TSTP Solution File: LCL957^6 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : LCL957^6 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 14:12:11 EDT 2022

% Result   : Theorem 2.06s 2.31s
% Output   : Proof 2.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   74
% Syntax   : Number of formulae    :   87 (  27 unt;  13 typ;  18 def)
%            Number of atoms       :  256 (  19 equ;   0 cnn)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  546 (  53   ~;  24   |;   0   &; 333   @)
%                                         (  24 <=>; 110  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   23 (  23   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   51 (  48 usr;  48 con; 0-3 aty)
%                                         (   2  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  125 (  31   ^  94   !;   0   ?; 125   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_mworld,type,
    mworld: $tType ).

thf(ty_eigen__6,type,
    eigen__6: mworld ).

thf(ty_eigen__7,type,
    eigen__7: mworld ).

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

thf(ty_eigen__0,type,
    eigen__0: mworld ).

thf(ty_eigen__4,type,
    eigen__4: $i ).

thf(ty_eigen__5,type,
    eigen__5: mworld ).

thf(ty_mrel,type,
    mrel: mworld > mworld > $o ).

thf(ty_eigen__3,type,
    eigen__3: mworld ).

thf(ty_eigen__8,type,
    eigen__8: $i ).

thf(ty_eigen__9,type,
    eigen__9: mworld ).

thf(ty_big_r,type,
    big_r: $i > $i > mworld > $o ).

thf(ty_mactual,type,
    mactual: mworld ).

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

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ eigen__0 @ X1 )
           => ! [X2: $i,X3: mworld] :
                ( ( mrel @ X1 @ X3 )
               => ( ! [X4: mworld] :
                      ( ( mrel @ X3 @ X4 )
                     => ( big_r @ eigen__1 @ eigen__1 @ X4 ) )
                 => ! [X4: mworld] :
                      ( ( mrel @ X3 @ X4 )
                     => ( big_r @ X2 @ X2 @ X4 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(eigendef_eigen__6,definition,
    ( eigen__6
    = ( eps__0
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ eigen__5 @ X1 )
           => ( big_r @ eigen__4 @ eigen__4 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__6])]) ).

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ mactual @ X1 )
           => ( ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( ~ ! [X3: $i] :
                          ~ ! [X4: mworld] :
                              ( ( mrel @ X2 @ X4 )
                             => ( big_r @ X3 @ X3 @ X4 ) )
                   => ! [X3: mworld] :
                        ( ( mrel @ X2 @ X3 )
                       => ! [X4: $i,X5: mworld] :
                            ( ( mrel @ X3 @ X5 )
                           => ( big_r @ X4 @ X4 @ X5 ) ) ) ) )
             => ~ ! [X2: $i] :
                    ~ ! [X3: mworld] :
                        ( ( mrel @ X1 @ X3 )
                       => ! [X4: $i,X5: mworld] :
                            ( ( mrel @ X3 @ X5 )
                           => ( ! [X6: mworld] :
                                  ( ( mrel @ X5 @ X6 )
                                 => ( big_r @ X2 @ X2 @ X6 ) )
                             => ! [X6: mworld] :
                                  ( ( mrel @ X5 @ X6 )
                                 => ( big_r @ X4 @ X4 @ X6 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(h1,assumption,
    ! [X1: $i > $o,X2: $i] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__8,definition,
    ( eigen__8
    = ( eps__1
      @ ^ [X1: $i] :
          ~ ! [X2: mworld] :
              ( ( mrel @ eigen__7 @ X2 )
             => ( ! [X3: mworld] :
                    ( ( mrel @ X2 @ X3 )
                   => ( big_r @ eigen__4 @ eigen__4 @ X3 ) )
               => ! [X3: mworld] :
                    ( ( mrel @ X2 @ X3 )
                   => ( big_r @ X1 @ X1 @ X3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__8])]) ).

thf(eigendef_eigen__4,definition,
    ( eigen__4
    = ( eps__1
      @ ^ [X1: $i] :
          ~ ! [X2: mworld] :
              ( ( mrel @ eigen__3 @ X2 )
             => ( ! [X3: mworld] :
                    ( ( mrel @ X2 @ X3 )
                   => ( big_r @ eigen__1 @ eigen__1 @ X3 ) )
               => ! [X3: mworld] :
                    ( ( mrel @ X2 @ X3 )
                   => ( big_r @ X1 @ X1 @ X3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__4])]) ).

thf(eigendef_eigen__9,definition,
    ( eigen__9
    = ( eps__0
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ eigen__7 @ X1 )
           => ( ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( big_r @ eigen__4 @ eigen__4 @ X2 ) )
             => ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( big_r @ eigen__8 @ eigen__8 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__9])]) ).

thf(eigendef_eigen__7,definition,
    ( eigen__7
    = ( eps__0
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ eigen__0 @ X1 )
           => ! [X2: $i,X3: mworld] :
                ( ( mrel @ X1 @ X3 )
               => ( ! [X4: mworld] :
                      ( ( mrel @ X3 @ X4 )
                     => ( big_r @ eigen__4 @ eigen__4 @ X4 ) )
                 => ! [X4: mworld] :
                      ( ( mrel @ X3 @ X4 )
                     => ( big_r @ X2 @ X2 @ X4 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__7])]) ).

