TSTP Solution File: SET907^7 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SET907^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n028.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 15:19:06 EDT 2023

% Result   : Theorem 0.19s 0.75s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_mu,type,
    mu: $tType ).

thf(ty_qmltpeq,type,
    qmltpeq: mu > mu > $i > $o ).

thf(ty_eigen__1,type,
    eigen__1: mu ).

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

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

thf(ty_set_union2,type,
    set_union2: mu > mu > mu ).

thf(ty_eigen__2,type,
    eigen__2: mu ).

thf(ty_subset,type,
    subset: mu > mu > $i > $o ).

thf(ty_unordered_pair,type,
    unordered_pair: mu > mu > mu ).

thf(ty_exists_in_world,type,
    exists_in_world: mu > $i > $o ).

thf(ty_eigen__3,type,
    eigen__3: mu ).

thf(sP1,plain,
    ( sP1
  <=> ( in @ eigen__1 @ eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: mu,X2: mu] : ( exists_in_world @ ( unordered_pair @ X1 @ X2 ) @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( ( subset @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ eigen__2 @ eigen__0 )
       => ~ ( sP1
           => ~ ( in @ eigen__3 @ eigen__2 @ eigen__0 ) ) )
     => ~ ( ~ ( sP1
             => ~ ( in @ eigen__3 @ eigen__2 @ eigen__0 ) )
         => ( subset @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ eigen__2 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i,X2: mu,X3: mu] : ( exists_in_world @ ( unordered_pair @ X2 @ X3 ) @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP1
     => ~ ( in @ eigen__3 @ eigen__2 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( exists_in_world @ eigen__3 @ eigen__0 )
     => ! [X1: mu] :
          ( ( exists_in_world @ X1 @ eigen__0 )
         => ~ ( ( ( subset @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ X1 @ eigen__0 )
               => ~ ( ( in @ eigen__1 @ X1 @ eigen__0 )
                   => ~ ( in @ eigen__3 @ X1 @ eigen__0 ) ) )
             => ~ ( ~ ( ( in @ eigen__1 @ X1 @ eigen__0 )
                     => ~ ( in @ eigen__3 @ X1 @ eigen__0 ) )
                 => ( subset @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ X1 @ eigen__0 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( exists_in_world @ eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: mu] : ( exists_in_world @ ( unordered_pair @ eigen__1 @ X1 ) @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i,X2: mu] :
        ( ( exists_in_world @ X2 @ X1 )
       => ! [X3: mu] :
            ( ( exists_in_world @ X3 @ X1 )
           => ! [X4: mu] :
                ( ( exists_in_world @ X4 @ X1 )
               => ~ ( ( ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 )
                     => ~ ( ( in @ X2 @ X4 @ X1 )
                         => ~ ( in @ X3 @ X4 @ X1 ) ) )
                   => ~ ( ~ ( ( in @ X2 @ X4 @ X1 )
                           => ~ ( in @ X3 @ X4 @ X1 ) )
                       => ( subset @ ( unordered_pair @ X2 @ X3 ) @ X4 @ X1 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( in @ eigen__3 @ eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP7
     => ( ( subset @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ eigen__2 @ eigen__0 )
       => ( qmltpeq @ ( set_union2 @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ eigen__2 ) @ eigen__2 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( exists_in_world @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( subset @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( exists_in_world @ eigen__3 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i,X2: mu] :
        ( ( exists_in_world @ X2 @ X1 )
       => ! [X3: mu] :
            ( ( exists_in_world @ X3 @ X1 )
           => ( ( subset @ X2 @ X3 @ X1 )
             => ( qmltpeq @ ( set_union2 @ X2 @ X3 ) @ X3 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ( ( subset @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ X1 @ eigen__0 )
         => ( qmltpeq @ ( set_union2 @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ X1 ) @ X1 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( exists_in_world @ eigen__1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( sP7
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( sP13
     => ( qmltpeq @ ( set_union2 @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ eigen__2 ) @ eigen__2 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( sP17
     => ! [X1: mu] :
          ( ( exists_in_world @ X1 @ eigen__0 )
         => ! [X2: mu] :
              ( ( exists_in_world @ X2 @ eigen__0 )
             => ~ ( ( ( subset @ ( unordered_pair @ eigen__1 @ X1 ) @ X2 @ eigen__0 )
                   => ~ ( ( in @ eigen__1 @ X2 @ eigen__0 )
                       => ~ ( in @ X1 @ X2 @ eigen__0 ) ) )
                 => ~ ( ~ ( ( in @ eigen__1 @ X2 @ eigen__0 )
                         => ~ ( in @ X1 @ X2 @ eigen__0 ) )
                     => ( subset @ ( unordered_pair @ eigen__1 @ X1 ) @ X2 @ eigen__0 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ! [X2: mu] :
            ( ( exists_in_world @ X2 @ eigen__0 )
           => ( ( subset @ X1 @ X2 @ eigen__0 )
             => ( qmltpeq @ ( set_union2 @ X1 @ X2 ) @ X2 @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( ~ sP5
     => sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ! [X2: mu] :
            ( ( exists_in_world @ X2 @ eigen__0 )
           => ~ ( ( ( subset @ ( unordered_pair @ eigen__1 @ X1 ) @ X2 @ eigen__0 )
                 => ~ ( ( in @ eigen__1 @ X2 @ eigen__0 )
                     => ~ ( in @ X1 @ X2 @ eigen__0 ) ) )
               => ~ ( ~ ( ( in @ eigen__1 @ X2 @ eigen__0 )
                       => ~ ( in @ X1 @ X2 @ eigen__0 ) )
                   => ( subset @ ( unordered_pair @ eigen__1 @ X1 ) @ X2 @ eigen__0 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ! [X2: mu] :
            ( ( exists_in_world @ X2 @ eigen__0 )
           => ! [X3: mu] :
                ( ( exists_in_world @ X3 @ eigen__0 )
               => ~ ( ( ( subset @ ( unordered_pair @ X1 @ X2 ) @ X3 @ eigen__0 )
                     => ~ ( ( in @ X1 @ X3 @ eigen__0 )
                         => ~ ( in @ X2 @ X3 @ eigen__0 ) ) )
                   => ~ ( ~ ( ( in @ X1 @ X3 @ eigen__0 )
                           => ~ ( in @ X2 @ X3 @ eigen__0 ) )
                       => ( subset @ ( unordered_pair @ X1 @ X2 ) @ X3 @ eigen__0 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( sP12
     => sP16 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ~ ( ( ( subset @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ X1 @ eigen__0 )
             => ~ ( ( in @ eigen__1 @ X1 @ eigen__0 )
                 => ~ ( in @ eigen__3 @ X1 @ eigen__0 ) ) )
           => ~ ( ~ ( ( in @ eigen__1 @ X1 @ eigen__0 )
                   => ~ ( in @ eigen__3 @ X1 @ eigen__0 ) )
               => ( subset @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ X1 @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( qmltpeq @ ( set_union2 @ ( unordered_pair @ eigen__1 @ eigen__3 ) @ eigen__2 ) @ eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(def_mnot,definition,
    ( mnot
    = ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).

