How can anyone conclusively prove that God doesn't exist. Its not possible as long as all possiblities of Gods existence is proved to be wrong.
Forget all possiblities ,its not possible t0 just prove that God doesn't exist in each and every points in the space (universe). Even if we find a method to check the presence of God a point in space the time required to cover the entire universe is unlimited (non deterministic). so the problem is unsolvable.
Well the funny thing is that its also impossible to prove the absence of elfs, fairies under the garden, Aalis's wonderland, or a flying tea pot. The burden of proof for presence of god is then clearly with proponents of god. Will they be able to prove it ?? I don't believe so.