TSTP Solution File: SEU492^1 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU492^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n032.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 : Tue Jul 19 13:52:27 EDT 2022

% Result   : Theorem 0.13s 0.31s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__6,type,
    eigen__6: $i ).

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

thf(ty_eigen__7,type,
    eigen__7: $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__9,type,
    eigen__9: $i ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( eigen__0 @ eigen__6 @ X1 )
           => ~ ( eigen__0 @ X1 @ X2 ) )
       => ( eigen__0 @ eigen__6 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ~ ( ( eigen__0 @ X1 @ X2 )
           => ~ ( eigen__0 @ X2 @ X3 ) )
       => ( eigen__0 @ X1 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( eigen__0 @ eigen__7 @ eigen__8 )
     => ~ ( eigen__0 @ eigen__8 @ eigen__9 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__0 @ eigen__3 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ~ ( ( eigen__0 @ eigen__2 @ eigen__3 )
         => ~ sP4 )
     => ( eigen__0 @ eigen__2 @ eigen__4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] :
        ( ( eigen__0 @ eigen__1 @ X1 )
       => ~ ( eigen__0 @ X1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__0 @ eigen__7 @ eigen__8 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__0 @ eigen__8 @ eigen__9 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( eigen__0 @ eigen__2 @ eigen__4 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( eigen__0 @ eigen__6 @ eigen__5 )
     => ~ ( eigen__0 @ eigen__5 @ eigen__6 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( eigen__0 @ eigen__7 @ X1 )
           => ~ ( eigen__0 @ X1 @ X2 ) )
       => ( eigen__0 @ eigen__7 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: $i] :
        ( ~ ( ( eigen__0 @ eigen__6 @ eigen__5 )
           => ~ ( eigen__0 @ eigen__5 @ X1 ) )
       => ( eigen__0 @ eigen__6 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

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

thf(sP14,plain,
    ( sP14
  <=> ( ( eigen__0 @ eigen__2 @ eigen__3 )
     => ~ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i] :
        ( ~ ( ( eigen__0 @ eigen__2 @ eigen__3 )
           => ~ ( eigen__0 @ eigen__3 @ X1 ) )
       => ( eigen__0 @ eigen__2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( eigen__0 @ eigen__7 @ eigen__9 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( eigen__0 @ eigen__6 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ! [X1: $i,X2: $i] :
        ( ( eigen__0 @ X1 @ X2 )
       => ~ ( eigen__0 @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( eigen__0 @ eigen__1 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( eigen__0 @ eigen__2 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: $i,X2: $i] :
        ( ~ ( ( eigen__0 @ eigen__2 @ X1 )
           => ~ ( eigen__0 @ X1 @ X2 ) )
       => ( eigen__0 @ eigen__2 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ! [X1: $i] :
        ( ~ ( sP7
           => ~ ( eigen__0 @ eigen__8 @ X1 ) )
       => ( eigen__0 @ eigen__7 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( eigen__0 @ eigen__5 @ eigen__6 ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( eigen__0 @ eigen__6 @ eigen__5 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( ~ sP3
     => sP16 ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( sP19
     => ~ sP19 ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( ~ sP10
     => sP17 ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

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

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

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

thf(def_infl,definition,
    ( infl
    = ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
        ! [X2: $i > $i > $o] : ( subrel @ X2 @ ( X1 @ X2 ) ) ) ) ).

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

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

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

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

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

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

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

thf(def_sc,definition,
    ( sc
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
          ( ~ ( X1 @ X3 @ X2 )
         => ( X1 @ X2 @ X3 ) ) ) ) ).

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

thf(def_tc,definition,
    ( tc
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
        ! [X4: $i > $i > $o] :
          ( ~ ( ( trans @ X4 )
             => ~ ( subrel @ X1 @ X4 ) )
         => ( X4 @ X2 @ X3 ) ) ) ) ).

thf(def_trc,definition,
    ( trc
    = ( ^ [X1: $i > $i > $o] : ( rc @ ( tc @ X1 ) ) ) ) ).

thf(def_trsc,definition,
    ( trsc
    = ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ) ).

thf(def_po,definition,
    ( po
    = ( ^ [X1: $i > $i > $o] :
          ~ ( ~ ( ( refl @ X1 )
               => ~ ( antisymm @ X1 ) )
           => ~ ( trans @ X1 ) ) ) ) ).

thf(def_so,definition,
    ( so
    = ( ^ [X1: $i > $i > $o] :
          ~ ( ( asymm @ X1 )
           => ~ ( trans @ X1 ) ) ) ) ).

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

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

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

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

thf(def_nfof,definition,
    ( nfof
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
          ~ ( ( trc @ X1 @ X3 @ X2 )
           => ~ ( innf @ X1 @ X2 ) ) ) ) ).

thf(def_norm,definition,
    ( norm
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i] :
          ~ ! [X3: $i] :
              ~ ( nfof @ X1 @ X3 @ X2 ) ) ) ).

