TSTP Solution File: SEU505^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU505^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 17:18:00 EDT 2023

% Result   : Theorem 41.18s 41.24s
% Output   : Proof 41.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   51
%            Number of leaves      :  248
% Syntax   : Number of formulae    :  337 ( 205 unt;  40 typ;  24 def)
%            Number of atoms       : 1041 ( 108 equ;   4 cnn)
%            Maximal formula atoms :   26 (   3 avg)
%            Number of connectives : 1788 ( 224   ~;  18   |;  18   &; 919   @)
%                                         (  39 <=>; 570  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   31 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   51 (  51   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   77 (  74 usr;  65 con; 0-2 aty)
%            Number of variables   :  450 (  78   ^; 358   !;  14   ?; 450   :)

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

thf(ty_descrp,type,
    descrp: $o ).

thf(ty_emptysetimpfalse,type,
    emptysetimpfalse: $o ).

thf(ty_setadjoinAx,type,
    setadjoinAx: $o ).

thf(ty_eigen__859,type,
    eigen__859: $i > $o ).

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

thf(ty_eigen__5,type,
    eigen__5: $i ).

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

thf(ty_emptysetAx,type,
    emptysetAx: $o ).

thf(ty_eigen__860,type,
    eigen__860: $i ).

thf(ty_emptysetE,type,
    emptysetE: $o ).

thf(ty_eigen__858,type,
    eigen__858: $i ).

thf(ty_dsetconstrI,type,
    dsetconstrI: $o ).

thf(ty_prop2setE,type,
    prop2setE: $o ).

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

thf(ty_eigen__857,type,
    eigen__857: $i > $o ).

thf(ty_foundationAx,type,
    foundationAx: $o ).

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

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

thf(ty_omega0Ax,type,
    omega0Ax: $o ).

thf(ty_powersetAx,type,
    powersetAx: $o ).

thf(ty_setunionAx,type,
    setunionAx: $o ).

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

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

thf(ty_replAx,type,
    replAx: $o ).

thf(ty_dsetconstrER,type,
    dsetconstrER: $o ).

thf(ty_setextAx,type,
    setextAx: $o ).

thf(ty_dsetconstrEL,type,
    dsetconstrEL: $o ).

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

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

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

thf(ty_eigen__861,type,
    eigen__861: $i > $o ).

thf(ty_exuE3e,type,
    exuE3e: $o ).

thf(ty_omegaIndAx,type,
    omegaIndAx: $o ).

thf(ty_omegaSAx,type,
    omegaSAx: $o ).

thf(ty_notinemptyset,type,
    notinemptyset: $o ).

thf(ty_eigen__862,type,
    eigen__862: $i ).

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

thf(ty_exuE1,type,
    exuE1: $o ).

thf(ty_wellorderingAx,type,
    wellorderingAx: $o ).

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

thf(eigendef_eigen__5,definition,
    ( eigen__5
    = ( eps__0
      @ ^ [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         != ( in @ X1 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__5])]) ).

thf(sP1,plain,
    ( sP1
  <=> setunionAx ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__1 )
       => ( in @ X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> emptysetE ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> dsetconstrER ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> notinemptyset ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X1 )
            = ( in @ X3 @ X2 ) )
       => ( X1 = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> setadjoinAx ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
        = ( in @ X1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> emptysetimpfalse ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
            = ( in @ X2 @ X1 ) )
       => ( eigen__0 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> omegaIndAx ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> omega0Ax ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

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

thf(sP14,plain,
    ( sP14
  <=> ( in @ eigen__5 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> exuE1 ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> dsetconstrEL ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ( in @ eigen__5 @ eigen__0 )
      = sP14 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> powersetAx ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( sP8
     => ( eigen__0 = eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> setextAx ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> replAx ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( in @ X1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( in @ eigen__5 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> emptysetAx ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( eigen__0 = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> prop2setE ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> dsetconstrI ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

