TPTP Problem File: SEU744^2.p
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% File : SEU744^2 : 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) -> (! Y:i.in Y (powerset A) ->
% (! x:i.in x A -> in x (setminus A (binunion X Y)) -> ~(in x X))))
% Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source : [Bro08]
% Names : ZFC246l [Bro08]
% Status : Theorem
% Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 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 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% Syntax : Number of formulae : 9 ( 2 unt; 6 typ; 2 def)
% Number of atoms : 18 ( 2 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 51 ( 4 ~; 0 |; 0 &; 36 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 0 ^; 11 !; 0 ?; 11 :)
% SPC : TH0_THM_EQU_NAR
% Comments : http://mathgate.info/detsetitem.php?id=306
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thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(setminus_type,type,
setminus: $i > $i > $i ).
thf(setminusER_type,type,
setminusER: $o ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ) ).
thf(binunionTILcontra_type,type,
binunionTILcontra: $o ).
thf(binunionTILcontra,definition,
( binunionTILcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
thf(inComplementUnionImpNotIn1,conjecture,
( setminusER
=> ( binunionTILcontra
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
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