I thought about that, but it automatically disqualifies every prophecy I can think of. I didn't want to start out with a big giant "No".
Yep, that's the same conclusion that I came to. You could even adjust it to be a little more lenient:
"There is no strong evidence that the prophecy was initially recorded only after the event prophesied"
And it would still eliminate most, of the fullfilled prophecy in the bible that fits your other rules. When I was trying to convince myself, years ago, that the bible must have been inspired, I went through a list of as many fullfilled prophecies that I could find and looking at them all objectively, the only prophecies that I concluded where reasonable to consider as inspired where those found in the book of Daniel. Come to find out, the book of Daniel appears to be written well after the prophecies where fullfilled.
Another rule to consider is that the description of the fullfillment of the prophecy must be independantly verifiable, at least if you're trying to use bible prophecy as a way to prove that the bible is god's word, as I was. If you already accept the bible as inerrant, then that won't matter to you much, and there will probably be a few prophecies that you could consider fullfilled. For me, the prophecies about Jesus weren't reliable because the only evidence of their fullfillment was a book that obviously only had any legitimacy if they described their fullfillment.