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

thf(sP29,plain,
    ( sP29
  <=> ( sP14
     => sP23 ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> wellorderingAx ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> exuE3e ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> omegaSAx ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( sP23
     => sP14 ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(setext,conjecture,
    ( sP20
   => ( sP24
     => ( sP7
       => ( sP18
         => ( sP1
           => ( sP12
             => ( sP32
               => ( sP11
                 => ( sP21
                   => ( sP28
                     => ( sP30
                       => ( sP13
                         => ( sP27
                           => ( sP16
                             => ( sP4
                               => ( sP15
                                 => ( sP26
                                   => ( sP3
                                     => ( sP9
                                       => ( sP5
                                         => ( sP31
                                           => ! [X1: $i,X2: $i] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ X2 ) )
                                               => ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ X1 ) )
                                                 => ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(h1,negated_conjecture,
    ~ ( sP20
     => ( sP24
       => ( sP7
         => ( sP18
           => ( sP1
             => ( sP12
               => ( sP32
                 => ( sP11
                   => ( sP21
                     => ( sP28
                       => ( sP30
                         => ( sP13
                           => ( sP27
                             => ( sP16
                               => ( sP4
                                 => ( sP15
                                   => ( sP26
                                     => ( sP3
                                       => ( sP9
                                         => ( sP5
                                           => ( sP31
                                             => ! [X1: $i,X2: $i] :
                                                  ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X1 )
                                                     => ( in @ X3 @ X2 ) )
                                                 => ( ! [X3: $i] :
                                                        ( ( in @ X3 @ X2 )
                                                       => ( in @ X3 @ X1 ) )
                                                   => ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[setext]) ).

thf(h2,assumption,
    sP20,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP24
     => ( sP7
       => ( sP18
         => ( sP1
           => ( sP12
             => ( sP32
               => ( sP11
                 => ( sP21
                   => ( sP28
                     => ( sP30
                       => ( sP13
                         => ( sP27
                           => ( sP16
                             => ( sP4
                               => ( sP15
                                 => ( sP26
                                   => ( sP3
                                     => ( sP9
                                       => ( sP5
                                         => ( sP31
                                           => ! [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(h4,assumption,
    sP24,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP7
     => ( sP18
       => ( sP1
         => ( sP12
           => ( sP32
             => ( sP11
               => ( sP21
                 => ( sP28
                   => ( sP30
                     => ( sP13
                       => ( sP27
                         => ( sP16
                           => ( sP4
                             => ( sP15
                               => ( sP26
                                 => ( sP3
                                   => ( sP9
                                     => ( sP5
                                       => ( sP31
                                         => ! [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(h6,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ( sP18
     => ( sP1
       => ( sP12
         => ( sP32
           => ( sP11
             => ( sP21
               => ( sP28
                 => ( sP30
                   => ( sP13
                     => ( sP27
                       => ( sP16
                         => ( sP4
                           => ( sP15
                             => ( sP26
                               => ( sP3
                                 => ( sP9
                                   => ( sP5
                                     => ( sP31
                                       => ! [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(h8,assumption,
    sP18,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( sP1
     => ( sP12
       => ( sP32
         => ( sP11
           => ( sP21
             => ( sP28
               => ( sP30
                 => ( sP13
                   => ( sP27
                     => ( sP16
                       => ( sP4
                         => ( sP15
                           => ( sP26
                             => ( sP3
                               => ( sP9
                                 => ( sP5
                                   => ( sP31
                                     => ! [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(h10,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ ( sP12
     => ( sP32
       => ( sP11
         => ( sP21
           => ( sP28
             => ( sP30
               => ( sP13
                 => ( sP27
                   => ( sP16
                     => ( sP4
                       => ( sP15
                         => ( sP26
                           => ( sP3
                             => ( sP9
                               => ( sP5
                                 => ( sP31
                                   => ! [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(h12,assumption,
    sP12,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ( sP32
     => ( sP11
       => ( sP21
         => ( sP28
           => ( sP30
             => ( sP13
               => ( sP27
                 => ( sP16
                   => ( sP4
                     => ( sP15
                       => ( sP26
                         => ( sP3
                           => ( sP9
                             => ( sP5
                               => ( sP31
                                 => ! [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(h14,assumption,
    sP32,
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ ( sP11
     => ( sP21
       => ( sP28
         => ( sP30
           => ( sP13
             => ( sP27
               => ( sP16
                 => ( sP4
                   => ( sP15
                     => ( sP26
                       => ( sP3
                         => ( sP9
                           => ( sP5
                             => ( sP31
                               => ! [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(h16,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(h17,assumption,
    ~ ( sP21
     => ( sP28
       => ( sP30
         => ( sP13
           => ( sP27
             => ( sP16
               => ( sP4
                 => ( sP15
                   => ( sP26
                     => ( sP3
                       => ( sP9
                         => ( sP5
                           => ( sP31
                             => ! [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(h18,assumption,
    sP21,
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ ( sP28
     => ( sP30
       => ( sP13
         => ( sP27
           => ( sP16
             => ( sP4
               => ( sP15
                 => ( sP26
                   => ( sP3
                     => ( sP9
                       => ( sP5
                         => ( sP31
                           => ! [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(h20,assumption,
    sP28,
    introduced(assumption,[]) ).

