TSTP Solution File: LCL865^1 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : LCL865^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n008.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 14:11:42 EDT 2022

% Result   : Theorem 1.59s 1.76s
% Output   : Proof 1.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :  145
% Syntax   : Number of formulae    :  179 (  94 unt;  12 typ;  32 def)
%            Number of atoms       :  352 (  41 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  610 ( 174   ~;  37   |;   0   &; 271   @)
%                                         (  37 <=>;  89  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   64 (  64   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   85 (  82 usr;  83 con; 0-2 aty)
%                                         (   2  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  143 (  48   ^  95   !;   0   ?; 143   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__14,type,
    eigen__14: $i ).

thf(ty_eigen__6,type,
    eigen__6: $i ).

thf(ty_eigen__12,type,
    eigen__12: $i ).

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

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

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

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

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

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

thf(ty_eigen__3,type,
    eigen__3: $i ).

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

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

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

thf(eigendef_eigen__12,definition,
    ( eigen__12
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ( eigen__0 @ eigen__8 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__12])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( eigen__0 @ X1 @ X2 )
           => ~ ( eigen__0 @ X1 @ X3 ) )
       => ( eigen__0 @ X2 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( ~ ( ( eigen__0 @ eigen__3 @ eigen__4 )
           => ~ ( eigen__0 @ eigen__3 @ X1 ) )
       => ( eigen__0 @ eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( eigen__0 @ eigen__5 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i] :
        ~ ( eigen__0 @ eigen__8 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( eigen__0 @ eigen__12 @ X1 )
           => ~ ( eigen__0 @ eigen__12 @ X2 ) )
       => ( eigen__0 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( eigen__0 @ eigen__3 @ eigen__4 )
     => ~ ( eigen__0 @ eigen__3 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__0 @ eigen__6 @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ~ ( sP3
         => ~ ( eigen__0 @ eigen__5 @ eigen__7 ) )
     => sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eigen__0 @ eigen__13 @ eigen__14 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i] :
        ( ( eigen__0 @ eigen__8 @ X1 )
       => ( eigen__0 @ X1 @ eigen__8 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ~ sP6
     => ( eigen__0 @ eigen__4 @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( eigen__0 @ eigen__8 @ eigen__8 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: $i] :
        ( ~ ( ( eigen__0 @ eigen__12 @ eigen__8 )
           => ~ ( eigen__0 @ eigen__12 @ X1 ) )
       => ( eigen__0 @ eigen__8 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( eigen__0 @ eigen__5 @ X1 )
           => ~ ( eigen__0 @ eigen__5 @ X2 ) )
       => ( eigen__0 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

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

thf(sP16,plain,
    ( sP16
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( eigen__0 @ eigen__13 @ X1 )
           => ~ ( eigen__0 @ eigen__13 @ X2 ) )
       => ( eigen__0 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ( eigen__0 @ eigen__12 @ eigen__8 )
     => ~ ( eigen__0 @ eigen__12 @ eigen__8 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( eigen__0 @ eigen__13 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ! [X1: $i] :
        ~ ! [X2: $i] :
            ~ ( eigen__0 @ X1 @ X2 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( eigen__0 @ eigen__3 @ X1 )
           => ~ ( eigen__0 @ eigen__3 @ X2 ) )
       => ( eigen__0 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( eigen__0 @ eigen__12 @ eigen__8 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ! [X1: $i] : ( eigen__0 @ X1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( eigen__0 @ eigen__1 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ! [X1: $i] :
        ~ ( eigen__0 @ eigen__1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( eigen__0 @ eigen__5 @ eigen__7 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ! [X1: $i] :
        ( ~ ( sP3
           => ~ ( eigen__0 @ eigen__5 @ X1 ) )
       => ( eigen__0 @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( eigen__0 @ eigen__8 @ eigen__12 ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( eigen__0 @ eigen__14 @ eigen__15 ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ( ~ ( sP9
         => ~ sP18 )
     => sP29 ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ( sP9
     => ~ sP18 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( sP28
     => sP22 ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ! [X1: $i,X2: $i] :
        ( ( eigen__0 @ X1 @ X2 )
       => ( eigen__0 @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ( ~ sP17
     => sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(sP35,plain,
    ( sP35
  <=> ( sP3
     => ~ sP26 ) ),
    introduced(definition,[new_symbols(definition,[sP35])]) ).

thf(sP36,plain,
    ( sP36
  <=> ( eigen__0 @ eigen__4 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP36])]) ).

thf(sP37,plain,
    ( sP37
  <=> ! [X1: $i] :
        ( ~ ( sP9
           => ~ ( eigen__0 @ eigen__13 @ X1 ) )
       => ( eigen__0 @ eigen__14 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP37])]) ).

thf(def_meq_ind,definition,
    ( meq_ind
    = ( ^ [X1: mu,X2: mu,X3: $i] : ( X1 = X2 ) ) ) ).

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

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

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_mforall_ind,definition,
    ( mforall_ind
    = ( ^ [X1: mu > $i > $o,X2: $i] :
        ! [X3: mu] : ( X1 @ X3 @ X2 ) ) ) ).

