@Val Killmore,
Try to conceive of the title this way, Val:
There are people who "believe" gods exist (or that a GOD exists).
I am not one of them.
I do not believe gods exist!
There are other people who "believe" there are no gods.
I am not one of them.
I do not believe there are no gods.
My title is exactly that: I do not believe gods exist...but I do not believe there are no gods.
As I explained within a couple of hours of posting the thread, the reason I wrote the title as I did was to show how the use of the words "belief" and "believe" can distort thinking.
Both of your "re-writes" make the mistake I was trying to illustrate. Both of your re-writes make a false assumption about what is being said. I will discuss this with you at length if you want.