thf(h21,assumption,
    ~ ( sP30
     => ( sP13
       => ( sP27
         => ( sP16
           => ( sP4
             => ( sP15
               => ( sP26
                 => ( sP3
                   => ( sP9
                     => ( sP5
                       => ( sP31
                         => ! [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(h22,assumption,
    sP30,
    introduced(assumption,[]) ).

thf(h23,assumption,
    ~ ( sP13
     => ( sP27
       => ( sP16
         => ( sP4
           => ( sP15
             => ( sP26
               => ( sP3
                 => ( sP9
                   => ( sP5
                     => ( sP31
                       => ! [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(h24,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(h25,assumption,
    ~ ( sP27
     => ( sP16
       => ( sP4
         => ( sP15
           => ( sP26
             => ( sP3
               => ( sP9
                 => ( sP5
                   => ( sP31
                     => ! [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(h26,assumption,
    sP27,
    introduced(assumption,[]) ).

thf(h27,assumption,
    ~ ( sP16
     => ( sP4
       => ( sP15
         => ( sP26
           => ( sP3
             => ( sP9
               => ( sP5
                 => ( sP31
                   => ! [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(h28,assumption,
    sP16,
    introduced(assumption,[]) ).

thf(h29,assumption,
    ~ ( sP4
     => ( sP15
       => ( sP26
         => ( sP3
           => ( sP9
             => ( sP5
               => ( sP31
                 => ! [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(h30,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h31,assumption,
    ~ ( sP15
     => ( sP26
       => ( sP3
         => ( sP9
           => ( sP5
             => ( sP31
               => ! [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(h32,assumption,
    sP15,
    introduced(assumption,[]) ).

thf(h33,assumption,
    ~ ( sP26
     => ( sP3
       => ( sP9
         => ( sP5
           => ( sP31
             => ! [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(h34,assumption,
    sP26,
    introduced(assumption,[]) ).

thf(h35,assumption,
    ~ ( sP3
     => ( sP9
       => ( sP5
         => ( sP31
           => ! [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(h36,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h37,assumption,
    ~ ( sP9
     => ( sP5
       => ( sP31
         => ! [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(h38,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h39,assumption,
    ~ ( sP5
     => ( sP31
       => ! [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(h40,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h41,assumption,
    ~ ( sP31
     => ! [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,
    sP31,
    introduced(assumption,[]) ).

thf(h43,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(h44,assumption,
    ~ ! [X1: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( in @ X2 @ X1 ) )
       => ( ! [X2: $i] :
              ( ( in @ X2 @ X1 )
             => ( in @ X2 @ eigen__0 ) )
         => ( eigen__0 = X1 ) ) ),
    introduced(assumption,[]) ).

thf(h45,assumption,
    ~ ( sP22
     => ( sP2
       => sP25 ) ),
    introduced(assumption,[]) ).

thf(h46,assumption,
    sP22,
    introduced(assumption,[]) ).

thf(h47,assumption,
    ~ ( sP2
     => sP25 ),
    introduced(assumption,[]) ).

thf(h48,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h49,assumption,
    ~ sP25,
    introduced(assumption,[]) ).

thf(h50,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h51,assumption,
    ~ sP20,
    introduced(assumption,[]) ).

thf(h52,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(h53,assumption,
    ! [X1: $i] :
      ~ ( in @ X1 @ emptyset ),
    introduced(assumption,[]) ).

thf(h54,assumption,
    ~ sP24,
    introduced(assumption,[]) ).

thf(h55,assumption,
    ~ ! [X1: $i] :
        ~ ( in @ X1 @ emptyset ),
    introduced(assumption,[]) ).

thf(h56,assumption,
    ! [X1: $i,X2: $i,X3: $i] :
      ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
      = ( ( X3 != X1 )
       => ( in @ X3 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h57,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(h58,assumption,
    ~ ! [X1: $i,X2: $i,X3: $i] :
        ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
        = ( ( X3 != X1 )
         => ( in @ X3 @ X2 ) ) ),
    introduced(assumption,[]) ).

