: $i] :
                                                                                                                        ( ( X1 @ X3 )
                                                                                                                       => ( X2 = X3 ) ) )
                                                                                                           => ( exu @ X1 ) )
                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                    ~ ( X1 @ X2 )
                                                                                                             => ( ! [X2: $i,X3: $i] :
                                                                                                                    ( ( X1 @ X2 )
                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                     => ( X2 = X3 ) ) )
                                                                                                               => ( exu @ X1 ) ) )
                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                      ~ ! [X3: $i] :
                                                                                                                          ( ( X1 @ X3 )
                                                                                                                          = ( X3 = X2 ) )
                                                                                                               => ( exu @ X1 ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                                      ( ( X3 = X4 )
                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                       => ( in @ X4 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                                        ( ( X3 = X4 )
                                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                                          = ( in @ X4 @ X2 ) ) ) )
                                                                                                               => ( ! [X1: $i > $o] :
                                                                                                                      ( ( exu @ X1 )
                                                                                                                     => ! [X2: $i,X3: $i] :
                                                                                                                          ( ( X1 @ X2 )
                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                           => ( X2 = X3 ) ) ) )
                                                                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                        ( ! [X3: $i,X4: $i] :
                                                                                                                            ( ( X3 = X4 )
                                                                                                                           => ( ( X1 @ X3 )
                                                                                                                              = ( X2 @ X4 ) ) )
                                                                                                                       => ( ( exu @ X1 )
                                                                                                                          = ( exu @ X2 ) ) )
                                                                                                                   => ( ( emptyset = emptyset )
                                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                                                ( ( X3 = X4 )
                                                                                                                               => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                       => ! [X1: $i,X2: $i] :
                                                                                                                            ( ( X1 = X2 )
                                                                                                                           => ( ( powerset @ X1 )
                                                                                                                              = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h23,assumption,
    ! [X1: $i > $o] :
      ( ( exu @ X1 )
     => ( X1 @ ( descr @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h24,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: $i > $o] :
                ( ( exu @ X1 )
               => ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) ) )
           => ( ! [X1: $o,X2: $i] :
                  ( ( in @ X2 @ ( prop2set @ X1 ) )
                 => X1 )
             => ( ! [X1: $i] :
                    ( ( in @ X1 @ emptyset )
                   => ! [X2: $o] : X2 )
               => ( ! [X1: $i] :
                      ~ ( in @ X1 @ emptyset )
                 => ( ! [X1: $i] :
                        ~ ( in @ X1 @ emptyset )
                   => ( ! [X1: $i > $o] :
                          ( ( exu @ X1 )
                         => ~ ! [X2: $i] :
                                ~ ( X1 @ X2 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( in @ X3 @ X2 ) )
                           => ( ! [X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ( in @ X3 @ X1 ) )
                             => ( X1 = X2 ) ) )
                       => ( ! [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] :
                                    ( ( nonempty @ X1 )
                                   => ~ ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 ) )
                               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( ( X2 @ X3 )
                                       => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                 => ( ! [X1: $i] :
                                        ( ~ ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 )
                                       => ( nonempty @ X1 ) )
                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                     => ( ( 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 ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                 => ( ( X3 != X1 )
                                                   => ( in @ X3 @ X2 ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ( dsetconstr @ X1
                                                      @ ^ [X2: $i] : ~ $false )
                                                    = X1 )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ! [X3: $i] :
                                                          ( ( in @ X3 @ X2 )
                                                         => ( in @ X3 @ X1 ) )
                                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                 => ( ! [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] :
                                                                    ( ( exu @ X1 )
                                                                   => ~ ! [X2: $i] :
                                                                          ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                              = ( X3 = X2 ) ) )
                                                               => ( ! [X1: $i] :
                                                                      ( ( nonempty @ X1 )
                                                                     => ~ ! [X2: $i] :
                                                                            ~ ( in @ X2 @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                       => ( X1 = X2 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 != X2 )
                                                                         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( ( X3 != X1 )
                                                                                 => ( X3 = X2 ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                      ( ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( X2 @ X3 ) )
                                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                                       != emptyset ) )
                                                                                 => ( ! [X1: $i > $o,X2: $i] :
                                                                                        ( ( in @ X2 @ emptyset )
                                                                                       => ( X1 @ X2 ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                          ( ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( X2 @ X3 ) )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( X2 @ X3 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                            ( ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( X2 @ X3 ) )
                                                                                           => ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                              ( ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                             => ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                ( ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( X2 @ X3 ) )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( X2 @ X3 ) ) )
                                                                                           => ( ! [X1: $o] :
                                                                                                  ( X1
                                                                                                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                             => ( ! [X1: $o] :
                                                                                                    ( X1
                                                                                                   => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                      ( ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( X2 @ X3 ) )
                                                                                                     => ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                                        ( ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( X2 @ X3 ) )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( in @ X3 @ X1 )
                                                                                                             => ( X2 @ X3 ) ) )
                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                ( ( X1 @ X2 )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( X1 @ X3 )
                                                                                                                     => ( X2 = X3 ) ) )
                                                                                                         => ( exu @ X1 ) )
                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                  ~ ( X1 @ X2 )
                                                                                                           => ( ! [X2: $i,X3: $i] :
                                                                                                                  ( ( X1 @ X2 )
                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                   => ( X2 = X3 ) ) )
                                                                                                             => ( exu @ X1 ) ) )
                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                              ( ~ ! [X2: $i] :
                                                                                                                    ~ ! [X3: $i] :
                                                                                                                        ( ( X1 @ X3 )
                                                                                                                        = ( X3 = X2 ) )
                                                                                                             => ( exu @ X1 ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                    ( ( X3 = X4 )
                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                     => ( in @ X4 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                                      ( ( X3 = X4 )
                                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                                        = ( in @ X4 @ X2 ) ) ) )
                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                    ( ( exu @ X1 )
                                                                                                                   => ! [X2: $i,X3: $i] :
                                                                                                                        ( ( X1 @ X2 )
                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                                                          ( ( X3 = X4 )
                                                                                                                         => ( ( X1 @ X3 )
                                                                                                                            = ( X2 @ X4 ) ) )
                                                                                                                     => ( ( exu @ X1 )
                                                                                                                        = ( exu @ X2 ) ) )
                                                                                                                 => ( ( emptyset = emptyset )
                                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                                              ( ( X3 = X4 )
                                                                                                                             => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                     => ! [X1: $i,X2: $i] :
                                                                                                                          ( ( X1 = X2 )
                                                                                                                         => ( ( powerset @ X1 )
                                                                                                                            = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h25,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( X2 @ X3 )
       => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h26,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: $i > $o] :
              ( ( exu @ X1 )
             => ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) ) )
         => ( ! [X1: $o,X2: $i] :
                ( ( in @ X2 @ ( prop2set @ X1 ) )
               => X1 )
           => ( ! [X1: $i] :
                  ( ( in @ X1 @ emptyset )
                 => ! [X2: $o] : X2 )
             => ( ! [X1: $i] :
                    ~ ( in @ X1 @ emptyset )
               => ( ! [X1: $i] :
                      ~ ( in @ X1 @ emptyset )
                 => ( ! [X1: $i > $o] :
                        ( ( exu @ X1 )
                       => ~ ! [X2: $i] :
                              ~ ( X1 @ X2 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( in @ X3 @ X2 ) )
                         => ( ! [X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ( in @ X3 @ X1 ) )
                           => ( X1 = X2 ) ) )
                     => ( ! [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] :
                                  ( ( nonempty @ X1 )
                                 => ~ ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 ) )
                             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( ( X2 @ X3 )
                                     => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                               => ( ! [X1: $i] :
                                      ( ~ ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 )
                                     => ( nonempty @ X1 ) )
                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                   => ( ( 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 ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                               => ( ( X3 != X1 )
                                                 => ( in @ X3 @ X2 ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ( dsetconstr @ X1
                                                    @ ^ [X2: $i] : ~ $false )
                                                  = X1 )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ X1 ) )
                                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                                               => ( ! [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] :
                                                                  ( ( exu @ X1 )
                                                                 => ~ ! [X2: $i] :
                                                                        ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                            = ( X3 = X2 ) ) )
                                                             => ( ! [X1: $i] :
                                                                    ( ( nonempty @ X1 )
                                                                   => ~ ! [X2: $i] :
                                                                          ~ ( in @ X2 @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                     => ( X1 = X2 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 != X2 )
                                                                       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( ( X3 != X1 )
                                                                               => ( X3 = X2 ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                    ( ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( X2 @ X3 ) )
                                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                                     != emptyset ) )
                                                                               => ( ! [X1: $i > $o,X2: $i] :
                                                                                      ( ( in @ X2 @ emptyset )
                                                                                     => ( X1 @ X2 ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                        ( ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( X2 @ X3 ) )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( X2 @ X3 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                          ( ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( X2 @ X3 ) )
                                                                                         => ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                            ( ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( X2 @ X3 ) )
                                                                                           => ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                              ( ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( X2 @ X3 ) )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( X2 @ X3 ) ) )
                                                                                         => ( ! [X1: $o] :
                                                                                                ( X1
                                                                                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                           => ( ! [X1: $o] :
                                                                                                  ( X1
                                                                                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                    ( ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                   => ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                      ( ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( X2 @ X3 ) )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                           => ( X2 @ X3 ) ) )
                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                        ( ~ ! [X2: $i] :
                                                                                                              ( ( X1 @ X2 )
                                                                                                             => ~ ! [X3: $i] :
                                                                                                                    ( ( X1 @ X3 )
                                                                                                                   => ( X2 = X3 ) ) )
                                                                                                       => ( exu @ X1 ) )
                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                ~ ( X1 @ X2 )
                                                                                                         => ( ! [X2: $i,X3: $i] :
                                                                                                                ( ( X1 @ X2 )
                                                                                                               => ( ( X1 @ X3 )
                                                                                                                 => ( X2 = X3 ) ) )
                                                                                                           => ( exu @ X1 ) ) )
                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                            ( ~ ! [X2: $i] :
                                                                                                                  ~ ! [X3: $i] :
                                                                                                                      ( ( X1 @ X3 )
                                                                                                                      = ( X3 = X2 ) )
                                                                                                           => ( exu @ X1 ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                  ( ( X3 = X4 )
                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                   => ( in @ X4 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                    ( ( X3 = X4 )
                                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                                      = ( in @ X4 @ X2 ) ) ) )
                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                  ( ( exu @ X1 )
                                                                                                                 => ! [X2: $i,X3: $i] :
                                                                                                                      ( ( X1 @ X2 )
                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                       => ( X2 = X3 ) ) ) )
                                                                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                    ( ! [X3: $i,X4: $i] :
                                                                                                                        ( ( X3 = X4 )
                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                          = ( X2 @ X4 ) ) )
                                                                                                                   => ( ( exu @ X1 )
                                                                                                                      = ( exu @ X2 ) ) )
                                                                                                               => ( ( emptyset = emptyset )
                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                            ( ( X3 = X4 )
                                                                                                                           => ( ( setadjoin @ X1 @ X3 )
                                                                                                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                   => ! [X1: $i,X2: $i] :
                                                                                                                        ( ( X1 = X2 )
                                                                                                                       => ( ( powerset @ X1 )
                                                                                                                          = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h27,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
     => ( in @ X3 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h28,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
         => ( X2 @ X3 ) )
     => ( ! [X1: $i > $o] :
            ( ( exu @ X1 )
           => ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) ) )
       => ( ! [X1: $o,X2: $i] :
              ( ( in @ X2 @ ( prop2set @ X1 ) )
             => X1 )
         => ( ! [X1: $i] :
                ( ( in @ X1 @ emptyset )
               => ! [X2: $o] : X2 )
           => ( ! [X1: $i] :
                  ~ ( in @ X1 @ emptyset )
             => ( ! [X1: $i] :
                    ~ ( in @ X1 @ emptyset )
               => ( ! [X1: $i > $o] :
                      ( ( exu @ X1 )
                     => ~ ! [X2: $i] :
                            ~ ( X1 @ X2 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( in @ X3 @ X2 ) )
                       => ( ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ( in @ X3 @ X1 ) )
                         => ( X1 = X2 ) ) )
                   => ( ! [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] :
                                ( ( nonempty @ X1 )
                               => ~ ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 ) )
                           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( ( X2 @ X3 )
                                   => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                             => ( ! [X1: $i] :
                                    ( ~ ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 )
                                   => ( nonempty @ X1 ) )
                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                 => ( ( 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 ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                             => ( ( X3 != X1 )
                                               => ( in @ X3 @ X2 ) ) )
                                         => ( ! [X1: $i] :
                                                ( ( dsetconstr @ X1
                                                  @ ^ [X2: $i] : ~ $false )
                                                = X1 )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ X1 ) )
                                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                                             => ( ! [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] :
                                                                ( ( exu @ X1 )
                                                               => ~ ! [X2: $i] :
                                                                      ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                          = ( X3 = X2 ) ) )
                                                           => ( ! [X1: $i] :
                                                                  ( ( nonempty @ X1 )
                                                                 => ~ ! [X2: $i] :
                                                                        ~ ( in @ X2 @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                   => ( X1 = X2 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 != X2 )
                                                                     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( ( X3 != X1 )
                                                                             => ( X3 = X2 ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                  ( ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( X2 @ X3 ) )
                                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                                   != emptyset ) )
                                                                             => ( ! [X1: $i > $o,X2: $i] :
                                                                                    ( ( in @ X2 @ emptyset )
                                                                                   => ( X1 @ X2 ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                      ( ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( X2 @ X3 ) )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( X2 @ X3 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                        ( ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( X2 @ X3 ) )
                                                                                       => ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                          ( ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( X2 @ X3 ) )
                                                                                         => ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                            ( ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( X2 @ X3 ) )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( X2 @ X3 ) ) )
                                                                                       => ( ! [X1: $o] :
                                                                                              ( X1
                                                                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                         => ( ! [X1: $o] :
                                                                                                ( X1
                                                                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                  ( ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                 => ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                    ( ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( X2 @ X3 ) )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( in @ X3 @ X1 )
                                                                                                         => ( X2 @ X3 ) ) )
                                                                                               => ( ! [X1: $i > $o] :
                                                                                                      ( ~ ! [X2: $i] :
                                                                                                            ( ( X1 @ X2 )
                                                                                                           => ~ ! [X3: $i] :
                                                                                                                  ( ( X1 @ X3 )
                                                                                                                 => ( X2 = X3 ) ) )
                                                                                                     => ( exu @ X1 ) )
                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                        ( ~ ! [X2: $i] :
                                                                                                              ~ ( X1 @ X2 )
                                                                                                       => ( ! [X2: $i,X3: $i] :
                                                                                                              ( ( X1 @ X2 )
                                                                                                             => ( ( X1 @ X3 )
                                                                                                               => ( X2 = X3 ) ) )
                                                                                                         => ( exu @ X1 ) ) )
                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                          ( ~ ! [X2: $i] :
                                                                                                                ~ ! [X3: $i] :
                                                                                                                    ( ( X1 @ X3 )
                                                                                                                    = ( X3 = X2 ) )
                                                                                                         => ( exu @ X1 ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                                ( ( X3 = X4 )
                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                 => ( in @ X4 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                  ( ( X3 = X4 )
                                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                                    = ( in @ X4 @ X2 ) ) ) )
                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                ( ( exu @ X1 )
                                                                                                               => ! [X2: $i,X3: $i] :
                                                                                                                    ( ( X1 @ X2 )
                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                     => ( X2 = X3 ) ) ) )
                                                                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                  ( ! [X3: $i,X4: $i] :
                                                                                                                      ( ( X3 = X4 )
                                                                                                                     => ( ( X1 @ X3 )
                                                                                                                        = ( X2 @ X4 ) ) )
                                                                                                                 => ( ( exu @ X1 )
                                                                                                                    = ( exu @ X2 ) ) )
                                                                                                             => ( ( emptyset = emptyset )
                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                          ( ( X3 = X4 )
                                                                                                                         => ( ( setadjoin @ X1 @ X3 )
                                                                                                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                 => ! [X1: $i,X2: $i] :
                                                                                                                      ( ( X1 = X2 )
                                                                                                                     => ( ( powerset @ X1 )
                                                                                                                        = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h29,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
     => ( X2 @ X3 ) ),
    introduced(assumption,[]) ).

thf(h30,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ( exu @ X1 )
         => ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) )
     => ( ! [X1: $o,X2: $i] :
            ( ( in @ X2 @ ( prop2set @ X1 ) )
           => X1 )
       => ( ! [X1: $i] :
              ( ( in @ X1 @ emptyset )
             => ! [X2: $o] : X2 )
         => ( ! [X1: $i] :
                ~ ( in @ X1 @ emptyset )
           => ( ! [X1: $i] :
                  ~ ( in @ X1 @ emptyset )
             => ( ! [X1: $i > $o] :
                    ( ( exu @ X1 )
                   => ~ ! [X2: $i] :
                          ~ ( X1 @ X2 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( in @ X3 @ X2 ) )
                     => ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ( in @ X3 @ X1 ) )
                       => ( X1 = X2 ) ) )
                 => ( ! [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] :
                              ( ( nonempty @ X1 )
                             => ~ ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 ) )
                         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( ( X2 @ X3 )
                                 => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                           => ( ! [X1: $i] :
                                  ( ~ ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 )
                                 => ( nonempty @ X1 ) )
                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                               => ( ( 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 ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                           => ( ( X3 != X1 )
                                             => ( in @ X3 @ X2 ) ) )
                                       => ( ! [X1: $i] :
                                              ( ( dsetconstr @ X1
                                                @ ^ [X2: $i] : ~ $false )
                                              = X1 )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X2 )
                                                   => ( in @ X3 @ X1 ) )
                                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                                           => ( ! [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] :
                                                              ( ( exu @ X1 )
                                                             => ~ ! [X2: $i] :
                                                                    ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                        = ( X3 = X2 ) ) )
                                                         => ( ! [X1: $i] :
                                                                ( ( nonempty @ X1 )
                                                               => ~ ! [X2: $i] :
                                                                      ~ ( in @ X2 @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                 => ( X1 = X2 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 != X2 )
                                                                   => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                       => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( ( X3 != X1 )
                                                                           => ( X3 = X2 ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                ( ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( X2 @ X3 ) )
                                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                                 != emptyset ) )
                                                                           => ( ! [X1: $i > $o,X2: $i] :
                                                                                  ( ( in @ X2 @ emptyset )
                                                                                 => ( X1 @ X2 ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                    ( ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( X2 @ X3 ) )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( X2 @ X3 ) ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                      ( ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( X2 @ X3 ) )
                                                                                     => ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                        ( ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( X2 @ X3 ) )
                                                                                       => ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                          ( ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( X2 @ X3 ) )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( X2 @ X3 ) ) )
                                                                                     => ( ! [X1: $o] :
                                                                                            ( X1
                                                                                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                       => ( ! [X1: $o] :
                                                                                              ( X1
                                                                                             => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                ( ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( X2 @ X3 ) )
                                                                                               => ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                  ( ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( X2 @ X3 ) )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                       => ( X2 @ X3 ) ) )
                                                                                             => ( ! [X1: $i > $o] :
                                                                                                    ( ~ ! [X2: $i] :
                                                                                                          ( ( X1 @ X2 )
                                                                                                         => ~ ! [X3: $i] :
                                                                                                                ( ( X1 @ X3 )
                                                                                                               => ( X2 = X3 ) ) )
                                                                                                   => ( exu @ X1 ) )
                                                                                               => ( ! [X1: $i > $o] :
                                                                                                      ( ~ ! [X2: $i] :
                                                                                                            ~ ( X1 @ X2 )
                                                                                                     => ( ! [X2: $i,X3: $i] :
                                                                                                            ( ( X1 @ X2 )
                                                                                                           => ( ( X1 @ X3 )
                                                                                                             => ( X2 = X3 ) ) )
                                                                                                       => ( exu @ X1 ) ) )
                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                        ( ~ ! [X2: $i] :
                                                                                                              ~ ! [X3: $i] :
                                                                                                                  ( ( X1 @ X3 )
                                                                                                                  = ( X3 = X2 ) )
                                                                                                       => ( exu @ X1 ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                              ( ( X3 = X4 )
                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                               => ( in @ X4 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                                ( ( X3 = X4 )
                                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                                  = ( in @ X4 @ X2 ) ) ) )
                                                                                                       => ( ! [X1: $i > $o] :
                                                                                                              ( ( exu @ X1 )
                                                                                                             => ! [X2: $i,X3: $i] :
                                                                                                                  ( ( X1 @ X2 )
                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                   => ( X2 = X3 ) ) ) )
                                                                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                ( ! [X3: $i,X4: $i] :
                                                                                                                    ( ( X3 = X4 )
                                                                                                                   => ( ( X1 @ X3 )
                                                                                                                      = ( X2 @ X4 ) ) )
                                                                                                               => ( ( exu @ X1 )
                                                                                                                  = ( exu @ X2 ) ) )
                                                                                                           => ( ( emptyset = emptyset )
                                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                                        ( ( X3 = X4 )
                                                                                                                       => ( ( setadjoin @ X1 @ X3 )
                                                                                                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                               => ! [X1: $i,X2: $i] :
                                                                                                                    ( ( X1 = X2 )
                                                                                                                   => ( ( powerset @ X1 )
                                                                                                                      = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h31,assumption,
    ! [X1: $i > $o] :
      ( ( exu @ X1 )
     => ~ ! [X2: $i] :
            ( ( X1 @ X2 )
           => ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h32,assumption,
    ~ ( ! [X1: $o,X2: $i] :
          ( ( in @ X2 @ ( prop2set @ X1 ) )
         => X1 )
     => ( ! [X1: $i] :
            ( ( in @ X1 @ emptyset )
           => ! [X2: $o] : X2 )
       => ( ! [X1: $i] :
              ~ ( in @ X1 @ emptyset )
         => ( ! [X1: $i] :
                ~ ( in @ X1 @ emptyset )
           => ( ! [X1: $i > $o] :
                  ( ( exu @ X1 )
                 => ~ ! [X2: $i] :
                        ~ ( X1 @ X2 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( in @ X3 @ X2 ) )
                   => ( ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ( in @ X3 @ X1 ) )
                     => ( X1 = X2 ) ) )
               => ( ! [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] :
                            ( ( nonempty @ X1 )
                           => ~ ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 ) )
                       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( ( X2 @ X3 )
                               => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                         => ( ! [X1: $i] :
                                ( ~ ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 )
                               => ( nonempty @ X1 ) )
                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                             => ( ( 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 ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                         => ( ( X3 != X1 )
                                           => ( in @ X3 @ X2 ) ) )
                                     => ( ! [X1: $i] :
                                            ( ( dsetconstr @ X1
                                              @ ^ [X2: $i] : ~ $false )
                                            = X1 )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X2 )
                                                 => ( in @ X3 @ X1 ) )
                                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                                         => ( ! [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] :
                                                            ( ( exu @ X1 )
                                                           => ~ ! [X2: $i] :
                                                                  ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                      = ( X3 = X2 ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ( nonempty @ X1 )
                                                             => ~ ! [X2: $i] :
                                                                    ~ ( in @ X2 @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                               => ( X1 = X2 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 != X2 )
                                                                 => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( ( X3 != X1 )
                                                                         => ( X3 = X2 ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                              ( ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( X2 @ X3 ) )
                                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                                               != emptyset ) )
                                                                         => ( ! [X1: $i > $o,X2: $i] :
                                                                                ( ( in @ X2 @ emptyset )
                                                                               => ( X1 @ X2 ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                  ( ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( X2 @ X3 ) )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( X2 @ X3 ) ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                    ( ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( X2 @ X3 ) )
                                                                                   => ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                      ( ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( X2 @ X3 ) )
                                                                                     => ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                        ( ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( X2 @ X3 ) )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( X2 @ X3 ) ) )
                                                                                   => ( ! [X1: $o] :
                                                                                          ( X1
                                                                                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                     => ( ! [X1: $o] :
                                                                                            ( X1
                                                                                           => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                              ( ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                             => ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                ( ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( X2 @ X3 ) )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                     => ( X2 @ X3 ) ) )
                                                                                           => ( ! [X1: $i > $o] :
                                                                                                  ( ~ ! [X2: $i] :
                                                                                                        ( ( X1 @ X2 )
                                                                                                       => ~ ! [X3: $i] :
                                                                                                              ( ( X1 @ X3 )
                                                                                                             => ( X2 = X3 ) ) )
                                                                                                 => ( exu @ X1 ) )
                                                                                             => ( ! [X1: $i > $o] :
                                                                                                    ( ~ ! [X2: $i] :
                                                                                                          ~ ( X1 @ X2 )
                                                                                                   => ( ! [X2: $i,X3: $i] :
                                                                                                          ( ( X1 @ X2 )
                                                                                                         => ( ( X1 @ X3 )
                                                                                                           => ( X2 = X3 ) ) )
                                                                                                     => ( exu @ X1 ) ) )
                                                                                               => ( ! [X1: $i > $o] :
                                                                                                      ( ~ ! [X2: $i] :
                                                                                                            ~ ! [X3: $i] :
                                                                                                                ( ( X1 @ X3 )
                                                                                                                = ( X3 = X2 ) )
                                                                                                     => ( exu @ X1 ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                            ( ( X3 = X4 )
                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                             => ( in @ X4 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                              ( ( X3 = X4 )
                                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                                = ( in @ X4 @ X2 ) ) ) )
                                                                                                     => ( ! [X1: $i > $o] :
                                                                                                            ( ( exu @ X1 )
                                                                                                           => ! [X2: $i,X3: $i] :
                                                                                                                ( ( X1 @ X2 )
                                                                                                               => ( ( X1 @ X3 )
                                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                              ( ! [X3: $i,X4: $i] :
                                                                                                                  ( ( X3 = X4 )
                                                                                                                 => ( ( X1 @ X3 )
                                                                                                                    = ( X2 @ X4 ) ) )
                                                                                                             => ( ( exu @ X1 )
                                                                                                                = ( exu @ X2 ) ) )
                                                                                                         => ( ( emptyset = emptyset )
                                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                                      ( ( X3 = X4 )
                                                                                                                     => ( ( setadjoin @ X1 @ X3 )
                                                                                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                             => ! [X1: $i,X2: $i] :
                                                                                                                  ( ( X1 = X2 )
                                                                                                                 => ( ( powerset @ X1 )
                                                                                                                    = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h33,assumption,
    ! [X1: $o,X2: $i] :
      ( ( in @ X2 @ ( prop2set @ X1 ) )
     => X1 ),
    introduced(assumption,[]) ).

