TSTP Solution File: SET617^5 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SET617^5 : 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 : n007.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 04:54:30 EDT 2022

% Result   : Theorem 0.12s 0.35s
% Output   : Proof 0.12s
% 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 ).

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

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

thf(sP2,plain,
    ( sP2
  <=> ( eigen__0 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(cBOOL_PROP_92_pme,conjecture,
    ! [X1: a > $o] :
      ~ ( ( ( ^ [X2: a] :
                ( ~ ( X1 @ X2 )
               => ~ ( $false
                   => ( X1 @ X2 ) ) ) )
          = X1 )
       => ( ( ^ [X2: a] :
                ( ( $false
                 => ( X1 @ X2 ) )
               => ( X1 @ X2 ) ) )
         != X1 ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: a > $o] :
        ~ ( ( ( ^ [X2: a] :
                  ( ~ ( X1 @ X2 )
                 => ~ ( $false
                     => ( X1 @ X2 ) ) ) )
            = X1 )
         => ( ( ^ [X2: a] :
                  ( ( $false
                   => ( X1 @ X2 ) )
                 => ( X1 @ X2 ) ) )
           != X1 ) ),
    inference(assume_negation,[status(cth)],[cBOOL_PROP_92_pme]) ).

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

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

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

thf(h4,assumption,
    ~ ! [X1: a] :
        ( ( ~ ( eigen__0 @ X1 )
         => ~ ( $false
             => ( eigen__0 @ X1 ) ) )
        = ( eigen__0 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ( ~ sP2
   => ~ ( $false
       => sP2 ) )
 != sP2,
    introduced(assumption,[]) ).

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

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

thf(h8,assumption,
    ~ ( ~ sP2
     => ~ ( $false
         => sP2 ) ),
    introduced(assumption,[]) ).

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

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

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

thf(h11,assumption,
    $false,
    introduced(assumption,[]) ).

thf(2,plain,
    $false,
    inference(tab_false,[status(thm),assumptions([h11,h9,h10,h6,h7,h5,h4,h2,h1,h0])],[h11]) ).

thf(3,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h10,h6,h7,h5,h4,h2,h1,h0]),tab_negimp(discharge,[h11,h9])],[h10,2,h11,h9]) ).

thf(4,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h6,h7,h5,h4,h2,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h10])],[h6,1,3,h7,h10]) ).

thf(h12,assumption,
    ( $false
   => sP2 ),
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ $false,
    introduced(assumption,[]) ).

thf(5,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h13,h9,h12,h8,h9,h5,h4,h2,h1,h0])],[h9,h9]) ).

thf(6,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h9,h12,h8,h9,h5,h4,h2,h1,h0])],[h7,h9]) ).

thf(7,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h9,h12,h8,h9,h5,h4,h2,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h7])],[h12,5,6,h13,h7]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h9,h5,h4,h2,h1,h0]),tab_negimp(discharge,[h9,h12])],[h8,7,h9,h12]) ).

thf(9,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h5,h4,h2,h1,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,4,8,h6,h7,h8,h9]) ).

thf(10,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__1)],[h4,9,h5]) ).

thf(11,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h4])],[h2,10,h4]) ).

thf(h14,assumption,
    ~ ! [X1: a] :
        ( ( ( $false
           => ( eigen__0 @ X1 ) )
         => ( eigen__0 @ X1 ) )
        = ( eigen__0 @ X1 ) ),
    introduced(assumption,[]) ).

thf(h15,assumption,
    ( ( $false
     => sP1 )
   => sP1 )
 != sP1,
    introduced(assumption,[]) ).

thf(h16,assumption,
    ( ( $false
     => sP1 )
   => sP1 ),
    introduced(assumption,[]) ).

thf(h17,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h18,assumption,
    ~ ( ( $false
       => sP1 )
     => sP1 ),
    introduced(assumption,[]) ).

thf(h19,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h20,assumption,
    ~ ( $false
     => sP1 ),
    introduced(assumption,[]) ).

thf(12,plain,
    $false,
    inference(tab_false,[status(thm),assumptions([h11,h19,h20,h16,h17,h15,h14,h3,h1,h0])],[h11]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h20,h16,h17,h15,h14,h3,h1,h0]),tab_negimp(discharge,[h11,h19])],[h20,12,h11,h19]) ).

thf(14,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h17,h16,h17,h15,h14,h3,h1,h0])],[h17,h17]) ).

thf(15,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h16,h17,h15,h14,h3,h1,h0]),tab_imp(discharge,[h20]),tab_imp(discharge,[h17])],[h16,13,14,h20,h17]) ).

thf(h21,assumption,
    ( $false
   => sP1 ),
    introduced(assumption,[]) ).

thf(16,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h13,h21,h19,h18,h19,h15,h14,h3,h1,h0])],[h19,h19]) ).

thf(17,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h17,h21,h19,h18,h19,h15,h14,h3,h1,h0])],[h17,h19]) ).

thf(18,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h21,h19,h18,h19,h15,h14,h3,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h17])],[h21,16,17,h13,h17]) ).

thf(19,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h18,h19,h15,h14,h3,h1,h0]),tab_negimp(discharge,[h21,h19])],[h18,18,h21,h19]) ).

thf(20,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h15,h14,h3,h1,h0]),tab_be(discharge,[h16,h17]),tab_be(discharge,[h18,h19])],[h15,15,19,h16,h17,h18,h19]) ).

thf(21,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h14,h3,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__2)],[h14,20,h15]) ).

thf(22,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h3,h1,h0]),tab_fe(discharge,[h14])],[h3,21,h14]) ).

thf(23,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h2]),tab_imp(discharge,[h3])],[h1,11,22,h2,h3]) ).

thf(24,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,23,h1]) ).

thf(0,theorem,
    ! [X1: a > $o] :
      ~ ( ( ( ^ [X2: a] :
                ( ~ ( X1 @ X2 )
               => ~ ( $false
                   => ( X1 @ X2 ) ) ) )
          = X1 )
       => ( ( ^ [X2: a] :
                ( ( $false
                 => ( X1 @ X2 ) )
               => ( X1 @ X2 ) ) )
         != X1 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[24,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SET617^5 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n007.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  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 22:48:47 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % SZS status Theorem
% 0.12/0.35  % Mode: mode213
% 0.12/0.35  % Inferences: 0
% 0.12/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------