%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV162^5 : 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 : Tue Jul 19 18:05:09 EDT 2022

% Result   : Theorem 2.01s 2.19s
% Output   : Proof 2.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   36 (  14 unt;   5 typ;   4 def)
%            Number of atoms       :   68 (   7 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   99 (  14   ~;  11   |;   0   &;  56   @)
%                                         (   8 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   37 (  37   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;  15 con; 0-2 aty)
%                                         (   7  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :   45 (  30   ^  15   !;   0   ?;  45   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_eigen__1,type,
    eigen__1: a ).

thf(ty_eigen__0,type,
    eigen__0: a > a > $o ).

thf(ty_eigen__4,type,
    eigen__4: ( a > a > a ) > a ).

thf(ty_eigen__3,type,
    eigen__3: a ).

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

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( eigen__0 @ eigen__1 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(eigendef_eigen__1,definition,
    ( eigen__1
    = ( eps__0
      @ ^ [X1: a] :
          ~ ( !! @ ( eigen__0 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__1])]) ).

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__1
      @ ^ [X1: a > a > $o] :
          ( ( ! [X2: a] : ( !! @ ( X1 @ X2 ) ) )
         != ( ! [X2: ( a > a > a ) > a] :
                ( X1
                @ ( X2
                  @ ^ [X3: a,X4: a] : X3 )
                @ ( X2
                  @ ^ [X3: a,X4: a] : X4 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(h2,assumption,
    ! [X1: ( ( a > a > a ) > a ) > $o,X2: ( a > a > a ) > a] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__2 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__4,definition,
    ( eigen__4
    = ( eps__2
      @ ^ [X1: ( a > a > a ) > a] :
          ~ ( eigen__0
            @ ( X1
              @ ^ [X2: a,X3: a] : X2 )
            @ ( X1
              @ ^ [X2: a,X3: a] : X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__4])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ( ! [X1: a] : ( !! @ ( eigen__0 @ X1 ) ) )
      = ( ! [X1: ( a > a > a ) > a] :
            ( eigen__0
            @ ( X1
              @ ^ [X2: a,X3: a] : X2 )
            @ ( X1
              @ ^ [X2: a,X3: a] : X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: ( a > a > a ) > a] :
        ( eigen__0
        @ ( X1
          @ ^ [X2: a,X3: a] : X2 )
        @ ( X1
          @ ^ [X2: a,X3: a] : X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( !!
      @ ( eigen__0
        @ ( eigen__4
          @ ^ [X1: a,X2: a] : X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: a] : ( !! @ ( eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a > a > $o] :
        ( ( ! [X2: a] : ( !! @ ( X1 @ X2 ) ) )
        = ( ! [X2: ( a > a > a ) > a] :
              ( X1
              @ ( X2
                @ ^ [X3: a,X4: a] : X3 )
              @ ( X2
                @ ^ [X3: a,X4: a] : X4 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( eigen__0 @ eigen__1 @ eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( eigen__0
      @ ( eigen__4
        @ ^ [X1: a,X2: a] : X1 )
      @ ( eigen__4
        @ ^ [X1: a,X2: a] : X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(cTHM184_pme,conjecture,
    sP6 ).

thf(h3,negated_conjecture,
    ~ sP6,
    inference(assume_negation,[status(cth)],[cTHM184_pme]) ).

thf(1,plain,
    ( ~ sP3
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP2
    | ~ sP8 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__4]) ).

thf(4,plain,
    ( ~ sP2
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP5
    | ~ sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(6,plain,
    ( sP4
    | ~ sP5 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(7,plain,
    ( sP1
    | ~ sP4
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP1
    | sP4
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP6
    | ~ sP1 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0]) ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,h3]) ).

thf(11,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[10,h2]) ).

thf(12,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[11,h1]) ).

thf(13,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[12,h0]) ).

thf(0,theorem,
    sP6,
    inference(contra,[status(thm),contra(discharge,[h3])],[10,h3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEV162^5 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 27 17:54:43 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.01/2.19  % SZS status Theorem
% 2.01/2.19  % Mode: mode506
% 2.01/2.19  % Inferences: 21504
% 2.01/2.19  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------