%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV391^5 : 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 : n004.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 19:34:26 EDT 2023

% Result   : Theorem 20.10s 20.43s
% Output   : Proof 20.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   30 (   7 unt;   5 typ;   1 def)
%            Number of atoms       :   57 (   1 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  116 (  26   ~;  10   |;   0   &;  59   @)
%                                         (   9 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   17 (  15 usr;  13 con; 0-3 aty)
%            Number of variables   :   10 (   1   ^;   9   !;   0   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_k,type,
    k: $i > $i ).

thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(ty_h,type,
    h: $i > $i ).

thf(ty_cP,type,
    cP: $i > $i > $i > $o ).

thf(ty_a,type,
    a: $i ).

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

thf(eigendef_eigen__0,definition,
    ( eigen__0
    = ( eps__0
      @ ^ [X1: $i] :
          ~ ~ ! [X2: $i] :
                ~ ( ( ~ ( cP @ a @ ( h @ X1 ) @ X1 )
                   => ( cP @ a @ ( k @ X1 ) @ X1 ) )
                 => ( cP @ a @ X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__0])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i] :
        ~ ! [X2: $i] :
            ~ ( ( ~ ( cP @ a @ ( h @ X1 ) @ X1 )
               => ( cP @ a @ ( k @ X1 ) @ X1 ) )
             => ( cP @ a @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( cP @ a @ ( h @ eigen__0 ) @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ~ sP2
     => ( cP @ a @ ( k @ eigen__0 ) @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP3
     => ( cP @ a @ ( k @ eigen__0 ) @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ~ ( sP3
         => ( cP @ a @ X1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i] :
        ~ ! [X2: $i] :
            ~ ! [X3: $i] :
                ~ ( ( ~ ( cP @ a @ ( h @ X2 ) @ X2 )
                   => ( cP @ X1 @ ( k @ X2 ) @ X2 ) )
                 => ( cP @ X1 @ X3 @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( cP @ a @ ( k @ eigen__0 ) @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP3
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( sP3
     => ( cP @ a @ a @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(cTHM87_pme,conjecture,
    ~ sP6 ).

thf(h1,negated_conjecture,
    sP6,
    inference(assume_negation,[status(cth)],[cTHM87_pme]) ).

thf(1,plain,
    ( sP4
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP8
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP5
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP5
    | ~ sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP3
    | sP2
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP9
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP5
    | ~ sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP1
    | sP5 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0]) ).

thf(9,plain,
    ( ~ sP6
    | ~ sP1 ),
    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,
    ~ sP6,
    inference(contra,[status(thm),contra(discharge,[h1])],[10,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEV391^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n004.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  : 300
% 0.13/0.34  % DateTime : Thu Aug 24 03:28:23 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 20.10/20.43  % SZS status Theorem
% 20.10/20.43  % Mode: cade22grackle2x798d
% 20.10/20.43  % Steps: 41
% 20.10/20.43  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------