TSTP Solution File: LCL958^18 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : LCL958^18 : 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 : n011.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 25.83s 26.14s
% Output   : Proof 25.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  118
% Syntax   : Number of formulae    :  131 (  29 unt;  15 typ;  18 def)
%            Number of atoms       :  403 (  19 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  804 ( 109   ~;  49   |;   0   &; 430   @)
%                                         (  45 <=>; 167  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   26 (  26   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   74 (  71 usr;  69 con; 0-2 aty)
%                                         (   4  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  139 (  31   ^ 108   !;   0   ?; 139   :)

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

thf(ty_eigen__14,type,
    eigen__14: mworld ).

thf(ty_eigen__12,type,
    eigen__12: mworld ).

thf(ty_eiw_di,type,
    eiw_di: $i > mworld > $o ).

thf(ty_eigen__1,type,
    eigen__1: mworld ).

thf(ty_eigen__15,type,
    eigen__15: mworld ).

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

thf(ty_eigen__19,type,
    eigen__19: mworld ).

thf(ty_eigen__11,type,
    eigen__11: $i ).

thf(ty_eigen__17,type,
    eigen__17: mworld ).

thf(ty_eigen__13,type,
    eigen__13: $i ).

thf(ty_big_p,type,
    big_p: $i > mworld > $o ).

thf(ty_big_q,type,
    big_q: $i > mworld > $o ).

thf(ty_mactual,type,
    mactual: mworld ).

thf(ty_eigen__18,type,
    eigen__18: $i ).

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

thf(eigendef_eigen__11,definition,
    ( eigen__11
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ( eiw_di @ X1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__11])]) ).

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

thf(eigendef_eigen__15,definition,
    ( eigen__15
    = ( eps__1
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ eigen__14 @ X1 )
           => ( big_p @ eigen__13 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__15])]) ).

thf(eigendef_eigen__17,definition,
    ( eigen__17
    = ( eps__1
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ mactual @ X1 )
           => ! [X2: $i] :
                ( ( eiw_di @ X2 @ X1 )
               => ! [X3: mworld] :
                    ( ( mrel @ X1 @ X3 )
                   => ( ! [X4: mworld] :
                          ( ( mrel @ X3 @ X4 )
                         => ( big_p @ eigen__13 @ X4 ) )
                     => ( ~ ! [X4: mworld] :
                              ( ( mrel @ X3 @ X4 )
                             => ( big_q @ eigen__13 @ X4 ) )
                       => ! [X4: mworld] :
                            ( ( mrel @ X3 @ X4 )
                           => ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__17])]) ).

thf(eigendef_eigen__14,definition,
    ( eigen__14
    = ( eps__1
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ eigen__12 @ X1 )
           => ( ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( big_p @ eigen__11 @ X2 ) )
             => ( ~ ! [X2: mworld] :
                      ( ( mrel @ X1 @ X2 )
                     => ( big_q @ eigen__11 @ X2 ) )
               => ! [X2: mworld] :
                    ( ( mrel @ X1 @ X2 )
                   => ( big_p @ eigen__13 @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__14])]) ).

thf(eigendef_eigen__12,definition,
    ( eigen__12
    = ( eps__1
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ mactual @ X1 )
           => ! [X2: $i] :
                ( ( eiw_di @ X2 @ X1 )
               => ! [X3: mworld] :
                    ( ( mrel @ X1 @ X3 )
                   => ( ! [X4: mworld] :
                          ( ( mrel @ X3 @ X4 )
                         => ( big_p @ eigen__11 @ X4 ) )
                     => ( ~ ! [X4: mworld] :
                              ( ( mrel @ X3 @ X4 )
                             => ( big_q @ eigen__11 @ X4 ) )
                       => ! [X4: mworld] :
                            ( ( mrel @ X3 @ X4 )
                           => ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__12])]) ).