thf(h34,assumption,
    ~ ( ! [X1: $i] :
          ( ( in @ X1 @ emptyset )
         => ! [X2: $o] : X2 )
     => ( ! [X1: $i] :
            ~ ( in @ X1 @ emptyset )
       => ( ! [X1: $i] :
              ~ ( in @ X1 @ emptyset )
         => ( ! [X1: $i > $o] :
                ( ( exu @ X1 )
               => ~ ! [X2: $i] :
                      ~ ( X1 @ X2 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( in @ X3 @ X2 ) )
                 => ( ! [X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ( in @ X3 @ X1 ) )
                   => ( X1 = X2 ) ) )
             => ( ! [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] :
                          ( ( nonempty @ X1 )
                         => ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 ) )
                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( ( X2 @ X3 )
                             => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                       => ( ! [X1: $i] :
                              ( ~ ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 )
                             => ( nonempty @ X1 ) )
                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                           => ( ( 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 ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                       => ( ( X3 != X1 )
                                         => ( in @ X3 @ X2 ) ) )
                                   => ( ! [X1: $i] :
                                          ( ( dsetconstr @ X1
                                            @ ^ [X2: $i] : ~ $false )
                                          = X1 )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X2 )
                                               => ( in @ X3 @ X1 ) )
                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                       => ( ! [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] :
                                                          ( ( exu @ X1 )
                                                         => ~ ! [X2: $i] :
                                                                ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                    = ( X3 = X2 ) ) )
                                                     => ( ! [X1: $i] :
                                                            ( ( nonempty @ X1 )
                                                           => ~ ! [X2: $i] :
                                                                  ~ ( in @ X2 @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                             => ( X1 = X2 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 != X2 )
                                                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( ( X3 != X1 )
                                                                       => ( X3 = X2 ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                            ( ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( X2 @ X3 ) )
                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                             != emptyset ) )
                                                                       => ( ! [X1: $i > $o,X2: $i] :
                                                                              ( ( in @ X2 @ emptyset )
                                                                             => ( X1 @ X2 ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                ( ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( X2 @ X3 ) )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( X2 @ X3 ) ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                  ( ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( X2 @ X3 ) )
                                                                                 => ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                    ( ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( X2 @ X3 ) )
                                                                                   => ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                      ( ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( X2 @ X3 ) )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( X2 @ X3 ) ) )
                                                                                 => ( ! [X1: $o] :
                                                                                        ( X1
                                                                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                   => ( ! [X1: $o] :
                                                                                          ( X1
                                                                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                            ( ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( X2 @ X3 ) )
                                                                                           => ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                              ( ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( X2 @ X3 ) )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                   => ( X2 @ X3 ) ) )
                                                                                         => ( ! [X1: $i > $o] :
                                                                                                ( ~ ! [X2: $i] :
                                                                                                      ( ( X1 @ X2 )
                                                                                                     => ~ ! [X3: $i] :
                                                                                                            ( ( X1 @ X3 )
                                                                                                           => ( X2 = X3 ) ) )
                                                                                               => ( exu @ X1 ) )
                                                                                           => ( ! [X1: $i > $o] :
                                                                                                  ( ~ ! [X2: $i] :
                                                                                                        ~ ( X1 @ X2 )
                                                                                                 => ( ! [X2: $i,X3: $i] :
                                                                                                        ( ( X1 @ X2 )
                                                                                                       => ( ( X1 @ X3 )
                                                                                                         => ( X2 = X3 ) ) )
                                                                                                   => ( exu @ X1 ) ) )
                                                                                             => ( ! [X1: $i > $o] :
                                                                                                    ( ~ ! [X2: $i] :
                                                                                                          ~ ! [X3: $i] :
                                                                                                              ( ( X1 @ X3 )
                                                                                                              = ( X3 = X2 ) )
                                                                                                   => ( exu @ X1 ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                          ( ( X3 = X4 )
                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                            ( ( X3 = X4 )
                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                          ( ( exu @ X1 )
                                                                                                         => ! [X2: $i,X3: $i] :
                                                                                                              ( ( X1 @ X2 )
                                                                                                             => ( ( X1 @ X3 )
                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                                ( ( X3 = X4 )
                                                                                                               => ( ( X1 @ X3 )
                                                                                                                  = ( X2 @ X4 ) ) )
                                                                                                           => ( ( exu @ X1 )
                                                                                                              = ( exu @ X2 ) ) )
                                                                                                       => ( ( emptyset = emptyset )
                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                    ( ( X3 = X4 )
                                                                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                           => ! [X1: $i,X2: $i] :
                                                                                                                ( ( X1 = X2 )
                                                                                                               => ( ( powerset @ X1 )
                                                                                                                  = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h35,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ emptyset )
     => ! [X2: $o] : X2 ),
    introduced(assumption,[]) ).

thf(h36,assumption,
    ~ ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset )
     => ( ! [X1: $i] :
            ~ ( in @ X1 @ emptyset )
       => ( ! [X1: $i > $o] :
              ( ( exu @ X1 )
             => ~ ! [X2: $i] :
                    ~ ( X1 @ X2 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( in @ X3 @ X2 ) )
               => ( ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ X1 ) )
                 => ( X1 = X2 ) ) )
           => ( ! [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] :
                        ( ( nonempty @ X1 )
                       => ~ ! [X2: $i] :
                              ~ ( in @ X2 @ X1 ) )
                   => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( ( X2 @ X3 )
                           => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                     => ( ! [X1: $i] :
                            ( ~ ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 )
                           => ( nonempty @ X1 ) )
                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                         => ( ( 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 ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                     => ( ( X3 != X1 )
                                       => ( in @ X3 @ X2 ) ) )
                                 => ( ! [X1: $i] :
                                        ( ( dsetconstr @ X1
                                          @ ^ [X2: $i] : ~ $false )
                                        = X1 )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X2 )
                                             => ( in @ X3 @ X1 ) )
                                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                                     => ( ! [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] :
                                                        ( ( exu @ X1 )
                                                       => ~ ! [X2: $i] :
                                                              ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                  = ( X3 = X2 ) ) )
                                                   => ( ! [X1: $i] :
                                                          ( ( nonempty @ X1 )
                                                         => ~ ! [X2: $i] :
                                                                ~ ( in @ X2 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                           => ( X1 = X2 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 != X2 )
                                                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( ( X3 != X1 )
                                                                     => ( X3 = X2 ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                          ( ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( X2 @ X3 ) )
                                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                                           != emptyset ) )
                                                                     => ( ! [X1: $i > $o,X2: $i] :
                                                                            ( ( in @ X2 @ emptyset )
                                                                           => ( X1 @ X2 ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                              ( ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( X2 @ X3 ) )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( X2 @ X3 ) ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                ( ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( X2 @ X3 ) )
                                                                               => ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                  ( ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( X2 @ X3 ) )
                                                                                 => ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                    ( ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( X2 @ X3 ) )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( X2 @ X3 ) ) )
                                                                               => ( ! [X1: $o] :
                                                                                      ( X1
                                                                                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                 => ( ! [X1: $o] :
                                                                                        ( X1
                                                                                       => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                          ( ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( X2 @ X3 ) )
                                                                                         => ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ~ ( X2 @ X3 ) ) )
                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                            ( ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( X2 @ X3 ) )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                 => ( X2 @ X3 ) ) )
                                                                                       => ( ! [X1: $i > $o] :
                                                                                              ( ~ ! [X2: $i] :
                                                                                                    ( ( X1 @ X2 )
                                                                                                   => ~ ! [X3: $i] :
                                                                                                          ( ( X1 @ X3 )
                                                                                                         => ( X2 = X3 ) ) )
                                                                                             => ( exu @ X1 ) )
                                                                                         => ( ! [X1: $i > $o] :
                                                                                                ( ~ ! [X2: $i] :
                                                                                                      ~ ( X1 @ X2 )
                                                                                               => ( ! [X2: $i,X3: $i] :
                                                                                                      ( ( X1 @ X2 )
                                                                                                     => ( ( X1 @ X3 )
                                                                                                       => ( X2 = X3 ) ) )
                                                                                                 => ( exu @ X1 ) ) )
                                                                                           => ( ! [X1: $i > $o] :
                                                                                                  ( ~ ! [X2: $i] :
                                                                                                        ~ ! [X3: $i] :
                                                                                                            ( ( X1 @ X3 )
                                                                                                            = ( X3 = X2 ) )
                                                                                                 => ( exu @ X1 ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                        ( ( X3 = X4 )
                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                         => ( in @ X4 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                          ( ( X3 = X4 )
                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                            = ( in @ X4 @ X2 ) ) ) )
                                                                                                 => ( ! [X1: $i > $o] :
                                                                                                        ( ( exu @ X1 )
                                                                                                       => ! [X2: $i,X3: $i] :
                                                                                                            ( ( X1 @ X2 )
                                                                                                           => ( ( X1 @ X3 )
                                                                                                             => ( X2 = X3 ) ) ) )
                                                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                          ( ! [X3: $i,X4: $i] :
                                                                                                              ( ( X3 = X4 )
                                                                                                             => ( ( X1 @ X3 )
                                                                                                                = ( X2 @ X4 ) ) )
                                                                                                         => ( ( exu @ X1 )
                                                                                                            = ( exu @ X2 ) ) )
                                                                                                     => ( ( emptyset = emptyset )
                                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                                  ( ( X3 = X4 )
                                                                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                         => ! [X1: $i,X2: $i] :
                                                                                                              ( ( X1 = X2 )
                                                                                                             => ( ( powerset @ X1 )
                                                                                                                = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h37,assumption,
    ~ ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset )
     => ( ! [X1: $i > $o] :
            ( ( exu @ X1 )
           => ~ ! [X2: $i] :
                  ~ ( X1 @ X2 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( in @ X3 @ X2 ) )
             => ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) )
               => ( X1 = X2 ) ) )
         => ( ! [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] :
                      ( ( nonempty @ X1 )
                     => ~ ! [X2: $i] :
                            ~ ( in @ X2 @ X1 ) )
                 => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( ( X2 @ X3 )
                         => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                   => ( ! [X1: $i] :
                          ( ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 )
                         => ( nonempty @ X1 ) )
                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                       => ( ( 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 ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                   => ( ( X3 != X1 )
                                     => ( in @ X3 @ X2 ) ) )
                               => ( ! [X1: $i] :
                                      ( ( dsetconstr @ X1
                                        @ ^ [X2: $i] : ~ $false )
                                      = X1 )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X2 )
                                           => ( in @ X3 @ X1 ) )
                                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                                   => ( ! [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] :
                                                      ( ( exu @ X1 )
                                                     => ~ ! [X2: $i] :
                                                            ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                                = ( X3 = X2 ) ) )
                                                 => ( ! [X1: $i] :
                                                        ( ( nonempty @ X1 )
                                                       => ~ ! [X2: $i] :
                                                              ~ ( in @ X2 @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                         => ( X1 = X2 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 != X2 )
                                                           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( ( X3 != X1 )
                                                                   => ( X3 = X2 ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                        ( ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( X2 @ X3 ) )
                                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                                         != emptyset ) )
                                                                   => ( ! [X1: $i > $o,X2: $i] :
                                                                          ( ( in @ X2 @ emptyset )
                                                                         => ( X1 @ X2 ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                            ( ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( X2 @ X3 ) )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( X2 @ X3 ) ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                              ( ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( X2 @ X3 ) )
                                                                             => ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                ( ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( X2 @ X3 ) )
                                                                               => ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                  ( ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( X2 @ X3 ) )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( X2 @ X3 ) ) )
                                                                             => ( ! [X1: $o] :
                                                                                    ( X1
                                                                                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                               => ( ! [X1: $o] :
                                                                                      ( X1
                                                                                     => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                        ( ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( X2 @ X3 ) )
                                                                                       => ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ~ ( X2 @ X3 ) ) )
                                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                                          ( ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( X2 @ X3 ) )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( in @ X3 @ X1 )
                                                                                               => ( X2 @ X3 ) ) )
                                                                                     => ( ! [X1: $i > $o] :
                                                                                            ( ~ ! [X2: $i] :
                                                                                                  ( ( X1 @ X2 )
                                                                                                 => ~ ! [X3: $i] :
                                                                                                        ( ( X1 @ X3 )
                                                                                                       => ( X2 = X3 ) ) )
                                                                                           => ( exu @ X1 ) )
                                                                                       => ( ! [X1: $i > $o] :
                                                                                              ( ~ ! [X2: $i] :
                                                                                                    ~ ( X1 @ X2 )
                                                                                             => ( ! [X2: $i,X3: $i] :
                                                                                                    ( ( X1 @ X2 )
                                                                                                   => ( ( X1 @ X3 )
                                                                                                     => ( X2 = X3 ) ) )
                                                                                               => ( exu @ X1 ) ) )
                                                                                         => ( ! [X1: $i > $o] :
                                                                                                ( ~ ! [X2: $i] :
                                                                                                      ~ ! [X3: $i] :
                                                                                                          ( ( X1 @ X3 )
                                                                                                          = ( X3 = X2 ) )
                                                                                               => ( exu @ X1 ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                      ( ( X3 = X4 )
                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                       => ( in @ X4 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                        ( ( X3 = X4 )
                                                                                                       => ( ( in @ X3 @ X1 )
                                                                                                          = ( in @ X4 @ X2 ) ) ) )
                                                                                               => ( ! [X1: $i > $o] :
                                                                                                      ( ( exu @ X1 )
                                                                                                     => ! [X2: $i,X3: $i] :
                                                                                                          ( ( X1 @ X2 )
                                                                                                         => ( ( X1 @ X3 )
                                                                                                           => ( X2 = X3 ) ) ) )
                                                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                        ( ! [X3: $i,X4: $i] :
                                                                                                            ( ( X3 = X4 )
                                                                                                           => ( ( X1 @ X3 )
                                                                                                              = ( X2 @ X4 ) ) )
                                                                                                       => ( ( exu @ X1 )
                                                                                                          = ( exu @ X2 ) ) )
                                                                                                   => ( ( emptyset = emptyset )
                                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                                ( ( X3 = X4 )
                                                                                                               => ( ( setadjoin @ X1 @ X3 )
                                                                                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                       => ! [X1: $i,X2: $i] :
                                                                                                            ( ( X1 = X2 )
                                                                                                           => ( ( powerset @ X1 )
                                                                                                              = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h38,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ( exu @ X1 )
         => ~ ! [X2: $i] :
                ~ ( X1 @ X2 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( in @ X3 @ X2 ) )
           => ( ! [X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ X1 ) )
             => ( X1 = X2 ) ) )
       => ( ! [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] :
                    ( ( nonempty @ X1 )
                   => ~ ! [X2: $i] :
                          ~ ( in @ X2 @ X1 ) )
               => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( ( X2 @ X3 )
                       => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                 => ( ! [X1: $i] :
                        ( ~ ! [X2: $i] :
                              ~ ( in @ X2 @ X1 )
                       => ( nonempty @ X1 ) )
                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                     => ( ( 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 ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                 => ( ( X3 != X1 )
                                   => ( in @ X3 @ X2 ) ) )
                             => ( ! [X1: $i] :
                                    ( ( dsetconstr @ X1
                                      @ ^ [X2: $i] : ~ $false )
                                    = X1 )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X2 )
                                         => ( in @ X3 @ X1 ) )
                                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                                 => ( ! [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] :
                                                    ( ( exu @ X1 )
                                                   => ~ ! [X2: $i] :
                                                          ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                              = ( X3 = X2 ) ) )
                                               => ( ! [X1: $i] :
                                                      ( ( nonempty @ X1 )
                                                     => ~ ! [X2: $i] :
                                                            ~ ( in @ X2 @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                       => ( X1 = X2 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 != X2 )
                                                         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( ( X3 != X1 )
                                                                 => ( X3 = X2 ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                      ( ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( X2 @ X3 ) )
                                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                                       != emptyset ) )
                                                                 => ( ! [X1: $i > $o,X2: $i] :
                                                                        ( ( in @ X2 @ emptyset )
                                                                       => ( X1 @ X2 ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                          ( ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( X2 @ X3 ) )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( X2 @ X3 ) ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( X2 @ X3 ) )
                                                                           => ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( X2 @ X3 ) ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                              ( ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( X2 @ X3 ) )
                                                                             => ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                ( ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( X2 @ X3 ) )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( X2 @ X3 ) ) )
                                                                           => ( ! [X1: $o] :
                                                                                  ( X1
                                                                                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                             => ( ! [X1: $o] :
                                                                                    ( X1
                                                                                   => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                      ( ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( X2 @ X3 ) )
                                                                                     => ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ~ ( X2 @ X3 ) ) )
                                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                                        ( ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( X2 @ X3 ) )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( in @ X3 @ X1 )
                                                                                             => ( X2 @ X3 ) ) )
                                                                                   => ( ! [X1: $i > $o] :
                                                                                          ( ~ ! [X2: $i] :
                                                                                                ( ( X1 @ X2 )
                                                                                               => ~ ! [X3: $i] :
                                                                                                      ( ( X1 @ X3 )
                                                                                                     => ( X2 = X3 ) ) )
                                                                                         => ( exu @ X1 ) )
                                                                                     => ( ! [X1: $i > $o] :
                                                                                            ( ~ ! [X2: $i] :
                                                                                                  ~ ( X1 @ X2 )
                                                                                           => ( ! [X2: $i,X3: $i] :
                                                                                                  ( ( X1 @ X2 )
                                                                                                 => ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) )
                                                                                             => ( exu @ X1 ) ) )
                                                                                       => ( ! [X1: $i > $o] :
                                                                                              ( ~ ! [X2: $i] :
                                                                                                    ~ ! [X3: $i] :
                                                                                                        ( ( X1 @ X3 )
                                                                                                        = ( X3 = X2 ) )
                                                                                             => ( exu @ X1 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                    ( ( X3 = X4 )
                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                     => ( in @ X4 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                      ( ( X3 = X4 )
                                                                                                     => ( ( in @ X3 @ X1 )
                                                                                                        = ( in @ X4 @ X2 ) ) ) )
                                                                                             => ( ! [X1: $i > $o] :
                                                                                                    ( ( exu @ X1 )
                                                                                                   => ! [X2: $i,X3: $i] :
                                                                                                        ( ( X1 @ X2 )
                                                                                                       => ( ( X1 @ X3 )
                                                                                                         => ( X2 = X3 ) ) ) )
                                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                                          ( ( X3 = X4 )
                                                                                                         => ( ( X1 @ X3 )
                                                                                                            = ( X2 @ X4 ) ) )
                                                                                                     => ( ( exu @ X1 )
                                                                                                        = ( exu @ X2 ) ) )
                                                                                                 => ( ( emptyset = emptyset )
                                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ! [X3: $i,X4: $i] :
                                                                                                              ( ( X3 = X4 )
                                                                                                             => ( ( setadjoin @ X1 @ X3 )
                                                                                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                     => ! [X1: $i,X2: $i] :
                                                                                                          ( ( X1 = X2 )
                                                                                                         => ( ( powerset @ X1 )
                                                                                                            = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h39,assumption,
    ! [X1: $i > $o] :
      ( ( exu @ X1 )
     => ~ ! [X2: $i] :
            ~ ( X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h40,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( in @ X3 @ X2 ) )
         => ( ! [X3: $i] :
                ( ( in @ X3 @ X2 )
               => ( in @ X3 @ X1 ) )
           => ( X1 = X2 ) ) )
     => ( ! [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] :
                  ( ( nonempty @ X1 )
                 => ~ ! [X2: $i] :
                        ~ ( in @ X2 @ X1 ) )
             => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( ( X2 @ X3 )
                     => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
               => ( ! [X1: $i] :
                      ( ~ ! [X2: $i] :
                            ~ ( in @ X2 @ X1 )
                     => ( nonempty @ X1 ) )
                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                   => ( ( 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 ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                               => ( ( X3 != X1 )
                                 => ( in @ X3 @ X2 ) ) )
                           => ( ! [X1: $i] :
                                  ( ( dsetconstr @ X1
                                    @ ^ [X2: $i] : ~ $false )
                                  = X1 )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X2 )
                                       => ( in @ X3 @ X1 ) )
                                   => ( in @ X2 @ ( powerset @ X1 ) ) )
                               => ( ! [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] :
                                                  ( ( exu @ X1 )
                                                 => ~ ! [X2: $i] :
                                                        ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                            = ( X3 = X2 ) ) )
                                             => ( ! [X1: $i] :
                                                    ( ( nonempty @ X1 )
                                                   => ~ ! [X2: $i] :
                                                          ~ ( in @ X2 @ X1 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                     => ( X1 = X2 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 != X2 )
                                                       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( ( X3 != X1 )
                                                               => ( X3 = X2 ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                    ( ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( X2 @ X3 ) )
                                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                                     != emptyset ) )
                                                               => ( ! [X1: $i > $o,X2: $i] :
                                                                      ( ( in @ X2 @ emptyset )
                                                                     => ( X1 @ X2 ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                        ( ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( X2 @ X3 ) )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( X2 @ X3 ) ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( X2 @ X3 ) )
                                                                         => ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( X2 @ X3 ) ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( X2 @ X3 ) )
                                                                           => ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( X2 @ X3 ) ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                              ( ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( X2 @ X3 ) )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( X2 @ X3 ) ) )
                                                                         => ( ! [X1: $o] :
                                                                                ( X1
                                                                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                           => ( ! [X1: $o] :
                                                                                  ( X1
                                                                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                    ( ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( X2 @ X3 ) )
                                                                                   => ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                      ( ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( X2 @ X3 ) )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( in @ X3 @ X1 )
                                                                                           => ( X2 @ X3 ) ) )
                                                                                 => ( ! [X1: $i > $o] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) )
                                                                                       => ( exu @ X1 ) )
                                                                                   => ( ! [X1: $i > $o] :
                                                                                          ( ~ ! [X2: $i] :
                                                                                                ~ ( X1 @ X2 )
                                                                                         => ( ! [X2: $i,X3: $i] :
                                                                                                ( ( X1 @ X2 )
                                                                                               => ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) )
                                                                                           => ( exu @ X1 ) ) )
                                                                                     => ( ! [X1: $i > $o] :
                                                                                            ( ~ ! [X2: $i] :
                                                                                                  ~ ! [X3: $i] :
                                                                                                      ( ( X1 @ X3 )
                                                                                                      = ( X3 = X2 ) )
                                                                                           => ( exu @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                  ( ( X3 = X4 )
                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                   => ( in @ X4 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                    ( ( X3 = X4 )
                                                                                                   => ( ( in @ X3 @ X1 )
                                                                                                      = ( in @ X4 @ X2 ) ) ) )
                                                                                           => ( ! [X1: $i > $o] :
                                                                                                  ( ( exu @ X1 )
                                                                                                 => ! [X2: $i,X3: $i] :
                                                                                                      ( ( X1 @ X2 )
                                                                                                     => ( ( X1 @ X3 )
                                                                                                       => ( X2 = X3 ) ) ) )
                                                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                    ( ! [X3: $i,X4: $i] :
                                                                                                        ( ( X3 = X4 )
                                                                                                       => ( ( X1 @ X3 )
                                                                                                          = ( X2 @ X4 ) ) )
                                                                                                   => ( ( exu @ X1 )
                                                                                                      = ( exu @ X2 ) ) )
                                                                                               => ( ( emptyset = emptyset )
                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                            ( ( X3 = X4 )
                                                                                                           => ( ( setadjoin @ X1 @ X3 )
                                                                                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                   => ! [X1: $i,X2: $i] :
                                                                                                        ( ( X1 = X2 )
                                                                                                       => ( ( powerset @ X1 )
                                                                                                          = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h41,assumption,
    ! [X1: $i,X2: $i] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( in @ X3 @ X2 ) )
     => ( ! [X3: $i] :
            ( ( in @ X3 @ X2 )
           => ( in @ X3 @ X1 ) )
       => ( X1 = X2 ) ) ),
    introduced(assumption,[]) ).

thf(h42,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] :
                ( ( nonempty @ X1 )
               => ~ ! [X2: $i] :
                      ~ ( in @ X2 @ X1 ) )
           => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( ( X2 @ X3 )
                   => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
             => ( ! [X1: $i] :
                    ( ~ ! [X2: $i] :
                          ~ ( in @ X2 @ X1 )
                   => ( nonempty @ X1 ) )
               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                 => ( ( 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 ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                             => ( ( X3 != X1 )
                               => ( in @ X3 @ X2 ) ) )
                         => ( ! [X1: $i] :
                                ( ( dsetconstr @ X1
                                  @ ^ [X2: $i] : ~ $false )
                                = X1 )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X2 )
                                     => ( in @ X3 @ X1 ) )
                                 => ( in @ X2 @ ( powerset @ X1 ) ) )
                             => ( ! [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] :
                                                ( ( exu @ X1 )
                                               => ~ ! [X2: $i] :
                                                      ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                          = ( X3 = X2 ) ) )
                                           => ( ! [X1: $i] :
                                                  ( ( nonempty @ X1 )
                                                 => ~ ! [X2: $i] :
                                                        ~ ( in @ X2 @ X1 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                   => ( X1 = X2 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 != X2 )
                                                     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( ( X3 != X1 )
                                                             => ( X3 = X2 ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                  ( ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( X2 @ X3 ) )
                                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                                   != emptyset ) )
                                                             => ( ! [X1: $i > $o,X2: $i] :
                                                                    ( ( in @ X2 @ emptyset )
                                                                   => ( X1 @ X2 ) )
                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                      ( ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( X2 @ X3 ) )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( X2 @ X3 ) ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                        ( ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( X2 @ X3 ) )
                                                                       => ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( X2 @ X3 ) ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( X2 @ X3 ) )
                                                                         => ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( X2 @ X3 ) ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                            ( ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( X2 @ X3 ) )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( X2 @ X3 ) ) )
                                                                       => ( ! [X1: $o] :
                                                                              ( X1
                                                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                         => ( ! [X1: $o] :
                                                                                ( X1
                                                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                  ( ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( X2 @ X3 ) )
                                                                                 => ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                    ( ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( X2 @ X3 ) )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( in @ X3 @ X1 )
                                                                                         => ( X2 @ X3 ) ) )
                                                                               => ( ! [X1: $i > $o] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) )
                                                                                     => ( exu @ X1 ) )
                                                                                 => ( ! [X1: $i > $o] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ~ ( X1 @ X2 )
                                                                                       => ( ! [X2: $i,X3: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) )
                                                                                         => ( exu @ X1 ) ) )
                                                                                   => ( ! [X1: $i > $o] :
                                                                                          ( ~ ! [X2: $i] :
                                                                                                ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                    = ( X3 = X2 ) )
                                                                                         => ( exu @ X1 ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                ( ( X3 = X4 )
                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                 => ( in @ X4 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                  ( ( X3 = X4 )
                                                                                                 => ( ( in @ X3 @ X1 )
                                                                                                    = ( in @ X4 @ X2 ) ) ) )
                                                                                         => ( ! [X1: $i > $o] :
                                                                                                ( ( exu @ X1 )
                                                                                               => ! [X2: $i,X3: $i] :
                                                                                                    ( ( X1 @ X2 )
                                                                                                   => ( ( X1 @ X3 )
                                                                                                     => ( X2 = X3 ) ) ) )
                                                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                  ( ! [X3: $i,X4: $i] :
                                                                                                      ( ( X3 = X4 )
                                                                                                     => ( ( X1 @ X3 )
                                                                                                        = ( X2 @ X4 ) ) )
                                                                                                 => ( ( exu @ X1 )
                                                                                                    = ( exu @ X2 ) ) )
                                                                                             => ( ( emptyset = emptyset )
                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                          ( ( X3 = X4 )
                                                                                                         => ( ( setadjoin @ X1 @ X3 )
                                                                                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                 => ! [X1: $i,X2: $i] :
                                                                                                      ( ( X1 = X2 )
                                                                                                     => ( ( powerset @ X1 )
                                                                                                        = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h43,assumption,
    ! [X1: $i] :
      ( ! [X2: $i] :
          ~ ( in @ X2 @ X1 )
     => ( X1 = emptyset ) ),
    introduced(assumption,[]) ).

