%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SET606^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -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  : 600s
% DateTime : Tue Jul 19 04:54:21 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_eigen__2,type,
    eigen__2: a ).

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

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

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

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

thf(cBOOL_PROP_77_pme,conjecture,
    ! [X1: a > $o,X2: a > $o] :
      ( ( ^ [X3: a] :
            ~ ( ( X1 @ X3 )
             => ~ ( ( X1 @ X3 )
                 => ~ ( X2 @ X3 ) ) ) )
      = ( ^ [X3: a] :
            ~ ( ( X1 @ X3 )
             => ( X2 @ X3 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > $o,X2: a > $o] :
        ( ( ^ [X3: a] :
              ~ ( ( X1 @ X3 )
               => ~ ( ( X1 @ X3 )
                   => ~ ( X2 @ X3 ) ) ) )
        = ( ^ [X3: a] :
              ~ ( ( X1 @ X3 )
               => ( X2 @ X3 ) ) ) ),
    inference(assume_negation,[status(cth)],[cBOOL_PROP_77_pme]) ).

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

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

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

thf(h4,assumption,
    ( ~ ( sP2
       => ~ ( sP2
           => ~ sP1 ) ) )
 != ( ~ ( sP2
       => sP1 ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP2
     => ~ ( sP2
         => ~ sP1 ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ( sP2
     => sP1 ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ( sP2
   => ~ ( sP2
       => ~ sP1 ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ( sP2
   => sP1 ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h10,assumption,
    ( sP2
   => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h12,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h13,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h11,h11,h9,h10,h5,h6,h4,h3,h2,h1,h0])],[h9,h11]) ).

thf(2,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h13,h11,h9,h10,h5,h6,h4,h3,h2,h1,h0])],[h9,h11]) ).

thf(3,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h11,h9,h10,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h13])],[h6,1,2,h11,h13]) ).

thf(4,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h11,h12,h9,h10,h5,h6,h4,h3,h2,h1,h0])],[h9,h11]) ).

thf(5,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h13,h12,h9,h10,h5,h6,h4,h3,h2,h1,h0])],[h13,h12]) ).

thf(6,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h12,h9,h10,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h13])],[h6,4,5,h11,h13]) ).

thf(7,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h9,h10,h5,h6,h4,h3,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h10,3,6,h11,h12]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h10])],[h5,7,h9,h10]) ).

thf(h14,assumption,
    ~ ( sP2
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(9,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h9,h12,h11,h7,h8,h4,h3,h2,h1,h0])],[h9,h11]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h7,h8,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h12])],[h8,9,h9,h12]) ).

thf(11,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h9,h12,h9,h13,h14,h7,h8,h4,h3,h2,h1,h0])],[h13,h12]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h13,h14,h7,h8,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h12])],[h8,11,h9,h12]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h7,h8,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h9,h13])],[h14,12,h9,h13]) ).

thf(14,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h7,h8,h4,h3,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h14])],[h7,10,13,h11,h14]) ).

thf(15,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h4,8,14,h5,h6,h7,h8]) ).

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

thf(17,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,16,h3]) ).

thf(18,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,17,h2]) ).

thf(19,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,18,h1]) ).

thf(0,theorem,
    ! [X1: a > $o,X2: a > $o] :
      ( ( ^ [X3: a] :
            ~ ( ( X1 @ X3 )
             => ~ ( ( X1 @ X3 )
                 => ~ ( X2 @ X3 ) ) ) )
      = ( ^ [X3: a] :
            ~ ( ( X1 @ X3 )
             => ( X2 @ X3 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[19,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET606^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n017.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  : 600
% 0.13/0.33  % DateTime : Mon Jul 11 08:33:48 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.35  % SZS status Theorem
% 0.13/0.35  % Mode: mode213
% 0.13/0.35  % Inferences: 0
% 0.13/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------