%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEV410^5 : 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 : n002.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 19:34:29 EDT 2023

% Result   : Theorem 0.21s 0.42s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   27 (   7 unt;   4 typ;   1 def)
%            Number of atoms       :   52 (   1 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   65 (  18   ~;   7   |;   0   &;  19   @)
%                                         (   7 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :    7 (   2   ^;   5   !;   0   ?;   7   :)

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

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

thf(ty_cB,type,
    cB: $i > $o ).

thf(ty_cA,type,
    cA: $i > $o ).

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] :
          ~ ( ( cA @ X1 )
           => ( ~ ( cA @ X1 )
             => ( cB @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( cP
      @ ^ [X1: $i] :
          ( ~ ( cA @ X1 )
         => ( cB @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

thf(sP3,plain,
    ( sP3
  <=> ( sP1
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ ( cA @ eigen__3 )
     => ( cB @ eigen__3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i > $o] :
        ( ( cP @ X1 )
       => ~ ! [X2: $i] :
              ( ( cA @ X2 )
             => ( X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

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

thf(sP7,plain,
    ( sP7
  <=> ( sP6
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(cSV1_pme,conjecture,
    ( sP1
   => ~ sP5 ) ).

thf(h1,negated_conjecture,
    ~ ( sP1
     => ~ sP5 ),
    inference(assume_negation,[status(cth)],[cSV1_pme]) ).

thf(h2,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(1,plain,
    ( sP4
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP7
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP7
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP2
    | ~ sP7 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(5,plain,
    ( ~ sP3
    | ~ sP1
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP5
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,7,h2,h3]) ).

thf(9,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[8,h0]) ).

thf(0,theorem,
    ( sP1
   => ~ sP5 ),
    inference(contra,[status(thm),contra(discharge,[h1])],[8,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEV410^5 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n002.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 02:31:16 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.21/0.42  % SZS status Theorem
% 0.21/0.42  % Mode: cade22grackle2xfee4
% 0.21/0.42  % Steps: 59
% 0.21/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------