Nothing is provable to the level you demand (well, pretty much nothing, cogito ergo sum and all that). Given that none of the omni* are well defined, the question doesn't mean much either.
Are you saying that it's an inference problem and after enough pieces of evidence we should just accept omnipotence (for instance) as the best hypothesis with a high degree of confidence, as we trust gravity now? How about the mind control problem?
Also, what you say about the omni* being not well defined sounds interesting. can you elaborate?
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