%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO292^5 : 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 : n018.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 19:31:17 EDT 2022

% Result   : Theorem 0.18s 0.35s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   21 (   9 unt;   3 typ;   2 def)
%            Number of atoms       :   36 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   47 (  11   ~;   4   |;   0   &;  19   @)
%                                         (   5 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   9 con; 0-2 aty)
%            Number of variables   :   11 (   2   ^   9   !;   0   ?;  11   :)

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

thf(ty_eigen__1,type,
    eigen__1: $i ).

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

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

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( $false
           => ( cP @ eigen__0 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

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

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i,X2: $i] :
        ( $false
       => ( cP @ X1 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( sP2
       => ( cP @ eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> ( sP2
     => ( cP @ eigen__0 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(cBLEDSOE5E,conjecture,
    ~ sP4 ).

thf(h1,negated_conjecture,
    sP4,
    inference(assume_negation,[status(cth)],[cBLEDSOE5E]) ).

thf(1,plain,
    ~ sP2,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP5
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP3
    | ~ sP5 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(4,plain,
    ( sP1
    | ~ sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(5,plain,
    ( ~ sP4
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,h1]) ).

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

thf(0,theorem,
    ~ sP4,
    inference(contra,[status(thm),contra(discharge,[h1])],[6,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYO292^5 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n018.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 : Sat Jul  9 00:09:41 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.35  % SZS status Theorem
% 0.18/0.35  % Mode: mode213
% 0.18/0.35  % Inferences: 48
% 0.18/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------