TSTP Solution File: SYN367^7 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYN367^7 : 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 : n031.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 : Fri Sep  1 03:20:40 EDT 2023

% Result   : Theorem 0.60s 0.79s
% Output   : Proof 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :  185
% Syntax   : Number of formulae    :  209 (  73 unt;  16 typ;  34 def)
%            Number of atoms       :  630 (  38 equ;   5 cnn)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives : 1210 ( 177   ~;  70   |;   8   &; 647   @)
%                                         (  58 <=>; 250  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   70 (  70   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  111 ( 107 usr; 105 con; 0-2 aty)
%            Number of variables   :  269 (  69   ^; 194   !;   6   ?; 269   :)

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

thf(ty_eigen__3,type,
    eigen__3: mu ).

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

thf(ty_eigen__6,type,
    eigen__6: mu ).

thf(ty_eigen__2,type,
    eigen__2: $i ).

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

thf(ty_p,type,
    p: $i > $o ).

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

thf(ty_eigen__7,type,
    eigen__7: $i ).

thf(ty_rel_s4,type,
    rel_s4: $i > $i > $o ).

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

thf(ty_eigen__15,type,
    eigen__15: $i ).

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

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

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

thf(ty_eigen__12,type,
    eigen__12: mu ).

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

thf(eigendef_eigen__15,definition,
    ( eigen__15
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( rel_s4 @ eigen__4 @ X1 )
           => ( p @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__15])]) ).

