%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : LCL738^5 : 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 : n004.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 : Sun Jul 17 14:10:40 EDT 2022

% Result   : Theorem 35.27s 35.52s
% Output   : Proof 35.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   21 (   9 unt;   2 typ;   1 def)
%            Number of atoms       :   34 (   1 equ;   0 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   80 (  26   ~;   6   |;   0   &;  33   @)
%                                         (   6 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   21 (  21   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   8 con; 0-2 aty)
%            Number of variables   :   23 (   1   ^  18   !;   0   ?;  23   :)
%                                         (   0  !>;   0  ?*;   0  @-;   4  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_b,type,
    b: $tType ).

thf(ty_eigen__4,type,
    eigen__4: b > $o ).

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

thf(eigendef_eigen__4,definition,
    ( eigen__4
    = ( eps__0
      @ ^ [X1: b > $o] :
          ~ ( ~ ! [X2: b] :
                  ~ ( X1 @ X2 )
           => ( X1
              @ @+[X2: b] : ( X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__4])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ~ ! [X1: b] :
            ~ ( eigen__4 @ X1 )
     => ( eigen__4
        @ @+[X1: b] : ( eigen__4 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: ( b > $o ) > b] :
        ~ ! [X2: b > $o] :
            ( ~ ! [X3: b] :
                  ~ ( X2 @ X3 )
           => ( X2 @ ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ~ ! [X1: ( b > $o ) > b > b > $o,X2: ( b > $o ) > b > b > $o] :
            ~ ( ! [X3: b > $o] :
                  ~ ! [X4: b] :
                      ~ ! [X5: b] :
                          ( ~ ( X2 @ X3 @ X4 @ X5 )
                         => ( X1 @ X3 @ X4 @ X5 ) )
             => ~ ! [X3: ( b > $o ) > b] :
                    ~ ! [X4: b > $o,X5: b] :
                        ( ~ ( X2 @ X4 @ ( X3 @ X4 ) @ X5 )
                       => ( X1 @ X4 @ ( X3 @ X4 ) @ X5 ) ) )
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> ( eigen__4
      @ @+[X1: b] : ( eigen__4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: b] :
        ~ ( eigen__4 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(cX5310_SUB,conjecture,
    sP3 ).

thf(h1,negated_conjecture,
    ~ sP3,
    inference(assume_negation,[status(cth)],[cX5310_SUB]) ).

thf(1,plain,
    ( sP5
    | sP6 ),
    inference(choice_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP1
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP1
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP4
    | ~ sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4]) ).

thf(5,plain,
    ( ~ sP2
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP3
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,h1]) ).

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

thf(0,theorem,
    sP3,
    inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL738^5 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n004.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 : Sun Jul  3 04:21:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 35.27/35.52  % SZS status Theorem
% 35.27/35.52  % Mode: mode466
% 35.27/35.52  % Inferences: 74609
% 35.27/35.52  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------