thf(h44,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] :
              ( ( nonempty @ X1 )
             => ~ ! [X2: $i] :
                    ~ ( in @ X2 @ X1 ) )
         => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( ( X2 @ X3 )
                 => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
           => ( ! [X1: $i] :
                  ( ~ ! [X2: $i] :
                        ~ ( in @ X2 @ X1 )
                 => ( nonempty @ X1 ) )
             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
               => ( ( 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 ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                           => ( ( X3 != X1 )
                             => ( in @ X3 @ X2 ) ) )
                       => ( ! [X1: $i] :
                              ( ( dsetconstr @ X1
                                @ ^ [X2: $i] : ~ $false )
                              = X1 )
                         => ( ! [X1: $i,X2: $i] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X2 )
                                   => ( in @ X3 @ X1 ) )
                               => ( in @ X2 @ ( powerset @ X1 ) ) )
                           => ( ! [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] :
                                              ( ( exu @ X1 )
                                             => ~ ! [X2: $i] :
                                                    ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                        = ( X3 = X2 ) ) )
                                         => ( ! [X1: $i] :
                                                ( ( nonempty @ X1 )
                                               => ~ ! [X2: $i] :
                                                      ~ ( in @ X2 @ X1 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                 => ( X1 = X2 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 != X2 )
                                                   => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                       => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( ( X3 != X1 )
                                                           => ( X3 = X2 ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                ( ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( X2 @ X3 ) )
                                                               => ( ( dsetconstr @ X1 @ X2 )
                                                                 != emptyset ) )
                                                           => ( ! [X1: $i > $o,X2: $i] :
                                                                  ( ( in @ X2 @ emptyset )
                                                                 => ( X1 @ X2 ) )
                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                    ( ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( X2 @ X3 ) )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( X2 @ X3 ) ) )
                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                      ( ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( X2 @ X3 ) )
                                                                     => ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( X2 @ X3 ) ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                        ( ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( X2 @ X3 ) )
                                                                       => ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( X2 @ X3 ) ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                          ( ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( X2 @ X3 ) )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( X2 @ X3 ) ) )
                                                                     => ( ! [X1: $o] :
                                                                            ( X1
                                                                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                       => ( ! [X1: $o] :
                                                                              ( X1
                                                                             => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                ( ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( X2 @ X3 ) )
                                                                               => ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ~ ( X2 @ X3 ) ) )
                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                  ( ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( X2 @ X3 ) )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( in @ X3 @ X1 )
                                                                                       => ( X2 @ X3 ) ) )
                                                                             => ( ! [X1: $i > $o] :
                                                                                    ( ~ ! [X2: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) )
                                                                                   => ( exu @ X1 ) )
                                                                               => ( ! [X1: $i > $o] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ~ ( X1 @ X2 )
                                                                                     => ( ! [X2: $i,X3: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) )
                                                                                       => ( exu @ X1 ) ) )
                                                                                 => ( ! [X1: $i > $o] :
                                                                                        ( ~ ! [X2: $i] :
                                                                                              ~ ! [X3: $i] :
                                                                                                  ( ( X1 @ X3 )
                                                                                                  = ( X3 = X2 ) )
                                                                                       => ( exu @ X1 ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ! [X3: $i,X4: $i] :
                                                                                              ( ( X3 = X4 )
                                                                                             => ( ( in @ X3 @ X1 )
                                                                                               => ( in @ X4 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                ( ( X3 = X4 )
                                                                                               => ( ( in @ X3 @ X1 )
                                                                                                  = ( in @ X4 @ X2 ) ) ) )
                                                                                       => ( ! [X1: $i > $o] :
                                                                                              ( ( exu @ X1 )
                                                                                             => ! [X2: $i,X3: $i] :
                                                                                                  ( ( X1 @ X2 )
                                                                                                 => ( ( X1 @ X3 )
                                                                                                   => ( X2 = X3 ) ) ) )
                                                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                ( ! [X3: $i,X4: $i] :
                                                                                                    ( ( X3 = X4 )
                                                                                                   => ( ( X1 @ X3 )
                                                                                                      = ( X2 @ X4 ) ) )
                                                                                               => ( ( exu @ X1 )
                                                                                                  = ( exu @ X2 ) ) )
                                                                                           => ( ( emptyset = emptyset )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ! [X3: $i,X4: $i] :
                                                                                                        ( ( X3 = X4 )
                                                                                                       => ( ( setadjoin @ X1 @ X3 )
                                                                                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                               => ! [X1: $i,X2: $i] :
                                                                                                    ( ( X1 = X2 )
                                                                                                   => ( ( powerset @ X1 )
                                                                                                      = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h45,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
            = ( X2 @ X3 ) ) )
     => ( ! [X1: $i] :
            ( ( nonempty @ X1 )
           => ~ ! [X2: $i] :
                  ~ ( in @ X2 @ X1 ) )
       => ( ! [X1: $i,X2: $i > $o,X3: $i] :
              ( ( in @ X3 @ X1 )
             => ( ( X2 @ X3 )
               => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
         => ( ! [X1: $i] :
                ( ~ ! [X2: $i] :
                      ~ ( in @ X2 @ X1 )
               => ( nonempty @ X1 ) )
           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
             => ( ( 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 ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                         => ( ( X3 != X1 )
                           => ( in @ X3 @ X2 ) ) )
                     => ( ! [X1: $i] :
                            ( ( dsetconstr @ X1
                              @ ^ [X2: $i] : ~ $false )
                            = X1 )
                       => ( ! [X1: $i,X2: $i] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X2 )
                                 => ( in @ X3 @ X1 ) )
                             => ( in @ X2 @ ( powerset @ X1 ) ) )
                         => ( ! [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] :
                                            ( ( exu @ X1 )
                                           => ~ ! [X2: $i] :
                                                  ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                      = ( X3 = X2 ) ) )
                                       => ( ! [X1: $i] :
                                              ( ( nonempty @ X1 )
                                             => ~ ! [X2: $i] :
                                                    ~ ( in @ X2 @ X1 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                               => ( X1 = X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 != X2 )
                                                 => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( ( X3 != X1 )
                                                         => ( X3 = X2 ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                              ( ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( X2 @ X3 ) )
                                                             => ( ( dsetconstr @ X1 @ X2 )
                                                               != emptyset ) )
                                                         => ( ! [X1: $i > $o,X2: $i] :
                                                                ( ( in @ X2 @ emptyset )
                                                               => ( X1 @ X2 ) )
                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                  ( ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( X2 @ X3 ) )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( X2 @ X3 ) ) )
                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                    ( ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( X2 @ X3 ) )
                                                                   => ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( X2 @ X3 ) ) )
                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                      ( ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( X2 @ X3 ) )
                                                                     => ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( X2 @ X3 ) ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                        ( ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( X2 @ X3 ) )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( X2 @ X3 ) ) )
                                                                   => ( ! [X1: $o] :
                                                                          ( X1
                                                                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                     => ( ! [X1: $o] :
                                                                            ( X1
                                                                           => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                              ( ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( X2 @ X3 ) )
                                                                             => ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ~ ( X2 @ X3 ) ) )
                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                ( ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( X2 @ X3 ) )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( in @ X3 @ X1 )
                                                                                     => ( X2 @ X3 ) ) )
                                                                           => ( ! [X1: $i > $o] :
                                                                                  ( ~ ! [X2: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) )
                                                                                 => ( exu @ X1 ) )
                                                                             => ( ! [X1: $i > $o] :
                                                                                    ( ~ ! [X2: $i] :
                                                                                          ~ ( X1 @ X2 )
                                                                                   => ( ! [X2: $i,X3: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) )
                                                                                     => ( exu @ X1 ) ) )
                                                                               => ( ! [X1: $i > $o] :
                                                                                      ( ~ ! [X2: $i] :
                                                                                            ~ ! [X3: $i] :
                                                                                                ( ( X1 @ X3 )
                                                                                                = ( X3 = X2 ) )
                                                                                     => ( exu @ X1 ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ! [X3: $i,X4: $i] :
                                                                                            ( ( X3 = X4 )
                                                                                           => ( ( in @ X3 @ X1 )
                                                                                             => ( in @ X4 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ! [X3: $i,X4: $i] :
                                                                                              ( ( X3 = X4 )
                                                                                             => ( ( in @ X3 @ X1 )
                                                                                                = ( in @ X4 @ X2 ) ) ) )
                                                                                     => ( ! [X1: $i > $o] :
                                                                                            ( ( exu @ X1 )
                                                                                           => ! [X2: $i,X3: $i] :
                                                                                                ( ( X1 @ X2 )
                                                                                               => ( ( X1 @ X3 )
                                                                                                 => ( X2 = X3 ) ) ) )
                                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                              ( ! [X3: $i,X4: $i] :
                                                                                                  ( ( X3 = X4 )
                                                                                                 => ( ( X1 @ X3 )
                                                                                                    = ( X2 @ X4 ) ) )
                                                                                             => ( ( exu @ X1 )
                                                                                                = ( exu @ X2 ) ) )
                                                                                         => ( ( emptyset = emptyset )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ! [X3: $i,X4: $i] :
                                                                                                      ( ( X3 = X4 )
                                                                                                     => ( ( setadjoin @ X1 @ X3 )
                                                                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                             => ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ( ( powerset @ X1 )
                                                                                                    = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h46,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
        = ( X2 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h47,assumption,
    ~ ( ! [X1: $i] :
          ( ( nonempty @ X1 )
         => ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 ) )
     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( ( X2 @ X3 )
             => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
       => ( ! [X1: $i] :
              ( ~ ! [X2: $i] :
                    ~ ( in @ X2 @ X1 )
             => ( nonempty @ X1 ) )
         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
           => ( ( 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 ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                       => ( ( X3 != X1 )
                         => ( in @ X3 @ X2 ) ) )
                   => ( ! [X1: $i] :
                          ( ( dsetconstr @ X1
                            @ ^ [X2: $i] : ~ $false )
                          = X1 )
                     => ( ! [X1: $i,X2: $i] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X2 )
                               => ( in @ X3 @ X1 ) )
                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                       => ( ! [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] :
                                          ( ( exu @ X1 )
                                         => ~ ! [X2: $i] :
                                                ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                    = ( X3 = X2 ) ) )
                                     => ( ! [X1: $i] :
                                            ( ( nonempty @ X1 )
                                           => ~ ! [X2: $i] :
                                                  ~ ( in @ X2 @ X1 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                             => ( X1 = X2 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 != X2 )
                                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( ( X3 != X1 )
                                                       => ( X3 = X2 ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                            ( ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( X2 @ X3 ) )
                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                             != emptyset ) )
                                                       => ( ! [X1: $i > $o,X2: $i] :
                                                              ( ( in @ X2 @ emptyset )
                                                             => ( X1 @ X2 ) )
                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                ( ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( X2 @ X3 ) )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( X2 @ X3 ) ) )
                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                  ( ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( X2 @ X3 ) )
                                                                 => ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( X2 @ X3 ) ) )
                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                    ( ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( X2 @ X3 ) )
                                                                   => ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( X2 @ X3 ) ) )
                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                      ( ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( X2 @ X3 ) )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( X2 @ X3 ) ) )
                                                                 => ( ! [X1: $o] :
                                                                        ( X1
                                                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                   => ( ! [X1: $o] :
                                                                          ( X1
                                                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( X2 @ X3 ) )
                                                                           => ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ~ ( X2 @ X3 ) ) )
                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                              ( ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( X2 @ X3 ) )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( in @ X3 @ X1 )
                                                                                   => ( X2 @ X3 ) ) )
                                                                         => ( ! [X1: $i > $o] :
                                                                                ( ~ ! [X2: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) )
                                                                               => ( exu @ X1 ) )
                                                                           => ( ! [X1: $i > $o] :
                                                                                  ( ~ ! [X2: $i] :
                                                                                        ~ ( X1 @ X2 )
                                                                                 => ( ! [X2: $i,X3: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) )
                                                                                   => ( exu @ X1 ) ) )
                                                                             => ( ! [X1: $i > $o] :
                                                                                    ( ~ ! [X2: $i] :
                                                                                          ~ ! [X3: $i] :
                                                                                              ( ( X1 @ X3 )
                                                                                              = ( X3 = X2 ) )
                                                                                   => ( exu @ X1 ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ! [X3: $i,X4: $i] :
                                                                                          ( ( X3 = X4 )
                                                                                         => ( ( in @ X3 @ X1 )
                                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ! [X3: $i,X4: $i] :
                                                                                            ( ( X3 = X4 )
                                                                                           => ( ( in @ X3 @ X1 )
                                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                                   => ( ! [X1: $i > $o] :
                                                                                          ( ( exu @ X1 )
                                                                                         => ! [X2: $i,X3: $i] :
                                                                                              ( ( X1 @ X2 )
                                                                                             => ( ( X1 @ X3 )
                                                                                               => ( X2 = X3 ) ) ) )
                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                ( ( X3 = X4 )
                                                                                               => ( ( X1 @ X3 )
                                                                                                  = ( X2 @ X4 ) ) )
                                                                                           => ( ( exu @ X1 )
                                                                                              = ( exu @ X2 ) ) )
                                                                                       => ( ( emptyset = emptyset )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                    ( ( X3 = X4 )
                                                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                           => ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 = X2 )
                                                                                               => ( ( powerset @ X1 )
                                                                                                  = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h48,assumption,
    ! [X1: $i] :
      ( ( nonempty @ X1 )
     => ~ ! [X2: $i] :
            ~ ( in @ X2 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h49,assumption,
    ~ ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( X2 @ X3 )
           => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
     => ( ! [X1: $i] :
            ( ~ ! [X2: $i] :
                  ~ ( in @ X2 @ X1 )
           => ( nonempty @ X1 ) )
       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
         => ( ( 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 ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                     => ( ( X3 != X1 )
                       => ( in @ X3 @ X2 ) ) )
                 => ( ! [X1: $i] :
                        ( ( dsetconstr @ X1
                          @ ^ [X2: $i] : ~ $false )
                        = X1 )
                   => ( ! [X1: $i,X2: $i] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X2 )
                             => ( in @ X3 @ X1 ) )
                         => ( in @ X2 @ ( powerset @ X1 ) ) )
                     => ( ! [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] :
                                        ( ( exu @ X1 )
                                       => ~ ! [X2: $i] :
                                              ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                  = ( X3 = X2 ) ) )
                                   => ( ! [X1: $i] :
                                          ( ( nonempty @ X1 )
                                         => ~ ! [X2: $i] :
                                                ~ ( in @ X2 @ X1 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                           => ( X1 = X2 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 != X2 )
                                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( ( X3 != X1 )
                                                     => ( X3 = X2 ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                          ( ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( X2 @ X3 ) )
                                                         => ( ( dsetconstr @ X1 @ X2 )
                                                           != emptyset ) )
                                                     => ( ! [X1: $i > $o,X2: $i] :
                                                            ( ( in @ X2 @ emptyset )
                                                           => ( X1 @ X2 ) )
                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                              ( ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( X2 @ X3 ) )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( X2 @ X3 ) ) )
                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                ( ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( X2 @ X3 ) )
                                                               => ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( X2 @ X3 ) ) )
                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                  ( ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( X2 @ X3 ) )
                                                                 => ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( X2 @ X3 ) ) )
                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                    ( ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( X2 @ X3 ) )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( X2 @ X3 ) ) )
                                                               => ( ! [X1: $o] :
                                                                      ( X1
                                                                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                 => ( ! [X1: $o] :
                                                                        ( X1
                                                                       => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                          ( ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( X2 @ X3 ) )
                                                                         => ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ~ ( X2 @ X3 ) ) )
                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                            ( ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( X2 @ X3 ) )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( in @ X3 @ X1 )
                                                                                 => ( X2 @ X3 ) ) )
                                                                       => ( ! [X1: $i > $o] :
                                                                              ( ~ ! [X2: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) )
                                                                             => ( exu @ X1 ) )
                                                                         => ( ! [X1: $i > $o] :
                                                                                ( ~ ! [X2: $i] :
                                                                                      ~ ( X1 @ X2 )
                                                                               => ( ! [X2: $i,X3: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) )
                                                                                 => ( exu @ X1 ) ) )
                                                                           => ( ! [X1: $i > $o] :
                                                                                  ( ~ ! [X2: $i] :
                                                                                        ~ ! [X3: $i] :
                                                                                            ( ( X1 @ X3 )
                                                                                            = ( X3 = X2 ) )
                                                                                 => ( exu @ X1 ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ! [X3: $i,X4: $i] :
                                                                                        ( ( X3 = X4 )
                                                                                       => ( ( in @ X3 @ X1 )
                                                                                         => ( in @ X4 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ! [X3: $i,X4: $i] :
                                                                                          ( ( X3 = X4 )
                                                                                         => ( ( in @ X3 @ X1 )
                                                                                            = ( in @ X4 @ X2 ) ) ) )
                                                                                 => ( ! [X1: $i > $o] :
                                                                                        ( ( exu @ X1 )
                                                                                       => ! [X2: $i,X3: $i] :
                                                                                            ( ( X1 @ X2 )
                                                                                           => ( ( X1 @ X3 )
                                                                                             => ( X2 = X3 ) ) ) )
                                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                          ( ! [X3: $i,X4: $i] :
                                                                                              ( ( X3 = X4 )
                                                                                             => ( ( X1 @ X3 )
                                                                                                = ( X2 @ X4 ) ) )
                                                                                         => ( ( exu @ X1 )
                                                                                            = ( exu @ X2 ) ) )
                                                                                     => ( ( emptyset = emptyset )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ! [X3: $i,X4: $i] :
                                                                                                  ( ( X3 = X4 )
                                                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                         => ! [X1: $i,X2: $i] :
                                                                                              ( ( X1 = X2 )
                                                                                             => ( ( powerset @ X1 )
                                                                                                = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h50,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( X2 @ X3 )
       => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h51,assumption,
    ~ ( ! [X1: $i] :
          ( ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 )
         => ( nonempty @ X1 ) )
     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
       => ( ( 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 ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                   => ( ( X3 != X1 )
                     => ( in @ X3 @ X2 ) ) )
               => ( ! [X1: $i] :
                      ( ( dsetconstr @ X1
                        @ ^ [X2: $i] : ~ $false )
                      = X1 )
                 => ( ! [X1: $i,X2: $i] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X2 )
                           => ( in @ X3 @ X1 ) )
                       => ( in @ X2 @ ( powerset @ X1 ) ) )
                   => ( ! [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] :
                                      ( ( exu @ X1 )
                                     => ~ ! [X2: $i] :
                                            ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                                = ( X3 = X2 ) ) )
                                 => ( ! [X1: $i] :
                                        ( ( nonempty @ X1 )
                                       => ~ ! [X2: $i] :
                                              ~ ( in @ X2 @ X1 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                         => ( X1 = X2 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 != X2 )
                                           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( ( X3 != X1 )
                                                   => ( X3 = X2 ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                        ( ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( X2 @ X3 ) )
                                                       => ( ( dsetconstr @ X1 @ X2 )
                                                         != emptyset ) )
                                                   => ( ! [X1: $i > $o,X2: $i] :
                                                          ( ( in @ X2 @ emptyset )
                                                         => ( X1 @ X2 ) )
                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                            ( ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( X2 @ X3 ) )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( X2 @ X3 ) ) )
                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                              ( ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( X2 @ X3 ) )
                                                             => ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( X2 @ X3 ) ) )
                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                ( ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( X2 @ X3 ) )
                                                               => ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( X2 @ X3 ) ) )
                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                  ( ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( X2 @ X3 ) )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( X2 @ X3 ) ) )
                                                             => ( ! [X1: $o] :
                                                                    ( X1
                                                                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                               => ( ! [X1: $o] :
                                                                      ( X1
                                                                     => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                        ( ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( X2 @ X3 ) )
                                                                       => ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ~ ( X2 @ X3 ) ) )
                                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                                          ( ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( X2 @ X3 ) )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( in @ X3 @ X1 )
                                                                               => ( X2 @ X3 ) ) )
                                                                     => ( ! [X1: $i > $o] :
                                                                            ( ~ ! [X2: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) )
                                                                           => ( exu @ X1 ) )
                                                                       => ( ! [X1: $i > $o] :
                                                                              ( ~ ! [X2: $i] :
                                                                                    ~ ( X1 @ X2 )
                                                                             => ( ! [X2: $i,X3: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) )
                                                                               => ( exu @ X1 ) ) )
                                                                         => ( ! [X1: $i > $o] :
                                                                                ( ~ ! [X2: $i] :
                                                                                      ~ ! [X3: $i] :
                                                                                          ( ( X1 @ X3 )
                                                                                          = ( X3 = X2 ) )
                                                                               => ( exu @ X1 ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ! [X3: $i,X4: $i] :
                                                                                      ( ( X3 = X4 )
                                                                                     => ( ( in @ X3 @ X1 )
                                                                                       => ( in @ X4 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ! [X3: $i,X4: $i] :
                                                                                        ( ( X3 = X4 )
                                                                                       => ( ( in @ X3 @ X1 )
                                                                                          = ( in @ X4 @ X2 ) ) ) )
                                                                               => ( ! [X1: $i > $o] :
                                                                                      ( ( exu @ X1 )
                                                                                     => ! [X2: $i,X3: $i] :
                                                                                          ( ( X1 @ X2 )
                                                                                         => ( ( X1 @ X3 )
                                                                                           => ( X2 = X3 ) ) ) )
                                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                        ( ! [X3: $i,X4: $i] :
                                                                                            ( ( X3 = X4 )
                                                                                           => ( ( X1 @ X3 )
                                                                                              = ( X2 @ X4 ) ) )
                                                                                       => ( ( exu @ X1 )
                                                                                          = ( exu @ X2 ) ) )
                                                                                   => ( ( emptyset = emptyset )
                                                                                     => ( ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ! [X3: $i,X4: $i] :
                                                                                                ( ( X3 = X4 )
                                                                                               => ( ( setadjoin @ X1 @ X3 )
                                                                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                       => ! [X1: $i,X2: $i] :
                                                                                            ( ( X1 = X2 )
                                                                                           => ( ( powerset @ X1 )
                                                                                              = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h52,assumption,
    ! [X1: $i] :
      ( ~ ! [X2: $i] :
            ~ ( in @ X2 @ X1 )
     => ( nonempty @ X1 ) ),
    introduced(assumption,[]) ).

thf(h53,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
     => ( ( 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 ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                 => ( ( X3 != X1 )
                   => ( in @ X3 @ X2 ) ) )
             => ( ! [X1: $i] :
                    ( ( dsetconstr @ X1
                      @ ^ [X2: $i] : ~ $false )
                    = X1 )
               => ( ! [X1: $i,X2: $i] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X2 )
                         => ( in @ X3 @ X1 ) )
                     => ( in @ X2 @ ( powerset @ X1 ) ) )
                 => ( ! [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] :
                                    ( ( exu @ X1 )
                                   => ~ ! [X2: $i] :
                                          ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                              = ( X3 = X2 ) ) )
                               => ( ! [X1: $i] :
                                      ( ( nonempty @ X1 )
                                     => ~ ! [X2: $i] :
                                            ~ ( in @ X2 @ X1 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                       => ( X1 = X2 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 != X2 )
                                         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( ( X3 != X1 )
                                                 => ( X3 = X2 ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                               => ( ! [X1: $i,X2: $i > $o] :
                                                      ( ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( X2 @ X3 ) )
                                                     => ( ( dsetconstr @ X1 @ X2 )
                                                       != emptyset ) )
                                                 => ( ! [X1: $i > $o,X2: $i] :
                                                        ( ( in @ X2 @ emptyset )
                                                       => ( X1 @ X2 ) )
                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                          ( ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( X2 @ X3 ) )
                                                         => ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( X2 @ X3 ) ) )
                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                            ( ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( X2 @ X3 ) )
                                                           => ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( X2 @ X3 ) ) )
                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                              ( ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( X2 @ X3 ) )
                                                             => ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( X2 @ X3 ) ) )
                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                ( ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( X2 @ X3 ) )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( X2 @ X3 ) ) )
                                                           => ( ! [X1: $o] :
                                                                  ( X1
                                                                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                             => ( ! [X1: $o] :
                                                                    ( X1
                                                                   => ( set2prop @ ( prop2set @ X1 ) ) )
                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                      ( ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( X2 @ X3 ) )
                                                                     => ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ~ ( X2 @ X3 ) ) )
                                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                                        ( ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( X2 @ X3 ) )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( in @ X3 @ X1 )
                                                                             => ( X2 @ X3 ) ) )
                                                                   => ( ! [X1: $i > $o] :
                                                                          ( ~ ! [X2: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) )
                                                                         => ( exu @ X1 ) )
                                                                     => ( ! [X1: $i > $o] :
                                                                            ( ~ ! [X2: $i] :
                                                                                  ~ ( X1 @ X2 )
                                                                           => ( ! [X2: $i,X3: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) )
                                                                             => ( exu @ X1 ) ) )
                                                                       => ( ! [X1: $i > $o] :
                                                                              ( ~ ! [X2: $i] :
                                                                                    ~ ! [X3: $i] :
                                                                                        ( ( X1 @ X3 )
                                                                                        = ( X3 = X2 ) )
                                                                             => ( exu @ X1 ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ! [X3: $i,X4: $i] :
                                                                                    ( ( X3 = X4 )
                                                                                   => ( ( in @ X3 @ X1 )
                                                                                     => ( in @ X4 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ! [X3: $i,X4: $i] :
                                                                                      ( ( X3 = X4 )
                                                                                     => ( ( in @ X3 @ X1 )
                                                                                        = ( in @ X4 @ X2 ) ) ) )
                                                                             => ( ! [X1: $i > $o] :
                                                                                    ( ( exu @ X1 )
                                                                                   => ! [X2: $i,X3: $i] :
                                                                                        ( ( X1 @ X2 )
                                                                                       => ( ( X1 @ X3 )
                                                                                         => ( X2 = X3 ) ) ) )
                                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                      ( ! [X3: $i,X4: $i] :
                                                                                          ( ( X3 = X4 )
                                                                                         => ( ( X1 @ X3 )
                                                                                            = ( X2 @ X4 ) ) )
                                                                                     => ( ( exu @ X1 )
                                                                                        = ( exu @ X2 ) ) )
                                                                                 => ( ( emptyset = emptyset )
                                                                                   => ( ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ! [X3: $i,X4: $i] :
                                                                                              ( ( X3 = X4 )
                                                                                             => ( ( setadjoin @ X1 @ X3 )
                                                                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                     => ! [X1: $i,X2: $i] :
                                                                                          ( ( X1 = X2 )
                                                                                         => ( ( powerset @ X1 )
                                                                                            = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h54,assumption,
    ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h55,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 ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
               => ( ( X3 != X1 )
                 => ( in @ X3 @ X2 ) ) )
           => ( ! [X1: $i] :
                  ( ( dsetconstr @ X1
                    @ ^ [X2: $i] : ~ $false )
                  = X1 )
             => ( ! [X1: $i,X2: $i] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X2 )
                       => ( in @ X3 @ X1 ) )
                   => ( in @ X2 @ ( powerset @ X1 ) ) )
               => ( ! [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] :
                                  ( ( exu @ X1 )
                                 => ~ ! [X2: $i] :
                                        ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                            = ( X3 = X2 ) ) )
                             => ( ! [X1: $i] :
                                    ( ( nonempty @ X1 )
                                   => ~ ! [X2: $i] :
                                          ~ ( in @ X2 @ X1 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                     => ( X1 = X2 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 != X2 )
                                       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i,X3: $i] :
                                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( ( X3 != X1 )
                                               => ( X3 = X2 ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                             => ( ! [X1: $i,X2: $i > $o] :
                                                    ( ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( X2 @ X3 ) )
                                                   => ( ( dsetconstr @ X1 @ X2 )
                                                     != emptyset ) )
                                               => ( ! [X1: $i > $o,X2: $i] :
                                                      ( ( in @ X2 @ emptyset )
                                                     => ( X1 @ X2 ) )
                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                        ( ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( X2 @ X3 ) )
                                                       => ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( X2 @ X3 ) ) )
                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                          ( ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( X2 @ X3 ) )
                                                         => ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( X2 @ X3 ) ) )
                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                            ( ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( X2 @ X3 ) )
                                                           => ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( X2 @ X3 ) ) )
                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                              ( ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( X2 @ X3 ) )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( X2 @ X3 ) ) )
                                                         => ( ! [X1: $o] :
                                                                ( X1
                                                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                           => ( ! [X1: $o] :
                                                                  ( X1
                                                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                    ( ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( X2 @ X3 ) )
                                                                   => ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ~ ( X2 @ X3 ) ) )
                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                      ( ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( X2 @ X3 ) )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( in @ X3 @ X1 )
                                                                           => ( X2 @ X3 ) ) )
                                                                 => ( ! [X1: $i > $o] :
                                                                        ( ~ ! [X2: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) )
                                                                       => ( exu @ X1 ) )
                                                                   => ( ! [X1: $i > $o] :
                                                                          ( ~ ! [X2: $i] :
                                                                                ~ ( X1 @ X2 )
                                                                         => ( ! [X2: $i,X3: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) )
                                                                           => ( exu @ X1 ) ) )
                                                                     => ( ! [X1: $i > $o] :
                                                                            ( ~ ! [X2: $i] :
                                                                                  ~ ! [X3: $i] :
                                                                                      ( ( X1 @ X3 )
                                                                                      = ( X3 = X2 ) )
                                                                           => ( exu @ X1 ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ! [X3: $i,X4: $i] :
                                                                                  ( ( X3 = X4 )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                   => ( in @ X4 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ! [X3: $i,X4: $i] :
                                                                                    ( ( X3 = X4 )
                                                                                   => ( ( in @ X3 @ X1 )
                                                                                      = ( in @ X4 @ X2 ) ) ) )
                                                                           => ( ! [X1: $i > $o] :
                                                                                  ( ( exu @ X1 )
                                                                                 => ! [X2: $i,X3: $i] :
                                                                                      ( ( X1 @ X2 )
                                                                                     => ( ( X1 @ X3 )
                                                                                       => ( X2 = X3 ) ) ) )
                                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                    ( ! [X3: $i,X4: $i] :
                                                                                        ( ( X3 = X4 )
                                                                                       => ( ( X1 @ X3 )
                                                                                          = ( X2 @ X4 ) ) )
                                                                                   => ( ( exu @ X1 )
                                                                                      = ( exu @ X2 ) ) )
                                                                               => ( ( emptyset = emptyset )
                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ! [X3: $i,X4: $i] :
                                                                                            ( ( X3 = X4 )
                                                                                           => ( ( setadjoin @ X1 @ X3 )
                                                                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                   => ! [X1: $i,X2: $i] :
                                                                                        ( ( X1 = X2 )
                                                                                       => ( ( powerset @ X1 )
                                                                                          = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h56,assumption,
    in @ emptyset @ ( setadjoin @ emptyset @ emptyset ),
    introduced(assumption,[]) ).