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

thf(h60,assumption,
    ~ sP18,
    introduced(assumption,[]) ).

thf(h61,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( in @ X2 @ ( powerset @ X1 ) )
        = ( ! [X3: $i] :
              ( ( in @ X3 @ X2 )
             => ( in @ X3 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

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

thf(h63,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

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

thf(h65,assumption,
    in @ emptyset @ omega,
    introduced(assumption,[]) ).

thf(h66,assumption,
    ~ sP12,
    introduced(assumption,[]) ).

thf(h67,assumption,
    ~ ( in @ emptyset @ omega ),
    introduced(assumption,[]) ).

thf(h68,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ omega )
     => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ),
    introduced(assumption,[]) ).

thf(h69,assumption,
    ~ sP32,
    introduced(assumption,[]) ).

thf(h70,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ omega )
       => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ),
    introduced(assumption,[]) ).

thf(h71,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(h72,assumption,
    ~ sP11,
    introduced(assumption,[]) ).

thf(h73,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(h74,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(h75,assumption,
    ~ sP21,
    introduced(assumption,[]) ).

thf(h76,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(h77,assumption,
    ! [X1: $i] :
      ( ~ ! [X2: $i] :
            ~ ( in @ X2 @ X1 )
     => ~ ! [X2: $i] :
            ( ( in @ X2 @ X1 )
           => ~ ! [X3: $i] :
                  ( ( in @ X3 @ X2 )
                 => ~ ( in @ X3 @ X1 ) ) ) ),
    introduced(assumption,[]) ).

thf(h78,assumption,
    ~ sP28,
    introduced(assumption,[]) ).

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

thf(h80,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(h81,assumption,
    ~ sP30,
    introduced(assumption,[]) ).

thf(h82,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(h83,assumption,
    ! [X1: $i > $o] :
      ( ( exu @ X1 )
     => ( X1 @ ( descr @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h84,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

thf(h85,assumption,
    ~ ! [X1: $i > $o] :
        ( ( exu @ X1 )
       => ( X1 @ ( descr @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h86,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ X1 )
     => ( ( X2 @ X3 )
       => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h87,assumption,
    ~ sP27,
    introduced(assumption,[]) ).

thf(h88,assumption,
    ~ ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3 @ X1 )
       => ( ( X2 @ X3 )
         => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h89,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
     => ( in @ X3 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h90,assumption,
    ~ sP16,
    introduced(assumption,[]) ).

thf(h91,assumption,
    ~ ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
       => ( in @ X3 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h92,assumption,
    ! [X1: $i,X2: $i > $o,X3: $i] :
      ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
     => ( X2 @ X3 ) ),
    introduced(assumption,[]) ).

thf(h93,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(h94,assumption,
    ~ ! [X1: $i,X2: $i > $o,X3: $i] :
        ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
       => ( X2 @ X3 ) ),
    introduced(assumption,[]) ).

thf(h95,assumption,
    ! [X1: $i > $o] :
      ( ( exu @ X1 )
     => ~ ! [X2: $i] :
            ( ( X1 @ X2 )
           => ~ ! [X3: $i] :
                  ( ( X1 @ X3 )
                 => ( X2 = X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h96,assumption,
    ~ sP15,
    introduced(assumption,[]) ).

thf(h97,assumption,
    ~ ! [X1: $i > $o] :
        ( ( exu @ X1 )
       => ~ ! [X2: $i] :
              ( ( X1 @ X2 )
             => ~ ! [X3: $i] :
                    ( ( X1 @ X3 )
                   => ( X2 = X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h98,assumption,
    ! [X1: $o,X2: $i] :
      ( ( in @ X2 @ ( prop2set @ X1 ) )
     => X1 ),
    introduced(assumption,[]) ).

