%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : LCL732^5 : 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 : n007.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 1.98s 2.24s
% Output   : Proof 1.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   26 (  10 unt;   4 typ;   2 def)
%            Number of atoms       :   45 (   2 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   62 (  24   ~;   6   |;   0   &;  18   @)
%                                         (   6 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;  12 con; 0-2 aty)
%            Number of variables   :   17 (   2   ^  15   !;   0   ?;  17   :)

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

thf(ty_p,type,
    p: $i > $o ).

thf(ty_eigen__1,type,
    eigen__1: b ).

thf(ty_y,type,
    y: $i ).

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

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: b] :
          ~ ~ ( ~ ! [X2: $i] :
                    ~ ( p @ X2 )
             => ( p @ y ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

thf(h1,assumption,
    ! [X1: ( b > $o ) > $o,X2: b > $o] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__1
      @ ^ [X1: b > $o] :
          ~ ( ~ ! [X2: $i] :
                  ~ ( p @ X2 )
           => ( p @ y ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: b > $o] :
        ~ ! [X2: b] :
            ~ ( ~ ! [X3: $i] :
                    ~ ( p @ X3 )
             => ( p @ y ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ( ~ ! [X1: $i] :
            ~ ( p @ X1 )
     => ( p @ y ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> ( sP1
     => ~ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: b > $o] : sP3 ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(cX5310_SUB3,conjecture,
    sP5 ).

thf(h2,negated_conjecture,
    ~ sP5,
    inference(assume_negation,[status(cth)],[cX5310_SUB3]) ).

thf(1,plain,
    ( sP6
    | ~ sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2]) ).

thf(2,plain,
    ( ~ sP4
    | ~ sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP2
    | sP3 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(4,plain,
    ( ~ sP1
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP5
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP5
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,h2]) ).

thf(8,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[7,h1]) ).

thf(9,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[8,h0]) ).

thf(0,theorem,
    sP5,
    inference(contra,[status(thm),contra(discharge,[h2])],[7,h2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : LCL732^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n007.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 : Mon Jul  4 14:28:12 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 1.98/2.24  % SZS status Theorem
% 1.98/2.24  % Mode: mode506
% 1.98/2.24  % Inferences: 71237
% 1.98/2.24  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------