%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SET173^5 : 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 : n017.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 15:16:19 EDT 2023

% Result   : Theorem 0.20s 0.38s
% 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__1,type,
    eigen__1: a > $o ).

thf(ty_eigen__2,type,
    eigen__2: a ).

thf(sP1,plain,
    ( sP1
  <=> ( ~ ( eigen__0 @ eigen__2 )
     => ( eigen__1 @ eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( eigen__0 @ eigen__2 )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( eigen__0 @ eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(cBOOL_PROP_68_pme,conjecture,
    ! [X1: a > $o,X2: a > $o] :
      ( ( ^ [X3: a] :
            ~ ( ( X1 @ X3 )
             => ~ ( ~ ( X1 @ X3 )
                 => ( X2 @ X3 ) ) ) )
      = X1 ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > $o,X2: a > $o] :
        ( ( ^ [X3: a] :
              ~ ( ( X1 @ X3 )
               => ~ ( ~ ( X1 @ X3 )
                   => ( X2 @ X3 ) ) ) )
        = X1 ),
    inference(assume_negation,[status(cth)],[cBOOL_PROP_68_pme]) ).

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

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

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

thf(h4,assumption,
    ( ~ sP2 != sP3 ),
    introduced(assumption,[]) ).

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

thf(h6,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h6,h9,h5,h6,h4,h3,h2,h1,h0])],[h6,h6]) ).

thf(2,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h6,h9])],[h5,1,h6,h9]) ).

thf(3,plain,
    ( sP1
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP2
    | ~ sP3
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h7,h8,h4,h3,h2,h1,h0])],[3,4,h7,h8]) ).

thf(6,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h4,2,5,h5,h6,h7,h8]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__2)],[h3,6,h4]) ).

thf(8,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,7,h3]) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,8,h2]) ).

thf(10,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1]) ).

thf(0,theorem,
    ! [X1: a > $o,X2: a > $o] :
      ( ( ^ [X3: a] :
            ~ ( ( X1 @ X3 )
             => ~ ( ~ ( X1 @ X3 )
                 => ( X2 @ X3 ) ) ) )
      = X1 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SET173^5 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 14:11:26 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.38  % SZS status Theorem
% 0.20/0.38  % Mode: cade22grackle2xfee4
% 0.20/0.38  % Steps: 4
% 0.20/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------