thf(h99,assumption,
    ~ sP26,
    introduced(assumption,[]) ).

thf(h100,assumption,
    ~ ! [X1: $o,X2: $i] :
        ( ( in @ X2 @ ( prop2set @ X1 ) )
       => X1 ),
    introduced(assumption,[]) ).

thf(h101,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ emptyset )
     => ! [X2: $o] : X2 ),
    introduced(assumption,[]) ).

thf(h102,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h103,assumption,
    ~ ! [X1: $i] :
        ( ( in @ X1 @ emptyset )
       => ! [X2: $o] : X2 ),
    introduced(assumption,[]) ).

thf(h104,assumption,
    ~ sP9,
    introduced(assumption,[]) ).

thf(h105,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h106,assumption,
    ! [X1: $i > $o] :
      ( ( exu @ X1 )
     => ~ ! [X2: $i] :
            ~ ( X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(h107,assumption,
    ~ sP31,
    introduced(assumption,[]) ).

thf(h108,assumption,
    ~ ! [X1: $i > $o] :
        ( ( exu @ X1 )
       => ~ ! [X2: $i] :
              ~ ( X1 @ X2 ) ),
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP29
    | ~ sP14
    | sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP33
    | ~ sP23
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP2
    | sP29 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP22
    | sP33 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP17
    | ~ sP23
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP17
    | sP23
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP8
    | ~ sP17 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).

thf(8,plain,
    ( ~ sP19
    | ~ sP8
    | sP25 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP10
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP6
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h42,h106,h40,h53,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,h50,h46,h48,h49]) ).

thf(h109,assumption,
    ~ ( ( exu @ eigen__857 )
     => ~ ! [X1: $i] :
            ~ ( eigen__857 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h110,assumption,
    exu @ eigen__857,
    introduced(assumption,[]) ).

thf(h111,assumption,
    ! [X1: $i] :
      ~ ( eigen__857 @ X1 ),
    introduced(assumption,[]) ).

thf(12,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h110,h111,h109,h107,h108,h40,h53,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h42,h107]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h109,h107,h108,h40,h53,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h110,h111])],[h109,12,h110,h111]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h107,h108,h40,h53,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h109]),tab_negall(eigenvar,eigen__857)],[h108,13,h109]) ).

thf(exuE3e,axiom,
    ( sP31
    = ( ! [X1: $i > $o] :
          ( ( exu @ X1 )
         => ~ ! [X2: $i] :
                ~ ( X1 @ X2 ) ) ) ) ).

thf(15,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h40,h53,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h42,h106]),tab_bq(discharge,[h107,h108])],[exuE3e,11,14,h42,h106,h107,h108]) ).

thf(h112,assumption,
    in @ eigen__858 @ emptyset,
    introduced(assumption,[]) ).

thf(16,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h42,h106,h112,h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h40,h105]) ).

thf(h113,assumption,
    ~ ( ( exu @ eigen__859 )
     => ~ ! [X1: $i] :
            ~ ( eigen__859 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h114,assumption,
    exu @ eigen__859,
    introduced(assumption,[]) ).

thf(h115,assumption,
    ! [X1: $i] :
      ~ ( eigen__859 @ X1 ),
    introduced(assumption,[]) ).

thf(17,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h114,h115,h113,h107,h108,h112,h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h42,h107]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h113,h107,h108,h112,h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h114,h115])],[h113,17,h114,h115]) ).

thf(19,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h107,h108,h112,h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h113]),tab_negall(eigenvar,eigen__859)],[h108,18,h113]) ).

thf(20,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h112,h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h42,h106]),tab_bq(discharge,[h107,h108])],[exuE3e,16,19,h42,h106,h107,h108]) ).

thf(21,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h105,h55,h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h112]),tab_negall(eigenvar,eigen__858)],[h55,20,h112]) ).

thf(notinemptyset,axiom,
    ( sP5
    = ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset ) ) ) ).

thf(22,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h38,h53,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h40,h53]),tab_bq(discharge,[h105,h55])],[notinemptyset,15,21,h40,h53,h105,h55]) ).

