TSTP Solution File: SEU573^2 by Lash---1.13

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%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU573^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n031.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 17:18:55 EDT 2023

% Result   : Theorem 0.20s 0.43s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   37
% Syntax   : Number of formulae    :   47 (  15 unt;   6 typ;   3 def)
%            Number of atoms       :  102 (   3 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  182 (  17   ~;  10   |;   0   &; 109   @)
%                                         (  11 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  20 usr;  18 con; 0-2 aty)
%            Number of variables   :   41 (   9   ^;  32   !;   0   ?;  41   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_powerset,type,
    powerset: $i > $i ).

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

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

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

thf(ty_in,type,
    in: $i > $i > $o ).

thf(ty_subset,type,
    subset: $i > $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] :
          ~ ( ( in @ X1 @ eigen__0 )
           => ( in @ X1 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(sP1,plain,
    ( sP1
  <=> ( subset @ eigen__0 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( in @ eigen__3 @ eigen__0 )
     => ( in @ eigen__3 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( sP1
       => ( ( in @ X1 @ eigen__0 )
         => ( in @ X1 @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ( in @ X1 @ eigen__1 ) )
     => ( in @ eigen__0 @ ( powerset @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] :
        ( ( in @ X1 @ eigen__0 )
       => ( in @ X1 @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i,X2: $i] :
        ( ( subset @ eigen__0 @ X1 )
       => ( ( in @ X2 @ eigen__0 )
         => ( in @ X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ X1 )
           => ( in @ X2 @ eigen__1 ) )
       => ( in @ X1 @ ( powerset @ eigen__1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP1
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i,X2: $i,X3: $i] :
        ( ( subset @ X1 @ X2 )
       => ( ( in @ X3 @ X1 )
         => ( in @ X3 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( in @ eigen__0 @ ( powerset @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i,X2: $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ X2 )
           => ( in @ X3 @ X1 ) )
       => ( in @ X2 @ ( powerset @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(def_powersetI,definition,
    ( powersetI
    = ( ! [X1: $i,X2: $i] :
          ( ^ [X3: $o,X4: $o] :
              ( X3
             => X4 )
          @ ! [X3: $i] :
              ( ^ [X4: $o,X5: $o] :
                  ( X4
                 => X5 )
              @ ( in @ X3 @ X2 )
              @ ( in @ X3 @ X1 ) )
          @ ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ).

thf(def_subsetE,definition,
    ( subsetE
    = ( ! [X1: $i,X2: $i,X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( subset @ X1 @ X2 )
          @ ( ^ [X4: $o,X5: $o] :
                ( X4
               => X5 )
            @ ( in @ X3 @ X1 )
            @ ( in @ X3 @ X2 ) ) ) ) ) ).

thf(subset2powerset,conjecture,
    ( sP11
   => ( sP9
     => ! [X1: $i,X2: $i] :
          ( ( subset @ X1 @ X2 )
         => ( in @ X1 @ ( powerset @ X2 ) ) ) ) ) ).

thf(h1,negated_conjecture,
    ~ ( sP11
     => ( sP9
       => ! [X1: $i,X2: $i] :
            ( ( subset @ X1 @ X2 )
           => ( in @ X1 @ ( powerset @ X2 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[subset2powerset]) ).

thf(h2,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP9
     => ! [X1: $i,X2: $i] :
          ( ( subset @ X1 @ X2 )
         => ( in @ X1 @ ( powerset @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: $i,X2: $i] :
        ( ( subset @ X1 @ X2 )
       => ( in @ X1 @ ( powerset @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ ! [X1: $i] :
        ( ( subset @ eigen__0 @ X1 )
       => ( in @ eigen__0 @ ( powerset @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ( sP1
     => sP10 ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP10,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP8
    | ~ sP1
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP5
    | ~ sP2 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(4,plain,
    ( ~ sP4
    | ~ sP5
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP7
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP11
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP6
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP9
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h6,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,h2,h4,h8,h9]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h7,h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,9,h8,h9]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__1)],[h6,10,h7]) ).

thf(12,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__0)],[h5,11,h6]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,12,h4,h5]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,13,h2,h3]) ).

thf(15,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[14,h0]) ).

thf(0,theorem,
    ( sP11
   => ( sP9
     => ! [X1: $i,X2: $i] :
          ( ( subset @ X1 @ X2 )
         => ( in @ X1 @ ( powerset @ X2 ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[14,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU573^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n031.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Wed Aug 23 16:09:35 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  % Mode: cade22grackle2xfee4
% 0.20/0.43  % Steps: 292
% 0.20/0.43  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------