%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU945^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n021.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  : 300s
% DateTime : Thu Aug 31 17:37:59 EDT 2023

% Result   : Theorem 0.22s 0.41s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   28 (   9 unt;   2 typ;   2 def)
%            Number of atoms       :   70 (  33 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   47 (  15   ~;   9   |;   0   &;   7   @)
%                                         (   9 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;  13 con; 0-2 aty)
%            Number of variables   :   24 (  14   ^;  10   !;   0   ?;  24   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
    eigen__2: $i ).

thf(ty_eigen__3,type,
    eigen__3: $i ).

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

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ( ( ( ^ [X2: $i] : ( eigen__2 = X2 ) )
              = ( ^ [X2: $i] : ( X1 = X2 ) ) )
           => ( eigen__2 = X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(eigendef_eigen__2,definition,
    ( eigen__2
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ! [X2: $i] :
              ( ( ( ^ [X3: $i] : ( X1 = X3 ) )
                = ( ^ [X3: $i] : ( X2 = X3 ) ) )
             => ( X1 = X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__2])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( ( eigen__2 = eigen__3 )
      = ~ $false ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( ( ^ [X1: $i] : ( eigen__2 = X1 ) )
        = ( ^ [X1: $i] : ( eigen__3 = X1 ) ) )
     => ( eigen__2 = eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ( eigen__2 = X1 )
        = ( eigen__3 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i,X2: $i] :
        ( ( ( ^ [X3: $i] : ( X1 = X3 ) )
          = ( ^ [X3: $i] : ( X2 = X3 ) ) )
       => ( X1 = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ( ( ( ^ [X2: $i] : ( eigen__2 = X2 ) )
          = ( ^ [X2: $i] : ( X1 = X2 ) ) )
       => ( eigen__2 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( eigen__2 = eigen__3 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i > $i > $o] :
        ~ ! [X2: $i,X3: $i] :
            ( ( ( X1 @ X2 )
              = ( X1 @ X3 ) )
           => ( X2 = X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( ^ [X1: $i] : ( eigen__2 = X1 ) )
      = ( ^ [X1: $i] : ( eigen__3 = X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(cTHM3_pme,conjecture,
    ~ sP7 ).

thf(h1,negated_conjecture,
    sP7,
    inference(assume_negation,[status(cth)],[cTHM3_pme]) ).

thf(1,plain,
    ( ~ sP1
    | sP6
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ~ sP9,
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP8
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP2
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP2
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP5
    | ~ sP2 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(8,plain,
    ( sP4
    | ~ sP5 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).

thf(9,plain,
    ( ~ sP7
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

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

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

thf(0,theorem,
    ~ sP7,
    inference(contra,[status(thm),contra(discharge,[h1])],[10,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU945^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.35  % Computer : n021.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Wed Aug 23 19:33:09 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.22/0.41  % SZS status Theorem
% 0.22/0.41  % Mode: cade22grackle2xfee4
% 0.22/0.41  % Steps: 416
% 0.22/0.41  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------