thf(h116,assumption,
    in @ eigen__860 @ emptyset,
    introduced(assumption,[]) ).

thf(23,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h42,h106,h40,h53,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h38,h104]) ).

thf(h117,assumption,
    ~ ( ( exu @ eigen__861 )
     => ~ ! [X1: $i] :
            ~ ( eigen__861 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h118,assumption,
    exu @ eigen__861,
    introduced(assumption,[]) ).

thf(h119,assumption,
    ! [X1: $i] :
      ~ ( eigen__861 @ X1 ),
    introduced(assumption,[]) ).

thf(24,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h118,h119,h117,h107,h108,h40,h53,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h42,h107]) ).

thf(25,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h117,h107,h108,h40,h53,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h118,h119])],[h117,24,h118,h119]) ).

thf(26,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h107,h108,h40,h53,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h117]),tab_negall(eigenvar,eigen__861)],[h108,25,h117]) ).

thf(27,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h40,h53,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h42,h106]),tab_bq(discharge,[h107,h108])],[exuE3e,23,26,h42,h106,h107,h108]) ).

thf(h120,assumption,
    in @ eigen__862 @ emptyset,
    introduced(assumption,[]) ).

thf(28,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h42,h106,h120,h105,h55,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h40,h105]) ).

thf(29,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h107,h108,h120,h105,h55,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h42,h107]) ).

thf(30,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h120,h105,h55,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h42,h106]),tab_bq(discharge,[h107,h108])],[exuE3e,28,29,h42,h106,h107,h108]) ).

thf(31,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h105,h55,h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h120]),tab_negall(eigenvar,eigen__862)],[h55,30,h120]) ).

thf(32,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h116,h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h40,h53]),tab_bq(discharge,[h105,h55])],[notinemptyset,27,31,h40,h53,h105,h55]) ).

thf(33,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h104,h55,h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h116]),tab_negall(eigenvar,eigen__860)],[h55,32,h116]) ).

thf(emptysetimpfalse,axiom,
    ( sP9
    = ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset ) ) ) ).

thf(34,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h36,h101,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h38,h53]),tab_bq(discharge,[h104,h55])],[emptysetimpfalse,22,33,h38,h53,h104,h55]) ).

thf(35,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h102,h103,h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h36,h102]) ).

thf(emptysetE,axiom,
    ( sP3
    = ( ! [X1: $i] :
          ( ( in @ X1 @ emptyset )
         => ! [X2: $o] : X2 ) ) ) ).

thf(36,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h34,h98,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h36,h101]),tab_bq(discharge,[h102,h103])],[emptysetE,34,35,h36,h101,h102,h103]) ).

thf(37,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h99,h100,h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h34,h99]) ).

thf(prop2setE,axiom,
    ( sP26
    = ( ! [X1: $o,X2: $i] :
          ( ( in @ X2 @ ( prop2set @ X1 ) )
         => X1 ) ) ) ).

thf(38,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h32,h95,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h34,h98]),tab_bq(discharge,[h99,h100])],[prop2setE,36,37,h34,h98,h99,h100]) ).

thf(39,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h96,h97,h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h32,h96]) ).

thf(exuE1,axiom,
    ( sP15
    = ( ! [X1: $i > $o] :
          ( ( exu @ X1 )
         => ~ ! [X2: $i] :
                ( ( X1 @ X2 )
               => ~ ! [X3: $i] :
                      ( ( X1 @ X3 )
                     => ( X2 = X3 ) ) ) ) ) ) ).

thf(40,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h30,h92,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h32,h95]),tab_bq(discharge,[h96,h97])],[exuE1,38,39,h32,h95,h96,h97]) ).

thf(41,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h93,h94,h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h30,h93]) ).

thf(dsetconstrER,axiom,
    ( sP4
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
         => ( X2 @ X3 ) ) ) ) ).

thf(42,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h28,h89,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h30,h92]),tab_bq(discharge,[h93,h94])],[dsetconstrER,40,41,h30,h92,h93,h94]) ).

thf(43,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h90,h91,h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h28,h90]) ).

thf(dsetconstrEL,axiom,
    ( sP16
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) )
         => ( in @ X3 @ X1 ) ) ) ) ).