thf(eigendef_eigen__18,definition,
    ( eigen__18
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( eiw_di @ X1 @ eigen__17 )
           => ! [X2: mworld] :
                ( ( mrel @ eigen__17 @ X2 )
               => ( ! [X3: mworld] :
                      ( ( mrel @ X2 @ X3 )
                     => ( big_p @ eigen__13 @ X3 ) )
                 => ( ~ ! [X3: mworld] :
                          ( ( mrel @ X2 @ X3 )
                         => ( big_q @ eigen__13 @ X3 ) )
                   => ! [X3: mworld] :
                        ( ( mrel @ X2 @ X3 )
                       => ( big_p @ X1 @ X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__18])]) ).

thf(eigendef_eigen__13,definition,
    ( eigen__13
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( eiw_di @ X1 @ eigen__12 )
           => ! [X2: mworld] :
                ( ( mrel @ eigen__12 @ X2 )
               => ( ! [X3: mworld] :
                      ( ( mrel @ X2 @ X3 )
                     => ( big_p @ eigen__11 @ X3 ) )
                 => ( ~ ! [X3: mworld] :
                          ( ( mrel @ X2 @ X3 )
                         => ( big_q @ eigen__11 @ X3 ) )
                   => ! [X3: mworld] :
                        ( ( mrel @ X2 @ X3 )
                       => ( big_p @ X1 @ X3 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__13])]) ).

