TPTP Problem File: SEU602^2.p

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% File     : SEU602^2 : TPTP v7.0.0. Released v3.7.0.
% Domain   : Set Theory
% Problem  : Preliminary Notions - Operations on Sets - Set Difference
% Version  : Especial > Reduced > Especial.
% English  : (! A:i.! B:i.! x:i.in x (setminus A B) -> in x A)

% Refs     : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source   : [Bro08]
% Names    : ZFC104l [Bro08]

% Status   : Theorem
% Rating   : 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% Syntax   : Number of formulae    :    7 (   0 unit;   4 type;   2 defn)
%            Number of atoms       :   27 (   2 equality;  14 variable)
%            Maximal formula depth :   10 (   6 average)
%            Number of connectives :   21 (   1   ~;   0   |;   0   &;  17   @)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4   :;   0   =)
%            Number of variables   :   10 (   0 sgn;   6   !;   0   ?;   4   ^)
%                                         (  10   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : http://mathgate.info/detsetitem.php?id=270
%          : 
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thf(in_type,type,(
    in: $i > $i > $o )).

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

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(setminus_type,type,(
    setminus: $i > $i > $i )).

thf(setminus,definition,
    ( setminus
    = ( ^ [A: $i,B: $i] :
          ( dsetconstr @ A
          @ ^ [Xx: $i] :
              ~ ( in @ Xx @ B ) ) ) )).

thf(setminusEL,conjecture,
    ( dsetconstrEL
   => ! [A: $i,B: $i,Xx: $i] :
        ( ( in @ Xx @ ( setminus @ A @ B ) )
       => ( in @ Xx @ A ) ) )).

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