Up until 10-12 I was relatively religious I guess as that was how I'd been raised... sort of. Well, my mother and her side of the family were religious. My dad wasn't. When we drive 30+ miles on Sunday to go to church (before we moved when I was 9) my dad would sit in the car while the rest of us went in.
The first revelation (excuse the pun) I had was that these religious people around me (teachers, nuns, priests and so on) didn't had some direct line to God. They were flawed as any of the rest of us. This came at about age 10 largely due to being blamed for something I didn't do.
Of course the mantra is that "people are flawed", "God works in mysterious ways" and other such platitudes but in my case the foundations were already crumbling. I basically rejected organized religion by age 11-12 and never looked back.
At this time and for awhile afterwards I took the "sitting on the fence" approach and described myself as agnostic (as many do I think). Basically this is a cop out though. It's simply not taking a position. But I guess not everyone needs to take a position but agnostic is basically saying "I don't care (one way or the other)" (although some would phrase this more along the lines of simply not knowing).
But some time later I eventually gave this up and essentially became a hardline atheist. Personally, I find the notion of a divine being--any divine being--to be ridiculous and simply the byproduct of the human fallacy to see patterns in randomness ("I prayed for rain today and it rained therefore there is a God. Last month I prayed for rain and there was no rain so I guess God Has A Plan [tm].").
Not that I don't think religion is useful. It's really a form of community and moral enforcement. Some people need to be told what to do. Others simply need to fit in somewhere (we all do in different ways). Yet others find comfort in the idea that when you die you simply cease to exist (which is something we're not well-equipped to comprehend). I get all that.
Take that as you will.
My point was just that in a strict logical sense you can't prove that this belief is correct -- or put another way, I'm more militantly logical than I am militantly atheist.
I think it is reasonable to take everyday speech saying "does not exist" as meaning "appears not to exist, and if it does exist this is indistinguishable from not existing".
Come to think if it, I'm pretty sure I've never stated "invisible pink unicorns do not exist". On the other hand, I've never had to avoid saying it either; oddly enough, I've never felt any urge to comment on the possible existence of invisible pink unicorns until now.
But this is immaterial to the issue at hand, which is one of logical arguments, not mere validity of statements. I don't believe that invisible pink unicorns exist, but I would never state that I had logically proven that invisible pink unicorns do not exist.
The IPU is a poor analogy for disproving the existence of God because it gives up too much ground.
God is in the same category as a square circle. Something that is self-contradictory and therefore cannot exist.