thf(eigendef_eigen__19,definition,
    ( eigen__19
    = ( eps__1
      @ ^ [X1: mworld] :
          ~ ( ( mrel @ eigen__17 @ X1 )
           => ( ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( big_p @ eigen__13 @ X2 ) )
             => ( ~ ! [X2: mworld] :
                      ( ( mrel @ X1 @ X2 )
                     => ( big_q @ eigen__13 @ X2 ) )
               => ! [X2: mworld] :
                    ( ( mrel @ X1 @ X2 )
                   => ( big_p @ eigen__18 @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__19])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: mworld] :
        ~ ! [X2: $i] :
            ~ ( eiw_di @ X2 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( ( eiw_di @ X1 @ eigen__17 )
       => ! [X2: mworld] :
            ( ( mrel @ eigen__17 @ X2 )
           => ( ! [X3: mworld] :
                  ( ( mrel @ X2 @ X3 )
                 => ( big_p @ eigen__13 @ X3 ) )
             => ( ~ ! [X3: mworld] :
                      ( ( mrel @ X2 @ X3 )
                     => ( big_q @ eigen__13 @ X3 ) )
               => ! [X3: mworld] :
                    ( ( mrel @ X2 @ X3 )
                   => ( big_p @ X1 @ X3 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: mworld] :
        ( ( mrel @ eigen__17 @ X1 )
       => ( ! [X2: mworld] :
              ( ( mrel @ X1 @ X2 )
             => ( big_p @ eigen__13 @ X2 ) )
         => ( ~ ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( big_q @ eigen__13 @ X2 ) )
           => ! [X2: mworld] :
                ( ( mrel @ X1 @ X2 )
               => ( big_p @ eigen__18 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( mrel @ eigen__17 @ eigen__19 )
     => ( ! [X1: mworld] :
            ( ( mrel @ eigen__19 @ X1 )
           => ( big_p @ eigen__13 @ X1 ) )
       => ( ~ ! [X1: mworld] :
                ( ( mrel @ eigen__19 @ X1 )
               => ( big_q @ eigen__13 @ X1 ) )
         => ! [X1: mworld] :
              ( ( mrel @ eigen__19 @ X1 )
             => ( big_p @ eigen__18 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( eiw_di @ eigen__18 @ eigen__17 )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( mrel @ eigen__12 @ mactual ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( mrel @ eigen__14 @ eigen__15 )
     => ( big_p @ eigen__13 @ eigen__15 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: mworld] :
        ( ( mrel @ eigen__14 @ X1 )
       => ( big_p @ eigen__13 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eiw_di @ eigen__13 @ eigen__12 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP9
     => ! [X1: mworld] :
          ( ( mrel @ eigen__12 @ X1 )
         => ( ! [X2: mworld] :
                ( ( mrel @ X1 @ X2 )
               => ( big_p @ eigen__11 @ X2 ) )
           => ( ~ ! [X2: mworld] :
                    ( ( mrel @ X1 @ X2 )
                   => ( big_q @ eigen__11 @ X2 ) )
             => ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( big_p @ eigen__13 @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( !! @ ( mrel @ eigen__19 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( !! @ ( mrel @ eigen__12 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: $i] :
        ( ( eiw_di @ X1 @ eigen__12 )
       => ! [X2: mworld] :
            ( ( mrel @ eigen__12 @ X2 )
           => ( ! [X3: mworld] :
                  ( ( mrel @ X2 @ X3 )
                 => ( big_p @ eigen__11 @ X3 ) )
             => ( ~ ! [X3: mworld] :
                      ( ( mrel @ X2 @ X3 )
                     => ( big_q @ eigen__11 @ X3 ) )
               => ! [X3: mworld] :
                    ( ( mrel @ X2 @ X3 )
                   => ( big_p @ X1 @ X3 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i] :
        ( ~ ( ( eiw_di @ X1 @ eigen__1 )
           => ~ ( mrel @ eigen__1 @ mactual ) )
       => ( eiw_di @ X1 @ mactual ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( mrel @ eigen__1 @ mactual ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( big_p @ eigen__13 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ~ ( ( eiw_di @ eigen__11 @ eigen__1 )
         => ~ sP15 )
     => ( eiw_di @ eigen__11 @ mactual ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( !! @ ( mrel @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( ( mrel @ eigen__19 @ eigen__15 )
     => sP16 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( ( eiw_di @ eigen__13 @ mactual )
     => ~ ! [X1: mworld] :
            ( ( mrel @ mactual @ X1 )
           => ! [X2: $i] :
                ( ( eiw_di @ X2 @ X1 )
               => ! [X3: mworld] :
                    ( ( mrel @ X1 @ X3 )
                   => ( ! [X4: mworld] :
                          ( ( mrel @ X3 @ X4 )
                         => ( big_p @ eigen__13 @ X4 ) )
                     => ( ~ ! [X4: mworld] :
                              ( ( mrel @ X3 @ X4 )
                             => ( big_q @ eigen__13 @ X4 ) )
                       => ! [X4: mworld] :
                            ( ( mrel @ X3 @ X4 )
                           => ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( mrel @ eigen__19 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( ( mrel @ mactual @ eigen__17 )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( ! [X1: mworld] :
          ( ( mrel @ eigen__14 @ X1 )
         => ( big_p @ eigen__11 @ X1 ) )
     => ( ~ ! [X1: mworld] :
              ( ( mrel @ eigen__14 @ X1 )
