TPTP Problem File: SEU500^2.p
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% File : SEU500^2 : TPTP v9.0.0. Released v3.7.0.
% Domain : Set Theory
% Problem : Preliminary Notions - Propositions as Sets
% Version : Especial > Reduced > Especial.
% English : (! phi:o.! x:i.in x (prop2set phi) -> phi)
% Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source : [Bro08]
% Names : ZFC002l [Bro08]
% Status : Theorem
% Rating : 0.00 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.29 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 v3.7.0
% Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% Number of atoms : 6 ( 2 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 15 ( 0 ~; 0 |; 0 &; 12 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 3 ^; 5 !; 0 ?; 8 :)
% SPC : TH0_THM_EQU_NAR
% Comments : http://mathgate.info/detsetitem.php?id=53
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thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ) ).
thf(prop2set_type,type,
prop2set: $o > $i ).
thf(prop2set,definition,
( prop2set
= ( ^ [Xphi: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Xx: $i] : Xphi ) ) ) ).
thf(prop2setE,conjecture,
( dsetconstrER
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ).
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