TSTP Solution File: LCL865^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : LCL865^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 08:05:22 EDT 2023

% Result   : Theorem 2.81s 2.90s
% Output   : Proof 2.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  104
% Syntax   : Number of formulae    :  119 (  58 unt;   6 typ;  36 def)
%            Number of atoms       :  280 (  45 equ;   4 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  524 ( 116   ~;  39   |;   8   &; 273   @)
%                                         (  28 <=>;  60  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   66 (  66   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   71 (  67 usr;  69 con; 0-2 aty)
%            Number of variables   :  163 (  70   ^;  87   !;   6   ?; 163   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
    eigen__2: $i ).

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

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

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

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

thf(ty_eigen__23,type,
    eigen__23: $i ).

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

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( eigen__0 @ eigen__2 @ X1 )
           => ( eigen__0 @ X1 @ eigen__2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ! [X2: $i] :
                ~ ( eigen__0 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(eigendef_eigen__23,definition,
    ( eigen__23
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ( eigen__0 @ eigen__13 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__23])]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ! [X2: $i] :
              ( ( eigen__0 @ X1 @ X2 )
             => ( eigen__0 @ X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(eigendef_eigen__13,definition,
    ( eigen__13
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( eigen__0 @ X1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__13])]) ).

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__1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ~ ( ( eigen__0 @ eigen__2 @ eigen__3 )
           => ~ ( eigen__0 @ eigen__2 @ X1 ) )
       => ( eigen__0 @ eigen__3 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__0 @ eigen__2 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] :
        ( ~ ( ( eigen__0 @ eigen__23 @ eigen__13 )
           => ~ ( eigen__0 @ eigen__23 @ X1 ) )
       => ( eigen__0 @ eigen__13 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i,X2: $i] :
        ( ( eigen__0 @ X1 @ X2 )
       => ( eigen__0 @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__0 @ eigen__23 @ eigen__13 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ~ ( sP8
         => ~ sP8 )
     => ( eigen__0 @ eigen__13 @ eigen__13 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( eigen__0 @ eigen__13 @ eigen__23 )
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP4
     => ( eigen__0 @ eigen__3 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( eigen__0 @ eigen__3 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: $i] :
        ~ ( eigen__0 @ eigen__13 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

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

thf(sP15,plain,
    ( sP15
  <=> ( ~ ( sP5
         => ~ sP7 )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ~ ( sP4
         => ~ ( eigen__0 @ eigen__2 @ eigen__2 ) )
     => sP12 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ! [X1: $i] :
        ( ( eigen__0 @ eigen__13 @ X1 )
       => ( eigen__0 @ X1 @ eigen__13 ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

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

thf(sP19,plain,
    ( sP19
  <=> ! [X1: $i] :
        ( ( eigen__0 @ eigen__2 @ X1 )
       => ( eigen__0 @ X1 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( eigen__0 @ eigen__2 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ( eigen__0 @ eigen__13 @ eigen__23 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( sP8
     => ~ sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( sP14
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( eigen__0 @ eigen__23 @ X1 )
           => ~ ( eigen__0 @ eigen__23 @ X2 ) )
       => ( eigen__0 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( eigen__0 @ eigen__2 @ X1 )
           => ~ ( eigen__0 @ eigen__2 @ X2 ) )
       => ( eigen__0 @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( sP5
     => ~ sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( sP4
     => ~ sP20 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( eigen__0 @ eigen__1 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

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,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_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] : $true ) ) ).

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] :
          ( ^ [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_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] :
        ? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).

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 != ~ sP15 ),
    introduced(assumption,[]) ).

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

thf(h4,assumption,
    ~ sP15,
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP23,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP15,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP14,
    introduced(assumption,[]) ).

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

thf(1,plain,
    ( ~ sP14
    | sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | ~ sP28 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP27
    | ~ sP4
    | ~ sP20 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP16
    | sP27
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP3
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP25
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP14
    | sP20 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP1
    | sP25 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP11
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP11
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP19
    | ~ sP11 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(12,plain,
    ( sP7
    | ~ sP19 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(13,plain,
    ( sP5
    | sP2 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(14,plain,
    ( ~ sP26
    | ~ sP5
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP15
    | sP26
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h7,h8,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h7,h8,h4]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h3,16,h7,h8]) ).

thf(h9,assumption,
    ~ sP26,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(18,plain,
    ( ~ sP22
    | ~ sP8
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP9
    | sP22
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP6
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP24
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP10
    | ~ sP21
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP1
    | sP24 ),
    inference(all_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP17
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(25,plain,
    ( sP13
    | sP21 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__23]) ).

thf(26,plain,
    ( ~ sP7
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP5
    | ~ sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( sP14
    | ~ sP18 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__13]) ).

thf(29,plain,
    ( ~ sP23
    | ~ sP14
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(30,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h10,h11,h9,h8,h5,h6,h2,h1,h0])],[18,19,20,21,22,23,24,25,26,27,28,29,h5,h10,h11,h8]) ).

thf(31,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h8,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h9,30,h10,h11]) ).

thf(32,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_negimp(discharge,[h9,h8])],[h6,31,h9,h8]) ).

thf(33,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,17,32,h3,h4,h5,h6]) ).

thf(34,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,33,h2]) ).

thf(35,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[34,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])],[34,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL865^1 : TPTP v8.1.2. Bugfixed v5.0.0.
% 0.07/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n002.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Aug 25 03:40:47 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 2.81/2.90  % SZS status Theorem
% 2.81/2.90  % Mode: cade22grackle2xfee4
% 2.81/2.90  % Steps: 34163
% 2.81/2.90  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------