             => ( big_q @ eigen__11 @ X1 ) )
       => sP8 ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( sP9
     => ~ sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( ( mrel @ mactual @ eigen__12 )
     => sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ! [X1: mworld] :
        ( ( mrel @ mactual @ X1 )
       => ! [X2: $i] :
            ( ( eiw_di @ X2 @ X1 )
           => ! [X3: mworld] :
                ( ( mrel @ X1 @ X3 )
               => ( ! [X4: mworld] :
                      ( ( mrel @ X3 @ X4 )
                     => ( big_p @ eigen__13 @ X4 ) )
                 => ( ~ ! [X4: mworld] :
                          ( ( mrel @ X3 @ X4 )
                         => ( big_q @ eigen__13 @ X4 ) )
                   => ! [X4: mworld] :
                        ( ( mrel @ X3 @ X4 )
                       => ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: mworld,X2: $i] :
        ( ~ ( ( eiw_di @ X2 @ eigen__12 )
           => ~ ( mrel @ eigen__12 @ X1 ) )
       => ( eiw_di @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ! [X1: mworld,X2: $i] :
        ( ~ ( ( eiw_di @ X2 @ eigen__1 )
           => ~ ( mrel @ eigen__1 @ X1 ) )
       => ( eiw_di @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( ( eiw_di @ eigen__11 @ eigen__1 )
     => ~ sP15 ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( ( eiw_di @ eigen__11 @ mactual )
     => ~ ! [X1: mworld] :
            ( ( mrel @ mactual @ X1 )
           => ! [X2: $i] :
                ( ( eiw_di @ X2 @ X1 )
               => ! [X3: mworld] :
                    ( ( mrel @ X1 @ X3 )
                   => ( ! [X4: mworld] :
                          ( ( mrel @ X3 @ X4 )
                         => ( big_p @ eigen__11 @ X4 ) )
                     => ( ~ ! [X4: mworld] :
                              ( ( mrel @ X3 @ X4 )
                             => ( big_q @ eigen__11 @ X4 ) )
                       => ! [X4: mworld] :
                            ( ( mrel @ X3 @ X4 )
                           => ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ! [X1: mworld,X2: mworld,X3: $i] :
        ( ~ ( ( eiw_di @ X3 @ X1 )
           => ~ ( mrel @ X1 @ X2 ) )
       => ( eiw_di @ X3 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ! [X1: mworld] :
        ( ( mrel @ eigen__19 @ X1 )
       => ( big_p @ eigen__13 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ! [X1: mworld] : ( !! @ ( mrel @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: mworld] :
        ( ( mrel @ eigen__12 @ X1 )
       => ( ! [X2: mworld] :
              ( ( mrel @ X1 @ X2 )
             => ( big_p @ eigen__11 @ X2 ) )
         => ( ~ ! [X2: mworld] :
                  ( ( mrel @ X1 @ X2 )
                 => ( big_q @ eigen__11 @ X2 ) )
           => ! [X2: mworld] :
                ( ( mrel @ X1 @ X2 )
               => ( big_p @ eigen__13 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( sP32
     => ( ~ ! [X1: mworld] :
              ( ( mrel @ eigen__19 @ X1 )
             => ( big_q @ eigen__13 @ X1 ) )
       => ! [X1: mworld] :
            ( ( mrel @ eigen__19 @ X1 )
           => ( big_p @ eigen__18 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( ( mrel @ eigen__12 @ eigen__14 )
     => sP23 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ! [X1: $i] :
        ~ ( eiw_di @ X1 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ! [X1: $i] :
        ( ~ ( ( eiw_di @ X1 @ eigen__12 )
           => ~ sP6 )
       => ( eiw_di @ X1 @ mactual ) ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( ~ sP24
     => ( eiw_di @ eigen__13 @ mactual ) ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ! [X1: mworld] :
        ( ( mrel @ mactual @ X1 )
       => ! [X2: $i] :
            ( ( eiw_di @ X2 @ X1 )
           => ! [X3: mworld] :
                ( ( mrel @ X1 @ X3 )
               => ( ! [X4: mworld] :
                      ( ( mrel @ X3 @ X4 )
                     => ( big_p @ eigen__11 @ X4 ) )
                 => ( ~ ! [X4: mworld] :
                          ( ( mrel @ X3 @ X4 )
                         => ( big_q @ eigen__11 @ X4 ) )
                   => ! [X4: mworld] :
                        ( ( mrel @ X3 @ X4 )
                       => ( big_p @ X2 @ X4 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ( ~ ! [X1: mworld] :
            ( ( mrel @ eigen__14 @ X1 )
           => ( big_q @ eigen__11 @ X1 ) )
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ( eiw_di @ eigen__13 @ mactual ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ! [X1: $i] :
        ( ( eiw_di @ X1 @ mactual )
       => ~ ! [X2: mworld] :
              ( ( mrel @ mactual @ X2 )
             => ! [X3: $i] :
                  ( ( eiw_di @ X3 @ X2 )
                 => ! [X4: mworld] :
                      ( ( mrel @ X2 @ X4 )
                     => ( ! [X5: mworld] :
                            ( ( mrel @ X4 @ X5 )
                           => ( big_p @ X1 @ X5 ) )
                       => ( ~ ! [X5: mworld] :
                                ( ( mrel @ X4 @ X5 )
                               => ( big_q @ X1 @ X5 ) )
                         => ! [X5: mworld] :
                              ( ( mrel @ X4 @ X5 )
                             => ( big_p @ X3 @ X5 ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ( eiw_di @ eigen__11 @ mactual ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ( eiw_di @ eigen__11 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