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

thf(eigendef_eigen__12,definition,
    ( eigen__12
    = ( eps__1
      @ ^ [X1: mu] :
          ~ ~ ( exists_in_world @ X1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__12])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i] : ( rel_s4 @ X1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( exists_in_world @ eigen__6 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ( rel_s4 @ eigen__2 @ X1 )
       => ~ ! [X2: $i] :
              ( ( rel_s4 @ X1 @ X2 )
             => ( p @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__2 )
       => ( ( ! [X2: $i] :
                ( ( rel_s4 @ eigen__2 @ X2 )
               => ( p @ X2 ) )
           => ~ ! [X2: $i] :
                  ( ( rel_s4 @ eigen__2 @ X2 )
                 => ( big_q @ X1 @ X2 ) ) )
         => ~ ( sP3
             => ~ ! [X2: $i] :
                    ( ( rel_s4 @ eigen__2 @ X2 )
                   => ( big_r @ X1 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( rel_s4 @ eigen__2 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( rel_s4 @ eigen__1 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( exists_in_world @ eigen__12 @ eigen__1 )
     => ( ( ! [X1: $i] :
              ( ( rel_s4 @ eigen__1 @ X1 )
             => ( p @ X1 ) )
         => ~ ! [X1: $i] :
                ( ( rel_s4 @ eigen__1 @ X1 )
               => ( big_q @ eigen__12 @ X1 ) ) )
       => ~ ( ! [X1: $i] :
                ( ( rel_s4 @ eigen__1 @ X1 )
               => ~ ! [X2: $i] :
                      ( ( rel_s4 @ X1 @ X2 )
                     => ( p @ X2 ) ) )
           => ~ ! [X1: $i] :
                  ( ( rel_s4 @ eigen__1 @ X1 )
                 => ( big_r @ eigen__12 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( rel_s4 @ eigen__1 @ eigen__2 )
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( big_r @ eigen__6 @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i] :
        ( ( rel_s4 @ eigen__1 @ X1 )
       => ~ ! [X2: $i] :
              ( ( rel_s4 @ X1 @ X2 )
             => ( p @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: mu] :
        ~ ( exists_in_world @ X1 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( rel_s4 @ eigen__1 @ X1 )
           => ~ ( rel_s4 @ X1 @ X2 ) )
       => ( rel_s4 @ eigen__1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( sP5
     => ~ ! [X1: $i] :
            ( ( rel_s4 @ eigen__4 @ X1 )
           => ( p @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i] :
        ( ( rel_s4 @ eigen__5 @ X1 )
       => ( big_r @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i] :
        ( ( rel_s4 @ eigen__5 @ X1 )
       => ( p @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ( ! [X1: $i] :
            ( ( rel_s4 @ eigen__2 @ X1 )
           => ( p @ X1 ) )
       => ~ ! [X1: $i] :
              ( ( rel_s4 @ eigen__2 @ X1 )
             => ( big_q @ eigen__3 @ X1 ) ) )
     => ~ ( sP3
         => ~ ! [X1: $i] :
                ( ( rel_s4 @ eigen__2 @ X1 )
               => ( big_r @ eigen__3 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( sP5
     => ( big_q @ eigen__3 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( ( rel_s4 @ eigen__5 @ eigen__7 )
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( ~ ( sP5
         => ~ ( rel_s4 @ eigen__4 @ eigen__15 ) )
     => ( rel_s4 @ eigen__2 @ eigen__15 ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( rel_s4 @ eigen__5 @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i] :
        ( ~ ( ( rel_s4 @ eigen__1 @ eigen__2 )
           => ~ ( rel_s4 @ eigen__2 @ X1 ) )
       => ( rel_s4 @ eigen__1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ! [X1: $i] :
        ( ~ ( sP5
           => ~ ( rel_s4 @ eigen__4 @ X1 ) )
       => ( rel_s4 @ eigen__2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( sP10
     => ~ ! [X1: $i] :
            ( ( rel_s4 @ eigen__1 @ X1 )
           => ( big_r @ eigen__12 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( rel_s4 @ eigen__2 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( sP6
     => ! [X1: mu] :
          ( ( exists_in_world @ X1 @ eigen__1 )
         => ( ( ! [X2: $i] :
                  ( ( rel_s4 @ eigen__1 @ X2 )
                 => ( p @ X2 ) )
             => ~ ! [X2: $i] :
                    ( ( rel_s4 @ eigen__1 @ X2 )
                   => ( big_q @ X1 @ X2 ) ) )
           => ~ ( sP10
               => ~ ! [X2: $i] :
                      ( ( rel_s4 @ eigen__1 @ X2 )
                     => ( big_r @ X1 @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( rel_s4 @ eigen__1 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( rel_s4 @ eigen__4 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ! [X1: $i] :
        ( ( rel_s4 @ eigen__1 @ X1 )
       => ! [X2: mu] :
            ( ( exists_in_world @ X2 @ X1 )
           => ( ( ! [X3: $i] :
                    ( ( rel_s4 @ X1 @ X3 )
                   => ( p @ X3 ) )
               => ~ ! [X3: $i] :
                      ( ( rel_s4 @ X1 @ X3 )
                     => ( big_q @ X2 @ X3 ) ) )
             => ~ ( ! [X3: $i] :
                      ( ( rel_s4 @ X1 @ X3 )
                     => ~ ! [X4: $i] :
                            ( ( rel_s4 @ X3 @ X4 )
                           => ( p @ X4 ) ) )
                 => ~ ! [X3: $i] :
                        ( ( rel_s4 @ X1 @ X3 )
                       => ( big_r @ X2 @ X3 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ! [X1: $i] :
        ( ( rel_s4 @ eigen__2 @ X1 )
       => ( big_q @ eigen__3 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( big_q @ eigen__3 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( exists_in_world @ eigen__3 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( ! [X1: $i] :
          ( ( rel_s4 @ eigen__5 @ X1 )
         => ~ ! [X2: $i] :
                ( ( rel_s4 @ X1 @ X2 )
               => ( p @ X2 ) ) )
     => ~ sP14 ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( ( rel_s4 @ eigen__1 @ eigen__5 )
     => ! [X1: mu] :
          ( ( exists_in_world @ X1 @ eigen__5 )
         => ( ( sP15
             => ~ ! [X2: $i] :
                    ( ( rel_s4 @ eigen__5 @ X2 )
                   => ( big_q @ X1 @ X2 ) ) )
           => ~ ( ! [X2: $i] :
                    ( ( rel_s4 @ eigen__5 @ X2 )
                   => ~ ! [X3: $i] :
                          ( ( rel_s4 @ X2 @ X3 )
                         => ( p @ X3 ) ) )
               => ~ ! [X2: $i] :
                      ( ( rel_s4 @ eigen__5 @ X2 )
                     => ( big_r @ X1 @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ( exists_in_world @ eigen__12 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( rel_s4 @ X1 @ X2 )
           => ~ ( rel_s4 @ X2 @ X3 ) )
       => ( rel_s4 @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ! [X1: $i] :
        ~ ! [X2: mu] :
            ~ ( exists_in_world @ X2 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ( sP27
     => ( p @ eigen__15 ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(sP38,plain,
    ( sP38
  <=> ( ~ ( ( rel_s4 @ eigen__1 @ eigen__2 )
         => ~ sP24 )
     => sP26 ) ),
    introduced(definition,[new_symbols(definition,[sP38])]) ).

