On the matter of proving nonexistence, this is possible. The problem lies with the definition of a god. Whenever you try to proof anything, you assume the worl

On the matter of proving nonexistence, this is possible. The problem lies with the definition of a god. Whenever you try to proof anything, you assume the world is causal/deterministic. An omnipotent influence is therefore also deterministic. This makes any god equal to a law of nature. Define your 'law that is a god' and it can be proven to exist/not-exist in theory.