TPTP Problem File: SEU720^2.p
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% File : SEU720^2 : TPTP v9.0.0. Released v3.7.0.
% Domain : Set Theory
% Problem : Typed Set Theory - Laws for Typed Sets
% Version : Especial > Reduced > Especial.
% English : (! A:i.! X:i.in X (powerset A) -> (! x:i.in x A ->
% ~(in x (setminus A X)) -> in x X))
% Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source : [Bro08]
% Names : ZFC222l [Bro08]
% Status : Theorem
% Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 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 v3.7.0
% Syntax : Number of formulae : 6 ( 1 unt; 4 typ; 1 def)
% Number of atoms : 10 ( 1 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 27 ( 2 ~; 0 |; 0 &; 19 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 6 !; 0 ?; 6 :)
% SPC : TH0_THM_EQU_NAR
% Comments : http://mathgate.info/detsetitem.php?id=280
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thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(setminus_type,type,
setminus: $i > $i > $i ).
thf(setminusI_type,type,
setminusI: $o ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
thf(complementTE1,conjecture,
( setminusI
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ X ) ) ) ) ) ).
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