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

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

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

thf(def_mdia,definition,
    ( mdia
    = ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ 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] :
          ( ( 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] :
          ( ~ ( ( X1 @ X2 @ X3 )
             => ~ ( X1 @ X3 @ X4 ) )
         => ( X1 @ X2 @ X4 ) ) ) ) ).

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

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

thf(def_mvalid,definition,
    mvalid = !! ).

thf(def_minvalid,definition,
    ( minvalid
    = ( ^ [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] :
          ~ ( !! @ X1 ) ) ) ).

thf(conj,conjecture,
    ! [X1: $i > $i > $o] :
      ( ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X2 @ X4 ) )
                 => ( X1 @ X3 @ X4 ) ) ) )
      = ( ~ ( ~ ( ! [X2: $i] :
                    ~ ! [X3: $i] :
                        ~ ( X1 @ X2 @ X3 )
               => ~ ! [X2: $i,X3: $i] :
                      ( ( X1 @ X2 @ X3 )
                     => ( X1 @ X3 @ X2 ) ) )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X2 @ X4 ) )
                 => ( X1 @ X3 @ X4 ) ) ) ) ) ).

thf(h1,negated_conjecture,
    ~ ! [X1: $i > $i > $o] :
        ( ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
             => ~ ! [X2: $i,X3: $i,X4: $i] :
                    ( ~ ( ( X1 @ X2 @ X3 )
                       => ~ ( X1 @ X2 @ X4 ) )
                   => ( X1 @ X3 @ X4 ) ) ) )
        = ( ~ ( ~ ( ! [X2: $i] :
                      ~ ! [X3: $i] :
                          ~ ( X1 @ X2 @ X3 )
                 => ~ ! [X2: $i,X3: $i] :
                        ( ( X1 @ X2 @ X3 )
                       => ( X1 @ X3 @ X2 ) ) )
             => ~ ! [X2: $i,X3: $i,X4: $i] :
                    ( ~ ( ( X1 @ X2 @ X3 )
                       => ~ ( X1 @ X2 @ X4 ) )
                   => ( X1 @ X3 @ X4 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[conj]) ).

thf(h2,assumption,
    ( ~ ( sP23
       => ~ sP1 ) )
 != ( ~ ( ~ ( sP20
           => ~ sP33 )
       => ~ sP1 ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP23
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( ~ ( sP20
         => ~ sP33 )
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ( sP23
   => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ( ~ ( sP20
       => ~ sP33 )
   => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP23,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ( sP20
   => ~ sP33 ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ sP20,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP33,
    introduced(assumption,[]) ).

thf(h13,assumption,
    sP25,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP25
    | ~ sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP23
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h13,h11,h9,h7,h8,h3,h4,h2,h1,h0])],[1,2,h7,h13]) ).

thf(4,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h11,h9,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__1)],[h11,3,h13]) ).

thf(h14,assumption,
    ~ ! [X1: $i] :
        ( ( eigen__0 @ eigen__3 @ X1 )
       => ( eigen__0 @ X1 @ eigen__3 ) ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ ( sP19
     => sP36 ),
    introduced(assumption,[]) ).

thf(h16,assumption,
    sP19,
    introduced(assumption,[]) ).

thf(h17,assumption,
    ~ sP36,
    introduced(assumption,[]) ).

thf(5,plain,
    ( ~ sP23
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP1
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP21
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP2
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP11
    | sP6
    | sP36 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP6
    | ~ sP19
    | ~ sP15 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h16,h17,h15,h14,h12,h9,h7,h8,h3,h4,h2,h1,h0])],[5,6,7,8,9,10,h7,h8,h16,h17]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h15,h14,h12,h9,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h16,h17])],[h15,11,h16,h17]) ).

thf(13,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h14,h12,h9,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__4)],[h14,12,h15]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h12,h9,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h12,13,h14]) ).

thf(15,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h9,h7,h8,h3,h4,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h9,4,14,h11,h12]) ).

thf(h18,assumption,
    ~ sP14,
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ sP27,
    introduced(assumption,[]) ).

thf(h20,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(h21,assumption,
    ~ sP35,
    introduced(assumption,[]) ).

thf(h22,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(h23,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h24,assumption,
    sP26,
    introduced(assumption,[]) ).

thf(16,plain,
    ( ~ sP1
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP14
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP27
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP8
    | sP35
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP35
    | ~ sP3
    | ~ sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h23,h24,h21,h22,h20,h19,h18,h10,h7,h8,h3,h4,h2,h1,h0])],[16,17,18,19,20,h8,h23,h24,h22]) ).

thf(22,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h21,h22,h20,h19,h18,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h23,h24])],[h21,21,h23,h24]) ).

thf(23,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h20,h19,h18,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h21,h22])],[h20,22,h21,h22]) ).

thf(24,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h19,h18,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__7)],[h19,23,h20]) ).