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

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

thf(def_sconfl,definition,
    ( sconfl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ~ ( ( X1 @ X2 @ X4 )
             => ~ ( trc @ X1 @ X2 @ X3 ) )
         => ( join @ X1 @ X4 @ X3 ) ) ) ) ).

thf(def_confl,definition,
    ( confl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ~ ( ( trc @ X1 @ X2 @ X4 )
             => ~ ( trc @ X1 @ X2 @ X3 ) )
         => ( join @ X1 @ X4 @ X3 ) ) ) ) ).

thf(def_cr,definition,
    ( cr
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i] :
          ( ( trsc @ X1 @ X2 @ X3 )
         => ( join @ X1 @ X2 @ X3 ) ) ) ) ).

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

thf(h0,negated_conjecture,
    ( ^ [X1: $i > $i > $o] :
        ~ ( ! [X2: $i,X3: $i] :
              ( ( X1 @ X2 @ X3 )
             => ~ ( X1 @ X3 @ X2 ) )
         => ~ ! [X2: $i,X3: $i,X4: $i] :
                ( ~ ( ( X1 @ X2 @ X3 )
                   => ~ ( X1 @ X3 @ X4 ) )
               => ( X1 @ X2 @ X4 ) ) ) )
 != ( ^ [X1: $i > $i > $o] :
        ~ ( ! [X2: $i] :
              ~ ( X1 @ X2 @ X2 )
         => ~ ! [X2: $i,X3: $i,X4: $i] :
                ( ~ ( ( X1 @ X2 @ X3 )
                   => ~ ( X1 @ X3 @ X4 ) )
               => ( X1 @ X2 @ X4 ) ) ) ),
    inference(assume_negation,[status(cth)],[alternative_definition_of_strict_order]) ).

thf(h1,assumption,
    ~ ! [X1: $i > $i > $o] :
        ( ( ~ ( ! [X2: $i,X3: $i] :
                  ( ( X1 @ X2 @ X3 )
                 => ~ ( X1 @ X3 @ X2 ) )
             => ~ ! [X2: $i,X3: $i,X4: $i] :
                    ( ~ ( ( X1 @ X2 @ X3 )
                       => ~ ( X1 @ X3 @ X4 ) )
                   => ( X1 @ X2 @ X4 ) ) ) )
        = ( ~ ( ! [X2: $i] :
                  ~ ( X1 @ X2 @ X2 )
             => ~ ! [X2: $i,X3: $i,X4: $i] :
                    ( ~ ( ( X1 @ X2 @ X3 )
                       => ~ ( X1 @ X3 @ X4 ) )
                   => ( X1 @ X2 @ X4 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ( ~ ( sP18
       => ~ sP2 ) )
 != ( ~ ( sP13
       => ~ sP2 ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP18
     => ~ sP2 ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sP13
     => ~ sP2 ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ( sP18
   => ~ sP2 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ( sP13
   => ~ sP2 ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP18,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP19,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP18
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP6
    | sP26 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP26
    | ~ sP19
    | ~ sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h11,h9,h7,h8,h3,h4,h2,h1,h0])],[1,2,3,h7,h11]) ).

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h9,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__1)],[h9,4,h11]) ).

thf(h12,assumption,
    ~ sP21,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ sP15,
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h15,assumption,
    ~ sP14,
    introduced(assumption,[]) ).

thf(h16,assumption,
    ~ sP9,
    introduced(assumption,[]) ).

thf(h17,assumption,
    sP20,
    introduced(assumption,[]) ).

thf(h18,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(6,plain,
    ( ~ sP2
    | sP21 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP21
    | sP15 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP15
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP5
    | sP14
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP14
    | ~ sP20
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h17,h18,h15,h16,h14,h13,h12,h10,h7,h8,h3,h4,h2,h1,h0])],[6,7,8,9,10,h8,h17,h18,h16]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h15,h16,h14,h13,h12,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h17,h18])],[h15,11,h17,h18]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h13,h12,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,12,h15,h16]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h13,h12,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__4)],[h13,13,h14]) ).

thf(15,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h12,h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__3)],[h12,14,h13]) ).

thf(16,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h10,h7,h8,h3,h4,h2,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__2)],[h10,15,h12]) ).

thf(17,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h7,h8,h3,h4,h2,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h4,5,16,h9,h10]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h3,17,h7,h8]) ).

thf(h19,assumption,
    ~ sP18,
    introduced(assumption,[]) ).

thf(h20,assumption,
    ~ ! [X1: $i] :
        ( ( eigen__0 @ eigen__5 @ X1 )
       => ~ ( eigen__0 @ X1 @ eigen__5 ) ),
    introduced(assumption,[]) ).

