%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : LCL734^5 : 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 : n003.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 14:10:39 EDT 2022

% Result   : Theorem 33.21s 33.43s
% Output   : Proof 33.21s
% 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 :   74 (  24   ~;   6   |;   0   &;  29   @)
%                                         (   6 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   8 con; 0-2 aty)
%            Number of variables   :   21 (   1   ^  16   !;   0   ?;  21   :)
%                                         (   0  !>;   0  ?*;   0  @-;   4  @+)

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

thf(ty_eigen__71,type,
    eigen__71: b > $o ).

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

thf(eigendef_eigen__71,definition,
    ( eigen__71
    = ( eps__0
      @ ^ [X1: b > $o] :
          ~ ( ~ ! [X2: b] :
                  ~ ( X1 @ X2 )
           => ( X1
              @ @+[X2: b] : ( X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__71])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: b > $o] :
        ( ~ ! [X2: b] :
              ~ ( X1 @ X2 )
       => ( X1
          @ @+[X2: b] : ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ ! [X1: b] :
            ~ ( eigen__71 @ X1 )
     => ( eigen__71
        @ @+[X1: b] : ( eigen__71 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: b] :
        ~ ( eigen__71 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> ( ! [X1: ( b > $o ) > b > $o,X2: ( b > $o ) > b > $o] :
          ( ! [X3: b > $o] :
              ~ ! [X4: b] :
                  ~ ( ~ ( X1 @ X3 @ X4 )
                   => ( X2 @ X3 @ X4 ) )
         => ~ ! [X3: ( b > $o ) > b] :
                ~ ! [X4: b > $o] :
                    ( ~ ( X1 @ X4 @ ( X3 @ X4 ) )
                   => ( X2 @ X4 @ ( X3 @ X4 ) ) ) )
     => ~ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__71
      @ @+[X1: b] : ( eigen__71 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(cX5310B,conjecture,
    sP5 ).

thf(h1,negated_conjecture,
    ~ sP5,
    inference(assume_negation,[status(cth)],[cX5310B]) ).

thf(1,plain,
    ( sP6
    | sP3 ),
    inference(choice_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP2
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP2
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP1
    | ~ sP2 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__71]) ).

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

thf(6,plain,
    ( sP5
    | sP4 ),
    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,
    sP5,
    inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : LCL734^5 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33  % Computer : n003.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sun Jul  3 06:17:09 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 33.21/33.43  % SZS status Theorem
% 33.21/33.43  % Mode: mode448
% 33.21/33.43  % Inferences: 807
% 33.21/33.43  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------