%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO258^5 : 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 : n023.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 : Thu Jul 21 19:31:07 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   26 (   9 unt;   5 typ;   1 def)
%            Number of atoms       :   55 (   1 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  108 (  34   ~;   3   |;   0   &;  42   @)
%                                         (   4 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  10 usr;  10 con; 0-2 aty)
%                                         (   5  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   13 (   4   ^   9   !;   0   ?;  13   :)

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

thf(ty_cP,type,
    cP: $i > $i > $o ).

thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(ty_b,type,
    b: $i ).

thf(ty_cQ,type,
    cQ: $i > ( $i > $o ) > $o ).

thf(h0,assumption,
    ! [X1: $i > $o,X2: $i] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( $false
           => ~ ( ~ ! [X2: $i] :
                      ( ( cP @ X1 @ X2 )
                     => ~ ( cQ @ X2
                          @ ^ [X3: $i] : $false ) )
               => ~ $false ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(sP1,plain,
    ( sP1
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( sP1
       => ~ ( ~ ! [X2: $i] :
                  ( ( cP @ X1 @ X2 )
                 => ~ ( cQ @ X2
                      @ ^ [X3: $i] : sP1 ) )
           => ~ sP1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( sP1
     => ~ ( ~ ! [X1: $i] :
                ( ( cP @ eigen__0 @ X1 )
               => ~ ( cQ @ X1
                    @ ^ [X2: $i] : sP1 ) )
         => ~ sP1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i > $o] :
        ~ ! [X2: $i] :
            ( ( X1 @ X2 )
           => ~ ( ~ ! [X3: $i] :
                      ( ( cP @ X2 @ X3 )
                     => ~ ( cQ @ X3 @ X1 ) )
               => ~ ( X1 @ a ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(cBLEDSOE_FENG_6,conjecture,
    ( ~ ( ( cP @ a @ b )
       => ~ ( !! @ ( cQ @ b ) ) )
   => ~ sP4 ) ).

thf(h1,negated_conjecture,
    ~ ( ~ ( ( cP @ a @ b )
         => ~ ( !! @ ( cQ @ b ) ) )
     => ~ sP4 ),
    inference(assume_negation,[status(cth)],[cBLEDSOE_FENG_6]) ).

thf(h2,assumption,
    ~ ( ( cP @ a @ b )
     => ~ ( !! @ ( cQ @ b ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP4,
    introduced(assumption,[]) ).

thf(h4,assumption,
    cP @ a @ b,
    introduced(assumption,[]) ).

thf(h5,assumption,
    !! @ ( cQ @ b ),
    introduced(assumption,[]) ).

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

thf(2,plain,
    ( sP3
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP2
    | ~ sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(4,plain,
    ( ~ sP4
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h5,h2,h3,h1,h0])],[1,2,3,4,h3]) ).

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

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

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

thf(0,theorem,
    ( ~ ( ( cP @ a @ b )
       => ~ ( !! @ ( cQ @ b ) ) )
   => ~ sP4 ),
    inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SYO258^5 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n023.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jul  8 18:00:41 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.36  % SZS status Theorem
% 0.12/0.36  % Mode: mode213
% 0.12/0.36  % Inferences: 51
% 0.12/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------