Here’s some great logic for you:

1. If there are frogs, they are purple.
2. If a purple frog exists, no ribbetting will be heard.
3. Ribbetting is heard.
4. No purple frog exists (from 2 and 3).
5. Hence, there are no frogs (from 1 and 4).

Thus by the Argument from Ranine Hiddenness we are able to conclude that no frog exists, even though our conclusion flies in the face of the observable fact that something out there – though clearly not a frog! – can be heard going ribbet, ribbet. And frankly, I think I’d be more impressed with the intellectual prowess exhibited by the average frog’s ribbets than by the cretins who produced this illogical drivel.

This is an accurate, parallel syllogism for the atheist’s Divine Hiddenness argument.