What are some good checkmate arguments against religion?

[Rampant.A.I.]

Name a logically sound ontological argument.

You should read more carefully. I said there are, so far as I can tell, logical proofs of God's existence. What I mean is that the arguments in question are valid, i.e the conclusion follows from the premises. I don't think the actual premises are true/sound, otherwise I wouldn't be an atheist/naturalist. And to be honest, the least we should be surprised by is logical validity. After all, the following, is logically valid:

All men men are bald;
MindForgedManacle is a man;
Therefore MindForgedManacle is bald.

But we clearly known the argument is unsound.

Now, logically valid ontological arguments would include:

Plantinga's modal ontological argument, the higher-order ontological argument, the mereological ontological argument and (I think) Anselm's ontological argument.

But as I say, I contest each of those.

Plantinga himself admits the modal ontological argument is unconvincing and flawed: One must presuppose the conclusion to allow the premises.

I'm unsure why you would provide four examples of circular reasoning when I asked you for a logically sound ontological argument, but judging from past responses and your post here, you simply fail to understand why circular reasoning is logically invalid.

Two words that can be used against any and all theist arguments: Prove it.

Strictly speaking, theists can provide a logical proof of God's existence (think ontological arguments in particular). The real question should be what actually follows from those proofs, i.e if successful, do they necessarily establish God's existence?

You should learn not to describe presuppositional arguments as "logical proofs," and then condescend to anyone who disagrees with an invalid ontological argument being defined as a "logical proof" like an arrogant 21 year-old suffering from the Dunning-Kreuger effect.