Atheist Hope for Logical Refutation of God

I asked ChatGPT to prove that logic isn’t logical. On the technical basis it advanced several points. On the semantic issue it said that well, logic is logic implicitly. Then it cited Godel’s incompleteness theorems to mention that in any sufficiently complex system some formal statements can’t be proven within the system and hence logic cannot prove it’s own foundation. Those may be useful points to keep handy when asserting propositions about the unknown . Atheists necessarily must stipulate they don’t know God.

Apparently neither Euclid's axioms or proportional logic are able to represent complex arithmetical concepts and hence are exempt from Godel's Incompleteness theorems. It was mentioned that even simple systems can be incomplete however. An example made was Euclid's axioms and postulates if he had omitted the parallel postulate.