thf(sP39,plain,
    ( sP39
  <=> ( ( rel_s4 @ eigen__1 @ eigen__2 )
     => ~ sP24 ) ),
    introduced(definition,[new_symbols(definition,[sP39])]) ).

thf(sP40,plain,
    ( sP40
  <=> ( rel_s4 @ eigen__1 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP40])]) ).

thf(sP41,plain,
    ( sP41
  <=> ! [X1: $i] :
        ( ( rel_s4 @ eigen__1 @ X1 )
       => ( p @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP41])]) ).

thf(sP42,plain,
    ( sP42
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__5 )
       => ( ( sP15
           => ~ ! [X2: $i] :
                  ( ( rel_s4 @ eigen__5 @ X2 )
                 => ( big_q @ X1 @ X2 ) ) )
         => ~ ( ! [X2: $i] :
                  ( ( rel_s4 @ eigen__5 @ X2 )
                 => ~ ! [X3: $i] :
                        ( ( rel_s4 @ X2 @ X3 )
                       => ( p @ X3 ) ) )
             => ~ ! [X2: $i] :
                    ( ( rel_s4 @ eigen__5 @ X2 )
                   => ( big_r @ X1 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP42])]) ).

thf(sP43,plain,
    ( sP43
  <=> ( rel_s4 @ eigen__1 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP43])]) ).

thf(sP44,plain,
    ( sP44
  <=> ( ! [X1: $i] :
          ( ( rel_s4 @ eigen__2 @ X1 )
         => ( p @ X1 ) )
     => ~ sP29 ) ),
    introduced(definition,[new_symbols(definition,[sP44])]) ).

thf(sP45,plain,
    ( sP45
  <=> ( sP40
     => ~ sP15 ) ),
    introduced(definition,[new_symbols(definition,[sP45])]) ).

thf(sP46,plain,
    ( sP46
  <=> ( sP26
     => ( p @ eigen__15 ) ) ),
    introduced(definition,[new_symbols(definition,[sP46])]) ).

thf(sP47,plain,
    ( sP47
  <=> ( sP31
     => sP16 ) ),
    introduced(definition,[new_symbols(definition,[sP47])]) ).

thf(sP48,plain,
    ( sP48
  <=> ( sP3
     => ~ ! [X1: $i] :
            ( ( rel_s4 @ eigen__2 @ X1 )
           => ( big_r @ eigen__3 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP48])]) ).

thf(sP49,plain,
    ( sP49
  <=> ( sP2
     => ( ( sP15
         => ~ ! [X1: $i] :
                ( ( rel_s4 @ eigen__5 @ X1 )
               => ( big_q @ eigen__6 @ X1 ) ) )
       => ~ sP32 ) ) ),
    introduced(definition,[new_symbols(definition,[sP49])]) ).

thf(sP50,plain,
    ( sP50
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__1 )
       => ( ( sP41
           => ~ ! [X2: $i] :
                  ( ( rel_s4 @ eigen__1 @ X2 )
                 => ( big_q @ X1 @ X2 ) ) )
         => ~ ( sP10
             => ~ ! [X2: $i] :
                    ( ( rel_s4 @ eigen__1 @ X2 )
                   => ( big_r @ X1 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP50])]) ).

thf(sP51,plain,
    ( sP51
  <=> ( ( sP15
       => ~ ! [X1: $i] :
              ( ( rel_s4 @ eigen__5 @ X1 )
             => ( big_q @ eigen__6 @ X1 ) ) )
     => ~ sP32 ) ),
    introduced(definition,[new_symbols(definition,[sP51])]) ).

thf(sP52,plain,
    ( sP52
  <=> ( ( sP41
       => ~ ! [X1: $i] :
              ( ( rel_s4 @ eigen__1 @ X1 )
             => ( big_q @ eigen__12 @ X1 ) ) )
     => ~ sP23 ) ),
    introduced(definition,[new_symbols(definition,[sP52])]) ).