thf(eigendef_eigen__5,definition,
    ( eigen__5
    = ( eps__0
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ eigen__3 @ X1 )
           => ( ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( big_r @ eigen__1 @ eigen__1 @ X2 ) )
             => ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( big_r @ eigen__4 @ eigen__4 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__5])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ( mrel @ eigen__5 @ eigen__6 )
     => ( big_r @ eigen__4 @ eigen__4 @ eigen__6 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: mworld] : ( !! @ ( mrel @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ! [X1: mworld] :
          ( ( mrel @ eigen__9 @ X1 )
         => ( big_r @ eigen__4 @ eigen__4 @ X1 ) )
     => ! [X1: mworld] :
          ( ( mrel @ eigen__9 @ X1 )
         => ( big_r @ eigen__8 @ eigen__8 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i] :
        ~ ! [X2: mworld] :
            ( ( mrel @ eigen__0 @ X2 )
           => ! [X3: $i,X4: mworld] :
                ( ( mrel @ X2 @ X4 )
               => ( ! [X5: mworld] :
                      ( ( mrel @ X4 @ X5 )
                     => ( big_r @ X1 @ X1 @ X5 ) )
                 => ! [X5: mworld] :
                      ( ( mrel @ X4 @ X5 )
                     => ( big_r @ X3 @ X3 @ X5 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i,X2: mworld] :
        ( ( mrel @ eigen__7 @ X2 )
       => ( ! [X3: mworld] :
              ( ( mrel @ X2 @ X3 )
             => ( big_r @ eigen__4 @ eigen__4 @ X3 ) )
         => ! [X3: mworld] :
              ( ( mrel @ X2 @ X3 )
             => ( big_r @ X1 @ X1 @ X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( mrel @ eigen__7 @ eigen__9 )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( mrel @ eigen__0 @ eigen__7 )
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ! [X1: mworld] :
          ( ( mrel @ eigen__0 @ X1 )
         => ( ~ ! [X2: $i] :
                  ~ ! [X3: mworld] :
                      ( ( mrel @ X1 @ X3 )
                     => ( big_r @ X2 @ X2 @ X3 ) )
           => ! [X2: mworld] :
                ( ( mrel @ X1 @ X2 )
               => ! [X3: $i,X4: mworld] :
                    ( ( mrel @ X2 @ X4 )
                   => ( big_r @ X3 @ X3 @ X4 ) ) ) ) )
     => ~ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: mworld] :
        ( ( mrel @ eigen__9 @ X1 )
       => ( big_r @ eigen__4 @ eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( big_r @ eigen__4 @ eigen__4 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( !! @ ( mrel @ eigen__9 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: mworld] :
        ( ( mrel @ eigen__7 @ X1 )
       => ( ! [X2: mworld] :
              ( ( mrel @ X1 @ X2 )
             => ( big_r @ eigen__4 @ eigen__4 @ X2 ) )
         => ! [X2: mworld] :
              ( ( mrel @ X1 @ X2 )
             => ( big_r @ eigen__8 @ eigen__8 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ! [X1: mworld] :
          ( ( mrel @ eigen__5 @ X1 )
         => ( big_r @ eigen__1 @ eigen__1 @ X1 ) )
     => ! [X1: mworld] :
          ( ( mrel @ eigen__5 @ X1 )
         => ( big_r @ eigen__4 @ eigen__4 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: mworld] :
        ( ( mrel @ eigen__5 @ X1 )
       => ( big_r @ eigen__4 @ eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i,X2: mworld] :
        ( ( mrel @ eigen__3 @ X2 )
       => ( ! [X3: mworld] :
              ( ( mrel @ X2 @ X3 )
             => ( big_r @ eigen__1 @ eigen__1 @ X3 ) )
         => ! [X3: mworld] :
              ( ( mrel @ X2 @ X3 )
             => ( big_r @ X1 @ X1 @ X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ( mrel @ eigen__0 @ eigen__3 )
     => sP15 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( mrel @ eigen__9 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: mworld] :
        ( ( mrel @ eigen__0 @ X1 )
       => ! [X2: $i,X3: mworld] :
            ( ( mrel @ X1 @ X3 )
           => ( ! [X4: mworld] :
                  ( ( mrel @ X3 @ X4 )
                 => ( big_r @ eigen__4 @ eigen__4 @ X4 ) )
             => ! [X4: mworld] :
                  ( ( mrel @ X3 @ X4 )
                 => ( big_r @ X2 @ X2 @ X4 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

