TPTP Problem File: SEU580^2.p
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% File : SEU580^2 : TPTP v8.2.0. Released v3.7.0.
% Domain : Set Theory
% Problem : Preliminary Notions - Relations on Sets - Subsets
% Version : Especial > Reduced > Especial.
% English : (! A:i.! phi:i>o.in (dsetconstr A (^ x:i.phi x)) (powerset A))
% Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source : [Bro08]
% Names : ZFC082l [Bro08]
% Status : Theorem
% Rating : 0.00 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v4.1.0, 0.33 v3.7.0
% Syntax : Number of formulae : 8 ( 2 unt; 5 typ; 2 def)
% Number of atoms : 12 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 25 ( 0 ~; 0 |; 0 &; 20 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 2 ^; 8 !; 0 ?; 10 :)
% SPC : TH0_THM_EQU_NAR
% Comments : http://mathgate.info/detsetitem.php?id=258
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thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
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(powersetI_type,type,
powersetI: $o ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ) ).
thf(sepInPowerset,conjecture,
( dsetconstrEL
=> ( powersetI
=> ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ) ).
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