%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : LCL730^5 : 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 : n005.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 14:10:38 EDT 2022

% Result   : Theorem 33.22s 33.51s
% Output   : Proof 33.22s
% 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 :   65 (  22   ~;   6   |;   0   &;  24   @)
%                                         (   6 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   8 con; 0-2 aty)
%            Number of variables   :   20 (   1   ^  15   !;   0   ?;  20   :)
%                                         (   0  !>;   0  ?*;   0  @-;   4  @+)

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

thf(ty_eigen__81,type,
    eigen__81: b > $o ).

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

thf(eigendef_eigen__81,definition,
    ( eigen__81
    = ( eps__0
      @ ^ [X1: b > $o] :
          ~ ( ~ ! [X2: b] :
                  ~ ( X1 @ X2 )
           => ( X1
              @ @+[X2: b] : ( X1 @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__81])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ~ ! [X1: b] :
            ~ ( eigen__81 @ X1 )
     => ( eigen__81
        @ @+[X1: b] : ( eigen__81 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ! [X1: b] :
        ~ ( eigen__81 @ 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] :
              ~ ! [X3: b] :
                  ~ ( X1 @ X2 @ X3 )
         => ~ ! [X2: ( b > $o ) > b] :
                ~ ! [X3: b > $o] : ( X1 @ X3 @ ( X2 @ X3 ) ) )
     => ~ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__81
      @ @+[X1: b] : ( eigen__81 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(cX5310,conjecture,
    sP5 ).

thf(h1,negated_conjecture,
    ~ sP5,
    inference(assume_negation,[status(cth)],[cX5310]) ).

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

thf(2,plain,
    ( sP1
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP1
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP2
    | ~ sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__81]) ).

thf(5,plain,
    ( ~ sP4
    | ~ sP2 ),
    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
% 0.07/0.14  % Problem  : LCL730^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.15  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.37  % Computer : n005.cluster.edu
% 0.13/0.37  % Model    : x86_64 x86_64
% 0.13/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37  % Memory   : 8042.1875MB
% 0.13/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37  % CPULimit : 300
% 0.13/0.37  % WCLimit  : 600
% 0.13/0.37  % DateTime : Sun Jul  3 22:30:37 EDT 2022
% 0.13/0.37  % CPUTime  : 
% 33.22/33.51  % SZS status Theorem
% 33.22/33.51  % Mode: mode448
% 33.22/33.51  % Inferences: 781
% 33.22/33.51  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------