thf(44,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h26,h86,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h28,h89]),tab_bq(discharge,[h90,h91])],[dsetconstrEL,42,43,h28,h89,h90,h91]) ).

thf(45,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h87,h88,h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h26,h87]) ).

thf(dsetconstrI,axiom,
    ( sP27
    = ( ! [X1: $i,X2: $i > $o,X3: $i] :
          ( ( in @ X3 @ X1 )
         => ( ( X2 @ X3 )
           => ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ) ) ) ).

thf(46,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h24,h83,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h26,h86]),tab_bq(discharge,[h87,h88])],[dsetconstrI,44,45,h26,h86,h87,h88]) ).

thf(47,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h84,h85,h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h24,h84]) ).

thf(descrp,axiom,
    ( sP13
    = ( ! [X1: $i > $o] :
          ( ( exu @ X1 )
         => ( X1 @ ( descr @ X1 ) ) ) ) ) ).

thf(48,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h22,h80,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h24,h83]),tab_bq(discharge,[h84,h85])],[descrp,46,47,h24,h83,h84,h85]) ).

thf(49,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h81,h82,h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h22,h81]) ).

thf(wellorderingAx,axiom,
    ( sP30
    = ( ! [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(50,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h20,h77,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h22,h80]),tab_bq(discharge,[h81,h82])],[wellorderingAx,48,49,h22,h80,h81,h82]) ).

thf(51,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h78,h79,h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h20,h78]) ).

thf(foundationAx,axiom,
    ( sP28
    = ( ! [X1: $i] :
          ( ~ ! [X2: $i] :
                ~ ( in @ X2 @ X1 )
         => ~ ! [X2: $i] :
                ( ( in @ X2 @ X1 )
               => ~ ! [X3: $i] :
                      ( ( in @ X3 @ X2 )
                     => ~ ( in @ X3 @ X1 ) ) ) ) ) ) ).

thf(52,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h18,h74,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h20,h77]),tab_bq(discharge,[h78,h79])],[foundationAx,50,51,h20,h77,h78,h79]) ).

thf(53,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h75,h76,h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h18,h75]) ).

thf(replAx,axiom,
    ( sP21
    = ( ! [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(54,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h16,h71,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h18,h74]),tab_bq(discharge,[h75,h76])],[replAx,52,53,h18,h74,h75,h76]) ).

thf(55,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h72,h73,h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h16,h72]) ).

thf(omegaIndAx,axiom,
    ( sP11
    = ( ! [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(56,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h14,h68,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h16,h71]),tab_bq(discharge,[h72,h73])],[omegaIndAx,54,55,h16,h71,h72,h73]) ).

thf(57,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h69,h70,h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h14,h69]) ).

thf(omegaSAx,axiom,
    ( sP32
    = ( ! [X1: $i] :
          ( ( in @ X1 @ omega )
         => ( in @ ( setadjoin @ X1 @ X1 ) @ omega ) ) ) ) ).

thf(58,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h12,h65,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h14,h68]),tab_bq(discharge,[h69,h70])],[omegaSAx,56,57,h14,h68,h69,h70]) ).

thf(59,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h66,h67,h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h12,h66]) ).

thf(omega0Ax,axiom,
    ( sP12
    = ( in @ emptyset @ omega ) ) ).

thf(60,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h10,h62,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h12,h65]),tab_bq(discharge,[h66,h67])],[omega0Ax,58,59,h12,h65,h66,h67]) ).

thf(61,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h63,h64,h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h10,h63]) ).

thf(setunionAx,axiom,
    ( sP1
    = ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( setunion @ X1 ) )
          = ( ~ ! [X3: $i] :
                  ( ( in @ X2 @ X3 )
                 => ~ ( in @ X3 @ X1 ) ) ) ) ) ) ).

thf(62,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h8,h59,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h10,h62]),tab_bq(discharge,[h63,h64])],[setunionAx,60,61,h10,h62,h63,h64]) ).

thf(63,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h60,h61,h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h8,h60]) ).

thf(powersetAx,axiom,
    ( sP18
    = ( ! [X1: $i,X2: $i] :
          ( ( in @ X2 @ ( powerset @ X1 ) )
          = ( ! [X3: $i] :
                ( ( in @ X3 @ X2 )
               => ( in @ X3 @ X1 ) ) ) ) ) ) ).