thf(sP53,plain,
    ( sP53
  <=> ( sP41
     => ~ ! [X1: $i] :
            ( ( rel_s4 @ eigen__1 @ X1 )
           => ( big_q @ eigen__12 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP53])]) ).

thf(sP54,plain,
    ( sP54
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( rel_s4 @ eigen__2 @ X1 )
           => ~ ( rel_s4 @ X1 @ X2 ) )
       => ( rel_s4 @ eigen__2 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP54])]) ).

thf(sP55,plain,
    ( sP55
  <=> ( sP5
     => ~ sP27 ) ),
    introduced(definition,[new_symbols(definition,[sP55])]) ).

thf(sP56,plain,
    ( sP56
  <=> ( sP15
     => ~ ! [X1: $i] :
            ( ( rel_s4 @ eigen__5 @ X1 )
           => ( big_q @ eigen__6 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP56])]) ).

thf(sP57,plain,
    ( sP57
  <=> ( p @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP57])]) ).

thf(sP58,plain,
    ( sP58
  <=> ! [X1: $i] :
        ( ( rel_s4 @ eigen__4 @ X1 )
       => ( p @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP58])]) ).

thf(def_meq_prop,definition,
    ( meq_prop
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X1 @ X3 )
          = ( X2 @ X3 ) ) ) ) ).

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_mbox,definition,
    ( mbox
    = ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
        ! [X4: $i] :
          ( ( (~) @ ( X1 @ X3 @ X4 ) )
          | ( X2 @ X4 ) ) ) ) ).

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

thf(def_mtrue,definition,
    ( mtrue
    = ( ^ [X1: $i] : $true ) ) ).

thf(def_mfalse,definition,
    ( mfalse
    = ( mnot @ mtrue ) ) ).

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_mimplied,definition,
    ( mimplied
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X2 ) @ X1 ) ) ) ).

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

thf(def_mxor,definition,
    ( mxor
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).

thf(def_mdia,definition,
    ( mdia
    = ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).

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_mexists_ind,definition,
    ( mexists_ind
    = ( ^ [X1: mu > $i > $o] :
          ( mnot
          @ ( mforall_ind
            @ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).

thf(def_mexists_prop,definition,
    ( mexists_prop
    = ( ^ [X1: ( $i > $o ) > $i > $o] :
          ( mnot
          @ ( mforall_prop
            @ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).

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

thf(def_msymmetric,definition,
    ( msymmetric
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( X1 @ X2 @ X3 )
          @ ( X1 @ X3 @ X2 ) ) ) ) ).

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

thf(def_mtransitive,definition,
    ( mtransitive
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X3 @ X4 ) )
          @ ( X1 @ X2 @ X4 ) ) ) ) ).

thf(def_meuclidean,definition,
    ( meuclidean
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X2 @ X4 ) )
          @ ( X1 @ X3 @ X4 ) ) ) ) ).

thf(def_mpartially_functional,definition,
    ( mpartially_functional
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X2 @ X4 ) )
          @ ( X3 = X4 ) ) ) ) ).

thf(def_mfunctional,definition,
    ( mfunctional
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i] :
        ? [X3: $i] :
          ( ( X1 @ X2 @ X3 )
          & ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( X1 @ X2 @ X4 )
              @ ( X3 = X4 ) ) ) ) ) ).

thf(def_mweakly_dense,definition,
    ( mweakly_dense
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( X1 @ X2 @ X3 )
          @ ? [X5: $i] :
              ( ( X1 @ X2 @ X5 )
              & ( X1 @ X5 @ X3 ) ) ) ) ) ).

thf(def_mweakly_connected,definition,
    ( mweakly_connected
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X2 @ X4 ) )
          @ ( ( X1 @ X3 @ X4 )
            | ( X3 = X4 )
            | ( X1 @ X4 @ X3 ) ) ) ) ) ).

thf(def_mweakly_directed,definition,
    ( mweakly_directed
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X2 @ X4 ) )
          @ ? [X5: $i] :
              ( ( X1 @ X3 @ X5 )
              & ( X1 @ X4 @ X5 ) ) ) ) ) ).