thf(h57,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 ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
             => ( ( X3 != X1 )
               => ( in @ X3 @ X2 ) ) )
         => ( ! [X1: $i] :
                ( ( dsetconstr @ X1
                  @ ^ [X2: $i] : ~ $false )
                = X1 )
           => ( ! [X1: $i,X2: $i] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ( in @ X3 @ X1 ) )
                 => ( in @ X2 @ ( powerset @ X1 ) ) )
             => ( ! [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] :
                                ( ( exu @ X1 )
                               => ~ ! [X2: $i] :
                                      ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                          = ( X3 = X2 ) ) )
                           => ( ! [X1: $i] :
                                  ( ( nonempty @ X1 )
                                 => ~ ! [X2: $i] :
                                        ~ ( in @ X2 @ X1 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                   => ( X1 = X2 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 != X2 )
                                     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i,X3: $i] :
                                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( ( X3 != X1 )
                                             => ( X3 = X2 ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                           => ( ! [X1: $i,X2: $i > $o] :
                                                  ( ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( X2 @ X3 ) )
                                                 => ( ( dsetconstr @ X1 @ X2 )
                                                   != emptyset ) )
                                             => ( ! [X1: $i > $o,X2: $i] :
                                                    ( ( in @ X2 @ emptyset )
                                                   => ( X1 @ X2 ) )
                                               => ( ! [X1: $i,X2: $i > $o] :
                                                      ( ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( X2 @ X3 ) )
                                                     => ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                        ( ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( X2 @ X3 ) )
                                                       => ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( X2 @ X3 ) ) )
                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                          ( ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( X2 @ X3 ) )
                                                         => ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( X2 @ X3 ) ) )
                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                            ( ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( X2 @ X3 ) )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( X2 @ X3 ) ) )
                                                       => ( ! [X1: $o] :
                                                              ( X1
                                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                         => ( ! [X1: $o] :
                                                                ( X1
                                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                  ( ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( X2 @ X3 ) )
                                                                 => ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ~ ( X2 @ X3 ) ) )
                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                    ( ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( X2 @ X3 ) )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( in @ X3 @ X1 )
                                                                         => ( X2 @ X3 ) ) )
                                                               => ( ! [X1: $i > $o] :
                                                                      ( ~ ! [X2: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) )
                                                                     => ( exu @ X1 ) )
                                                                 => ( ! [X1: $i > $o] :
                                                                        ( ~ ! [X2: $i] :
                                                                              ~ ( X1 @ X2 )
                                                                       => ( ! [X2: $i,X3: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) )
                                                                         => ( exu @ X1 ) ) )
                                                                   => ( ! [X1: $i > $o] :
                                                                          ( ~ ! [X2: $i] :
                                                                                ~ ! [X3: $i] :
                                                                                    ( ( X1 @ X3 )
                                                                                    = ( X3 = X2 ) )
                                                                         => ( exu @ X1 ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ! [X3: $i,X4: $i] :
                                                                                ( ( X3 = X4 )
                                                                               => ( ( in @ X3 @ X1 )
                                                                                 => ( in @ X4 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ! [X3: $i,X4: $i] :
                                                                                  ( ( X3 = X4 )
                                                                                 => ( ( in @ X3 @ X1 )
                                                                                    = ( in @ X4 @ X2 ) ) ) )
                                                                         => ( ! [X1: $i > $o] :
                                                                                ( ( exu @ X1 )
                                                                               => ! [X2: $i,X3: $i] :
                                                                                    ( ( X1 @ X2 )
                                                                                   => ( ( X1 @ X3 )
                                                                                     => ( X2 = X3 ) ) ) )
                                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                  ( ! [X3: $i,X4: $i] :
                                                                                      ( ( X3 = X4 )
                                                                                     => ( ( X1 @ X3 )
                                                                                        = ( X2 @ X4 ) ) )
                                                                                 => ( ( exu @ X1 )
                                                                                    = ( exu @ X2 ) ) )
                                                                             => ( ( emptyset = emptyset )
                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ! [X3: $i,X4: $i] :
                                                                                          ( ( X3 = X4 )
                                                                                         => ( ( setadjoin @ X1 @ X3 )
                                                                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                 => ! [X1: $i,X2: $i] :
                                                                                      ( ( X1 = X2 )
                                                                                     => ( ( powerset @ X1 )
                                                                                        = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h58,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ X2 )
     => ( in @ X3 @ ( setadjoin @ X1 @ 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 ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
           => ( ( X3 != X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( ! [X1: $i] :
              ( ( dsetconstr @ X1
                @ ^ [X2: $i] : ~ $false )
              = X1 )
         => ( ! [X1: $i,X2: $i] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) )
               => ( in @ X2 @ ( powerset @ X1 ) ) )
           => ( ! [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] :
                              ( ( exu @ X1 )
                             => ~ ! [X2: $i] :
                                    ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                        = ( X3 = X2 ) ) )
                         => ( ! [X1: $i] :
                                ( ( nonempty @ X1 )
                               => ~ ! [X2: $i] :
                                      ~ ( in @ X2 @ X1 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                 => ( X1 = X2 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 != X2 )
                                   => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                       => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i,X3: $i] :
                                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( ( X3 != X1 )
                                           => ( X3 = X2 ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                         => ( ! [X1: $i,X2: $i > $o] :
                                                ( ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( X2 @ X3 ) )
                                               => ( ( dsetconstr @ X1 @ X2 )
                                                 != emptyset ) )
                                           => ( ! [X1: $i > $o,X2: $i] :
                                                  ( ( in @ X2 @ emptyset )
                                                 => ( X1 @ X2 ) )
                                             => ( ! [X1: $i,X2: $i > $o] :
                                                    ( ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( X2 @ X3 ) )
                                                   => ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( X2 @ X3 ) ) )
                                               => ( ! [X1: $i,X2: $i > $o] :
                                                      ( ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( X2 @ X3 ) )
                                                     => ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                        ( ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( X2 @ X3 ) )
                                                       => ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( X2 @ X3 ) ) )
                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                          ( ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( X2 @ X3 ) )
                                                         => ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( X2 @ X3 ) ) )
                                                     => ( ! [X1: $o] :
                                                            ( X1
                                                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                       => ( ! [X1: $o] :
                                                              ( X1
                                                             => ( set2prop @ ( prop2set @ X1 ) ) )
                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                ( ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( X2 @ X3 ) )
                                                               => ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ~ ( X2 @ X3 ) ) )
                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                  ( ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( X2 @ X3 ) )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( in @ X3 @ X1 )
                                                                       => ( X2 @ X3 ) ) )
                                                             => ( ! [X1: $i > $o] :
                                                                    ( ~ ! [X2: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) )
                                                                   => ( exu @ X1 ) )
                                                               => ( ! [X1: $i > $o] :
                                                                      ( ~ ! [X2: $i] :
                                                                            ~ ( X1 @ X2 )
                                                                     => ( ! [X2: $i,X3: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) )
                                                                       => ( exu @ X1 ) ) )
                                                                 => ( ! [X1: $i > $o] :
                                                                        ( ~ ! [X2: $i] :
                                                                              ~ ! [X3: $i] :
                                                                                  ( ( X1 @ X3 )
                                                                                  = ( X3 = X2 ) )
                                                                       => ( exu @ X1 ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ! [X3: $i,X4: $i] :
                                                                              ( ( X3 = X4 )
                                                                             => ( ( in @ X3 @ X1 )
                                                                               => ( in @ X4 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ! [X3: $i,X4: $i] :
                                                                                ( ( X3 = X4 )
                                                                               => ( ( in @ X3 @ X1 )
                                                                                  = ( in @ X4 @ X2 ) ) ) )
                                                                       => ( ! [X1: $i > $o] :
                                                                              ( ( exu @ X1 )
                                                                             => ! [X2: $i,X3: $i] :
                                                                                  ( ( X1 @ X2 )
                                                                                 => ( ( X1 @ X3 )
                                                                                   => ( X2 = X3 ) ) ) )
                                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                ( ! [X3: $i,X4: $i] :
                                                                                    ( ( X3 = X4 )
                                                                                   => ( ( X1 @ X3 )
                                                                                      = ( X2 @ X4 ) ) )
                                                                               => ( ( exu @ X1 )
                                                                                  = ( exu @ X2 ) ) )
                                                                           => ( ( emptyset = emptyset )
                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ! [X3: $i,X4: $i] :
                                                                                        ( ( X3 = X4 )
                                                                                       => ( ( setadjoin @ X1 @ X3 )
                                                                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                               => ! [X1: $i,X2: $i] :
                                                                                    ( ( X1 = X2 )
                                                                                   => ( ( powerset @ X1 )
                                                                                      = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h60,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(h61,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
         => ( ( X3 != X1 )
           => ( in @ X3 @ X2 ) ) )
     => ( ! [X1: $i] :
            ( ( dsetconstr @ X1
              @ ^ [X2: $i] : ~ $false )
            = X1 )
       => ( ! [X1: $i,X2: $i] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ( in @ X3 @ X1 ) )
             => ( in @ X2 @ ( powerset @ X1 ) ) )
         => ( ! [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] :
                            ( ( exu @ X1 )
                           => ~ ! [X2: $i] :
                                  ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                      = ( X3 = X2 ) ) )
                       => ( ! [X1: $i] :
                              ( ( nonempty @ X1 )
                             => ~ ! [X2: $i] :
                                    ~ ( in @ X2 @ X1 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                               => ( X1 = X2 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 != X2 )
                                 => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( ( X3 != X1 )
                                         => ( X3 = X2 ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                       => ( ! [X1: $i,X2: $i > $o] :
                                              ( ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( X2 @ X3 ) )
                                             => ( ( dsetconstr @ X1 @ X2 )
                                               != emptyset ) )
                                         => ( ! [X1: $i > $o,X2: $i] :
                                                ( ( in @ X2 @ emptyset )
                                               => ( X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i > $o] :
                                                  ( ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( X2 @ X3 ) )
                                                 => ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( X2 @ X3 ) ) )
                                             => ( ! [X1: $i,X2: $i > $o] :
                                                    ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( X2 @ X3 ) )
                                                   => ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( X2 @ X3 ) ) )
                                               => ( ! [X1: $i,X2: $i > $o] :
                                                      ( ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( X2 @ X3 ) )
                                                     => ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                        ( ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( X2 @ X3 ) )
                                                       => ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( X2 @ X3 ) ) )
                                                   => ( ! [X1: $o] :
                                                          ( X1
                                                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                     => ( ! [X1: $o] :
                                                            ( X1
                                                           => ( set2prop @ ( prop2set @ X1 ) ) )
                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                              ( ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( X2 @ X3 ) )
                                                             => ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ~ ( X2 @ X3 ) ) )
                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                ( ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( X2 @ X3 ) )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( in @ X3 @ X1 )
                                                                     => ( X2 @ X3 ) ) )
                                                           => ( ! [X1: $i > $o] :
                                                                  ( ~ ! [X2: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) )
                                                                 => ( exu @ X1 ) )
                                                             => ( ! [X1: $i > $o] :
                                                                    ( ~ ! [X2: $i] :
                                                                          ~ ( X1 @ X2 )
                                                                   => ( ! [X2: $i,X3: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) )
                                                                     => ( exu @ X1 ) ) )
                                                               => ( ! [X1: $i > $o] :
                                                                      ( ~ ! [X2: $i] :
                                                                            ~ ! [X3: $i] :
                                                                                ( ( X1 @ X3 )
                                                                                = ( X3 = X2 ) )
                                                                     => ( exu @ X1 ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ! [X3: $i,X4: $i] :
                                                                            ( ( X3 = X4 )
                                                                           => ( ( in @ X3 @ X1 )
                                                                             => ( in @ X4 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ! [X3: $i,X4: $i] :
                                                                              ( ( X3 = X4 )
                                                                             => ( ( in @ X3 @ X1 )
                                                                                = ( in @ X4 @ X2 ) ) ) )
                                                                     => ( ! [X1: $i > $o] :
                                                                            ( ( exu @ X1 )
                                                                           => ! [X2: $i,X3: $i] :
                                                                                ( ( X1 @ X2 )
                                                                               => ( ( X1 @ X3 )
                                                                                 => ( X2 = X3 ) ) ) )
                                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                              ( ! [X3: $i,X4: $i] :
                                                                                  ( ( X3 = X4 )
                                                                                 => ( ( X1 @ X3 )
                                                                                    = ( X2 @ X4 ) ) )
                                                                             => ( ( exu @ X1 )
                                                                                = ( exu @ X2 ) ) )
                                                                         => ( ( emptyset = emptyset )
                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ! [X3: $i,X4: $i] :
                                                                                      ( ( X3 = X4 )
                                                                                     => ( ( setadjoin @ X1 @ X3 )
                                                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                             => ! [X1: $i,X2: $i] :
                                                                                  ( ( X1 = X2 )
                                                                                 => ( ( powerset @ X1 )
                                                                                    = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h62,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
     => ( ( X3 != X1 )
       => ( in @ X3 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h63,assumption,
    ~ ( ! [X1: $i] :
          ( ( dsetconstr @ X1
            @ ^ [X2: $i] : ~ $false )
          = X1 )
     => ( ! [X1: $i,X2: $i] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X2 )
               => ( in @ X3 @ X1 ) )
           => ( in @ X2 @ ( powerset @ X1 ) ) )
       => ( ! [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] :
                          ( ( exu @ X1 )
                         => ~ ! [X2: $i] :
                                ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                    = ( X3 = X2 ) ) )
                     => ( ! [X1: $i] :
                            ( ( nonempty @ X1 )
                           => ~ ! [X2: $i] :
                                  ~ ( in @ X2 @ X1 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                             => ( X1 = X2 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 != X2 )
                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( ( X3 != X1 )
                                       => ( X3 = X2 ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                     => ( ! [X1: $i,X2: $i > $o] :
                                            ( ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( X2 @ X3 ) )
                                           => ( ( dsetconstr @ X1 @ X2 )
                                             != emptyset ) )
                                       => ( ! [X1: $i > $o,X2: $i] :
                                              ( ( in @ X2 @ emptyset )
                                             => ( X1 @ X2 ) )
                                         => ( ! [X1: $i,X2: $i > $o] :
                                                ( ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( X2 @ X3 ) )
                                               => ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( X2 @ X3 ) ) )
                                           => ( ! [X1: $i,X2: $i > $o] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( X2 @ X3 ) )
                                                 => ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( X2 @ X3 ) ) )
                                             => ( ! [X1: $i,X2: $i > $o] :
                                                    ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( X2 @ X3 ) )
                                                   => ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( X2 @ X3 ) ) )
                                               => ( ! [X1: $i,X2: $i > $o] :
                                                      ( ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( X2 @ X3 ) )
                                                     => ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $o] :
                                                        ( X1
                                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                   => ( ! [X1: $o] :
                                                          ( X1
                                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                            ( ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( X2 @ X3 ) )
                                                           => ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ~ ( X2 @ X3 ) ) )
                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                              ( ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( X2 @ X3 ) )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( in @ X3 @ X1 )
                                                                   => ( X2 @ X3 ) ) )
                                                         => ( ! [X1: $i > $o] :
                                                                ( ~ ! [X2: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) )
                                                               => ( exu @ X1 ) )
                                                           => ( ! [X1: $i > $o] :
                                                                  ( ~ ! [X2: $i] :
                                                                        ~ ( X1 @ X2 )
                                                                 => ( ! [X2: $i,X3: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) )
                                                                   => ( exu @ X1 ) ) )
                                                             => ( ! [X1: $i > $o] :
                                                                    ( ~ ! [X2: $i] :
                                                                          ~ ! [X3: $i] :
                                                                              ( ( X1 @ X3 )
                                                                              = ( X3 = X2 ) )
                                                                   => ( exu @ X1 ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ! [X3: $i,X4: $i] :
                                                                          ( ( X3 = X4 )
                                                                         => ( ( in @ X3 @ X1 )
                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ! [X3: $i,X4: $i] :
                                                                            ( ( X3 = X4 )
                                                                           => ( ( in @ X3 @ X1 )
                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                   => ( ! [X1: $i > $o] :
                                                                          ( ( exu @ X1 )
                                                                         => ! [X2: $i,X3: $i] :
                                                                              ( ( X1 @ X2 )
                                                                             => ( ( X1 @ X3 )
                                                                               => ( X2 = X3 ) ) ) )
                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                            ( ! [X3: $i,X4: $i] :
                                                                                ( ( X3 = X4 )
                                                                               => ( ( X1 @ X3 )
                                                                                  = ( X2 @ X4 ) ) )
                                                                           => ( ( exu @ X1 )
                                                                              = ( exu @ X2 ) ) )
                                                                       => ( ( emptyset = emptyset )
                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ! [X3: $i,X4: $i] :
                                                                                    ( ( X3 = X4 )
                                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                           => ! [X1: $i,X2: $i] :
                                                                                ( ( X1 = X2 )
                                                                               => ( ( powerset @ X1 )
                                                                                  = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h64,assumption,
    ! [X1: $i] :
      ( ( dsetconstr @ X1
        @ ^ [X2: $i] : ~ $false )
      = X1 ),
    introduced(assumption,[]) ).

thf(h65,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X2 )
             => ( in @ X3 @ X1 ) )
         => ( in @ X2 @ ( powerset @ X1 ) ) )
     => ( ! [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] :
                        ( ( exu @ X1 )
                       => ~ ! [X2: $i] :
                              ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                  = ( X3 = X2 ) ) )
                   => ( ! [X1: $i] :
                          ( ( nonempty @ X1 )
                         => ~ ! [X2: $i] :
                                ~ ( in @ X2 @ X1 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                           => ( X1 = X2 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 != X2 )
                             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i,X3: $i] :
                                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( ( X3 != X1 )
                                     => ( X3 = X2 ) ) )
                               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                   => ( ! [X1: $i,X2: $i > $o] :
                                          ( ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( X2 @ X3 ) )
                                         => ( ( dsetconstr @ X1 @ X2 )
                                           != emptyset ) )
                                     => ( ! [X1: $i > $o,X2: $i] :
                                            ( ( in @ X2 @ emptyset )
                                           => ( X1 @ X2 ) )
                                       => ( ! [X1: $i,X2: $i > $o] :
                                              ( ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( X2 @ X3 ) )
                                             => ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( X2 @ X3 ) ) )
                                         => ( ! [X1: $i,X2: $i > $o] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( X2 @ X3 ) )
                                               => ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( X2 @ X3 ) ) )
                                           => ( ! [X1: $i,X2: $i > $o] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( X2 @ X3 ) )
                                                 => ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( X2 @ X3 ) ) )
                                             => ( ! [X1: $i,X2: $i > $o] :
                                                    ( ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( X2 @ X3 ) )
                                                   => ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( X2 @ X3 ) ) )
                                               => ( ! [X1: $o] :
                                                      ( X1
                                                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                 => ( ! [X1: $o] :
                                                        ( X1
                                                       => ( set2prop @ ( prop2set @ X1 ) ) )
                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                          ( ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( X2 @ X3 ) )
                                                         => ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ~ ( X2 @ X3 ) ) )
                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                            ( ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( X2 @ X3 ) )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( in @ X3 @ X1 )
                                                                 => ( X2 @ X3 ) ) )
                                                       => ( ! [X1: $i > $o] :
                                                              ( ~ ! [X2: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) )
                                                             => ( exu @ X1 ) )
                                                         => ( ! [X1: $i > $o] :
                                                                ( ~ ! [X2: $i] :
                                                                      ~ ( X1 @ X2 )
                                                               => ( ! [X2: $i,X3: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) )
                                                                 => ( exu @ X1 ) ) )
                                                           => ( ! [X1: $i > $o] :
                                                                  ( ~ ! [X2: $i] :
                                                                        ~ ! [X3: $i] :
                                                                            ( ( X1 @ X3 )
                                                                            = ( X3 = X2 ) )
                                                                 => ( exu @ X1 ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ! [X3: $i,X4: $i] :
                                                                        ( ( X3 = X4 )
                                                                       => ( ( in @ X3 @ X1 )
                                                                         => ( in @ X4 @ X2 ) ) ) )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ! [X3: $i,X4: $i] :
                                                                          ( ( X3 = X4 )
                                                                         => ( ( in @ X3 @ X1 )
                                                                            = ( in @ X4 @ X2 ) ) ) )
                                                                 => ( ! [X1: $i > $o] :
                                                                        ( ( exu @ X1 )
                                                                       => ! [X2: $i,X3: $i] :
                                                                            ( ( X1 @ X2 )
                                                                           => ( ( X1 @ X3 )
                                                                             => ( X2 = X3 ) ) ) )
                                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                          ( ! [X3: $i,X4: $i] :
                                                                              ( ( X3 = X4 )
                                                                             => ( ( X1 @ X3 )
                                                                                = ( X2 @ X4 ) ) )
                                                                         => ( ( exu @ X1 )
                                                                            = ( exu @ X2 ) ) )
                                                                     => ( ( emptyset = emptyset )
                                                                       => ( ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ! [X3: $i,X4: $i] :
                                                                                  ( ( X3 = X4 )
                                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                         => ! [X1: $i,X2: $i] :
                                                                              ( ( X1 = X2 )
                                                                             => ( ( powerset @ X1 )
                                                                                = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

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

thf(h67,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] :
                      ( ( exu @ X1 )
                     => ~ ! [X2: $i] :
                            ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                                = ( X3 = X2 ) ) )
                 => ( ! [X1: $i] :
                        ( ( nonempty @ X1 )
                       => ~ ! [X2: $i] :
                              ~ ( in @ X2 @ X1 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                         => ( X1 = X2 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 != X2 )
                           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i,X3: $i] :
                                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( ( X3 != X1 )
                                   => ( X3 = X2 ) ) )
                             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                 => ( ! [X1: $i,X2: $i > $o] :
                                        ( ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( X2 @ X3 ) )
                                       => ( ( dsetconstr @ X1 @ X2 )
                                         != emptyset ) )
                                   => ( ! [X1: $i > $o,X2: $i] :
                                          ( ( in @ X2 @ emptyset )
                                         => ( X1 @ X2 ) )
                                     => ( ! [X1: $i,X2: $i > $o] :
                                            ( ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( X2 @ X3 ) )
                                           => ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( X2 @ X3 ) ) )
                                       => ( ! [X1: $i,X2: $i > $o] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( X2 @ X3 ) )
                                             => ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( X2 @ X3 ) ) )
                                         => ( ! [X1: $i,X2: $i > $o] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( X2 @ X3 ) )
                                               => ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( X2 @ X3 ) ) )
                                           => ( ! [X1: $i,X2: $i > $o] :
                                                  ( ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( X2 @ X3 ) )
                                                 => ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( X2 @ X3 ) ) )
                                             => ( ! [X1: $o] :
                                                    ( X1
                                                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                               => ( ! [X1: $o] :
                                                      ( X1
                                                     => ( set2prop @ ( prop2set @ X1 ) ) )
                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                        ( ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( X2 @ X3 ) )
                                                       => ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ~ ( X2 @ X3 ) ) )
                                                   => ( ! [X1: $i,X2: $i > $o] :
                                                          ( ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( X2 @ X3 ) )
                                                         => ~ ! [X3: $i] :
                                                                ( ( in @ X3 @ X1 )
                                                               => ( X2 @ X3 ) ) )
                                                     => ( ! [X1: $i > $o] :
                                                            ( ~ ! [X2: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) )
                                                           => ( exu @ X1 ) )
                                                       => ( ! [X1: $i > $o] :
                                                              ( ~ ! [X2: $i] :
                                                                    ~ ( X1 @ X2 )
                                                             => ( ! [X2: $i,X3: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) )
                                                               => ( exu @ X1 ) ) )
                                                         => ( ! [X1: $i > $o] :
                                                                ( ~ ! [X2: $i] :
                                                                      ~ ! [X3: $i] :
                                                                          ( ( X1 @ X3 )
                                                                          = ( X3 = X2 ) )
                                                               => ( exu @ X1 ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ! [X3: $i,X4: $i] :
                                                                      ( ( X3 = X4 )
                                                                     => ( ( in @ X3 @ X1 )
                                                                       => ( in @ X4 @ X2 ) ) ) )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ! [X3: $i,X4: $i] :
                                                                        ( ( X3 = X4 )
                                                                       => ( ( in @ X3 @ X1 )
                                                                          = ( in @ X4 @ X2 ) ) ) )
                                                               => ( ! [X1: $i > $o] :
                                                                      ( ( exu @ X1 )
                                                                     => ! [X2: $i,X3: $i] :
                                                                          ( ( X1 @ X2 )
                                                                         => ( ( X1 @ X3 )
                                                                           => ( X2 = X3 ) ) ) )
                                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                        ( ! [X3: $i,X4: $i] :
                                                                            ( ( X3 = X4 )
                                                                           => ( ( X1 @ X3 )
                                                                              = ( X2 @ X4 ) ) )
                                                                       => ( ( exu @ X1 )
                                                                          = ( exu @ X2 ) ) )
                                                                   => ( ( emptyset = emptyset )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ! [X3: $i,X4: $i] :
                                                                                ( ( X3 = X4 )
                                                                               => ( ( setadjoin @ X1 @ X3 )
                                                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                       => ! [X1: $i,X2: $i] :
                                                                            ( ( X1 = X2 )
                                                                           => ( ( powerset @ X1 )
                                                                              = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h68,assumption,
    ! [X1: $i] : ( in @ emptyset @ ( powerset @ X1 ) ),
    introduced(assumption,[]) ).

