IF formula with 4 conditions...

Hi all. Currently trying to wrestle IF formulas.

Here is a screenshot of my sheet:

The formula will go in column K. The top three rows are real data, but the bottom line that I have selected (which is row 9) is 'dummy' data that I'm using to check the formula works.

SShot.png

What I'm trying to achieve:
If I9 is blank, show nothing (i.e. blank cell)
If J9 is blank, show nothing (like above)
If J9 is between H9 and I9, show "true"
IF J9 is after I9, show "False"

The final complication is that if *today's date* is after I9, then K9 should show false, even if I9 is blank.

(I've used conditional formatting in column K to show a background and font colour of green if the cell says true, and red if it says false, hence why you can't actually see any text in those cells).

I'm not sure if what I want is even possible, but any help or advice would be greatly appreciated!