While these sorts of logical arguments support my disbelief in the various religious god claims they do not result in my complete knowledge that "a god" does not or can not exist.
Mathematicians have the same problem with existence proofs vs constructive proofs. In an existence proof, if you prove something possible or impossible, you are done. In a constructive proof, one - you are proving something possible, two - you are demonstrating an example. I exist, and am a demi-god, so that meets the requirement of number two.