thf(h69,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] :
                    ( ( exu @ X1 )
                   => ~ ! [X2: $i] :
                          ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                              = ( X3 = X2 ) ) )
               => ( ! [X1: $i] :
                      ( ( nonempty @ X1 )
                     => ~ ! [X2: $i] :
                            ~ ( in @ X2 @ X1 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                       => ( X1 = X2 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 != X2 )
                         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i,X3: $i] :
                                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                               => ( ( X3 != X1 )
                                 => ( X3 = X2 ) ) )
                           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                               => ( ! [X1: $i,X2: $i > $o] :
                                      ( ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( X2 @ X3 ) )
                                     => ( ( dsetconstr @ X1 @ X2 )
                                       != emptyset ) )
                                 => ( ! [X1: $i > $o,X2: $i] :
                                        ( ( in @ X2 @ emptyset )
                                       => ( X1 @ X2 ) )
                                   => ( ! [X1: $i,X2: $i > $o] :
                                          ( ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( X2 @ X3 ) )
                                         => ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( X2 @ X3 ) ) )
                                     => ( ! [X1: $i,X2: $i > $o] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( X2 @ X3 ) )
                                           => ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( X2 @ X3 ) ) )
                                       => ( ! [X1: $i,X2: $i > $o] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( X2 @ X3 ) )
                                             => ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( X2 @ X3 ) ) )
                                         => ( ! [X1: $i,X2: $i > $o] :
                                                ( ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( X2 @ X3 ) )
                                               => ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( X2 @ X3 ) ) )
                                           => ( ! [X1: $o] :
                                                  ( X1
                                                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                             => ( ! [X1: $o] :
                                                    ( X1
                                                   => ( set2prop @ ( prop2set @ X1 ) ) )
                                               => ( ! [X1: $i,X2: $i > $o] :
                                                      ( ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( X2 @ X3 ) )
                                                     => ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ~ ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i,X2: $i > $o] :
                                                        ( ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( X2 @ X3 ) )
                                                       => ~ ! [X3: $i] :
                                                              ( ( in @ X3 @ X1 )
                                                             => ( X2 @ X3 ) ) )
                                                   => ( ! [X1: $i > $o] :
                                                          ( ~ ! [X2: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) )
                                                         => ( exu @ X1 ) )
                                                     => ( ! [X1: $i > $o] :
                                                            ( ~ ! [X2: $i] :
                                                                  ~ ( X1 @ X2 )
                                                           => ( ! [X2: $i,X3: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) )
                                                             => ( exu @ X1 ) ) )
                                                       => ( ! [X1: $i > $o] :
                                                              ( ~ ! [X2: $i] :
                                                                    ~ ! [X3: $i] :
                                                                        ( ( X1 @ X3 )
                                                                        = ( X3 = X2 ) )
                                                             => ( exu @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ! [X3: $i,X4: $i] :
                                                                    ( ( X3 = X4 )
                                                                   => ( ( in @ X3 @ X1 )
                                                                     => ( in @ X4 @ X2 ) ) ) )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ! [X3: $i,X4: $i] :
                                                                      ( ( X3 = X4 )
                                                                     => ( ( in @ X3 @ X1 )
                                                                        = ( in @ X4 @ X2 ) ) ) )
                                                             => ( ! [X1: $i > $o] :
                                                                    ( ( exu @ X1 )
                                                                   => ! [X2: $i,X3: $i] :
                                                                        ( ( X1 @ X2 )
                                                                       => ( ( X1 @ X3 )
                                                                         => ( X2 = X3 ) ) ) )
                                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                      ( ! [X3: $i,X4: $i] :
                                                                          ( ( X3 = X4 )
                                                                         => ( ( X1 @ X3 )
                                                                            = ( X2 @ X4 ) ) )
                                                                     => ( ( exu @ X1 )
                                                                        = ( exu @ X2 ) ) )
                                                                 => ( ( emptyset = emptyset )
                                                                   => ( ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ! [X3: $i,X4: $i] :
                                                                              ( ( X3 = X4 )
                                                                             => ( ( setadjoin @ X1 @ X3 )
                                                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                     => ! [X1: $i,X2: $i] :
                                                                          ( ( X1 = X2 )
                                                                         => ( ( powerset @ X1 )
                                                                            = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h70,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] :
                  ( ( exu @ X1 )
                 => ~ ! [X2: $i] :
                        ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                            = ( X3 = X2 ) ) )
             => ( ! [X1: $i] :
                    ( ( nonempty @ X1 )
                   => ~ ! [X2: $i] :
                          ~ ( in @ X2 @ X1 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                     => ( X1 = X2 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 != X2 )
                       => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i,X3: $i] :
                              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                             => ( ( X3 != X1 )
                               => ( X3 = X2 ) ) )
                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                             => ( ! [X1: $i,X2: $i > $o] :
                                    ( ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( X2 @ X3 ) )
                                   => ( ( dsetconstr @ X1 @ X2 )
                                     != emptyset ) )
                               => ( ! [X1: $i > $o,X2: $i] :
                                      ( ( in @ X2 @ emptyset )
                                     => ( X1 @ X2 ) )
                                 => ( ! [X1: $i,X2: $i > $o] :
                                        ( ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( X2 @ X3 ) )
                                       => ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( X2 @ X3 ) ) )
                                   => ( ! [X1: $i,X2: $i > $o] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( X2 @ X3 ) )
                                         => ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( X2 @ X3 ) ) )
                                     => ( ! [X1: $i,X2: $i > $o] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( X2 @ X3 ) )
                                           => ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( X2 @ X3 ) ) )
                                       => ( ! [X1: $i,X2: $i > $o] :
                                              ( ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( X2 @ X3 ) )
                                             => ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( X2 @ X3 ) ) )
                                         => ( ! [X1: $o] :
                                                ( X1
                                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                           => ( ! [X1: $o] :
                                                  ( X1
                                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                                             => ( ! [X1: $i,X2: $i > $o] :
                                                    ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( X2 @ X3 ) )
                                                   => ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ~ ( X2 @ X3 ) ) )
                                               => ( ! [X1: $i,X2: $i > $o] :
                                                      ( ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( X2 @ X3 ) )
                                                     => ~ ! [X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( X2 @ X3 ) ) )
                                                 => ( ! [X1: $i > $o] :
                                                        ( ~ ! [X2: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) )
                                                       => ( exu @ X1 ) )
                                                   => ( ! [X1: $i > $o] :
                                                          ( ~ ! [X2: $i] :
                                                                ~ ( X1 @ X2 )
                                                         => ( ! [X2: $i,X3: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) )
                                                           => ( exu @ X1 ) ) )
                                                     => ( ! [X1: $i > $o] :
                                                            ( ~ ! [X2: $i] :
                                                                  ~ ! [X3: $i] :
                                                                      ( ( X1 @ X3 )
                                                                      = ( X3 = X2 ) )
                                                           => ( exu @ X1 ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ! [X3: $i,X4: $i] :
                                                                  ( ( X3 = X4 )
                                                                 => ( ( in @ X3 @ X1 )
                                                                   => ( in @ X4 @ X2 ) ) ) )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ! [X3: $i,X4: $i] :
                                                                    ( ( X3 = X4 )
                                                                   => ( ( in @ X3 @ X1 )
                                                                      = ( in @ X4 @ X2 ) ) ) )
                                                           => ( ! [X1: $i > $o] :
                                                                  ( ( exu @ X1 )
                                                                 => ! [X2: $i,X3: $i] :
                                                                      ( ( X1 @ X2 )
                                                                     => ( ( X1 @ X3 )
                                                                       => ( X2 = X3 ) ) ) )
                                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                    ( ! [X3: $i,X4: $i] :
                                                                        ( ( X3 = X4 )
                                                                       => ( ( X1 @ X3 )
                                                                          = ( X2 @ X4 ) ) )
                                                                   => ( ( exu @ X1 )
                                                                      = ( exu @ X2 ) ) )
                                                               => ( ( emptyset = emptyset )
                                                                 => ( ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ! [X3: $i,X4: $i] :
                                                                            ( ( X3 = X4 )
                                                                           => ( ( setadjoin @ X1 @ X3 )
                                                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                   => ! [X1: $i,X2: $i] :
                                                                        ( ( X1 = X2 )
                                                                       => ( ( powerset @ X1 )
                                                                          = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

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

thf(h72,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] :
                ( ( exu @ X1 )
               => ~ ! [X2: $i] :
                      ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                          = ( X3 = X2 ) ) )
           => ( ! [X1: $i] :
                  ( ( nonempty @ X1 )
                 => ~ ! [X2: $i] :
                        ~ ( in @ X2 @ X1 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                   => ( X1 = X2 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 != X2 )
                     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i,X3: $i] :
                            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                           => ( ( X3 != X1 )
                             => ( X3 = X2 ) ) )
                       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                           => ( ! [X1: $i,X2: $i > $o] :
                                  ( ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( X2 @ X3 ) )
                                 => ( ( dsetconstr @ X1 @ X2 )
                                   != emptyset ) )
                             => ( ! [X1: $i > $o,X2: $i] :
                                    ( ( in @ X2 @ emptyset )
                                   => ( X1 @ X2 ) )
                               => ( ! [X1: $i,X2: $i > $o] :
                                      ( ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( X2 @ X3 ) )
                                     => ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( X2 @ X3 ) ) )
                                 => ( ! [X1: $i,X2: $i > $o] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( X2 @ X3 ) )
                                       => ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( X2 @ X3 ) ) )
                                   => ( ! [X1: $i,X2: $i > $o] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( X2 @ X3 ) )
                                         => ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( X2 @ X3 ) ) )
                                     => ( ! [X1: $i,X2: $i > $o] :
                                            ( ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( X2 @ X3 ) )
                                           => ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( X2 @ X3 ) ) )
                                       => ( ! [X1: $o] :
                                              ( X1
                                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                         => ( ! [X1: $o] :
                                                ( X1
                                               => ( set2prop @ ( prop2set @ X1 ) ) )
                                           => ( ! [X1: $i,X2: $i > $o] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( X2 @ X3 ) )
                                                 => ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ~ ( X2 @ X3 ) ) )
                                             => ( ! [X1: $i,X2: $i > $o] :
                                                    ( ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( X2 @ X3 ) )
                                                   => ~ ! [X3: $i] :
                                                          ( ( in @ X3 @ X1 )
                                                         => ( X2 @ X3 ) ) )
                                               => ( ! [X1: $i > $o] :
                                                      ( ~ ! [X2: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) )
                                                     => ( exu @ X1 ) )
                                                 => ( ! [X1: $i > $o] :
                                                        ( ~ ! [X2: $i] :
                                                              ~ ( X1 @ X2 )
                                                       => ( ! [X2: $i,X3: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) )
                                                         => ( exu @ X1 ) ) )
                                                   => ( ! [X1: $i > $o] :
                                                          ( ~ ! [X2: $i] :
                                                                ~ ! [X3: $i] :
                                                                    ( ( X1 @ X3 )
                                                                    = ( X3 = X2 ) )
                                                         => ( exu @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ! [X3: $i,X4: $i] :
                                                                ( ( X3 = X4 )
                                                               => ( ( in @ X3 @ X1 )
                                                                 => ( in @ X4 @ X2 ) ) ) )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ! [X3: $i,X4: $i] :
                                                                  ( ( X3 = X4 )
                                                                 => ( ( in @ X3 @ X1 )
                                                                    = ( in @ X4 @ X2 ) ) ) )
                                                         => ( ! [X1: $i > $o] :
                                                                ( ( exu @ X1 )
                                                               => ! [X2: $i,X3: $i] :
                                                                    ( ( X1 @ X2 )
                                                                   => ( ( X1 @ X3 )
                                                                     => ( X2 = X3 ) ) ) )
                                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                  ( ! [X3: $i,X4: $i] :
                                                                      ( ( X3 = X4 )
                                                                     => ( ( X1 @ X3 )
                                                                        = ( X2 @ X4 ) ) )
                                                                 => ( ( exu @ X1 )
                                                                    = ( exu @ X2 ) ) )
                                                             => ( ( emptyset = emptyset )
                                                               => ( ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ! [X3: $i,X4: $i] :
                                                                          ( ( X3 = X4 )
                                                                         => ( ( setadjoin @ X1 @ X3 )
                                                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                 => ! [X1: $i,X2: $i] :
                                                                      ( ( X1 = X2 )
                                                                     => ( ( powerset @ X1 )
                                                                        = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h73,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X2 @ X3 )
     => ( ( in @ X3 @ X1 )
       => ( in @ X2 @ ( setunion @ X1 ) ) ) ),
    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 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X2 @ X1 )
           => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
       => ( ! [X1: $i > $o] :
              ( ( exu @ X1 )
             => ~ ! [X2: $i] :
                    ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                        = ( X3 = X2 ) ) )
         => ( ! [X1: $i] :
                ( ( nonempty @ X1 )
               => ~ ! [X2: $i] :
                      ~ ( in @ X2 @ X1 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                 => ( X1 = X2 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 != X2 )
                   => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                       => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i,X3: $i] :
                          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                         => ( ( X3 != X1 )
                           => ( X3 = X2 ) ) )
                     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                         => ( ! [X1: $i,X2: $i > $o] :
                                ( ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( X2 @ X3 ) )
                               => ( ( dsetconstr @ X1 @ X2 )
                                 != emptyset ) )
                           => ( ! [X1: $i > $o,X2: $i] :
                                  ( ( in @ X2 @ emptyset )
                                 => ( X1 @ X2 ) )
                             => ( ! [X1: $i,X2: $i > $o] :
                                    ( ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( X2 @ X3 ) )
                                   => ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( X2 @ X3 ) ) )
                               => ( ! [X1: $i,X2: $i > $o] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( X2 @ X3 ) )
                                     => ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( X2 @ X3 ) ) )
                                 => ( ! [X1: $i,X2: $i > $o] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( X2 @ X3 ) )
                                       => ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( X2 @ X3 ) ) )
                                   => ( ! [X1: $i,X2: $i > $o] :
                                          ( ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( X2 @ X3 ) )
                                         => ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( X2 @ X3 ) ) )
                                     => ( ! [X1: $o] :
                                            ( X1
                                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                       => ( ! [X1: $o] :
                                              ( X1
                                             => ( set2prop @ ( prop2set @ X1 ) ) )
                                         => ( ! [X1: $i,X2: $i > $o] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( X2 @ X3 ) )
                                               => ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ~ ( X2 @ X3 ) ) )
                                           => ( ! [X1: $i,X2: $i > $o] :
                                                  ( ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( X2 @ X3 ) )
                                                 => ~ ! [X3: $i] :
                                                        ( ( in @ X3 @ X1 )
                                                       => ( X2 @ X3 ) ) )
                                             => ( ! [X1: $i > $o] :
                                                    ( ~ ! [X2: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) )
                                                   => ( exu @ X1 ) )
                                               => ( ! [X1: $i > $o] :
                                                      ( ~ ! [X2: $i] :
                                                            ~ ( X1 @ X2 )
                                                     => ( ! [X2: $i,X3: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) )
                                                       => ( exu @ X1 ) ) )
                                                 => ( ! [X1: $i > $o] :
                                                        ( ~ ! [X2: $i] :
                                                              ~ ! [X3: $i] :
                                                                  ( ( X1 @ X3 )
                                                                  = ( X3 = X2 ) )
                                                       => ( exu @ X1 ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ! [X3: $i,X4: $i] :
                                                              ( ( X3 = X4 )
                                                             => ( ( in @ X3 @ X1 )
                                                               => ( in @ X4 @ X2 ) ) ) )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ! [X3: $i,X4: $i] :
                                                                ( ( X3 = X4 )
                                                               => ( ( in @ X3 @ X1 )
                                                                  = ( in @ X4 @ X2 ) ) ) )
                                                       => ( ! [X1: $i > $o] :
                                                              ( ( exu @ X1 )
                                                             => ! [X2: $i,X3: $i] :
                                                                  ( ( X1 @ X2 )
                                                                 => ( ( X1 @ X3 )
                                                                   => ( X2 = X3 ) ) ) )
                                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                ( ! [X3: $i,X4: $i] :
                                                                    ( ( X3 = X4 )
                                                                   => ( ( X1 @ X3 )
                                                                      = ( X2 @ X4 ) ) )
                                                               => ( ( exu @ X1 )
                                                                  = ( exu @ X2 ) ) )
                                                           => ( ( emptyset = emptyset )
                                                             => ( ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ! [X3: $i,X4: $i] :
                                                                        ( ( X3 = X4 )
                                                                       => ( ( setadjoin @ X1 @ X3 )
                                                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                                                               => ! [X1: $i,X2: $i] :
                                                                    ( ( X1 = X2 )
                                                                   => ( ( powerset @ X1 )
                                                                      = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h75,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ ( setunion @ X1 ) )
     => ! [X3: $o] :
          ( ! [X4: $i] :
              ( ( in @ X2 @ X4 )
             => ( ( in @ X4 @ X1 )
               => X3 ) )
         => X3 ) ),
    introduced(assumption,[]) ).

thf(h76,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ X1 )
         => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) )
     => ( ! [X1: $i > $o] :
            ( ( exu @ X1 )
           => ~ ! [X2: $i] :
                  ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                      = ( X3 = X2 ) ) )
       => ( ! [X1: $i] :
              ( ( nonempty @ X1 )
             => ~ ! [X2: $i] :
                    ~ ( in @ X2 @ X1 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
               => ( X1 = X2 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 != X2 )
                 => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i,X3: $i] :
                        ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                       => ( ( X3 != X1 )
                         => ( X3 = X2 ) ) )
                   => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                       => ( ! [X1: $i,X2: $i > $o] :
                              ( ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( X2 @ X3 ) )
                             => ( ( dsetconstr @ X1 @ X2 )
                               != emptyset ) )
                         => ( ! [X1: $i > $o,X2: $i] :
                                ( ( in @ X2 @ emptyset )
                               => ( X1 @ X2 ) )
                           => ( ! [X1: $i,X2: $i > $o] :
                                  ( ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( X2 @ X3 ) )
                                 => ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( X2 @ X3 ) ) )
                             => ( ! [X1: $i,X2: $i > $o] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( X2 @ X3 ) )
                                   => ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( X2 @ X3 ) ) )
                               => ( ! [X1: $i,X2: $i > $o] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( X2 @ X3 ) )
                                     => ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( X2 @ X3 ) ) )
                                 => ( ! [X1: $i,X2: $i > $o] :
                                        ( ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( X2 @ X3 ) )
                                       => ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( X2 @ X3 ) ) )
                                   => ( ! [X1: $o] :
                                          ( X1
                                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                     => ( ! [X1: $o] :
                                            ( X1
                                           => ( set2prop @ ( prop2set @ X1 ) ) )
                                       => ( ! [X1: $i,X2: $i > $o] :
                                              ( ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( X2 @ X3 ) )
                                             => ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ~ ( X2 @ X3 ) ) )
                                         => ( ! [X1: $i,X2: $i > $o] :
                                                ( ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( X2 @ X3 ) )
                                               => ~ ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( X2 @ X3 ) ) )
                                           => ( ! [X1: $i > $o] :
                                                  ( ~ ! [X2: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) )
                                                 => ( exu @ X1 ) )
                                             => ( ! [X1: $i > $o] :
                                                    ( ~ ! [X2: $i] :
                                                          ~ ( X1 @ X2 )
                                                   => ( ! [X2: $i,X3: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) )
                                                     => ( exu @ X1 ) ) )
                                               => ( ! [X1: $i > $o] :
                                                      ( ~ ! [X2: $i] :
                                                            ~ ! [X3: $i] :
                                                                ( ( X1 @ X3 )
                                                                = ( X3 = X2 ) )
                                                     => ( exu @ X1 ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ! [X3: $i,X4: $i] :
                                                            ( ( X3 = X4 )
                                                           => ( ( in @ X3 @ X1 )
                                                             => ( in @ X4 @ X2 ) ) ) )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ! [X3: $i,X4: $i] :
                                                              ( ( X3 = X4 )
                                                             => ( ( in @ X3 @ X1 )
                                                                = ( in @ X4 @ X2 ) ) ) )
                                                     => ( ! [X1: $i > $o] :
                                                            ( ( exu @ X1 )
                                                           => ! [X2: $i,X3: $i] :
                                                                ( ( X1 @ X2 )
                                                               => ( ( X1 @ X3 )
                                                                 => ( X2 = X3 ) ) ) )
                                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                                              ( ! [X3: $i,X4: $i] :
                                                                  ( ( X3 = X4 )
                                                                 => ( ( X1 @ X3 )
                                                                    = ( X2 @ X4 ) ) )
                                                             => ( ( exu @ X1 )
                                                                = ( exu @ X2 ) ) )
                                                         => ( ( emptyset = emptyset )
                                                           => ( ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ! [X3: $i,X4: $i] :
                                                                      ( ( X3 = X4 )
                                                                     => ( ( setadjoin @ X1 @ X3 )
                                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                                             => ! [X1: $i,X2: $i] :
                                                                  ( ( X1 = X2 )
                                                                 => ( ( powerset @ X1 )
                                                                    = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h77,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X2 @ X1 )
     => ( in @ X2 @ ( powerset @ ( setunion @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h78,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ( exu @ X1 )
         => ~ ! [X2: $i] :
                ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                    = ( X3 = X2 ) ) )
     => ( ! [X1: $i] :
            ( ( nonempty @ X1 )
           => ~ ! [X2: $i] :
                  ~ ( in @ X2 @ X1 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
             => ( X1 = X2 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 != X2 )
               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i,X3: $i] :
                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                     => ( ( X3 != X1 )
                       => ( X3 = X2 ) ) )
                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                     => ( ! [X1: $i,X2: $i > $o] :
                            ( ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( X2 @ X3 ) )
                           => ( ( dsetconstr @ X1 @ X2 )
                             != emptyset ) )
                       => ( ! [X1: $i > $o,X2: $i] :
                              ( ( in @ X2 @ emptyset )
                             => ( X1 @ X2 ) )
                         => ( ! [X1: $i,X2: $i > $o] :
                                ( ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( X2 @ X3 ) )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( X2 @ X3 ) ) )
                           => ( ! [X1: $i,X2: $i > $o] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( X2 @ X3 ) )
                                 => ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( X2 @ X3 ) ) )
                             => ( ! [X1: $i,X2: $i > $o] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( X2 @ X3 ) )
                                   => ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( X2 @ X3 ) ) )
                               => ( ! [X1: $i,X2: $i > $o] :
                                      ( ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( X2 @ X3 ) )
                                     => ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( X2 @ X3 ) ) )
                                 => ( ! [X1: $o] :
                                        ( X1
                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                   => ( ! [X1: $o] :
                                          ( X1
                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                     => ( ! [X1: $i,X2: $i > $o] :
                                            ( ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( X2 @ X3 ) )
                                           => ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ~ ( X2 @ X3 ) ) )
                                       => ( ! [X1: $i,X2: $i > $o] :
                                              ( ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( X2 @ X3 ) )
                                             => ~ ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( X2 @ X3 ) ) )
                                         => ( ! [X1: $i > $o] :
                                                ( ~ ! [X2: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) )
                                               => ( exu @ X1 ) )
                                           => ( ! [X1: $i > $o] :
                                                  ( ~ ! [X2: $i] :
                                                        ~ ( X1 @ X2 )
                                                 => ( ! [X2: $i,X3: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                                   => ( exu @ X1 ) ) )
                                             => ( ! [X1: $i > $o] :
                                                    ( ~ ! [X2: $i] :
                                                          ~ ! [X3: $i] :
                                                              ( ( X1 @ X3 )
                                                              = ( X3 = X2 ) )
                                                   => ( exu @ X1 ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ! [X3: $i,X4: $i] :
                                                          ( ( X3 = X4 )
                                                         => ( ( in @ X3 @ X1 )
                                                           => ( in @ X4 @ X2 ) ) ) )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ! [X3: $i,X4: $i] :
                                                            ( ( X3 = X4 )
                                                           => ( ( in @ X3 @ X1 )
                                                              = ( in @ X4 @ X2 ) ) ) )
                                                   => ( ! [X1: $i > $o] :
                                                          ( ( exu @ X1 )
                                                         => ! [X2: $i,X3: $i] :
                                                              ( ( X1 @ X2 )
                                                             => ( ( X1 @ X3 )
                                                               => ( X2 = X3 ) ) ) )
                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                            ( ! [X3: $i,X4: $i] :
                                                                ( ( X3 = X4 )
                                                               => ( ( X1 @ X3 )
                                                                  = ( X2 @ X4 ) ) )
                                                           => ( ( exu @ X1 )
                                                              = ( exu @ X2 ) ) )
                                                       => ( ( emptyset = emptyset )
                                                         => ( ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ! [X3: $i,X4: $i] :
                                                                    ( ( X3 = X4 )
                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                           => ! [X1: $i,X2: $i] :
                                                                ( ( X1 = X2 )
                                                               => ( ( powerset @ X1 )
                                                                  = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h79,assumption,
    ! [X1: $i > $o] :
      ( ( exu @ X1 )
     => ~ ! [X2: $i] :
            ~ ! [X3: $i] :
                ( ( X1 @ X3 )
                = ( X3 = X2 ) ) ),
    introduced(assumption,[]) ).