thf(64,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h6,h56,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h8,h59]),tab_bq(discharge,[h60,h61])],[powersetAx,62,63,h8,h59,h60,h61]) ).

thf(65,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h57,h58,h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h6,h57]) ).

thf(setadjoinAx,axiom,
    ( sP7
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
          = ( ( X3 != X1 )
           => ( in @ X3 @ X2 ) ) ) ) ) ).

thf(66,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h4,h53,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h6,h56]),tab_bq(discharge,[h57,h58])],[setadjoinAx,64,65,h6,h56,h57,h58]) ).

thf(67,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h54,h55,h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h4,h54]) ).

thf(emptysetAx,axiom,
    ( sP24
    = ( ! [X1: $i] :
          ~ ( in @ X1 @ emptyset ) ) ) ).

thf(68,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h2,h50,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h4,h53]),tab_bq(discharge,[h54,h55])],[emptysetAx,66,67,h4,h53,h54,h55]) ).

thf(69,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h51,h52,h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[h2,h51]) ).

thf(setextAx,axiom,
    sP20 = sP6 ).

thf(70,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h48,h49,h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_bq(discharge,[h2,h50]),tab_bq(discharge,[h51,h52])],[setextAx,68,69,h2,h50,h51,h52]) ).

thf(71,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h46,h47,h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h48,h49])],[h47,70,h48,h49]) ).

thf(72,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h45,h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h46,h47])],[h45,71,h46,h47]) ).

thf(73,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h44,h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h45]),tab_negall(eigenvar,eigen__1)],[h44,72,h45]) ).

thf(74,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h42,h43,h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h44]),tab_negall(eigenvar,eigen__0)],[h43,73,h44]) ).

thf(75,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h40,h41,h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h42,h43])],[h41,74,h42,h43]) ).

thf(76,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h38,h39,h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h40,h41])],[h39,75,h40,h41]) ).

thf(77,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h38,h39])],[h37,76,h38,h39]) ).

thf(78,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h36,h37])],[h35,77,h36,h37]) ).

thf(79,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h34,h35])],[h33,78,h34,h35]) ).

thf(80,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h32,h33])],[h31,79,h32,h33]) ).

thf(81,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h30,h31])],[h29,80,h30,h31]) ).

thf(82,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,81,h28,h29]) ).

thf(83,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h26,h27])],[h25,82,h26,h27]) ).

thf(84,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,83,h24,h25]) ).

thf(85,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,84,h22,h23]) ).

thf(86,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,85,h20,h21]) ).

thf(87,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,86,h18,h19]) ).

thf(88,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,87,h16,h17]) ).

thf(89,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,88,h14,h15]) ).

thf(90,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,89,h12,h13]) ).

thf(91,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,90,h10,h11]) ).

thf(92,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,91,h8,h9]) ).

thf(93,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,92,h6,h7]) ).

thf(94,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,93,h4,h5]) ).

thf(95,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,94,h2,h3]) ).

thf(96,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[95,h0]) ).

thf(0,theorem,
    ( sP20
   => ( sP24
     => ( sP7
       => ( sP18
         => ( sP1
           => ( sP12
             => ( sP32
               => ( sP11
                 => ( sP21
                   => ( sP28
                     => ( sP30
                       => ( sP13
                         => ( sP27
                           => ( sP16
                             => ( sP4
                               => ( sP15
                                 => ( sP26
                                   => ( sP3
                                     => ( sP9
                                       => ( sP5
                                         => ( sP31
                                           => ! [X1: $i,X2: $i] :
                                                ( ! [X3: $i] :
                                                    ( ( in @ X3 @ X1 )
                                                   => ( in @ X3 @ X2 ) )
                                               => ( ! [X3: $i] :
                                                      ( ( in @ X3 @ X2 )
                                                     => ( in @ X3 @ X1 ) )
                                                 => ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[95,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU505^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Wed Aug 23 19:30:53 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 41.18/41.24  % SZS status Theorem
% 41.18/41.24  % Mode: cade22grackle2x6987
% 41.18/41.24  % Steps: 22891
% 41.18/41.24  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------