thf(25,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h18,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h19]),tab_negall(eigenvar,eigen__6)],[h18,24,h19]) ).

thf(26,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h18]),tab_negall(eigenvar,eigen__5)],[h10,25,h18]) ).

thf(27,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h7,h8,h3,h4,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h4,15,26,h9,h10]) ).

thf(28,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h3,27,h7,h8]) ).

thf(h25,assumption,
    ~ sP23,
    introduced(assumption,[]) ).

thf(h26,assumption,
    ~ sP12,
    introduced(assumption,[]) ).

thf(h27,assumption,
    ~ ( sP20
     => ~ sP33 ),
    introduced(assumption,[]) ).

thf(h28,assumption,
    sP20,
    introduced(assumption,[]) ).

thf(h29,assumption,
    sP33,
    introduced(assumption,[]) ).

thf(29,plain,
    ( ~ sP13
    | sP34 ),
    inference(all_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP34
    | sP17
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP17
    | ~ sP22
    | ~ sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP5
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP1
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP10
    | sP32 ),
    inference(all_rule,[status(thm)],]) ).

thf(35,plain,
    ( ~ sP32
    | ~ sP28
    | sP22 ),
    inference(prop_rule,[status(thm)],]) ).

thf(36,plain,
    ( sP4
    | sP28 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12]) ).

thf(37,plain,
    ( ~ sP20
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(38,plain,
    ( ~ sP33
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(39,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h28,h29,h27,h8,h26,h25,h5,h6,h2,h1,h0])],[29,30,31,32,33,34,35,36,37,38,h26,h28,h29,h8]) ).

thf(40,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h27,h8,h26,h25,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,39,h28,h29]) ).

thf(41,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h26,h25,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h27,h8])],[h6,40,h27,h8]) ).

thf(42,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h25,h5,h6,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__8)],[h25,41,h26]) ).

thf(h30,assumption,
    ~ sP16,
    introduced(assumption,[]) ).

thf(h31,assumption,
    ~ sP37,
    introduced(assumption,[]) ).

thf(h32,assumption,
    ~ sP30,
    introduced(assumption,[]) ).

thf(h33,assumption,
    ~ sP31,
    introduced(assumption,[]) ).

thf(h34,assumption,
    ~ sP29,
    introduced(assumption,[]) ).

thf(h35,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h36,assumption,
    sP18,
    introduced(assumption,[]) ).

thf(43,plain,
    ( ~ sP1
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(44,plain,
    ( ~ sP16
    | sP37 ),
    inference(all_rule,[status(thm)],]) ).

thf(45,plain,
    ( ~ sP37
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(46,plain,
    ( ~ sP30
    | sP31
    | sP29 ),
    inference(prop_rule,[status(thm)],]) ).

thf(47,plain,
    ( ~ sP31
    | ~ sP9
    | ~ sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(48,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h28,h29,h27,h8,h35,h36,h33,h34,h32,h31,h30,h10,h5,h6,h2,h1,h0])],[43,44,45,46,47,h35,h36,h34,h8]) ).

thf(49,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h27,h8,h35,h36,h33,h34,h32,h31,h30,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,48,h28,h29]) ).

thf(50,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h35,h36,h33,h34,h32,h31,h30,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h27,h8])],[h6,49,h27,h8]) ).

thf(51,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h33,h34,h32,h31,h30,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h35,h36])],[h33,50,h35,h36]) ).

thf(52,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h32,h31,h30,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h33,h34])],[h32,51,h33,h34]) ).

thf(53,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h31,h30,h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h32]),tab_negall(eigenvar,eigen__15)],[h31,52,h32]) ).

thf(54,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h30,h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h31]),tab_negall(eigenvar,eigen__14)],[h30,53,h31]) ).

thf(55,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h30]),tab_negall(eigenvar,eigen__13)],[h10,54,h30]) ).

thf(56,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_imp(discharge,[h25]),tab_imp(discharge,[h10])],[h5,42,55,h25,h10]) ).

thf(57,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,28,56,h3,h4,h5,h6]) ).

thf(58,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,57,h2]) ).

thf(59,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[58,h0]) ).

thf(0,theorem,
    ! [X1: $i > $i > $o] :
      ( ( ~ ( ! [X2: $i] : ( X1 @ X2 @ X2 )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X2 @ X4 ) )
                 => ( X1 @ X3 @ X4 ) ) ) )
      = ( ~ ( ~ ( ! [X2: $i] :
                    ~ ! [X3: $i] :
                        ~ ( X1 @ X2 @ X3 )
               => ~ ! [X2: $i,X3: $i] :
                      ( ( X1 @ X2 @ X3 )
                     => ( X1 @ X3 @ X2 ) ) )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X2 @ X4 ) )
                 => ( X1 @ X3 @ X4 ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[58,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : LCL865^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n008.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 : Mon Jul  4 00:54:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.59/1.76  % SZS status Theorem
% 1.59/1.76  % Mode: mode213
% 1.59/1.76  % Inferences: 12558
% 1.59/1.76  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------