%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SET008^5 : 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 : n006.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 15:15:03 EDT 2023

% Result   : Theorem 0.19s 0.38s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

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

thf(ty_eigen__1,type,
    eigen__1: a > $o ).

thf(ty_eigen__2,type,
    eigen__2: a ).

thf(sP1,plain,
    ( sP1
  <=> ( eigen__1 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(cBOOL_PROP_78_pme,conjecture,
    ! [X1: a > $o,X2: a > $o] :
      ( ( ^ [X3: a] :
            ~ ( ~ ( ( X1 @ X3 )
                 => ( X2 @ X3 ) )
             => ~ ( X2 @ X3 ) ) )
      = ( ^ [X3: a] : $false ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > $o,X2: a > $o] :
        ( ( ^ [X3: a] :
              ~ ( ~ ( ( X1 @ X3 )
                   => ( X2 @ X3 ) )
               => ~ ( X2 @ X3 ) ) )
        = ( ^ [X3: a] : $false ) ),
    inference(assume_negation,[status(cth)],[cBOOL_PROP_78_pme]) ).

thf(h1,assumption,
    ~ ! [X1: a > $o] :
        ( ( ^ [X2: a] :
              ~ ( ~ ( ( eigen__0 @ X2 )
                   => ( X1 @ X2 ) )
               => ~ ( X1 @ X2 ) ) )
        = ( ^ [X2: a] : $false ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ( ( ^ [X1: a] :
          ~ ( ~ ( ( eigen__0 @ X1 )
               => ( eigen__1 @ X1 ) )
           => ~ ( eigen__1 @ X1 ) ) )
   != ( ^ [X1: a] : $false ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ! [X1: a] :
        ( ( ~ ( ~ ( ( eigen__0 @ X1 )
                 => ( eigen__1 @ X1 ) )
             => ~ ( eigen__1 @ X1 ) ) )
        = $false ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( ~ ( ( eigen__0 @ eigen__2 )
         => sP1 )
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( ( eigen__0 @ eigen__2 )
     => sP1 ),
    introduced(assumption,[]) ).

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

thf(h7,assumption,
    eigen__0 @ eigen__2,
    introduced(assumption,[]) ).

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

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h8,h5,h6,h4,h3,h2,h1,h0])],[h6,h8]) ).

thf(2,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h5,1,h7,h8]) ).

thf(3,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,2,h5,h6]) ).

thf(4,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,3,h4]) ).

thf(5,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,4,h3]) ).

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,5,h2]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1]) ).

thf(0,theorem,
    ! [X1: a > $o,X2: a > $o] :
      ( ( ^ [X3: a] :
            ~ ( ~ ( ( X1 @ X3 )
                 => ( X2 @ X3 ) )
             => ~ ( X2 @ X3 ) ) )
      = ( ^ [X3: a] : $false ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET008^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Aug 26 10:52:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.38  % SZS status Theorem
% 0.19/0.38  % Mode: cade22grackle2xfee4
% 0.19/0.38  % Steps: 0
% 0.19/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------