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] :
          ( ( eiw_di @ X3 @ X2 )
         => ( X1 @ X3 @ X2 ) ) ) ) ).

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

thf(x2137,conjecture,
    ~ sP43 ).

thf(h2,negated_conjecture,
    sP43,
    inference(assume_negation,[status(cth)],[x2137]) ).

thf(1,plain,
    ( ~ sP11
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP33
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP12
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP32
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP19
    | ~ sP21
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP35
    | sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP4
    | ~ sP35 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP3
    | ~ sP4 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__19]) ).

thf(9,plain,
    ( sP5
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP2
    | ~ sP5 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__18]) ).

thf(11,plain,
    ( sP22
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP26
    | ~ sP22 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__17]) ).

thf(13,plain,
    ( ~ sP43
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP20
    | ~ sP42
    | ~ sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP38
    | sP39 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP39
    | sP24
    | sP42 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP24
    | ~ sP9
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP27
    | sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP31
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP33
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP18
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( sP7
    | ~ sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( sP8
    | ~ sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__15]) ).

thf(24,plain,
    ( sP41
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( sP23
    | ~ sP41 ),
    inference(prop_rule,[status(thm)],]) ).

thf(26,plain,
    ( sP36
    | ~ sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( sP34
    | ~ sP36 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__14]) ).

thf(28,plain,
    ( sP10
    | ~ sP34 ),
    inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
    ( sP10
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(30,plain,
    ( sP13
    | ~ sP10 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).

thf(31,plain,
    ( sP25
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
    ( sP40
    | ~ sP25 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).

thf(33,plain,
    ( ~ sP43
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP30
    | ~ sP44
    | ~ sP40 ),
    inference(prop_rule,[status(thm)],]) ).

thf(35,plain,
    ( ~ sP14
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP17
    | sP29
    | sP44 ),
    inference(prop_rule,[status(thm)],]) ).

thf(37,plain,
    ( ~ sP29
    | ~ sP45
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(38,plain,
    ( sP37
    | sP45 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__11]) ).

thf(39,plain,
    ( ~ sP28
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(40,plain,
    ( ~ sP31
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(41,plain,
    ( ~ sP1
    | ~ sP37 ),
    inference(all_rule,[status(thm)],]) ).

thf(42,plain,
    ( ~ sP33
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(eiw_di_cumul,axiom,
    sP31 ).

thf(eiw_di_nonempty,axiom,
    sP1 ).

thf(mrel_universal,axiom,
    sP33 ).

thf(43,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,h2,eiw_di_cumul,eiw_di_nonempty,mrel_universal]) ).

thf(44,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[43,h1]) ).

thf(45,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[44,h0]) ).

thf(0,theorem,
    ~ sP43,
    inference(contra,[status(thm),contra(discharge,[h2])],[43,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : LCL958^18 : TPTP v8.1.0. Released v8.1.0.
% 0.04/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n011.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  : 600
% 0.13/0.34  % DateTime : Mon Jul  4 23:56:52 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 25.83/26.14  % SZS status Theorem
% 25.83/26.14  % Mode: mode461
% 25.83/26.14  % Inferences: 2016
% 25.83/26.14  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------