%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SET587^5 : 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 : n015.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 15:17:37 EDT 2023

% Result   : Theorem 0.20s 0.42s
% Output   : Proof 0.20s
% 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__3,type,
    eigen__3: a ).

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

thf(ty_eigen__2,type,
    eigen__2: a ).

thf(sP1,plain,
    ( sP1
  <=> ( eigen__0 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( eigen__0 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( sP1
     => ( eigen__1 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( eigen__1 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP2
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

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

thf(sP7,plain,
    ( sP7
  <=> ( eigen__1 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: a] :
        ( ( eigen__0 @ X1 )
       => ( eigen__1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(cBOOL_PROP_45_pme,conjecture,
    ! [X1: a > $o,X2: a > $o] :
      ( ( ( ^ [X3: a] :
              ~ ( ( X1 @ X3 )
               => ( X2 @ X3 ) ) )
        = ( ^ [X3: a] : $false ) )
      = ( ! [X3: a] :
            ( ( X1 @ X3 )
           => ( X2 @ X3 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > $o,X2: a > $o] :
        ( ( ( ^ [X3: a] :
                ~ ( ( X1 @ X3 )
                 => ( X2 @ X3 ) ) )
          = ( ^ [X3: a] : $false ) )
        = ( ! [X3: a] :
              ( ( X1 @ X3 )
             => ( X2 @ X3 ) ) ) ),
    inference(assume_negation,[status(cth)],[cBOOL_PROP_45_pme]) ).

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

thf(h2,assumption,
    sP6 != sP8,
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP8,
    introduced(assumption,[]) ).

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

thf(h6,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

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

thf(h9,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP3
    | ~ sP1
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP8
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP6
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

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

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

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h4,5,h7]) ).

thf(h10,assumption,
    ~ ! [X1: a] :
        ( ( ~ ( ( eigen__0 @ X1 )
             => ( eigen__1 @ X1 ) ) )
        = $false ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ sP5,
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ sP4,
    introduced(assumption,[]) ).

thf(7,plain,
    ( ~ sP5
    | ~ sP2
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP8
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h12,h13,h11,h10,h5,h6,h2,h1,h0])],[7,8,h12,h13,h6]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h10,h5,h6,h2,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,9,h12,h13]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h10,h5,h6,h2,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__3)],[h10,10,h11]) ).

thf(12,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h5,h6,h2,h1,h0]),tab_fe(discharge,[h10])],[h5,11,h10]) ).

thf(13,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h2,h1,h0]),tab_be(discharge,[h3,h4]),tab_be(discharge,[h5,h6])],[h2,6,12,h3,h4,h5,h6]) ).

thf(14,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,13,h2]) ).

thf(15,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,14,h1]) ).

thf(0,theorem,
    ! [X1: a > $o,X2: a > $o] :
      ( ( ( ^ [X3: a] :
              ~ ( ( X1 @ X3 )
               => ( X2 @ X3 ) ) )
        = ( ^ [X3: a] : $false ) )
      = ( ! [X3: a] :
            ( ( X1 @ X3 )
           => ( X2 @ X3 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.15  % Problem  : SET587^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.16  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36  % Computer : n015.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sat Aug 26 15:02:23 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 0.20/0.42  % SZS status Theorem
% 0.20/0.42  % Mode: cade22grackle2xfee4
% 0.20/0.42  % Steps: 21
% 0.20/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------