%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYN051^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n019.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 03:19:38 EDT 2023

% Result   : Theorem 0.13s 0.38s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_cF,type,
    cF: $i > $o ).

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

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

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

thf(sP1,plain,
    ( sP1
  <=> ( ( cF @ eigen__1 )
     => p ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( p
       => ( cF @ eigen__1 ) )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> p ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( sP4
       => ( cF @ eigen__0 ) )
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP4
     => ( cF @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i] :
        ( ( sP4
         => ( cF @ X1 ) )
       => ~ ( ( cF @ X1 )
           => sP4 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

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

thf(cPELL21,conjecture,
    ( ~ ( ~ ! [X1: $i] :
              ~ ( sP4
               => ( cF @ X1 ) )
       => ! [X1: $i] :
            ~ ( ( cF @ X1 )
             => sP4 ) )
   => ~ sP7 ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ! [X1: $i] :
                ~ ( sP4
                 => ( cF @ X1 ) )
         => ! [X1: $i] :
              ~ ( ( cF @ X1 )
               => sP4 ) )
     => ~ sP7 ),
    inference(assume_negation,[status(cth)],[cPELL21]) ).

thf(h1,assumption,
    ~ ( ~ ! [X1: $i] :
            ~ ( sP4
             => ( cF @ X1 ) )
     => ! [X1: $i] :
          ~ ( ( cF @ X1 )
           => sP4 ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: $i] :
        ~ ( sP4
         => ( cF @ X1 ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: $i] :
        ~ ( ( cF @ X1 )
         => sP4 ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP3
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP5
    | ~ sP6
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP7
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP8
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP2
    | ~ sP8
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP7
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h6,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,h5,h6,h2]) ).

thf(8,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h4,7,h6]) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h3,8,h5]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,9,h3,h4]) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,10,h1,h2]) ).

thf(0,theorem,
    ( ~ ( ~ ! [X1: $i] :
              ~ ( sP4
               => ( cF @ X1 ) )
       => ! [X1: $i] :
            ~ ( ( cF @ X1 )
             => sP4 ) )
   => ~ sP7 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN051^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n019.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sat Aug 26 18:39:43 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.13/0.38  % SZS status Theorem
% 0.13/0.38  % Mode: cade22grackle2xfee4
% 0.13/0.38  % Steps: 20
% 0.13/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------