thf(def_mor,definition,
    ( mor
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X1 @ X3 )
          | ( X2 @ X3 ) ) ) ) ).

thf(def_mand,definition,
    ( mand
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).

thf(def_mimplies,definition,
    ( mimplies
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).

thf(def_mequiv,definition,
    ( mequiv
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).

thf(def_mforall_ind,definition,
    ( mforall_ind
    = ( ^ [X1: mu > $i > $o,X2: $i] :
        ! [X3: mu] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( exists_in_world @ X3 @ X2 )
          @ ( X1 @ X3 @ X2 ) ) ) ) ).

thf(def_mvalid,definition,
    ( mvalid
    = ( ^ [X1: $i > $o] :
        ! [X2: $i] : ( X1 @ X2 ) ) ) ).

thf(t48_zfmisc_1,conjecture,
    ! [X1: $i,X2: mu] :
      ( ( exists_in_world @ X2 @ X1 )
     => ! [X3: mu] :
          ( ( exists_in_world @ X3 @ X1 )
         => ! [X4: mu] :
              ( ( exists_in_world @ X4 @ X1 )
             => ( ~ ( ( in @ X2 @ X3 @ X1 )
                   => ~ ( in @ X4 @ X3 @ X1 ) )
               => ( qmltpeq @ ( set_union2 @ ( unordered_pair @ X2 @ X4 ) @ X3 ) @ X3 @ X1 ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i,X2: mu] :
        ( ( exists_in_world @ X2 @ X1 )
       => ! [X3: mu] :
            ( ( exists_in_world @ X3 @ X1 )
           => ! [X4: mu] :
                ( ( exists_in_world @ X4 @ X1 )
               => ( ~ ( ( in @ X2 @ X3 @ X1 )
                     => ~ ( in @ X4 @ X3 @ X1 ) )
                 => ( qmltpeq @ ( set_union2 @ ( unordered_pair @ X2 @ X4 ) @ X3 ) @ X3 @ X1 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[t48_zfmisc_1]) ).

