%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO381^5 : 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 : n011.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 : Fri Sep  1 04:46:30 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   22 (   7 unt;   3 typ;   1 def)
%            Number of atoms       :   41 (   4 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   51 (  18   ~;   8   |;   0   &;  18   @)
%                                         (   6 <=>;   1  =>;   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     :   12 (  10 usr;  10 con; 0-2 aty)
%            Number of variables   :   13 (   1   ^;  12   !;   0   ?;  13   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(ty_eigen__1,type,
    eigen__1: $i ).

thf(ty_cR,type,
    cR: $i > $i > $o ).

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

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

thf(sP1,plain,
    ( sP1
  <=> ( ( ~ ! [X1: $i] :
              ~ ! [X2: $i] : ( cR @ X1 @ X2 ) )
      = ( ! [X1: $i] : ( cR @ eigen__0 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] : ( cR @ eigen__1 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ~ ! [X2: $i] : ( cR @ X1 @ X2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> ( ~ sP3 = sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] : ( cR @ eigen__0 @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(cX_2002_12_17,conjecture,
    ~ sP4 ).

thf(h1,negated_conjecture,
    sP4,
    inference(assume_negation,[status(cth)],[cX_2002_12_17]) ).

thf(1,plain,
    ( sP5
    | sP3
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | ~ sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | ~ sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP3
    | sP2 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1]) ).

thf(5,plain,
    ( sP1
    | ~ sP3
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP4
    | ~ sP1 ),
    inference(all_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,
    ~ sP4,
    inference(contra,[status(thm),contra(discharge,[h1])],[7,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYO381^5 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n011.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  : 300
% 0.12/0.33  % DateTime : Sat Aug 26 01:44:24 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.59  % SZS status Theorem
% 0.19/0.59  % Mode: cade22grackle2xfee4
% 0.19/0.59  % Steps: 5058
% 0.19/0.59  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------