thf(h21,assumption,
    ~ ( sP23
     => ~ sP24 ),
    introduced(assumption,[]) ).

thf(h22,assumption,
    sP23,
    introduced(assumption,[]) ).

thf(h23,assumption,
    sP24,
    introduced(assumption,[]) ).

thf(h24,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(19,plain,
    ( ~ sP13
    | ~ sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    ( ~ sP2
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(21,plain,
    ( ~ sP1
    | sP12 ),
    inference(all_rule,[status(thm)],]) ).

thf(22,plain,
    ( ~ sP12
    | sP27 ),
    inference(all_rule,[status(thm)],]) ).

thf(23,plain,
    ( ~ sP27
    | sP10
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(24,plain,
    ( ~ sP10
    | ~ sP24
    | ~ sP23 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h24,h8,h22,h23,h21,h20,h19,h5,h6,h2,h1,h0])],[19,20,21,22,23,24,h22,h23,h24,h8]) ).

thf(26,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h22,h23,h21,h20,h19,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h24,h8])],[h6,25,h24,h8]) ).

thf(27,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h21,h20,h19,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h22,h23])],[h21,26,h22,h23]) ).

thf(28,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h20,h19,h5,h6,h2,h1,h0]),tab_negall(discharge,[h21]),tab_negall(eigenvar,eigen__6)],[h20,27,h21]) ).

thf(29,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h19,h5,h6,h2,h1,h0]),tab_negall(discharge,[h20]),tab_negall(eigenvar,eigen__5)],[h19,28,h20]) ).

thf(h25,assumption,
    ~ sP11,
    introduced(assumption,[]) ).

thf(h26,assumption,
    ~ sP22,
    introduced(assumption,[]) ).

thf(h27,assumption,
    ~ sP25,
    introduced(assumption,[]) ).

thf(h28,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h29,assumption,
    ~ sP16,
    introduced(assumption,[]) ).

thf(h30,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h31,assumption,
    sP8,
    introduced(assumption,[]) ).

thf(30,plain,
    ( ~ sP2
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP11
    | sP22 ),
    inference(all_rule,[status(thm)],]) ).

thf(32,plain,
    ( ~ sP22
    | sP25 ),
    inference(all_rule,[status(thm)],]) ).

thf(33,plain,
    ( ~ sP25
    | sP3
    | sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(34,plain,
    ( ~ sP3
    | ~ sP7
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(35,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h24,h8,h30,h31,h28,h29,h27,h26,h25,h10,h5,h6,h2,h1,h0])],[30,31,32,33,34,h30,h31,h29,h8]) ).

thf(36,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h30,h31,h28,h29,h27,h26,h25,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h24,h8])],[h6,35,h24,h8]) ).

thf(37,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h28,h29,h27,h26,h25,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h30,h31])],[h28,36,h30,h31]) ).

thf(38,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h27,h26,h25,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h28,h29])],[h27,37,h28,h29]) ).

thf(39,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h26,h25,h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h27]),tab_negall(eigenvar,eigen__9)],[h26,38,h27]) ).

thf(40,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h25,h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h26]),tab_negall(eigenvar,eigen__8)],[h25,39,h26]) ).

thf(41,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__7)],[h10,40,h25]) ).

thf(42,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_imp(discharge,[h19]),tab_imp(discharge,[h10])],[h5,29,41,h19,h10]) ).

thf(43,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,18,42,h3,h4,h5,h6]) ).

thf(44,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,43,h2]) ).

thf(45,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,44,h1]) ).

thf(0,theorem,
    ( ( ^ [X1: $i > $i > $o] :
          ~ ( ! [X2: $i,X3: $i] :
                ( ( X1 @ X2 @ X3 )
               => ~ ( X1 @ X3 @ X2 ) )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) ) )
    = ( ^ [X1: $i > $i > $o] :
          ~ ( ! [X2: $i] :
                ~ ( X1 @ X2 @ X2 )
           => ~ ! [X2: $i,X3: $i,X4: $i] :
                  ( ~ ( ( X1 @ X2 @ X3 )
                     => ~ ( X1 @ X3 @ X4 ) )
                 => ( X1 @ X2 @ X4 ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[45,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09  % Problem  : SEU492^1 : TPTP v8.1.0. Released v3.6.0.
% 0.06/0.09  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.28  % Computer : n032.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 600
% 0.09/0.28  % DateTime : Sun Jun 19 22:31:33 EDT 2022
% 0.09/0.28  % CPUTime  : 
% 0.13/0.31  % SZS status Theorem
% 0.13/0.31  % Mode: mode213
% 0.13/0.31  % Inferences: 18
% 0.13/0.31  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------