%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SET604^5 : 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 : n028.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 04:54:19 EDT 2022

% Result   : Theorem 0.17s 0.34s
% Output   : Proof 0.17s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_eigen__1,type,
    eigen__1: a ).

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

thf(cBOOL_PROP_75_pme,conjecture,
    ! [X1: a > $o] :
      ( ( ^ [X2: a] :
            ~ ( $false
             => ( X1 @ X2 ) ) )
      = ( ^ [X2: a] : $false ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > $o] :
        ( ( ^ [X2: a] :
              ~ ( $false
               => ( X1 @ X2 ) ) )
        = ( ^ [X2: a] : $false ) ),
    inference(assume_negation,[status(cth)],[cBOOL_PROP_75_pme]) ).

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

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

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

thf(h4,assumption,
    ~ ( $false
     => ( eigen__0 @ eigen__1 ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    $false,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ( $false
   => ( eigen__0 @ eigen__1 ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ $false,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( eigen__0 @ eigen__1 ),
    introduced(assumption,[]) ).

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

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

thf(h9,assumption,
    eigen__0 @ eigen__1,
    introduced(assumption,[]) ).

thf(3,plain,
    $false,
    inference(tab_false,[status(thm),assumptions([h7,h6,h7,h3,h2,h1,h0])],[h7]) ).

thf(4,plain,
    $false,
    inference(tab_false,[status(thm),assumptions([h9,h6,h7,h3,h2,h1,h0])],[h7]) ).

thf(5,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h6,h7,h3,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h9])],[h6,3,4,h7,h9]) ).

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

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,6,h3]) ).

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

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

thf(0,theorem,
    ! [X1: a > $o] :
      ( ( ^ [X2: a] :
            ~ ( $false
             => ( X1 @ X2 ) ) )
      = ( ^ [X2: a] : $false ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SET604^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32  % Computer : n028.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sun Jul 10 07:48:27 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.17/0.34  % SZS status Theorem
% 0.17/0.34  % Mode: mode213
% 0.17/0.34  % Inferences: 0
% 0.17/0.34  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------