thf(h1,assumption,
    ~ ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ! [X2: mu] :
            ( ( exists_in_world @ X2 @ eigen__0 )
           => ! [X3: mu] :
                ( ( exists_in_world @ X3 @ eigen__0 )
               => ( ~ ( ( in @ X1 @ X2 @ eigen__0 )
                     => ~ ( in @ X3 @ X2 @ eigen__0 ) )
                 => ( qmltpeq @ ( set_union2 @ ( unordered_pair @ X1 @ X3 ) @ X2 ) @ X2 @ eigen__0 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP17
     => ! [X1: mu] :
          ( ( exists_in_world @ X1 @ eigen__0 )
         => ! [X2: mu] :
              ( ( exists_in_world @ X2 @ eigen__0 )
             => ( ~ ( ( in @ eigen__1 @ X1 @ eigen__0 )
                   => ~ ( in @ X2 @ X1 @ eigen__0 ) )
               => ( qmltpeq @ ( set_union2 @ ( unordered_pair @ eigen__1 @ X2 ) @ X1 ) @ X1 @ eigen__0 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP17,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ! [X2: mu] :
            ( ( exists_in_world @ X2 @ eigen__0 )
           => ( ~ ( ( in @ eigen__1 @ X1 @ eigen__0 )
                 => ~ ( in @ X2 @ X1 @ eigen__0 ) )
             => ( qmltpeq @ ( set_union2 @ ( unordered_pair @ eigen__1 @ X2 ) @ X1 ) @ X1 @ eigen__0 ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP7
     => ! [X1: mu] :
          ( ( exists_in_world @ X1 @ eigen__0 )
         => ( ~ ( sP1
               => ~ ( in @ X1 @ eigen__2 @ eigen__0 ) )
           => ( qmltpeq @ ( set_union2 @ ( unordered_pair @ eigen__1 @ X1 ) @ eigen__2 ) @ eigen__2 @ eigen__0 ) ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ( ~ ( sP1
             => ~ ( in @ X1 @ eigen__2 @ eigen__0 ) )
         => ( qmltpeq @ ( set_union2 @ ( unordered_pair @ eigen__1 @ X1 ) @ eigen__2 ) @ eigen__2 @ eigen__0 ) ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( sP14
     => ( ~ sP5
       => sP27 ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP14,
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ( ~ sP5
     => sP27 ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP27,
    introduced(assumption,[]) ).

thf(h13,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h14,assumption,
    sP10,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP19
    | ~ sP13
    | sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP11
    | ~ sP7
    | sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP16
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP25
    | ~ sP12
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP21
    | sP25 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP5
    | ~ sP1
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP22
    | sP5
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP3
    | sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP18
    | ~ sP7
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP26
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP6
    | ~ sP14
    | sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP23
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP20
    | ~ sP17
    | sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP24
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP8
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP2
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP4
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP15
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP9
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(t38_zfmisc_1,axiom,
    sP9 ).

thf(t12_xboole_1,axiom,
    sP15 ).

thf(existence_of_unordered_pair_ax,axiom,
    sP4 ).

thf(20,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h8,h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,h3,h6,h9,h13,h14,h12,t38_zfmisc_1,t12_xboole_1,existence_of_unordered_pair_ax]) ).

thf(21,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h8,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h11,20,h13,h14]) ).

thf(22,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h10,h8,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h12])],[h10,21,h11,h12]) ).

thf(23,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,22,h9,h10]) ).

thf(24,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h8]),tab_negall(eigenvar,eigen__3)],[h7,23,h8]) ).

thf(25,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,24,h6,h7]) ).

thf(26,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,25,h5]) ).

thf(27,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,26,h3,h4]) ).

thf(28,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,27,h2]) ).

thf(29,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,28,h1]) ).

thf(0,theorem,
    ! [X1: $i,X2: mu] :
      ( ( exists_in_world @ X2 @ X1 )
     => ! [X3: mu] :
          ( ( exists_in_world @ X3 @ X1 )
         => ! [X4: mu] :
              ( ( exists_in_world @ X4 @ X1 )
             => ( ~ ( ( in @ X2 @ X3 @ X1 )
                   => ~ ( in @ X4 @ X3 @ X1 ) )
               => ( qmltpeq @ ( set_union2 @ ( unordered_pair @ X2 @ X4 ) @ X3 ) @ X3 @ X1 ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[29,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET907^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sat Aug 26 13:08:22 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.75  % SZS status Theorem
% 0.19/0.75  % Mode: cade22sinegrackle2x6978
% 0.19/0.75  % Steps: 4702
% 0.19/0.75  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------