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

thf(def_msatisfiable,definition,
    ( msatisfiable
    = ( ^ [X1: $i > $o] :
        ? [X2: $i] : ( X1 @ X2 ) ) ) ).

thf(def_mcountersatisfiable,definition,
    ( mcountersatisfiable
    = ( ^ [X1: $i > $o] :
        ? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).

thf(def_minvalid,definition,
    ( minvalid
    = ( ^ [X1: $i > $o] :
        ! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).

thf(def_mbox_s4,definition,
    ( mbox_s4
    = ( ^ [X1: $i > $o,X2: $i] :
        ! [X3: $i] :
          ( ( (~) @ ( rel_s4 @ X2 @ X3 ) )
          | ( X1 @ X3 ) ) ) ) ).

thf(def_mdia_s4,definition,
    ( mdia_s4
    = ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X1 ) ) ) ) ) ).

thf(x2118,conjecture,
    ! [X1: $i,X2: $i] :
      ( ( rel_s4 @ X1 @ X2 )
     => ( ! [X3: $i] :
            ( ( rel_s4 @ X2 @ X3 )
           => ! [X4: mu] :
                ( ( exists_in_world @ X4 @ X3 )
               => ( ( ! [X5: $i] :
                        ( ( rel_s4 @ X3 @ X5 )
                       => ( p @ X5 ) )
                   => ~ ! [X5: $i] :
                          ( ( rel_s4 @ X3 @ X5 )
                         => ( big_q @ X4 @ X5 ) ) )
                 => ~ ( ! [X5: $i] :
                          ( ( rel_s4 @ X3 @ X5 )
                         => ~ ! [X6: $i] :
                                ( ( rel_s4 @ X5 @ X6 )
                               => ( p @ X6 ) ) )
                     => ~ ! [X5: $i] :
                            ( ( rel_s4 @ X3 @ X5 )
                           => ( big_r @ X4 @ X5 ) ) ) ) ) )
       => ( ~ ! [X3: $i] :
                ( ( rel_s4 @ X2 @ X3 )
               => ! [X4: mu] :
                    ( ( exists_in_world @ X4 @ X3 )
                   => ! [X5: $i] :
                        ( ( rel_s4 @ X3 @ X5 )
                       => ( big_q @ X4 @ X5 ) ) ) )
         => ! [X3: $i] :
              ( ( rel_s4 @ X2 @ X3 )
             => ! [X4: mu] :
                  ( ( exists_in_world @ X4 @ X3 )
                 => ! [X5: $i] :
                      ( ( rel_s4 @ X3 @ X5 )
                     => ( big_r @ X4 @ X5 ) ) ) ) ) ) ) ).

thf(h2,negated_conjecture,
    ~ ! [X1: $i,X2: $i] :
        ( ( rel_s4 @ X1 @ X2 )
       => ( ! [X3: $i] :
              ( ( rel_s4 @ X2 @ X3 )
             => ! [X4: mu] :
                  ( ( exists_in_world @ X4 @ X3 )
                 => ( ( ! [X5: $i] :
                          ( ( rel_s4 @ X3 @ X5 )
                         => ( p @ X5 ) )
                     => ~ ! [X5: $i] :
                            ( ( rel_s4 @ X3 @ X5 )
                           => ( big_q @ X4 @ X5 ) ) )
                   => ~ ( ! [X5: $i] :
                            ( ( rel_s4 @ X3 @ X5 )
                           => ~ ! [X6: $i] :
                                  ( ( rel_s4 @ X5 @ X6 )
                                 => ( p @ X6 ) ) )
                       => ~ ! [X5: $i] :
                              ( ( rel_s4 @ X3 @ X5 )
                             => ( big_r @ X4 @ X5 ) ) ) ) ) )
         => ( ~ ! [X3: $i] :
                  ( ( rel_s4 @ X2 @ X3 )
                 => ! [X4: mu] :
                      ( ( exists_in_world @ X4 @ X3 )
                     => ! [X5: $i] :
                          ( ( rel_s4 @ X3 @ X5 )
                         => ( big_q @ X4 @ X5 ) ) ) )
           => ! [X3: $i] :
                ( ( rel_s4 @ X2 @ X3 )
               => ! [X4: mu] :
                    ( ( exists_in_world @ X4 @ X3 )
                   => ! [X5: $i] :
                        ( ( rel_s4 @ X3 @ X5 )
                       => ( big_r @ X4 @ X5 ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[x2118]) ).

