TPTP Problem File: SEU517^2.p

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% File     : SEU517^2 : TPTP v7.4.0. Released v3.7.0.
% Domain   : Set Theory
% Problem  : Preliminary Notions - Power Sets and Unions
% Version  : Especial > Reduced > Especial.
% English  : (! A:i.dsetconstr A (^ x:i.true) = A)

% Refs     : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source   : [Bro08]
% Names    : ZFC019l [Bro08]

% Status   : Theorem
% Rating   : 0.29 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v3.7.0
% Syntax   : Number of formulae    :    9 (   0 unit;   5 type;   3 defn)
%            Number of atoms       :   49 (   5 equality;  26 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :   35 (   0   ~;   0   |;   0   &;  25   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5   :;   0   =)
%            Number of variables   :   14 (   1 sgn;  11   !;   0   ?;   3   ^)
%                                         (  14   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : http://mathgate.info/detsetitem.php?id=466
%          : 
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thf(in_type,type,(
    in: $i > $i > $o )).

thf(dsetconstr_type,type,(
    dsetconstr: $i > ( $i > $o ) > $i )).

thf(dsetconstrI_type,type,(
    dsetconstrI: $o )).

thf(dsetconstrI,definition,
    ( dsetconstrI
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx @ A )
         => ( ( Xphi @ Xx )
           => ( in @ Xx
              @ ( dsetconstr @ A
                @ ^ [Xy: $i] :
                    ( Xphi @ Xy ) ) ) ) ) ) )).

thf(dsetconstrEL_type,type,(
    dsetconstrEL: $o )).

thf(dsetconstrEL,definition,
    ( dsetconstrEL
    = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
          ( ( in @ Xx
            @ ( dsetconstr @ A
              @ ^ [Xy: $i] :
                  ( Xphi @ Xy ) ) )
         => ( in @ Xx @ A ) ) ) )).

thf(setext_type,type,(
    setext: $o )).

thf(setext,definition,
    ( setext
    = ( ! [A: $i,B: $i] :
          ( ! [Xx: $i] :
              ( ( in @ Xx @ A )
             => ( in @ Xx @ B ) )
         => ( ! [Xx: $i] :
                ( ( in @ Xx @ B )
               => ( in @ Xx @ A ) )
           => ( A = B ) ) ) ) )).

thf(setoftrueEq,conjecture,
    ( dsetconstrI
   => ( dsetconstrEL
     => ( setext
       => ! [A: $i] :
            ( ( dsetconstr @ A
              @ ^ [Xx: $i] : $true )
            = A ) ) ) )).

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