thf(h80,assumption,
    ~ ( ! [X1: $i] :
          ( ( nonempty @ X1 )
         => ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
           => ( X1 = X2 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 != X2 )
             => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                 => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i,X3: $i] :
                    ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                   => ( ( X3 != X1 )
                     => ( X3 = X2 ) ) )
               => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                   => ( ! [X1: $i,X2: $i > $o] :
                          ( ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( X2 @ X3 ) )
                         => ( ( dsetconstr @ X1 @ X2 )
                           != emptyset ) )
                     => ( ! [X1: $i > $o,X2: $i] :
                            ( ( in @ X2 @ emptyset )
                           => ( X1 @ X2 ) )
                       => ( ! [X1: $i,X2: $i > $o] :
                              ( ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( X2 @ X3 ) )
                             => ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( X2 @ X3 ) ) )
                         => ( ! [X1: $i,X2: $i > $o] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( X2 @ X3 ) )
                               => ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( X2 @ X3 ) ) )
                           => ( ! [X1: $i,X2: $i > $o] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( X2 @ X3 ) )
                                 => ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( X2 @ X3 ) ) )
                             => ( ! [X1: $i,X2: $i > $o] :
                                    ( ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( X2 @ X3 ) )
                                   => ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( X2 @ X3 ) ) )
                               => ( ! [X1: $o] :
                                      ( X1
                                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                 => ( ! [X1: $o] :
                                        ( X1
                                       => ( set2prop @ ( prop2set @ X1 ) ) )
                                   => ( ! [X1: $i,X2: $i > $o] :
                                          ( ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( X2 @ X3 ) )
                                         => ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ~ ( X2 @ X3 ) ) )
                                     => ( ! [X1: $i,X2: $i > $o] :
                                            ( ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( X2 @ X3 ) )
                                           => ~ ! [X3: $i] :
                                                  ( ( in @ X3 @ X1 )
                                                 => ( X2 @ X3 ) ) )
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) )
                                             => ( exu @ X1 ) )
                                         => ( ! [X1: $i > $o] :
                                                ( ~ ! [X2: $i] :
                                                      ~ ( X1 @ X2 )
                                               => ( ! [X2: $i,X3: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) )
                                                 => ( exu @ X1 ) ) )
                                           => ( ! [X1: $i > $o] :
                                                  ( ~ ! [X2: $i] :
                                                        ~ ! [X3: $i] :
                                                            ( ( X1 @ X3 )
                                                            = ( X3 = X2 ) )
                                                 => ( exu @ X1 ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ! [X3: $i,X4: $i] :
                                                        ( ( X3 = X4 )
                                                       => ( ( in @ X3 @ X1 )
                                                         => ( in @ X4 @ X2 ) ) ) )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ! [X3: $i,X4: $i] :
                                                          ( ( X3 = X4 )
                                                         => ( ( in @ X3 @ X1 )
                                                            = ( in @ X4 @ X2 ) ) ) )
                                                 => ( ! [X1: $i > $o] :
                                                        ( ( exu @ X1 )
                                                       => ! [X2: $i,X3: $i] :
                                                            ( ( X1 @ X2 )
                                                           => ( ( X1 @ X3 )
                                                             => ( X2 = X3 ) ) ) )
                                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                                          ( ! [X3: $i,X4: $i] :
                                                              ( ( X3 = X4 )
                                                             => ( ( X1 @ X3 )
                                                                = ( X2 @ X4 ) ) )
                                                         => ( ( exu @ X1 )
                                                            = ( exu @ X2 ) ) )
                                                     => ( ( emptyset = emptyset )
                                                       => ( ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ! [X3: $i,X4: $i] :
                                                                  ( ( X3 = X4 )
                                                                 => ( ( setadjoin @ X1 @ X3 )
                                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                                         => ! [X1: $i,X2: $i] :
                                                              ( ( X1 = X2 )
                                                             => ( ( powerset @ X1 )
                                                                = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h81,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
         => ( X1 = X2 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 != X2 )
           => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
               => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i,X3: $i] :
                  ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                 => ( ( X3 != X1 )
                   => ( X3 = X2 ) ) )
             => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                 => ( ! [X1: $i,X2: $i > $o] :
                        ( ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( X2 @ X3 ) )
                       => ( ( dsetconstr @ X1 @ X2 )
                         != emptyset ) )
                   => ( ! [X1: $i > $o,X2: $i] :
                          ( ( in @ X2 @ emptyset )
                         => ( X1 @ X2 ) )
                     => ( ! [X1: $i,X2: $i > $o] :
                            ( ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( X2 @ X3 ) )
                           => ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( X2 @ X3 ) ) )
                       => ( ! [X1: $i,X2: $i > $o] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( X2 @ X3 ) )
                             => ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( X2 @ X3 ) ) )
                         => ( ! [X1: $i,X2: $i > $o] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( X2 @ X3 ) )
                               => ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( X2 @ X3 ) ) )
                           => ( ! [X1: $i,X2: $i > $o] :
                                  ( ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( X2 @ X3 ) )
                                 => ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( X2 @ X3 ) ) )
                             => ( ! [X1: $o] :
                                    ( X1
                                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                               => ( ! [X1: $o] :
                                      ( X1
                                     => ( set2prop @ ( prop2set @ X1 ) ) )
                                 => ( ! [X1: $i,X2: $i > $o] :
                                        ( ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( X2 @ X3 ) )
                                       => ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ~ ( X2 @ X3 ) ) )
                                   => ( ! [X1: $i,X2: $i > $o] :
                                          ( ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( X2 @ X3 ) )
                                         => ~ ! [X3: $i] :
                                                ( ( in @ X3 @ X1 )
                                               => ( X2 @ X3 ) ) )
                                     => ( ! [X1: $i > $o] :
                                            ( ~ ! [X2: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) )
                                           => ( exu @ X1 ) )
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ~ ( X1 @ X2 )
                                             => ( ! [X2: $i,X3: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) )
                                               => ( exu @ X1 ) ) )
                                         => ( ! [X1: $i > $o] :
                                                ( ~ ! [X2: $i] :
                                                      ~ ! [X3: $i] :
                                                          ( ( X1 @ X3 )
                                                          = ( X3 = X2 ) )
                                               => ( exu @ X1 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ! [X3: $i,X4: $i] :
                                                      ( ( X3 = X4 )
                                                     => ( ( in @ X3 @ X1 )
                                                       => ( in @ X4 @ X2 ) ) ) )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ! [X3: $i,X4: $i] :
                                                        ( ( X3 = X4 )
                                                       => ( ( in @ X3 @ X1 )
                                                          = ( in @ X4 @ X2 ) ) ) )
                                               => ( ! [X1: $i > $o] :
                                                      ( ( exu @ X1 )
                                                     => ! [X2: $i,X3: $i] :
                                                          ( ( X1 @ X2 )
                                                         => ( ( X1 @ X3 )
                                                           => ( X2 = X3 ) ) ) )
                                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                                        ( ! [X3: $i,X4: $i] :
                                                            ( ( X3 = X4 )
                                                           => ( ( X1 @ X3 )
                                                              = ( X2 @ X4 ) ) )
                                                       => ( ( exu @ X1 )
                                                          = ( exu @ X2 ) ) )
                                                   => ( ( emptyset = emptyset )
                                                     => ( ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ! [X3: $i,X4: $i] :
                                                                ( ( X3 = X4 )
                                                               => ( ( setadjoin @ X1 @ X3 )
                                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                                       => ! [X1: $i,X2: $i] :
                                                            ( ( X1 = X2 )
                                                           => ( ( powerset @ X1 )
                                                              = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h82,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
     => ( X1 = X2 ) ),
    introduced(assumption,[]) ).

thf(h83,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 != X2 )
         => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
             => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i,X3: $i] :
                ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
               => ( ( X3 != X1 )
                 => ( X3 = X2 ) ) )
           => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
               => ( ! [X1: $i,X2: $i > $o] :
                      ( ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( X2 @ X3 ) )
                     => ( ( dsetconstr @ X1 @ X2 )
                       != emptyset ) )
                 => ( ! [X1: $i > $o,X2: $i] :
                        ( ( in @ X2 @ emptyset )
                       => ( X1 @ X2 ) )
                   => ( ! [X1: $i,X2: $i > $o] :
                          ( ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( X2 @ X3 ) )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( X2 @ X3 ) ) )
                     => ( ! [X1: $i,X2: $i > $o] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( X2 @ X3 ) )
                           => ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( X2 @ X3 ) ) )
                       => ( ! [X1: $i,X2: $i > $o] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( X2 @ X3 ) )
                             => ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( X2 @ X3 ) ) )
                         => ( ! [X1: $i,X2: $i > $o] :
                                ( ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( X2 @ X3 ) )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( X2 @ X3 ) ) )
                           => ( ! [X1: $o] :
                                  ( X1
                                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                             => ( ! [X1: $o] :
                                    ( X1
                                   => ( set2prop @ ( prop2set @ X1 ) ) )
                               => ( ! [X1: $i,X2: $i > $o] :
                                      ( ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( X2 @ X3 ) )
                                     => ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ~ ( X2 @ X3 ) ) )
                                 => ( ! [X1: $i,X2: $i > $o] :
                                        ( ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( X2 @ X3 ) )
                                       => ~ ! [X3: $i] :
                                              ( ( in @ X3 @ X1 )
                                             => ( X2 @ X3 ) ) )
                                   => ( ! [X1: $i > $o] :
                                          ( ~ ! [X2: $i] :
                                                ( ( X1 @ X2 )
                                               => ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) )
                                         => ( exu @ X1 ) )
                                     => ( ! [X1: $i > $o] :
                                            ( ~ ! [X2: $i] :
                                                  ~ ( X1 @ X2 )
                                           => ( ! [X2: $i,X3: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) )
                                             => ( exu @ X1 ) ) )
                                       => ( ! [X1: $i > $o] :
                                              ( ~ ! [X2: $i] :
                                                    ~ ! [X3: $i] :
                                                        ( ( X1 @ X3 )
                                                        = ( X3 = X2 ) )
                                             => ( exu @ X1 ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ! [X3: $i,X4: $i] :
                                                    ( ( X3 = X4 )
                                                   => ( ( in @ X3 @ X1 )
                                                     => ( in @ X4 @ X2 ) ) ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ! [X3: $i,X4: $i] :
                                                      ( ( X3 = X4 )
                                                     => ( ( in @ X3 @ X1 )
                                                        = ( in @ X4 @ X2 ) ) ) )
                                             => ( ! [X1: $i > $o] :
                                                    ( ( exu @ X1 )
                                                   => ! [X2: $i,X3: $i] :
                                                        ( ( X1 @ X2 )
                                                       => ( ( X1 @ X3 )
                                                         => ( X2 = X3 ) ) ) )
                                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                                      ( ! [X3: $i,X4: $i] :
                                                          ( ( X3 = X4 )
                                                         => ( ( X1 @ X3 )
                                                            = ( X2 @ X4 ) ) )
                                                     => ( ( exu @ X1 )
                                                        = ( exu @ X2 ) ) )
                                                 => ( ( emptyset = emptyset )
                                                   => ( ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ! [X3: $i,X4: $i] :
                                                              ( ( X3 = X4 )
                                                             => ( ( setadjoin @ X1 @ X3 )
                                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                                     => ! [X1: $i,X2: $i] :
                                                          ( ( X1 = X2 )
                                                         => ( ( powerset @ X1 )
                                                            = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h84,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 != X2 )
     => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h85,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
           => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i,X3: $i] :
              ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
             => ( ( X3 != X1 )
               => ( X3 = X2 ) ) )
         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
             => ( ! [X1: $i,X2: $i > $o] :
                    ( ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( X2 @ X3 ) )
                   => ( ( dsetconstr @ X1 @ X2 )
                     != emptyset ) )
               => ( ! [X1: $i > $o,X2: $i] :
                      ( ( in @ X2 @ emptyset )
                     => ( X1 @ X2 ) )
                 => ( ! [X1: $i,X2: $i > $o] :
                        ( ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( X2 @ X3 ) )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( X2 @ X3 ) ) )
                   => ( ! [X1: $i,X2: $i > $o] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( X2 @ X3 ) )
                         => ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( X2 @ X3 ) ) )
                     => ( ! [X1: $i,X2: $i > $o] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( X2 @ X3 ) )
                           => ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( X2 @ X3 ) ) )
                       => ( ! [X1: $i,X2: $i > $o] :
                              ( ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( X2 @ X3 ) )
                             => ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( X2 @ X3 ) ) )
                         => ( ! [X1: $o] :
                                ( X1
                               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                           => ( ! [X1: $o] :
                                  ( X1
                                 => ( set2prop @ ( prop2set @ X1 ) ) )
                             => ( ! [X1: $i,X2: $i > $o] :
                                    ( ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( X2 @ X3 ) )
                                   => ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ~ ( X2 @ X3 ) ) )
                               => ( ! [X1: $i,X2: $i > $o] :
                                      ( ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( X2 @ X3 ) )
                                     => ~ ! [X3: $i] :
                                            ( ( in @ X3 @ X1 )
                                           => ( X2 @ X3 ) ) )
                                 => ( ! [X1: $i > $o] :
                                        ( ~ ! [X2: $i] :
                                              ( ( X1 @ X2 )
                                             => ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) )
                                       => ( exu @ X1 ) )
                                   => ( ! [X1: $i > $o] :
                                          ( ~ ! [X2: $i] :
                                                ~ ( X1 @ X2 )
                                         => ( ! [X2: $i,X3: $i] :
                                                ( ( X1 @ X2 )
                                               => ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) )
                                           => ( exu @ X1 ) ) )
                                     => ( ! [X1: $i > $o] :
                                            ( ~ ! [X2: $i] :
                                                  ~ ! [X3: $i] :
                                                      ( ( X1 @ X3 )
                                                      = ( X3 = X2 ) )
                                           => ( exu @ X1 ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ! [X3: $i,X4: $i] :
                                                  ( ( X3 = X4 )
                                                 => ( ( in @ X3 @ X1 )
                                                   => ( in @ X4 @ X2 ) ) ) )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ! [X3: $i,X4: $i] :
                                                    ( ( X3 = X4 )
                                                   => ( ( in @ X3 @ X1 )
                                                      = ( in @ X4 @ X2 ) ) ) )
                                           => ( ! [X1: $i > $o] :
                                                  ( ( exu @ X1 )
                                                 => ! [X2: $i,X3: $i] :
                                                      ( ( X1 @ X2 )
                                                     => ( ( X1 @ X3 )
                                                       => ( X2 = X3 ) ) ) )
                                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                                    ( ! [X3: $i,X4: $i] :
                                                        ( ( X3 = X4 )
                                                       => ( ( X1 @ X3 )
                                                          = ( X2 @ X4 ) ) )
                                                   => ( ( exu @ X1 )
                                                      = ( exu @ X2 ) ) )
                                               => ( ( emptyset = emptyset )
                                                 => ( ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ! [X3: $i,X4: $i] :
                                                            ( ( X3 = X4 )
                                                           => ( ( setadjoin @ X1 @ X3 )
                                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                                   => ! [X1: $i,X2: $i] :
                                                        ( ( X1 = X2 )
                                                       => ( ( powerset @ X1 )
                                                          = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h86,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h87,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
         => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
           => ( ( X3 != X1 )
             => ( X3 = X2 ) ) )
       => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
           => ( ! [X1: $i,X2: $i > $o] :
                  ( ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( X2 @ X3 ) )
                 => ( ( dsetconstr @ X1 @ X2 )
                   != emptyset ) )
             => ( ! [X1: $i > $o,X2: $i] :
                    ( ( in @ X2 @ emptyset )
                   => ( X1 @ X2 ) )
               => ( ! [X1: $i,X2: $i > $o] :
                      ( ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( X2 @ X3 ) )
                     => ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( X2 @ X3 ) ) )
                 => ( ! [X1: $i,X2: $i > $o] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( X2 @ X3 ) )
                       => ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( X2 @ X3 ) ) )
                   => ( ! [X1: $i,X2: $i > $o] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( X2 @ X3 ) )
                         => ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( X2 @ X3 ) ) )
                     => ( ! [X1: $i,X2: $i > $o] :
                            ( ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( X2 @ X3 ) )
                           => ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( X2 @ X3 ) ) )
                       => ( ! [X1: $o] :
                              ( X1
                             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                         => ( ! [X1: $o] :
                                ( X1
                               => ( set2prop @ ( prop2set @ X1 ) ) )
                           => ( ! [X1: $i,X2: $i > $o] :
                                  ( ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( X2 @ X3 ) )
                                 => ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ~ ( X2 @ X3 ) ) )
                             => ( ! [X1: $i,X2: $i > $o] :
                                    ( ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( X2 @ X3 ) )
                                   => ~ ! [X3: $i] :
                                          ( ( in @ X3 @ X1 )
                                         => ( X2 @ X3 ) ) )
                               => ( ! [X1: $i > $o] :
                                      ( ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) )
                                     => ( exu @ X1 ) )
                                 => ( ! [X1: $i > $o] :
                                        ( ~ ! [X2: $i] :
                                              ~ ( X1 @ X2 )
                                       => ( ! [X2: $i,X3: $i] :
                                              ( ( X1 @ X2 )
                                             => ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) )
                                         => ( exu @ X1 ) ) )
                                   => ( ! [X1: $i > $o] :
                                          ( ~ ! [X2: $i] :
                                                ~ ! [X3: $i] :
                                                    ( ( X1 @ X3 )
                                                    = ( X3 = X2 ) )
                                         => ( exu @ X1 ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ! [X3: $i,X4: $i] :
                                                ( ( X3 = X4 )
                                               => ( ( in @ X3 @ X1 )
                                                 => ( in @ X4 @ X2 ) ) ) )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ! [X3: $i,X4: $i] :
                                                  ( ( X3 = X4 )
                                                 => ( ( in @ X3 @ X1 )
                                                    = ( in @ X4 @ X2 ) ) ) )
                                         => ( ! [X1: $i > $o] :
                                                ( ( exu @ X1 )
                                               => ! [X2: $i,X3: $i] :
                                                    ( ( X1 @ X2 )
                                                   => ( ( X1 @ X3 )
                                                     => ( X2 = X3 ) ) ) )
                                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                                  ( ! [X3: $i,X4: $i] :
                                                      ( ( X3 = X4 )
                                                     => ( ( X1 @ X3 )
                                                        = ( X2 @ X4 ) ) )
                                                 => ( ( exu @ X1 )
                                                    = ( exu @ X2 ) ) )
                                             => ( ( emptyset = emptyset )
                                               => ( ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ! [X3: $i,X4: $i] :
                                                          ( ( X3 = X4 )
                                                         => ( ( setadjoin @ X1 @ X3 )
                                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                                 => ! [X1: $i,X2: $i] :
                                                      ( ( X1 = X2 )
                                                     => ( ( powerset @ X1 )
                                                        = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h88,assumption,
    ! [X1: $i,X2: $i] :
      ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
     => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h89,assumption,
    ~ ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ( X3 != X1 )
           => ( X3 = X2 ) ) )
     => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
         => ( ! [X1: $i,X2: $i > $o] :
                ( ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( X2 @ X3 ) )
               => ( ( dsetconstr @ X1 @ X2 )
                 != emptyset ) )
           => ( ! [X1: $i > $o,X2: $i] :
                  ( ( in @ X2 @ emptyset )
                 => ( X1 @ X2 ) )
             => ( ! [X1: $i,X2: $i > $o] :
                    ( ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( X2 @ X3 ) )
                   => ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( X2 @ X3 ) ) )
               => ( ! [X1: $i,X2: $i > $o] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( X2 @ X3 ) )
                     => ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( X2 @ X3 ) ) )
                 => ( ! [X1: $i,X2: $i > $o] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( X2 @ X3 ) )
                       => ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( X2 @ X3 ) ) )
                   => ( ! [X1: $i,X2: $i > $o] :
                          ( ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( X2 @ X3 ) )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( X2 @ X3 ) ) )
                     => ( ! [X1: $o] :
                            ( X1
                           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                       => ( ! [X1: $o] :
                              ( X1
                             => ( set2prop @ ( prop2set @ X1 ) ) )
                         => ( ! [X1: $i,X2: $i > $o] :
                                ( ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( X2 @ X3 ) )
                               => ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ~ ( X2 @ X3 ) ) )
                           => ( ! [X1: $i,X2: $i > $o] :
                                  ( ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( X2 @ X3 ) )
                                 => ~ ! [X3: $i] :
                                        ( ( in @ X3 @ X1 )
                                       => ( X2 @ X3 ) ) )
                             => ( ! [X1: $i > $o] :
                                    ( ~ ! [X2: $i] :
                                          ( ( X1 @ X2 )
                                         => ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) )
                                   => ( exu @ X1 ) )
                               => ( ! [X1: $i > $o] :
                                      ( ~ ! [X2: $i] :
                                            ~ ( X1 @ X2 )
                                     => ( ! [X2: $i,X3: $i] :
                                            ( ( X1 @ X2 )
                                           => ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) )
                                       => ( exu @ X1 ) ) )
                                 => ( ! [X1: $i > $o] :
                                        ( ~ ! [X2: $i] :
                                              ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                  = ( X3 = X2 ) )
                                       => ( exu @ X1 ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ! [X3: $i,X4: $i] :
                                              ( ( X3 = X4 )
                                             => ( ( in @ X3 @ X1 )
                                               => ( in @ X4 @ X2 ) ) ) )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ! [X3: $i,X4: $i] :
                                                ( ( X3 = X4 )
                                               => ( ( in @ X3 @ X1 )
                                                  = ( in @ X4 @ X2 ) ) ) )
                                       => ( ! [X1: $i > $o] :
                                              ( ( exu @ X1 )
                                             => ! [X2: $i,X3: $i] :
                                                  ( ( X1 @ X2 )
                                                 => ( ( X1 @ X3 )
                                                   => ( X2 = X3 ) ) ) )
                                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                                ( ! [X3: $i,X4: $i] :
                                                    ( ( X3 = X4 )
                                                   => ( ( X1 @ X3 )
                                                      = ( X2 @ X4 ) ) )
                                               => ( ( exu @ X1 )
                                                  = ( exu @ X2 ) ) )
                                           => ( ( emptyset = emptyset )
                                             => ( ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ! [X3: $i,X4: $i] :
                                                        ( ( X3 = X4 )
                                                       => ( ( setadjoin @ X1 @ X3 )
                                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                                               => ! [X1: $i,X2: $i] :
                                                    ( ( X1 = X2 )
                                                   => ( ( powerset @ X1 )
                                                      = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h90,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
     => ( ( X3 != X1 )
       => ( X3 = X2 ) ) ),
    introduced(assumption,[]) ).

thf(h91,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
       => ( ! [X1: $i,X2: $i > $o] :
              ( ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( X2 @ X3 ) )
             => ( ( dsetconstr @ X1 @ X2 )
               != emptyset ) )
         => ( ! [X1: $i > $o,X2: $i] :
                ( ( in @ X2 @ emptyset )
               => ( X1 @ X2 ) )
           => ( ! [X1: $i,X2: $i > $o] :
                  ( ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( X2 @ X3 ) )
                 => ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( X2 @ X3 ) ) )
             => ( ! [X1: $i,X2: $i > $o] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( X2 @ X3 ) )
                   => ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( X2 @ X3 ) ) )
               => ( ! [X1: $i,X2: $i > $o] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( X2 @ X3 ) )
                     => ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( X2 @ X3 ) ) )
                 => ( ! [X1: $i,X2: $i > $o] :
                        ( ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( X2 @ X3 ) )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( X2 @ X3 ) ) )
                   => ( ! [X1: $o] :
                          ( X1
                         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                     => ( ! [X1: $o] :
                            ( X1
                           => ( set2prop @ ( prop2set @ X1 ) ) )
                       => ( ! [X1: $i,X2: $i > $o] :
                              ( ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( X2 @ X3 ) )
                             => ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ~ ( X2 @ X3 ) ) )
                         => ( ! [X1: $i,X2: $i > $o] :
                                ( ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( X2 @ X3 ) )
                               => ~ ! [X3: $i] :
                                      ( ( in @ X3 @ X1 )
                                     => ( X2 @ X3 ) ) )
                           => ( ! [X1: $i > $o] :
                                  ( ~ ! [X2: $i] :
                                        ( ( X1 @ X2 )
                                       => ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) )
                                 => ( exu @ X1 ) )
                             => ( ! [X1: $i > $o] :
                                    ( ~ ! [X2: $i] :
                                          ~ ( X1 @ X2 )
                                   => ( ! [X2: $i,X3: $i] :
                                          ( ( X1 @ X2 )
                                         => ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) )
                                     => ( exu @ X1 ) ) )
                               => ( ! [X1: $i > $o] :
                                      ( ~ ! [X2: $i] :
                                            ~ ! [X3: $i] :
                                                ( ( X1 @ X3 )
                                                = ( X3 = X2 ) )
                                     => ( exu @ X1 ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ! [X3: $i,X4: $i] :
                                            ( ( X3 = X4 )
                                           => ( ( in @ X3 @ X1 )
                                             => ( in @ X4 @ X2 ) ) ) )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ! [X3: $i,X4: $i] :
                                              ( ( X3 = X4 )
                                             => ( ( in @ X3 @ X1 )
                                                = ( in @ X4 @ X2 ) ) ) )
                                     => ( ! [X1: $i > $o] :
                                            ( ( exu @ X1 )
                                           => ! [X2: $i,X3: $i] :
                                                ( ( X1 @ X2 )
                                               => ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) ) )
                                       => ( ! [X1: $i > $o,X2: $i > $o] :
                                              ( ! [X3: $i,X4: $i] :
                                                  ( ( X3 = X4 )
                                                 => ( ( X1 @ X3 )
                                                    = ( X2 @ X4 ) ) )
                                             => ( ( exu @ X1 )
                                                = ( exu @ X2 ) ) )
                                         => ( ( emptyset = emptyset )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ! [X3: $i,X4: $i] :
                                                      ( ( X3 = X4 )
                                                     => ( ( setadjoin @ X1 @ X3 )
                                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                                             => ! [X1: $i,X2: $i] :
                                                  ( ( X1 = X2 )
                                                 => ( ( powerset @ X1 )
                                                    = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h92,assumption,
    ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h93,assumption,
    ~ ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
     => ( ! [X1: $i,X2: $i > $o] :
            ( ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( X2 @ X3 ) )
           => ( ( dsetconstr @ X1 @ X2 )
             != emptyset ) )
       => ( ! [X1: $i > $o,X2: $i] :
              ( ( in @ X2 @ emptyset )
             => ( X1 @ X2 ) )
         => ( ! [X1: $i,X2: $i > $o] :
                ( ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( X2 @ X3 ) )
               => ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( X2 @ X3 ) ) )
           => ( ! [X1: $i,X2: $i > $o] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( X2 @ X3 ) )
                 => ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( X2 @ X3 ) ) )
             => ( ! [X1: $i,X2: $i > $o] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( X2 @ X3 ) )
                   => ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( X2 @ X3 ) ) )
               => ( ! [X1: $i,X2: $i > $o] :
                      ( ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( X2 @ X3 ) )
                     => ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( X2 @ X3 ) ) )
                 => ( ! [X1: $o] :
                        ( X1
                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                   => ( ! [X1: $o] :
                          ( X1
                         => ( set2prop @ ( prop2set @ X1 ) ) )
                     => ( ! [X1: $i,X2: $i > $o] :
                            ( ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( X2 @ X3 ) )
                           => ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ~ ( X2 @ X3 ) ) )
                       => ( ! [X1: $i,X2: $i > $o] :
                              ( ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( X2 @ X3 ) )
                             => ~ ! [X3: $i] :
                                    ( ( in @ X3 @ X1 )
                                   => ( X2 @ X3 ) ) )
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ( ( X1 @ X2 )
                                     => ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) )
                               => ( exu @ X1 ) )
                           => ( ! [X1: $i > $o] :
                                  ( ~ ! [X2: $i] :
                                        ~ ( X1 @ X2 )
                                 => ( ! [X2: $i,X3: $i] :
                                        ( ( X1 @ X2 )
                                       => ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                                   => ( exu @ X1 ) ) )
                             => ( ! [X1: $i > $o] :
                                    ( ~ ! [X2: $i] :
                                          ~ ! [X3: $i] :
                                              ( ( X1 @ X3 )
                                              = ( X3 = X2 ) )
                                   => ( exu @ X1 ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ! [X3: $i,X4: $i] :
                                          ( ( X3 = X4 )
                                         => ( ( in @ X3 @ X1 )
                                           => ( in @ X4 @ X2 ) ) ) )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ! [X3: $i,X4: $i] :
                                            ( ( X3 = X4 )
                                           => ( ( in @ X3 @ X1 )
                                              = ( in @ X4 @ X2 ) ) ) )
                                   => ( ! [X1: $i > $o] :
                                          ( ( exu @ X1 )
                                         => ! [X2: $i,X3: $i] :
                                              ( ( X1 @ X2 )
                                             => ( ( X1 @ X3 )
                                               => ( X2 = X3 ) ) ) )
                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                            ( ! [X3: $i,X4: $i] :
                                                ( ( X3 = X4 )
                                               => ( ( X1 @ X3 )
                                                  = ( X2 @ X4 ) ) )
                                           => ( ( exu @ X1 )
                                              = ( exu @ X2 ) ) )
                                       => ( ( emptyset = emptyset )
                                         => ( ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ! [X3: $i,X4: $i] :
                                                    ( ( X3 = X4 )
                                                   => ( ( setadjoin @ X1 @ X3 )
                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                           => ! [X1: $i,X2: $i] :
                                                ( ( X1 = X2 )
                                               => ( ( powerset @ X1 )
                                                  = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h94,assumption,
    ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ),
    introduced(assumption,[]) ).