thf(h3,assumption,
    ~ ! [X1: $i] :
        ( ( rel_s4 @ eigen__0 @ X1 )
       => ( ! [X2: $i] :
              ( ( rel_s4 @ X1 @ X2 )
             => ! [X3: mu] :
                  ( ( exists_in_world @ X3 @ X2 )
                 => ( ( ! [X4: $i] :
                          ( ( rel_s4 @ X2 @ X4 )
                         => ( p @ X4 ) )
                     => ~ ! [X4: $i] :
                            ( ( rel_s4 @ X2 @ X4 )
                           => ( big_q @ X3 @ X4 ) ) )
                   => ~ ( ! [X4: $i] :
                            ( ( rel_s4 @ X2 @ X4 )
                           => ~ ! [X5: $i] :
                                  ( ( rel_s4 @ X4 @ X5 )
                                 => ( p @ X5 ) ) )
                       => ~ ! [X4: $i] :
                              ( ( rel_s4 @ X2 @ X4 )
                             => ( big_r @ X3 @ X4 ) ) ) ) ) )
         => ( ~ ! [X2: $i] :
                  ( ( rel_s4 @ X1 @ X2 )
                 => ! [X3: mu] :
                      ( ( exists_in_world @ X3 @ X2 )
                     => ! [X4: $i] :
                          ( ( rel_s4 @ X2 @ X4 )
                         => ( big_q @ X3 @ X4 ) ) ) )
           => ! [X2: $i] :
                ( ( rel_s4 @ X1 @ X2 )
               => ! [X3: mu] :
                    ( ( exists_in_world @ X3 @ X2 )
                   => ! [X4: $i] :
                        ( ( rel_s4 @ X2 @ X4 )
                       => ( big_r @ X3 @ X4 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( ( rel_s4 @ eigen__0 @ eigen__1 )
     => ( sP28
       => ( ~ ! [X1: $i] :
                ( ( rel_s4 @ eigen__1 @ X1 )
               => ! [X2: mu] :
                    ( ( exists_in_world @ X2 @ X1 )
                   => ! [X3: $i] :
                        ( ( rel_s4 @ X1 @ X3 )
                       => ( big_q @ X2 @ X3 ) ) ) )
         => ! [X1: $i] :
              ( ( rel_s4 @ eigen__1 @ X1 )
             => ! [X2: mu] :
                  ( ( exists_in_world @ X2 @ X1 )
                 => ! [X3: $i] :
                      ( ( rel_s4 @ X1 @ X3 )
                     => ( big_r @ X2 @ X3 ) ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    rel_s4 @ eigen__0 @ eigen__1,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( sP28
     => ( ~ ! [X1: $i] :
              ( ( rel_s4 @ eigen__1 @ X1 )
             => ! [X2: mu] :
                  ( ( exists_in_world @ X2 @ X1 )
                 => ! [X3: $i] :
                      ( ( rel_s4 @ X1 @ X3 )
                     => ( big_q @ X2 @ X3 ) ) ) )
       => ! [X1: $i] :
            ( ( rel_s4 @ eigen__1 @ X1 )
           => ! [X2: mu] :
                ( ( exists_in_world @ X2 @ X1 )
               => ! [X3: $i] :
                    ( ( rel_s4 @ X1 @ X3 )
                   => ( big_r @ X2 @ X3 ) ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP28,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( ~ ! [X1: $i] :
            ( ( rel_s4 @ eigen__1 @ X1 )
           => ! [X2: mu] :
                ( ( exists_in_world @ X2 @ X1 )
               => ! [X3: $i] :
                    ( ( rel_s4 @ X1 @ X3 )
                   => ( big_q @ X2 @ X3 ) ) ) )
     => ! [X1: $i] :
          ( ( rel_s4 @ eigen__1 @ X1 )
         => ! [X2: mu] :
              ( ( exists_in_world @ X2 @ X1 )
             => ! [X3: $i] :
                  ( ( rel_s4 @ X1 @ X3 )
                 => ( big_r @ X2 @ X3 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ! [X1: $i] :
        ( ( rel_s4 @ eigen__1 @ X1 )
       => ! [X2: mu] :
            ( ( exists_in_world @ X2 @ X1 )
           => ! [X3: $i] :
                ( ( rel_s4 @ X1 @ X3 )
               => ( big_q @ X2 @ X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ ! [X1: $i] :
        ( ( rel_s4 @ eigen__1 @ X1 )
       => ! [X2: mu] :
            ( ( exists_in_world @ X2 @ X1 )
           => ! [X3: $i] :
                ( ( rel_s4 @ X1 @ X3 )
               => ( big_r @ X2 @ X3 ) ) ) ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ ( sP43
     => ! [X1: mu] :
          ( ( exists_in_world @ X1 @ eigen__2 )
         => ! [X2: $i] :
              ( ( rel_s4 @ eigen__2 @ X2 )
             => ( big_q @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP43,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__2 )
       => ! [X2: $i] :
            ( ( rel_s4 @ eigen__2 @ X2 )
           => ( big_q @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ ( sP31
     => sP29 ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    sP31,
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ sP29,
    introduced(assumption,[]) ).