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

thf(sP20,plain,
    ( sP20
  <=> ! [X1: mworld] :
        ( ( mrel @ mactual @ X1 )
       => ( ! [X2: mworld] :
              ( ( mrel @ X1 @ X2 )
             => ( ~ ! [X3: $i] :
                      ~ ! [X4: mworld] :
                          ( ( mrel @ X2 @ X4 )
                         => ( big_r @ X3 @ X3 @ X4 ) )
               => ! [X3: mworld] :
                    ( ( mrel @ X2 @ X3 )
                   => ! [X4: $i,X5: mworld] :
                        ( ( mrel @ X3 @ X5 )
                       => ( big_r @ X4 @ X4 @ X5 ) ) ) ) )
         => ~ ! [X2: $i] :
                ~ ! [X3: mworld] :
                    ( ( mrel @ X1 @ X3 )
                   => ! [X4: $i,X5: mworld] :
                        ( ( mrel @ X3 @ X5 )
                       => ( ! [X6: mworld] :
                              ( ( mrel @ X5 @ X6 )
                             => ( big_r @ X2 @ X2 @ X6 ) )
                         => ! [X6: mworld] :
                              ( ( mrel @ X5 @ X6 )
                             => ( big_r @ X4 @ X4 @ X6 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: mworld] :
        ( ( mrel @ eigen__0 @ X1 )
       => ! [X2: $i,X3: mworld] :
            ( ( mrel @ X1 @ X3 )
           => ( ! [X4: mworld] :
                  ( ( mrel @ X3 @ X4 )
                 => ( big_r @ eigen__1 @ eigen__1 @ X4 ) )
             => ! [X4: mworld] :
                  ( ( mrel @ X3 @ X4 )
                 => ( big_r @ X2 @ X2 @ X4 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( ( mrel @ eigen__3 @ eigen__5 )
     => sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ! [X1: mworld] :
        ( ( mrel @ eigen__3 @ X1 )
       => ( ! [X2: mworld] :
              ( ( mrel @ X1 @ X2 )
             => ( big_r @ eigen__1 @ eigen__1 @ X2 ) )
         => ! [X2: mworld] :
              ( ( mrel @ X1 @ X2 )
             => ( big_r @ eigen__4 @ eigen__4 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( sP17
     => sP10 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(def_mlocal,definition,
    ( mlocal
    = ( ^ [X1: mworld > $o] : ( X1 @ mactual ) ) ) ).

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

thf(def_mand,definition,
    ( mand
    = ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
          ~ ( ( X1 @ X3 )
           => ~ ( X2 @ X3 ) ) ) ) ).

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

thf(def_mimplies,definition,
    ( mimplies
    = ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
          ( ( X1 @ X3 )
         => ( X2 @ X3 ) ) ) ) ).

thf(def_mequiv,definition,
    ( mequiv
    = ( ^ [X1: mworld > $o,X2: mworld > $o,X3: mworld] :
          ( ( X1 @ X3 )
          = ( X2 @ X3 ) ) ) ) ).

thf(def_mbox,definition,
    ( mbox
    = ( ^ [X1: mworld > $o,X2: mworld] :
        ! [X3: mworld] :
          ( ( mrel @ X2 @ X3 )
         => ( X1 @ X3 ) ) ) ) ).

thf(def_mdia,definition,
    ( mdia
    = ( ^ [X1: mworld > $o,X2: mworld] :
          ~ ! [X3: mworld] :
              ( ( mrel @ X2 @ X3 )
             => ~ ( X1 @ X3 ) ) ) ) ).

thf(def_mforall_di,definition,
    ( mforall_di
    = ( ^ [X1: $i > mworld > $o,X2: mworld] :
        ! [X3: $i] : ( X1 @ X3 @ X2 ) ) ) ).

thf(def_mexists_di,definition,
    ( mexists_di
    = ( ^ [X1: $i > mworld > $o,X2: mworld] :
          ~ ! [X3: $i] :
              ~ ( X1 @ X3 @ X2 ) ) ) ).

thf(x2122,conjecture,
    sP20 ).

thf(h2,negated_conjecture,
    ~ sP20,
    inference(assume_negation,[status(cth)],[x2122]) ).

thf(1,plain,
    ( ~ sP11
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP9
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP24
    | ~ sP17
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP2
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP3
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP6
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP12
    | ~ sP6 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__9]) ).

thf(8,plain,
    ( sP5
    | ~ sP12 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__8]) ).

thf(9,plain,
    ( sP7
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP18
    | ~ sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__7]) ).

thf(11,plain,
    ( ~ sP4
    | ~ sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP1
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP14
    | ~ sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6]) ).

thf(14,plain,
    ( sP13
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( sP22
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( sP23
    | ~ sP22 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).

thf(17,plain,
    ( sP15
    | ~ sP23 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__4]) ).

thf(18,plain,
    ( sP16
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP21
    | ~ sP16 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(20,plain,
    ( ~ sP4
    | ~ sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP8
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( sP19
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( sP20
    | ~ sP19 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(mrel_universal,axiom,
    sP2 ).

thf(24,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,mrel_universal,h2]) ).

thf(25,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[24,h1]) ).

thf(26,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[25,h0]) ).

thf(0,theorem,
    sP20,
    inference(contra,[status(thm),contra(discharge,[h2])],[24,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL957^6 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul  3 14:38:43 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 2.06/2.31  % SZS status Theorem
% 2.06/2.31  % Mode: mode506
% 2.06/2.31  % Inferences: 40348
% 2.06/2.31  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------