thf(h95,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( X2 @ X3 ) )
         => ( ( dsetconstr @ X1 @ X2 )
           != emptyset ) )
     => ( ! [X1: $i > $o,X2: $i] :
            ( ( in @ X2 @ emptyset )
           => ( X1 @ X2 ) )
       => ( ! [X1: $i,X2: $i > $o] :
              ( ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( X2 @ X3 ) )
             => ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( X2 @ X3 ) ) )
         => ( ! [X1: $i,X2: $i > $o] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( X2 @ X3 ) )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( X2 @ X3 ) ) )
           => ( ! [X1: $i,X2: $i > $o] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( X2 @ X3 ) )
                 => ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( X2 @ X3 ) ) )
             => ( ! [X1: $i,X2: $i > $o] :
                    ( ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( X2 @ X3 ) )
                   => ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( X2 @ X3 ) ) )
               => ( ! [X1: $o] :
                      ( X1
                     => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                 => ( ! [X1: $o] :
                        ( X1
                       => ( set2prop @ ( prop2set @ X1 ) ) )
                   => ( ! [X1: $i,X2: $i > $o] :
                          ( ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( X2 @ X3 ) )
                         => ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ~ ( X2 @ X3 ) ) )
                     => ( ! [X1: $i,X2: $i > $o] :
                            ( ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( X2 @ X3 ) )
                           => ~ ! [X3: $i] :
                                  ( ( in @ X3 @ X1 )
                                 => ( X2 @ X3 ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ( ( X1 @ X2 )
                                   => ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) )
                             => ( exu @ X1 ) )
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ~ ( X1 @ X2 )
                               => ( ! [X2: $i,X3: $i] :
                                      ( ( X1 @ X2 )
                                     => ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) )
                                 => ( exu @ X1 ) ) )
                           => ( ! [X1: $i > $o] :
                                  ( ~ ! [X2: $i] :
                                        ~ ! [X3: $i] :
                                            ( ( X1 @ X3 )
                                            = ( X3 = X2 ) )
                                 => ( exu @ X1 ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ! [X3: $i,X4: $i] :
                                        ( ( X3 = X4 )
                                       => ( ( in @ X3 @ X1 )
                                         => ( in @ X4 @ X2 ) ) ) )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ! [X3: $i,X4: $i] :
                                          ( ( X3 = X4 )
                                         => ( ( in @ X3 @ X1 )
                                            = ( in @ X4 @ X2 ) ) ) )
                                 => ( ! [X1: $i > $o] :
                                        ( ( exu @ X1 )
                                       => ! [X2: $i,X3: $i] :
                                            ( ( X1 @ X2 )
                                           => ( ( X1 @ X3 )
                                             => ( X2 = X3 ) ) ) )
                                   => ( ! [X1: $i > $o,X2: $i > $o] :
                                          ( ! [X3: $i,X4: $i] :
                                              ( ( X3 = X4 )
                                             => ( ( X1 @ X3 )
                                                = ( X2 @ X4 ) ) )
                                         => ( ( exu @ X1 )
                                            = ( exu @ X2 ) ) )
                                     => ( ( emptyset = emptyset )
                                       => ( ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ! [X3: $i,X4: $i] :
                                                  ( ( X3 = X4 )
                                                 => ( ( setadjoin @ X1 @ X3 )
                                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                                         => ! [X1: $i,X2: $i] :
                                              ( ( X1 = X2 )
                                             => ( ( powerset @ X1 )
                                                = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h96,assumption,
    ! [X1: $i,X2: $i > $o] :
      ( ~ ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ~ ( X2 @ X3 ) )
     => ( ( dsetconstr @ X1 @ X2 )
       != emptyset ) ),
    introduced(assumption,[]) ).

thf(h97,assumption,
    ~ ( ! [X1: $i > $o,X2: $i] :
          ( ( in @ X2 @ emptyset )
         => ( X1 @ X2 ) )
     => ( ! [X1: $i,X2: $i > $o] :
            ( ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( X2 @ X3 ) )
           => ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( X2 @ X3 ) ) )
       => ( ! [X1: $i,X2: $i > $o] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( X2 @ X3 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( X2 @ X3 ) ) )
         => ( ! [X1: $i,X2: $i > $o] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( X2 @ X3 ) )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( X2 @ X3 ) ) )
           => ( ! [X1: $i,X2: $i > $o] :
                  ( ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( X2 @ X3 ) )
                 => ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( X2 @ X3 ) ) )
             => ( ! [X1: $o] :
                    ( X1
                   => ( in @ emptyset @ ( prop2set @ X1 ) ) )
               => ( ! [X1: $o] :
                      ( X1
                     => ( set2prop @ ( prop2set @ X1 ) ) )
                 => ( ! [X1: $i,X2: $i > $o] :
                        ( ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( X2 @ X3 ) )
                       => ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ~ ( X2 @ X3 ) ) )
                   => ( ! [X1: $i,X2: $i > $o] :
                          ( ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( X2 @ X3 ) )
                         => ~ ! [X3: $i] :
                                ( ( in @ X3 @ X1 )
                               => ( X2 @ X3 ) ) )
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ( ( X1 @ X2 )
                                 => ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) )
                           => ( exu @ X1 ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ~ ( X1 @ X2 )
                             => ( ! [X2: $i,X3: $i] :
                                    ( ( X1 @ X2 )
                                   => ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) )
                               => ( exu @ X1 ) ) )
                         => ( ! [X1: $i > $o] :
                                ( ~ ! [X2: $i] :
                                      ~ ! [X3: $i] :
                                          ( ( X1 @ X3 )
                                          = ( X3 = X2 ) )
                               => ( exu @ X1 ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ! [X3: $i,X4: $i] :
                                      ( ( X3 = X4 )
                                     => ( ( in @ X3 @ X1 )
                                       => ( in @ X4 @ X2 ) ) ) )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ! [X3: $i,X4: $i] :
                                        ( ( X3 = X4 )
                                       => ( ( in @ X3 @ X1 )
                                          = ( in @ X4 @ X2 ) ) ) )
                               => ( ! [X1: $i > $o] :
                                      ( ( exu @ X1 )
                                     => ! [X2: $i,X3: $i] :
                                          ( ( X1 @ X2 )
                                         => ( ( X1 @ X3 )
                                           => ( X2 = X3 ) ) ) )
                                 => ( ! [X1: $i > $o,X2: $i > $o] :
                                        ( ! [X3: $i,X4: $i] :
                                            ( ( X3 = X4 )
                                           => ( ( X1 @ X3 )
                                              = ( X2 @ X4 ) ) )
                                       => ( ( exu @ X1 )
                                          = ( exu @ X2 ) ) )
                                   => ( ( emptyset = emptyset )
                                     => ( ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ! [X3: $i,X4: $i] :
                                                ( ( X3 = X4 )
                                               => ( ( setadjoin @ X1 @ X3 )
                                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                                       => ! [X1: $i,X2: $i] :
                                            ( ( X1 = X2 )
                                           => ( ( powerset @ X1 )
                                              = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h98,assumption,
    ! [X1: $i > $o,X2: $i] :
      ( ( in @ X2 @ emptyset )
     => ( X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h99,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) )
         => ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) ) )
     => ( ! [X1: $i,X2: $i > $o] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( X2 @ X3 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( X2 @ X3 ) ) )
       => ( ! [X1: $i,X2: $i > $o] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( X2 @ X3 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( X2 @ X3 ) ) )
         => ( ! [X1: $i,X2: $i > $o] :
                ( ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( X2 @ X3 ) )
               => ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( X2 @ X3 ) ) )
           => ( ! [X1: $o] :
                  ( X1
                 => ( in @ emptyset @ ( prop2set @ X1 ) ) )
             => ( ! [X1: $o] :
                    ( X1
                   => ( set2prop @ ( prop2set @ X1 ) ) )
               => ( ! [X1: $i,X2: $i > $o] :
                      ( ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( X2 @ X3 ) )
                     => ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ~ ( X2 @ X3 ) ) )
                 => ( ! [X1: $i,X2: $i > $o] :
                        ( ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( X2 @ X3 ) )
                       => ~ ! [X3: $i] :
                              ( ( in @ X3 @ X1 )
                             => ( X2 @ X3 ) ) )
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ( ( X1 @ X2 )
                               => ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) )
                         => ( exu @ X1 ) )
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ~ ( X1 @ X2 )
                           => ( ! [X2: $i,X3: $i] :
                                  ( ( X1 @ X2 )
                                 => ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) )
                             => ( exu @ X1 ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ~ ! [X2: $i] :
                                    ~ ! [X3: $i] :
                                        ( ( X1 @ X3 )
                                        = ( X3 = X2 ) )
                             => ( exu @ X1 ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ! [X3: $i,X4: $i] :
                                    ( ( X3 = X4 )
                                   => ( ( in @ X3 @ X1 )
                                     => ( in @ X4 @ X2 ) ) ) )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ! [X3: $i,X4: $i] :
                                      ( ( X3 = X4 )
                                     => ( ( in @ X3 @ X1 )
                                        = ( in @ X4 @ X2 ) ) ) )
                             => ( ! [X1: $i > $o] :
                                    ( ( exu @ X1 )
                                   => ! [X2: $i,X3: $i] :
                                        ( ( X1 @ X2 )
                                       => ( ( X1 @ X3 )
                                         => ( X2 = X3 ) ) ) )
                               => ( ! [X1: $i > $o,X2: $i > $o] :
                                      ( ! [X3: $i,X4: $i] :
                                          ( ( X3 = X4 )
                                         => ( ( X1 @ X3 )
                                            = ( X2 @ X4 ) ) )
                                     => ( ( exu @ X1 )
                                        = ( exu @ X2 ) ) )
                                 => ( ( emptyset = emptyset )
                                   => ( ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ! [X3: $i,X4: $i] :
                                              ( ( X3 = X4 )
                                             => ( ( setadjoin @ X1 @ X3 )
                                                = ( setadjoin @ X2 @ X4 ) ) ) )
                                     => ! [X1: $i,X2: $i] :
                                          ( ( X1 = X2 )
                                         => ( ( powerset @ X1 )
                                            = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h100,assumption,
    ! [X1: $i,X2: $i > $o] :
      ( ~ ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( X2 @ X3 ) )
     => ~ ! [X3: $i] :
            ( ( in @ X3 @ X1 )
           => ( X2 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h101,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) ) )
     => ( ! [X1: $i,X2: $i > $o] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( X2 @ X3 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( X2 @ X3 ) ) )
       => ( ! [X1: $i,X2: $i > $o] :
              ( ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( X2 @ X3 ) )
             => ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( X2 @ X3 ) ) )
         => ( ! [X1: $o] :
                ( X1
               => ( in @ emptyset @ ( prop2set @ X1 ) ) )
           => ( ! [X1: $o] :
                  ( X1
                 => ( set2prop @ ( prop2set @ X1 ) ) )
             => ( ! [X1: $i,X2: $i > $o] :
                    ( ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( X2 @ X3 ) )
                   => ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ~ ( X2 @ X3 ) ) )
               => ( ! [X1: $i,X2: $i > $o] :
                      ( ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( X2 @ X3 ) )
                     => ~ ! [X3: $i] :
                            ( ( in @ X3 @ X1 )
                           => ( X2 @ X3 ) ) )
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ( ( X1 @ X2 )
                             => ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) )
                       => ( exu @ X1 ) )
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ~ ( X1 @ X2 )
                         => ( ! [X2: $i,X3: $i] :
                                ( ( X1 @ X2 )
                               => ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) )
                           => ( exu @ X1 ) ) )
                     => ( ! [X1: $i > $o] :
                            ( ~ ! [X2: $i] :
                                  ~ ! [X3: $i] :
                                      ( ( X1 @ X3 )
                                      = ( X3 = X2 ) )
                           => ( exu @ X1 ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ! [X3: $i,X4: $i] :
                                  ( ( X3 = X4 )
                                 => ( ( in @ X3 @ X1 )
                                   => ( in @ X4 @ X2 ) ) ) )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ! [X3: $i,X4: $i] :
                                    ( ( X3 = X4 )
                                   => ( ( in @ X3 @ X1 )
                                      = ( in @ X4 @ X2 ) ) ) )
                           => ( ! [X1: $i > $o] :
                                  ( ( exu @ X1 )
                                 => ! [X2: $i,X3: $i] :
                                      ( ( X1 @ X2 )
                                     => ( ( X1 @ X3 )
                                       => ( X2 = X3 ) ) ) )
                             => ( ! [X1: $i > $o,X2: $i > $o] :
                                    ( ! [X3: $i,X4: $i] :
                                        ( ( X3 = X4 )
                                       => ( ( X1 @ X3 )
                                          = ( X2 @ X4 ) ) )
                                   => ( ( exu @ X1 )
                                      = ( exu @ X2 ) ) )
                               => ( ( emptyset = emptyset )
                                 => ( ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ! [X3: $i,X4: $i] :
                                            ( ( X3 = X4 )
                                           => ( ( setadjoin @ X1 @ X3 )
                                              = ( setadjoin @ X2 @ X4 ) ) ) )
                                   => ! [X1: $i,X2: $i] :
                                        ( ( X1 = X2 )
                                       => ( ( powerset @ X1 )
                                          = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h102,assumption,
    ! [X1: $i,X2: $i > $o] :
      ( ! [X3: $i] :
          ( ( in @ X3 @ X1 )
         => ~ ( X2 @ X3 ) )
     => ! [X3: $i] :
          ( ( in @ X3 @ X1 )
         => ~ ( X2 @ X3 ) ) ),
    introduced(assumption,[]) ).

thf(h103,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) ) )
     => ( ! [X1: $i,X2: $i > $o] :
            ( ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( X2 @ X3 ) )
           => ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( X2 @ X3 ) ) )
       => ( ! [X1: $o] :
              ( X1
             => ( in @ emptyset @ ( prop2set @ X1 ) ) )
         => ( ! [X1: $o] :
                ( X1
               => ( set2prop @ ( prop2set @ X1 ) ) )
           => ( ! [X1: $i,X2: $i > $o] :
                  ( ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( X2 @ X3 ) )
                 => ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ~ ( X2 @ X3 ) ) )
             => ( ! [X1: $i,X2: $i > $o] :
                    ( ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( X2 @ X3 ) )
                   => ~ ! [X3: $i] :
                          ( ( in @ X3 @ X1 )
                         => ( X2 @ X3 ) ) )
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ( ( X1 @ X2 )
                           => ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) )
                     => ( exu @ X1 ) )
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ~ ( X1 @ X2 )
                       => ( ! [X2: $i,X3: $i] :
                              ( ( X1 @ X2 )
                             => ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) )
                         => ( exu @ X1 ) ) )
                   => ( ! [X1: $i > $o] :
                          ( ~ ! [X2: $i] :
                                ~ ! [X3: $i] :
                                    ( ( X1 @ X3 )
                                    = ( X3 = X2 ) )
                         => ( exu @ X1 ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ! [X3: $i,X4: $i] :
                                ( ( X3 = X4 )
                               => ( ( in @ X3 @ X1 )
                                 => ( in @ X4 @ X2 ) ) ) )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ! [X3: $i,X4: $i] :
                                  ( ( X3 = X4 )
                                 => ( ( in @ X3 @ X1 )
                                    = ( in @ X4 @ X2 ) ) ) )
                         => ( ! [X1: $i > $o] :
                                ( ( exu @ X1 )
                               => ! [X2: $i,X3: $i] :
                                    ( ( X1 @ X2 )
                                   => ( ( X1 @ X3 )
                                     => ( X2 = X3 ) ) ) )
                           => ( ! [X1: $i > $o,X2: $i > $o] :
                                  ( ! [X3: $i,X4: $i] :
                                      ( ( X3 = X4 )
                                     => ( ( X1 @ X3 )
                                        = ( X2 @ X4 ) ) )
                                 => ( ( exu @ X1 )
                                    = ( exu @ X2 ) ) )
                             => ( ( emptyset = emptyset )
                               => ( ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ! [X3: $i,X4: $i] :
                                          ( ( X3 = X4 )
                                         => ( ( setadjoin @ X1 @ X3 )
                                            = ( setadjoin @ X2 @ X4 ) ) ) )
                                 => ! [X1: $i,X2: $i] :
                                      ( ( X1 = X2 )
                                     => ( ( powerset @ X1 )
                                        = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h104,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) )
         => ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) ) )
     => ( ! [X1: $o] :
            ( X1
           => ( in @ emptyset @ ( prop2set @ X1 ) ) )
       => ( ! [X1: $o] :
              ( X1
             => ( set2prop @ ( prop2set @ X1 ) ) )
         => ( ! [X1: $i,X2: $i > $o] :
                ( ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( X2 @ X3 ) )
               => ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ~ ( X2 @ X3 ) ) )
           => ( ! [X1: $i,X2: $i > $o] :
                  ( ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( X2 @ X3 ) )
                 => ~ ! [X3: $i] :
                        ( ( in @ X3 @ X1 )
                       => ( X2 @ X3 ) ) )
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ( ( X1 @ X2 )
                         => ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) )
                   => ( exu @ X1 ) )
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ~ ( X1 @ X2 )
                     => ( ! [X2: $i,X3: $i] :
                            ( ( X1 @ X2 )
                           => ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) )
                       => ( exu @ X1 ) ) )
                 => ( ! [X1: $i > $o] :
                        ( ~ ! [X2: $i] :
                              ~ ! [X3: $i] :
                                  ( ( X1 @ X3 )
                                  = ( X3 = X2 ) )
                       => ( exu @ X1 ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ! [X3: $i,X4: $i] :
                              ( ( X3 = X4 )
                             => ( ( in @ X3 @ X1 )
                               => ( in @ X4 @ X2 ) ) ) )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ! [X3: $i,X4: $i] :
                                ( ( X3 = X4 )
                               => ( ( in @ X3 @ X1 )
                                  = ( in @ X4 @ X2 ) ) ) )
                       => ( ! [X1: $i > $o] :
                              ( ( exu @ X1 )
                             => ! [X2: $i,X3: $i] :
                                  ( ( X1 @ X2 )
                                 => ( ( X1 @ X3 )
                                   => ( X2 = X3 ) ) ) )
                         => ( ! [X1: $i > $o,X2: $i > $o] :
                                ( ! [X3: $i,X4: $i] :
                                    ( ( X3 = X4 )
                                   => ( ( X1 @ X3 )
                                      = ( X2 @ X4 ) ) )
                               => ( ( exu @ X1 )
                                  = ( exu @ X2 ) ) )
                           => ( ( emptyset = emptyset )
                             => ( ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ! [X3: $i,X4: $i] :
                                        ( ( X3 = X4 )
                                       => ( ( setadjoin @ X1 @ X3 )
                                          = ( setadjoin @ X2 @ X4 ) ) ) )
                               => ! [X1: $i,X2: $i] :
                                    ( ( X1 = X2 )
                                   => ( ( powerset @ X1 )
                                      = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h105,assumption,
    ~ ( ! [X1: $o] :
          ( X1
         => ( in @ emptyset @ ( prop2set @ X1 ) ) )
     => ( ! [X1: $o] :
            ( X1
           => ( set2prop @ ( prop2set @ X1 ) ) )
       => ( ! [X1: $i,X2: $i > $o] :
              ( ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( X2 @ X3 ) )
             => ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ~ ( X2 @ X3 ) ) )
         => ( ! [X1: $i,X2: $i > $o] :
                ( ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( X2 @ X3 ) )
               => ~ ! [X3: $i] :
                      ( ( in @ X3 @ X1 )
                     => ( X2 @ X3 ) ) )
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ( ( X1 @ X2 )
                       => ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) )
                 => ( exu @ X1 ) )
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ~ ( X1 @ X2 )
                   => ( ! [X2: $i,X3: $i] :
                          ( ( X1 @ X2 )
                         => ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) )
                     => ( exu @ X1 ) ) )
               => ( ! [X1: $i > $o] :
                      ( ~ ! [X2: $i] :
                            ~ ! [X3: $i] :
                                ( ( X1 @ X3 )
                                = ( X3 = X2 ) )
                     => ( exu @ X1 ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ! [X3: $i,X4: $i] :
                            ( ( X3 = X4 )
                           => ( ( in @ X3 @ X1 )
                             => ( in @ X4 @ X2 ) ) ) )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ! [X3: $i,X4: $i] :
                              ( ( X3 = X4 )
                             => ( ( in @ X3 @ X1 )
                                = ( in @ X4 @ X2 ) ) ) )
                     => ( ! [X1: $i > $o] :
                            ( ( exu @ X1 )
                           => ! [X2: $i,X3: $i] :
                                ( ( X1 @ X2 )
                               => ( ( X1 @ X3 )
                                 => ( X2 = X3 ) ) ) )
                       => ( ! [X1: $i > $o,X2: $i > $o] :
                              ( ! [X3: $i,X4: $i] :
                                  ( ( X3 = X4 )
                                 => ( ( X1 @ X3 )
                                    = ( X2 @ X4 ) ) )
                             => ( ( exu @ X1 )
                                = ( exu @ X2 ) ) )
                         => ( ( emptyset = emptyset )
                           => ( ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ! [X3: $i,X4: $i] :
                                      ( ( X3 = X4 )
                                     => ( ( setadjoin @ X1 @ X3 )
                                        = ( setadjoin @ X2 @ X4 ) ) ) )
                             => ! [X1: $i,X2: $i] :
                                  ( ( X1 = X2 )
                                 => ( ( powerset @ X1 )
                                    = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h106,assumption,
    ! [X1: $o] :
      ( X1
     => ( in @ emptyset @ ( prop2set @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h107,assumption,
    ~ ( ! [X1: $o] :
          ( X1
         => ( set2prop @ ( prop2set @ X1 ) ) )
     => ( ! [X1: $i,X2: $i > $o] :
            ( ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( X2 @ X3 ) )
           => ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ~ ( X2 @ X3 ) ) )
       => ( ! [X1: $i,X2: $i > $o] :
              ( ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( X2 @ X3 ) )
             => ~ ! [X3: $i] :
                    ( ( in @ X3 @ X1 )
                   => ( X2 @ X3 ) ) )
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ( ( X1 @ X2 )
                     => ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) )
               => ( exu @ X1 ) )
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ~ ( X1 @ X2 )
                 => ( ! [X2: $i,X3: $i] :
                        ( ( X1 @ X2 )
                       => ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) )
                   => ( exu @ X1 ) ) )
             => ( ! [X1: $i > $o] :
                    ( ~ ! [X2: $i] :
                          ~ ! [X3: $i] :
                              ( ( X1 @ X3 )
                              = ( X3 = X2 ) )
                   => ( exu @ X1 ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ! [X3: $i,X4: $i] :
                          ( ( X3 = X4 )
                         => ( ( in @ X3 @ X1 )
                           => ( in @ X4 @ X2 ) ) ) )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ! [X3: $i,X4: $i] :
                            ( ( X3 = X4 )
                           => ( ( in @ X3 @ X1 )
                              = ( in @ X4 @ X2 ) ) ) )
                   => ( ! [X1: $i > $o] :
                          ( ( exu @ X1 )
                         => ! [X2: $i,X3: $i] :
                              ( ( X1 @ X2 )
                             => ( ( X1 @ X3 )
                               => ( X2 = X3 ) ) ) )
                     => ( ! [X1: $i > $o,X2: $i > $o] :
                            ( ! [X3: $i,X4: $i] :
                                ( ( X3 = X4 )
                               => ( ( X1 @ X3 )
                                  = ( X2 @ X4 ) ) )
                           => ( ( exu @ X1 )
                              = ( exu @ X2 ) ) )
                       => ( ( emptyset = emptyset )
                         => ( ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ! [X3: $i,X4: $i] :
                                    ( ( X3 = X4 )
                                   => ( ( setadjoin @ X1 @ X3 )
                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                           => ! [X1: $i,X2: $i] :
                                ( ( X1 = X2 )
                               => ( ( powerset @ X1 )
                                  = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h108,assumption,
    ! [X1: $o] :
      ( X1
     => ( set2prop @ ( prop2set @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h109,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) )
         => ! [X3: $i] :
              ( ( in @ X3 @ X1 )
             => ~ ( X2 @ X3 ) ) )
     => ( ! [X1: $i,X2: $i > $o] :
            ( ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( X2 @ X3 ) )
           => ~ ! [X3: $i] :
                  ( ( in @ X3 @ X1 )
                 => ( X2 @ X3 ) ) )
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ( ( X1 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) )
             => ( exu @ X1 ) )
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ~ ( X1 @ X2 )
               => ( ! [X2: $i,X3: $i] :
                      ( ( X1 @ X2 )
                     => ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
                 => ( exu @ X1 ) ) )
           => ( ! [X1: $i > $o] :
                  ( ~ ! [X2: $i] :
                        ~ ! [X3: $i] :
                            ( ( X1 @ X3 )
                            = ( X3 = X2 ) )
                 => ( exu @ X1 ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ! [X3: $i,X4: $i] :
                        ( ( X3 = X4 )
                       => ( ( in @ X3 @ X1 )
                         => ( in @ X4 @ X2 ) ) ) )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ! [X3: $i,X4: $i] :
                          ( ( X3 = X4 )
                         => ( ( in @ X3 @ X1 )
                            = ( in @ X4 @ X2 ) ) ) )
                 => ( ! [X1: $i > $o] :
                        ( ( exu @ X1 )
                       => ! [X2: $i,X3: $i] :
                            ( ( X1 @ X2 )
                           => ( ( X1 @ X3 )
                             => ( X2 = X3 ) ) ) )
                   => ( ! [X1: $i > $o,X2: $i > $o] :
                          ( ! [X3: $i,X4: $i] :
                              ( ( X3 = X4 )
                             => ( ( X1 @ X3 )
                                = ( X2 @ X4 ) ) )
                         => ( ( exu @ X1 )
                            = ( exu @ X2 ) ) )
                     => ( ( emptyset = emptyset )
                       => ( ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ! [X3: $i,X4: $i] :
                                  ( ( X3 = X4 )
                                 => ( ( setadjoin @ X1 @ X3 )
                                    = ( setadjoin @ X2 @ X4 ) ) ) )
                         => ! [X1: $i,X2: $i] :
                              ( ( X1 = X2 )
                             => ( ( powerset @ X1 )
                                = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h110,assumption,
    ~ ( ! [X1: $i,X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) )
         => ~ ! [X3: $i] :
                ( ( in @ X3 @ X1 )
               => ( X2 @ X3 ) ) )
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ( ( X1 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) )
           => ( exu @ X1 ) )
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ~ ( X1 @ X2 )
             => ( ! [X2: $i,X3: $i] :
                    ( ( X1 @ X2 )
                   => ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
               => ( exu @ X1 ) ) )
         => ( ! [X1: $i > $o] :
                ( ~ ! [X2: $i] :
                      ~ ! [X3: $i] :
                          ( ( X1 @ X3 )
                          = ( X3 = X2 ) )
               => ( exu @ X1 ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ! [X3: $i,X4: $i] :
                      ( ( X3 = X4 )
                     => ( ( in @ X3 @ X1 )
                       => ( in @ X4 @ X2 ) ) ) )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ! [X3: $i,X4: $i] :
                        ( ( X3 = X4 )
                       => ( ( in @ X3 @ X1 )
                          = ( in @ X4 @ X2 ) ) ) )
               => ( ! [X1: $i > $o] :
                      ( ( exu @ X1 )
                     => ! [X2: $i,X3: $i] :
                          ( ( X1 @ X2 )
                         => ( ( X1 @ X3 )
                           => ( X2 = X3 ) ) ) )
                 => ( ! [X1: $i > $o,X2: $i > $o] :
                        ( ! [X3: $i,X4: $i] :
                            ( ( X3 = X4 )
                           => ( ( X1 @ X3 )
                              = ( X2 @ X4 ) ) )
                       => ( ( exu @ X1 )
                          = ( exu @ X2 ) ) )
                   => ( ( emptyset = emptyset )
                     => ( ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ! [X3: $i,X4: $i] :
                                ( ( X3 = X4 )
                               => ( ( setadjoin @ X1 @ X3 )
                                  = ( setadjoin @ X2 @ X4 ) ) ) )
                       => ! [X1: $i,X2: $i] :
                            ( ( X1 = X2 )
                           => ( ( powerset @ X1 )
                              = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h111,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) )
         => ( exu @ X1 ) )
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ~ ( X1 @ X2 )
           => ( ! [X2: $i,X3: $i] :
                  ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) )
             => ( exu @ X1 ) ) )
       => ( ! [X1: $i > $o] :
              ( ~ ! [X2: $i] :
                    ~ ! [X3: $i] :
                        ( ( X1 @ X3 )
                        = ( X3 = X2 ) )
             => ( exu @ X1 ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ! [X3: $i,X4: $i] :
                    ( ( X3 = X4 )
                   => ( ( in @ X3 @ X1 )
                     => ( in @ X4 @ X2 ) ) ) )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ! [X3: $i,X4: $i] :
                      ( ( X3 = X4 )
                     => ( ( in @ X3 @ X1 )
                        = ( in @ X4 @ X2 ) ) ) )
             => ( ! [X1: $i > $o] :
                    ( ( exu @ X1 )
                   => ! [X2: $i,X3: $i] :
                        ( ( X1 @ X2 )
                       => ( ( X1 @ X3 )
                         => ( X2 = X3 ) ) ) )
               => ( ! [X1: $i > $o,X2: $i > $o] :
                      ( ! [X3: $i,X4: $i] :
                          ( ( X3 = X4 )
                         => ( ( X1 @ X3 )
                            = ( X2 @ X4 ) ) )
                     => ( ( exu @ X1 )
                        = ( exu @ X2 ) ) )
                 => ( ( emptyset = emptyset )
                   => ( ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ! [X3: $i,X4: $i] :
                              ( ( X3 = X4 )
                             => ( ( setadjoin @ X1 @ X3 )
                                = ( setadjoin @ X2 @ X4 ) ) ) )
                     => ! [X1: $i,X2: $i] :
                          ( ( X1 = X2 )
                         => ( ( powerset @ X1 )
                            = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h112,assumption,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ( ( X1 @ X2 )
           => ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
     => ( exu @ X1 ) ),
    introduced(assumption,[]) ).