thf(h17,assumption,
    ~ sP17,
    introduced(assumption,[]) ).

thf(h18,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ sP30,
    introduced(assumption,[]) ).

thf(h20,assumption,
    ~ ( sP40
     => ! [X1: mu] :
          ( ( exists_in_world @ X1 @ eigen__5 )
         => ! [X2: $i] :
              ( ( rel_s4 @ eigen__5 @ X2 )
             => ( big_r @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h21,assumption,
    sP40,
    introduced(assumption,[]) ).

thf(h22,assumption,
    ~ ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__5 )
       => ! [X2: $i] :
            ( ( rel_s4 @ eigen__5 @ X2 )
           => ( big_r @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h23,assumption,
    ~ ( sP2
     => sP14 ),
    introduced(assumption,[]) ).

thf(h24,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h25,assumption,
    ~ sP14,
    introduced(assumption,[]) ).

thf(h26,assumption,
    ~ sP18,
    introduced(assumption,[]) ).

thf(h27,assumption,
    sP20,
    introduced(assumption,[]) ).

thf(h28,assumption,
    ~ sP9,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP39
    | ~ sP43
    | ~ sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP38
    | sP39
    | sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP55
    | ~ sP5
    | ~ sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP19
    | sP55
    | sP24 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP46
    | ~ sP26
    | sP57 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP41
    | sP46 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP21
    | sP38 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP22
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP23
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP53
    | sP41 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP52
    | ~ sP53
    | ~ sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP7
    | ~ sP34
    | sP52 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP50
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP13
    | ~ sP5
    | ~ sP58 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP3
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(16,plain,
    ( sP48
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP17
    | ~ sP5
    | sP30 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP29
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP44
    | sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP16
    | ~ sP44
    | ~ sP48 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP47
    | ~ sP31
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP4
    | sP47 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP8
    | ~ sP43
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP54
    | sP22 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP35
    | sP54 ),
    inference(all_rule,[status(thm)],]) ).

thf(26,plain,
    ( ~ sP28
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP12
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( sP37
    | ~ sP57 ),
    inference(prop_rule,[status(thm)],]) ).

thf(29,plain,
    ( sP37
    | sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(30,plain,
    ( sP58
    | ~ sP37 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__15]) ).

thf(31,plain,
    ( ~ sP45
    | ~ sP40
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP10
    | sP45 ),
    inference(all_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP25
    | ~ sP6
    | sP50 ),
    inference(prop_rule,[status(thm)],]) ).

thf(34,plain,
    ( sP11
    | sP34 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__12]) ).

thf(35,plain,
    ( ~ sP1
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(36,plain,
    ( ~ sP36
    | ~ sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(37,plain,
    ( ~ sP35
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(38,plain,
    ( ~ sP28
    | sP25 ),
    inference(all_rule,[status(thm)],]) ).

thf(39,plain,
    ( ~ sP18
    | ~ sP20
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(40,plain,
    ( ~ sP14
    | sP18 ),
    inference(all_rule,[status(thm)],]) ).

