I'm developing a rebuttal to Biblical literalists and I'd like to know whether the following is a recognized/named type of syllogism or other type of argument (and if so, what it's called): Verse X prophesied that <whatever> would happen <whatever> happened in verse Y Therefore, the prophecy was fulfilled (If this is not a recognized/named type of syllogism or other type of argument, could it be made so by adding one or two lines?)

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This is still a little confusing to me, but I take it that you may be looking for the term:

Vaticinium ex eventu

This occurs when a writer (whether Biblical or not) offers a prophecy that some event will occur when (it is assumed) that the writer already knows the event has taken place. In the context of the Bible, perhaps the most salient case that is the subject of controversy is the New Testament recording of Jesus predicting that the Temple will be destroyed, which it was some forty years after his death. It is not obvious, though, whether this is a case of writing ex eventu. It is possible that Jesus could have foreseen the destruction of the Temple, especially when you consider the evidence available during Jesus' lifetime of how Rome responds to rebellion and recent past cases of Jewish resistance to Roman imperial power.

This is more a matter of history, than philosophy per se, though philosophers have long had an interest in thinking about the miraculous and whether it can ever be reasonable to believe in miracles. See the Stanford Encyclopedia of Philosophy on Hume and the entry Philosophy of Religion.

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