thf(h113,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ~ ( X1 @ X2 )
         => ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) )
           => ( exu @ X1 ) ) )
     => ( ! [X1: $i > $o] :
            ( ~ ! [X2: $i] :
                  ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                      = ( X3 = X2 ) )
           => ( exu @ X1 ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ! [X3: $i,X4: $i] :
                  ( ( X3 = X4 )
                 => ( ( in @ X3 @ X1 )
                   => ( in @ X4 @ X2 ) ) ) )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ! [X3: $i,X4: $i] :
                    ( ( X3 = X4 )
                   => ( ( in @ X3 @ X1 )
                      = ( in @ X4 @ X2 ) ) ) )
           => ( ! [X1: $i > $o] :
                  ( ( exu @ X1 )
                 => ! [X2: $i,X3: $i] :
                      ( ( X1 @ X2 )
                     => ( ( X1 @ X3 )
                       => ( X2 = X3 ) ) ) )
             => ( ! [X1: $i > $o,X2: $i > $o] :
                    ( ! [X3: $i,X4: $i] :
                        ( ( X3 = X4 )
                       => ( ( X1 @ X3 )
                          = ( X2 @ X4 ) ) )
                   => ( ( exu @ X1 )
                      = ( exu @ X2 ) ) )
               => ( ( emptyset = emptyset )
                 => ( ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ! [X3: $i,X4: $i] :
                            ( ( X3 = X4 )
                           => ( ( setadjoin @ X1 @ X3 )
                              = ( setadjoin @ X2 @ X4 ) ) ) )
                   => ! [X1: $i,X2: $i] :
                        ( ( X1 = X2 )
                       => ( ( powerset @ X1 )
                          = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h114,assumption,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ~ ( X1 @ X2 )
     => ( ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 )
           => ( ( X1 @ X3 )
             => ( X2 = X3 ) ) )
       => ( exu @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h115,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ~ ! [X2: $i] :
                ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                    = ( X3 = X2 ) )
         => ( exu @ X1 ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ! [X3: $i,X4: $i] :
                ( ( X3 = X4 )
               => ( ( in @ X3 @ X1 )
                 => ( in @ X4 @ X2 ) ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ! [X3: $i,X4: $i] :
                  ( ( X3 = X4 )
                 => ( ( in @ X3 @ X1 )
                    = ( in @ X4 @ X2 ) ) ) )
         => ( ! [X1: $i > $o] :
                ( ( exu @ X1 )
               => ! [X2: $i,X3: $i] :
                    ( ( X1 @ X2 )
                   => ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) )
           => ( ! [X1: $i > $o,X2: $i > $o] :
                  ( ! [X3: $i,X4: $i] :
                      ( ( X3 = X4 )
                     => ( ( X1 @ X3 )
                        = ( X2 @ X4 ) ) )
                 => ( ( exu @ X1 )
                    = ( exu @ X2 ) ) )
             => ( ( emptyset = emptyset )
               => ( ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ! [X3: $i,X4: $i] :
                          ( ( X3 = X4 )
                         => ( ( setadjoin @ X1 @ X3 )
                            = ( setadjoin @ X2 @ X4 ) ) ) )
                 => ! [X1: $i,X2: $i] :
                      ( ( X1 = X2 )
                     => ( ( powerset @ X1 )
                        = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h116,assumption,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ~ ! [X3: $i] :
                ( ( X1 @ X3 )
                = ( X3 = X2 ) )
     => ( exu @ X1 ) ),
    introduced(assumption,[]) ).

thf(h117,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( in @ X3 @ X1 )
               => ( in @ X4 @ X2 ) ) ) )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ! [X3: $i,X4: $i] :
                ( ( X3 = X4 )
               => ( ( in @ X3 @ X1 )
                  = ( in @ X4 @ X2 ) ) ) )
       => ( ! [X1: $i > $o] :
              ( ( exu @ X1 )
             => ! [X2: $i,X3: $i] :
                  ( ( X1 @ X2 )
                 => ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) )
         => ( ! [X1: $i > $o,X2: $i > $o] :
                ( ! [X3: $i,X4: $i] :
                    ( ( X3 = X4 )
                   => ( ( X1 @ X3 )
                      = ( X2 @ X4 ) ) )
               => ( ( exu @ X1 )
                  = ( exu @ X2 ) ) )
           => ( ( emptyset = emptyset )
             => ( ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ! [X3: $i,X4: $i] :
                        ( ( X3 = X4 )
                       => ( ( setadjoin @ X1 @ X3 )
                          = ( setadjoin @ X2 @ X4 ) ) ) )
               => ! [X1: $i,X2: $i] :
                    ( ( X1 = X2 )
                   => ( ( powerset @ X1 )
                      = ( powerset @ X2 ) ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h118,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ! [X3: $i,X4: $i] :
          ( ( X3 = X4 )
         => ( ( in @ X3 @ X1 )
           => ( in @ X4 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h119,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( in @ X3 @ X1 )
                = ( in @ X4 @ X2 ) ) ) )
     => ( ! [X1: $i > $o] :
            ( ( exu @ X1 )
           => ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 )
               => ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) )
       => ( ! [X1: $i > $o,X2: $i > $o] :
              ( ! [X3: $i,X4: $i] :
                  ( ( X3 = X4 )
                 => ( ( X1 @ X3 )
                    = ( X2 @ X4 ) ) )
             => ( ( exu @ X1 )
                = ( exu @ X2 ) ) )
         => ( ( emptyset = emptyset )
           => ( ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ! [X3: $i,X4: $i] :
                      ( ( X3 = X4 )
                     => ( ( setadjoin @ X1 @ X3 )
                        = ( setadjoin @ X2 @ X4 ) ) ) )
             => ! [X1: $i,X2: $i] :
                  ( ( X1 = X2 )
                 => ( ( powerset @ X1 )
                    = ( powerset @ X2 ) ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h120,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ! [X3: $i,X4: $i] :
          ( ( X3 = X4 )
         => ( ( in @ X3 @ X1 )
            = ( in @ X4 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h121,assumption,
    ~ ( ! [X1: $i > $o] :
          ( ( exu @ X1 )
         => ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 )
             => ( ( X1 @ X3 )
               => ( X2 = X3 ) ) ) )
     => ( ! [X1: $i > $o,X2: $i > $o] :
            ( ! [X3: $i,X4: $i] :
                ( ( X3 = X4 )
               => ( ( X1 @ X3 )
                  = ( X2 @ X4 ) ) )
           => ( ( exu @ X1 )
              = ( exu @ X2 ) ) )
       => ( ( emptyset = emptyset )
         => ( ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ! [X3: $i,X4: $i] :
                    ( ( X3 = X4 )
                   => ( ( setadjoin @ X1 @ X3 )
                      = ( setadjoin @ X2 @ X4 ) ) ) )
           => ! [X1: $i,X2: $i] :
                ( ( X1 = X2 )
               => ( ( powerset @ X1 )
                  = ( powerset @ X2 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h122,assumption,
    ! [X1: $i > $o] :
      ( ( exu @ X1 )
     => ! [X2: $i,X3: $i] :
          ( ( X1 @ X2 )
         => ( ( X1 @ X3 )
           => ( X2 = X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h123,assumption,
    ~ ( ! [X1: $i > $o,X2: $i > $o] :
          ( ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( X1 @ X3 )
                = ( X2 @ X4 ) ) )
         => ( ( exu @ X1 )
            = ( exu @ X2 ) ) )
     => ( ( emptyset = emptyset )
       => ( ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ! [X3: $i,X4: $i] :
                  ( ( X3 = X4 )
                 => ( ( setadjoin @ X1 @ X3 )
                    = ( setadjoin @ X2 @ X4 ) ) ) )
         => ! [X1: $i,X2: $i] :
              ( ( X1 = X2 )
             => ( ( powerset @ X1 )
                = ( powerset @ X2 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h124,assumption,
    ! [X1: $i > $o,X2: $i > $o] :
      ( ! [X3: $i,X4: $i] :
          ( ( X3 = X4 )
         => ( ( X1 @ X3 )
            = ( X2 @ X4 ) ) )
     => ( ( exu @ X1 )
        = ( exu @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h125,assumption,
    ~ ( ( emptyset = emptyset )
     => ( ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ! [X3: $i,X4: $i] :
                ( ( X3 = X4 )
               => ( ( setadjoin @ X1 @ X3 )
                  = ( setadjoin @ X2 @ X4 ) ) ) )
       => ! [X1: $i,X2: $i] :
            ( ( X1 = X2 )
           => ( ( powerset @ X1 )
              = ( powerset @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h126,assumption,
    emptyset = emptyset,
    introduced(assumption,[]) ).

thf(h127,assumption,
    ~ ( ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ! [X3: $i,X4: $i] :
              ( ( X3 = X4 )
             => ( ( setadjoin @ X1 @ X3 )
                = ( setadjoin @ X2 @ X4 ) ) ) )
     => ! [X1: $i,X2: $i] :
          ( ( X1 = X2 )
         => ( ( powerset @ X1 )
            = ( powerset @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h128,assumption,
    ! [X1: $i,X2: $i] :
      ( ( X1 = X2 )
     => ! [X3: $i,X4: $i] :
          ( ( X3 = X4 )
         => ( ( setadjoin @ X1 @ X3 )
            = ( setadjoin @ X2 @ X4 ) ) ) ),
    introduced(assumption,[]) ).

thf(h129,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( X1 = X2 )
       => ( ( powerset @ X1 )
          = ( powerset @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h130,assumption,
    ~ ! [X1: $i] :
        ( ( eigen__0 = X1 )
       => ( ( powerset @ eigen__0 )
          = ( powerset @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h131,assumption,
    ~ ( ( eigen__0 = eigen__1 )
     => ( ( powerset @ eigen__0 )
        = ( powerset @ eigen__1 ) ) ),
    introduced(assumption,[]) ).

thf(h132,assumption,
    eigen__0 = eigen__1,
    introduced(assumption,[]) ).

thf(h133,assumption,
    ( powerset @ eigen__0 )
 != ( powerset @ eigen__1 ),
    introduced(assumption,[]) ).

thf(pax2,axiom,
    ( p2
   => ( f__0 = f__1 ) ),
    file('<stdin>',pax2) ).

thf(nax1,axiom,
    ( p1
   <= ( ( fpowerset @ f__0 )
      = ( fpowerset @ f__1 ) ) ),
    file('<stdin>',nax1) ).

thf(ax19,axiom,
    p2,
    file('<stdin>',ax19) ).

thf(ax20,axiom,
    ~ p1,
    file('<stdin>',ax20) ).

thf(c_0_4,plain,
    ( ~ p2
    | ( f__0 = f__1 ) ),
    inference(fof_nnf,[status(thm)],[pax2]) ).

thf(c_0_5,plain,
    ( ( ( fpowerset @ f__0 )
     != ( fpowerset @ f__1 ) )
    | p1 ),
    inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])]) ).

thf(c_0_6,plain,
    ( ( f__0 = f__1 )
    | ~ p2 ),
    inference(split_conjunct,[status(thm)],[c_0_4]) ).

thf(c_0_7,plain,
    p2,
    inference(split_conjunct,[status(thm)],[ax19]) ).

thf(c_0_8,plain,
    ~ p1,
    inference(fof_simplification,[status(thm)],[ax20]) ).

thf(c_0_9,plain,
    ( p1
    | ( ( fpowerset @ f__0 )
     != ( fpowerset @ f__1 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

thf(c_0_10,plain,
    f__1 = f__0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]) ).

thf(c_0_11,plain,
    ~ p1,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_12,plain,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10])]),c_0_11]),
    [proof] ).

thf(1,plain,
    $false,
    inference(eprover,[status(thm),assumptions([h132,h133,h131,h130,h128,h129,h126,h127,h124,h125,h122,h123,h120,h121,h118,h119,h116,h117,h114,h115,h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],]) ).

thf(2,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h131,h130,h128,h129,h126,h127,h124,h125,h122,h123,h120,h121,h118,h119,h116,h117,h114,h115,h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h132,h133])],[h131,1,h132,h133]) ).

thf(3,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h130,h128,h129,h126,h127,h124,h125,h122,h123,h120,h121,h118,h119,h116,h117,h114,h115,h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h131]),tab_negall(eigenvar,eigen__1)],[h130,2,h131]) ).

thf(4,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h128,h129,h126,h127,h124,h125,h122,h123,h120,h121,h118,h119,h116,h117,h114,h115,h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negall(discharge,[h130]),tab_negall(eigenvar,eigen__0)],[h129,3,h130]) ).

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h126,h127,h124,h125,h122,h123,h120,h121,h118,h119,h116,h117,h114,h115,h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h128,h129])],[h127,4,h128,h129]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h124,h125,h122,h123,h120,h121,h118,h119,h116,h117,h114,h115,h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h126,h127])],[h125,5,h126,h127]) ).

thf(7,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h122,h123,h120,h121,h118,h119,h116,h117,h114,h115,h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h124,h125])],[h123,6,h124,h125]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h120,h121,h118,h119,h116,h117,h114,h115,h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h122,h123])],[h121,7,h122,h123]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h118,h119,h116,h117,h114,h115,h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h120,h121])],[h119,8,h120,h121]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h116,h117,h114,h115,h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h118,h119])],[h117,9,h118,h119]) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h114,h115,h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h116,h117])],[h115,10,h116,h117]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h112,h113,h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h114,h115])],[h113,11,h114,h115]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h100,h111,h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h112,h113])],[h111,12,h112,h113]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h102,h110,h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h100,h111])],[h110,13,h100,h111]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h108,h109,h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h102,h110])],[h109,14,h102,h110]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h106,h107,h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h108,h109])],[h107,15,h108,h109]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h100,h105,h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h106,h107])],[h105,16,h106,h107]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h102,h104,h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h100,h105])],[h104,17,h100,h105]) ).

thf(19,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h102,h103,h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h102,h104])],[h103,18,h102,h104]) ).

thf(20,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h100,h101,h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h102,h103])],[h101,19,h102,h103]) ).

thf(21,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h98,h99,h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h100,h101])],[h99,20,h100,h101]) ).

thf(22,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h96,h97,h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h98,h99])],[h97,21,h98,h99]) ).

thf(23,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h94,h95,h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h96,h97])],[h95,22,h96,h97]) ).

thf(24,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h92,h93,h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h94,h95])],[h93,23,h94,h95]) ).

thf(25,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h90,h91,h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h92,h93])],[h91,24,h92,h93]) ).

thf(26,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h88,h89,h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h90,h91])],[h89,25,h90,h91]) ).

thf(27,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h86,h87,h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h88,h89])],[h87,26,h88,h89]) ).

thf(28,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h84,h85,h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h86,h87])],[h85,27,h86,h87]) ).

thf(29,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h82,h83,h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h84,h85])],[h83,28,h84,h85]) ).

thf(30,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h48,h81,h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h82,h83])],[h81,29,h82,h83]) ).

thf(31,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h79,h80,h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h48,h81])],[h80,30,h48,h81]) ).

thf(32,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h77,h78,h75,h76,h73,h74,h71,h72,h68,h70,h68,h69,h66,h67,h64,h65,h62,h63,h60,h61,h58,h59,h56,h57,h54,h55,h52,h53,h50,h51,h48,h49,h46,h47,h43,h45,h43,h44,h41,h42,h39,h40,h3,h38,h3,h37,h35,h36,h33,h34,h31,h32,h29,h30,h27,h28,h25,h26,h23,h24,h21,h22,h19,h20,h17,h18,h15,h16,h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h79,h80])],[h78,31,h79,h80]) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(70,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h6,69,h7,h8]) ).

thf(71,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,70,h5,h6]) ).

thf(72,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,71,h3,h4]) ).

thf(73,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,72,h1,h2]) ).

thf(0,theorem,
    ( ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
            = ( in @ X3 @ X2 ) )
       => ( X1 = X2 ) )
   => ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset )
     => ( ! [X1: $i,X2: $i,X3: $i] :
            ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
            = ( ( X3 != X1 )
             => ( in @ X3 @ X2 ) ) )
       => ( ! [X1: $i,X2: $i] :
              ( ( in @ X2 @ ( powerset @ X1 ) )
              = ( ! [X3: $i] :
                    ( ( in @ X3 @ X2 )
                   => ( in @ X3 @ X1 ) ) ) )
         => ( ! [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 )
                           => ( exu @ ( X1 @ X3 ) ) )
                       => ~ ! [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] :
                              ( ( exu @ X1 )
                             => ( 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: $i > $o] :
                                      ( ( exu @ X1 )
                                     => ~ ! [X2: $i] :
                                            ( ( X1 @ X2 )
                                           => ~ ! [X3: $i] :
                                                  ( ( X1 @ X3 )
                                                 => ( X2 = X3 ) ) ) )
                                 => ( ! [X1: $o,X2: $i] :
                                        ( ( in @ X2 @ ( prop2set @ X1 ) )
                                       => X1 )
                                   => ( ! [X1: $i] :
                                          ( ( in @ X1 @ emptyset )
                                         => ! [X2: $o] : X2 )
                                     => ( ! [X1: $i] :
                                            ~ ( in @ X1 @ emptyset )
                                       => ( ! [X1: $i] :
                                              ~ ( in @ X1 @ emptyset )
                                         => ( ! [X1: $i > $o] :
                                                ( ( exu @ X1 )
                                               => ~ ! [X2: $i] :
                                                      ~ ( X1 @ X2 ) )
                                           => ( ! [X1: $i,X2: $i] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( in @ X3 @ X2 ) )
                                                 => ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ X1 ) )
                                                   => ( X1 = X2 ) ) )
                                             => ( ! [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] :
                                                          ( ( nonempty @ X1 )
                                                         => ~ ! [X2: $i] :
                                                                ~ ( in @ X2 @ X1 ) )
                                                     => ( ! [X1: $i,X2: $i > $o,X3: $i] :
                                                            ( ( in @ X3 @ X1 )
                                                           => ( ( X2 @ X3 )
                                                             => ( nonempty @ ( dsetconstr @ X1 @ X2 ) ) ) )
                                                       => ( ! [X1: $i] :
                                                              ( ~ ! [X2: $i] :
                                                                    ~ ( in @ X2 @ X1 )
                                                             => ( nonempty @ X1 ) )
                                                         => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ X2 ) )
                                                           => ( ( 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 ) ) )
                                                                 => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
                                                                       => ( ( X3 != X1 )
                                                                         => ( in @ X3 @ X2 ) ) )
                                                                   => ( ! [X1: $i] :
                                                                          ( ( dsetconstr @ X1
                                                                            @ ^ [X2: $i] : ~ $false )
                                                                          = X1 )
                                                                     => ( ! [X1: $i,X2: $i] :
                                                                            ( ! [X3: $i] :
                                                                                ( ( in @ X3 @ X2 )
                                                                               => ( in @ X3 @ X1 ) )
                                                                           => ( in @ X2 @ ( powerset @ X1 ) ) )
                                                                       => ( ! [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] :
                                                                                          ( ( exu @ X1 )
                                                                                         => ~ ! [X2: $i] :
                                                                                                ~ ! [X3: $i] :
                                                                                                    ( ( X1 @ X3 )
                                                                                                    = ( X3 = X2 ) ) )
                                                                                     => ( ! [X1: $i] :
                                                                                            ( ( nonempty @ X1 )
                                                                                           => ~ ! [X2: $i] :
                                                                                                  ~ ( in @ X2 @ X1 ) )
                                                                                       => ( ! [X1: $i,X2: $i] :
                                                                                              ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                             => ( X1 = X2 ) )
                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                ( ( X1 != X2 )
                                                                                               => ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                           => ( ! [X1: $i,X2: $i] :
                                                                                                  ( ( X1 = X2 )
                                                                                                 => ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                             => ( ! [X1: $i,X2: $i] :
                                                                                                    ( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
                                                                                                   => ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
                                                                                               => ( ! [X1: $i,X2: $i,X3: $i] :
                                                                                                      ( ( in @ X3 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ( X3 != X1 )
                                                                                                       => ( X3 = X2 ) ) )
                                                                                                 => ( ! [X1: $i,X2: $i] : ( in @ X1 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                   => ( ! [X1: $i,X2: $i] : ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                            ( ~ ! [X3: $i] :
                                                                                                                  ( ( in @ X3 @ X1 )
                                                                                                                 => ~ ( X2 @ X3 ) )
                                                                                                           => ( ( dsetconstr @ X1 @ X2 )
                                                                                                             != emptyset ) )
                                                                                                       => ( ! [X1: $i > $o,X2: $i] :
                                                                                                              ( ( in @ X2 @ emptyset )
                                                                                                             => ( X1 @ X2 ) )
                                                                                                         => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                ( ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( X2 @ X3 ) )
                                                                                                               => ~ ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ( X2 @ X3 ) ) )
                                                                                                           => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                  ( ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) )
                                                                                                                 => ! [X3: $i] :
                                                                                                                      ( ( in @ X3 @ X1 )
                                                                                                                     => ~ ( X2 @ X3 ) ) )
                                                                                                             => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                    ( ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) )
                                                                                                                   => ! [X3: $i] :
                                                                                                                        ( ( in @ X3 @ X1 )
                                                                                                                       => ~ ( X2 @ X3 ) ) )
                                                                                                               => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                      ( ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( X2 @ X3 ) )
                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                            ( ( in @ X3 @ X1 )
                                                                                                                           => ( X2 @ X3 ) ) )
                                                                                                                 => ( ! [X1: $o] :
                                                                                                                        ( X1
                                                                                                                       => ( in @ emptyset @ ( prop2set @ X1 ) ) )
                                                                                                                   => ( ! [X1: $o] :
                                                                                                                          ( X1
                                                                                                                         => ( set2prop @ ( prop2set @ X1 ) ) )
                                                                                                                     => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                            ( ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ~ ( X2 @ X3 ) )
                                                                                                                           => ! [X3: $i] :
                                                                                                                                ( ( in @ X3 @ X1 )
                                                                                                                               => ~ ( X2 @ X3 ) ) )
                                                                                                                       => ( ! [X1: $i,X2: $i > $o] :
                                                                                                                              ( ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( X2 @ X3 ) )
                                                                                                                             => ~ ! [X3: $i] :
                                                                                                                                    ( ( in @ X3 @ X1 )
                                                                                                                                   => ( X2 @ X3 ) ) )
                                                                                                                         => ( ! [X1: $i > $o] :
                                                                                                                                ( ~ ! [X2: $i] :
                                                                                                                                      ( ( X1 @ X2 )
                                                                                                                                     => ~ ! [X3: $i] :
                                                                                                                                            ( ( X1 @ X3 )
                                                                                                                                           => ( X2 = X3 ) ) )
                                                                                                                               => ( exu @ X1 ) )
                                                                                                                           => ( ! [X1: $i > $o] :
                                                                                                                                  ( ~ ! [X2: $i] :
                                                                                                                                        ~ ( X1 @ X2 )
                                                                                                                                 => ( ! [X2: $i,X3: $i] :
                                                                                                                                        ( ( X1 @ X2 )
                                                                                                                                       => ( ( X1 @ X3 )
                                                                                                                                         => ( X2 = X3 ) ) )
                                                                                                                                   => ( exu @ X1 ) ) )
                                                                                                                             => ( ! [X1: $i > $o] :
                                                                                                                                    ( ~ ! [X2: $i] :
                                                                                                                                          ~ ! [X3: $i] :
                                                                                                                                              ( ( X1 @ X3 )
                                                                                                                                              = ( X3 = X2 ) )
                                                                                                                                   => ( exu @ X1 ) )
                                                                                                                               => ( ! [X1: $i,X2: $i] :
                                                                                                                                      ( ( X1 = X2 )
                                                                                                                                     => ! [X3: $i,X4: $i] :
                                                                                                                                          ( ( X3 = X4 )
                                                                                                                                         => ( ( in @ X3 @ X1 )
                                                                                                                                           => ( in @ X4 @ X2 ) ) ) )
                                                                                                                                 => ( ! [X1: $i,X2: $i] :
                                                                                                                                        ( ( X1 = X2 )
                                                                                                                                       => ! [X3: $i,X4: $i] :
                                                                                                                                            ( ( X3 = X4 )
                                                                                                                                           => ( ( in @ X3 @ X1 )
                                                                                                                                              = ( in @ X4 @ X2 ) ) ) )
                                                                                                                                   => ( ! [X1: $i > $o] :
                                                                                                                                          ( ( exu @ X1 )
                                                                                                                                         => ! [X2: $i,X3: $i] :
                                                                                                                                              ( ( X1 @ X2 )
                                                                                                                                             => ( ( X1 @ X3 )
                                                                                                                                               => ( X2 = X3 ) ) ) )
                                                                                                                                     => ( ! [X1: $i > $o,X2: $i > $o] :
                                                                                                                                            ( ! [X3: $i,X4: $i] :
                                                                                                                                                ( ( X3 = X4 )
                                                                                                                                               => ( ( X1 @ X3 )
                                                                                                                                                  = ( X2 @ X4 ) ) )
                                                                                                                                           => ( ( exu @ X1 )
                                                                                                                                              = ( exu @ X2 ) ) )
                                                                                                                                       => ( ( emptyset = emptyset )
                                                                                                                                         => ( ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                               => ! [X3: $i,X4: $i] :
                                                                                                                                                    ( ( X3 = X4 )
                                                                                                                                                   => ( ( setadjoin @ X1 @ X3 )
                                                                                                                                                      = ( setadjoin @ X2 @ X4 ) ) ) )
                                                                                                                                           => ! [X1: $i,X2: $i] :
                                                                                                                                                ( ( X1 = X2 )
                                                                                                                                               => ( ( powerset @ X1 )
                                                                                                                                                  = ( powerset @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[73,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SEU553^1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n008.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  : 600
% 0.12/0.33  % DateTime : Sun Jun 19 06:48:52 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.40  % SZS status Theorem
% 0.18/0.40  % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.18/0.40  % Inferences: 0
% 0.18/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------