thf(41,plain,
    ( sP32
    | sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(42,plain,
    ( sP56
    | sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(43,plain,
    ( ~ sP51
    | ~ sP56
    | ~ sP32 ),
    inference(prop_rule,[status(thm)],]) ).

thf(44,plain,
    ( ~ sP49
    | ~ sP2
    | sP51 ),
    inference(prop_rule,[status(thm)],]) ).

thf(45,plain,
    ( ~ sP42
    | sP49 ),
    inference(all_rule,[status(thm)],]) ).

thf(46,plain,
    ( ~ sP33
    | ~ sP40
    | sP42 ),
    inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
    ( ~ sP28
    | sP33 ),
    inference(all_rule,[status(thm)],]) ).

thf(a2,axiom,
    sP35 ).

thf(a1,axiom,
    sP1 ).

thf(nonempty_ax,axiom,
    sP36 ).

thf(48,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h27,h28,h26,h24,h25,h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,h7,h12,h15,h18,h19,h21,h24,h27,h28,a2,a1,nonempty_ax]) ).

thf(49,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h26,h24,h25,h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h27,h28])],[h26,48,h27,h28]) ).

thf(50,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h24,h25,h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__7)],[h25,49,h26]) ).

thf(51,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h23,h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h24,h25])],[h23,50,h24,h25]) ).

thf(52,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h21,h22,h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h23]),tab_negall(eigenvar,eigen__6)],[h22,51,h23]) ).

thf(53,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h20,h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,52,h21,h22]) ).

thf(54,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h18,h19,h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h10,53,h20]) ).

thf(55,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h17,h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,54,h18,h19]) ).

thf(56,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h16,55,h17]) ).

thf(57,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,56,h15,h16]) ).

thf(58,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h13,57,h14]) ).

thf(59,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,58,h12,h13]) ).

thf(60,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h9,59,h11]) ).

thf(61,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,60,h9,h10]) ).

thf(62,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,61,h7,h8]) ).

thf(63,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,62,h5,h6]) ).

thf(64,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,63,h4]) ).

thf(65,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__0)],[h2,64,h3]) ).

thf(66,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[65,h1]) ).

thf(67,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[66,h0]) ).

thf(0,theorem,
    ! [X1: $i,X2: $i] :
      ( ( rel_s4 @ X1 @ X2 )
     => ( ! [X3: $i] :
            ( ( rel_s4 @ X2 @ X3 )
           => ! [X4: mu] :
                ( ( exists_in_world @ X4 @ X3 )
               => ( ( ! [X5: $i] :
                        ( ( rel_s4 @ X3 @ X5 )
                       => ( p @ X5 ) )
                   => ~ ! [X5: $i] :
                          ( ( rel_s4 @ X3 @ X5 )
                         => ( big_q @ X4 @ X5 ) ) )
                 => ~ ( ! [X5: $i] :
                          ( ( rel_s4 @ X3 @ X5 )
                         => ~ ! [X6: $i] :
                                ( ( rel_s4 @ X5 @ X6 )
                               => ( p @ X6 ) ) )
                     => ~ ! [X5: $i] :
                            ( ( rel_s4 @ X3 @ X5 )
                           => ( big_r @ X4 @ X5 ) ) ) ) ) )
       => ( ~ ! [X3: $i] :
                ( ( rel_s4 @ X2 @ X3 )
               => ! [X4: mu] :
                    ( ( exists_in_world @ X4 @ X3 )
                   => ! [X5: $i] :
                        ( ( rel_s4 @ X3 @ X5 )
                       => ( big_q @ X4 @ X5 ) ) ) )
         => ! [X3: $i] :
              ( ( rel_s4 @ X2 @ X3 )
             => ! [X4: mu] :
                  ( ( exists_in_world @ X4 @ X3 )
                 => ! [X5: $i] :
                      ( ( rel_s4 @ X3 @ X5 )
                     => ( big_r @ X4 @ X5 ) ) ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h2])],[65,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : SYN367^7 : TPTP v8.1.2. Released v5.5.0.
% 0.13/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n031.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sat Aug 26 19:05:53 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.60/0.79  % SZS status Theorem
% 0.60/0.79  % Mode: cade22grackle2xfee4
% 0.60/0.79  % Steps: 5441
% 0.60/0.79  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------