And what claims. That Socrates not believed in Zeus. What else did he do in Delphi? Which god did he obeyed by his own claims, if it wasn't Zeus? And what better that would be?

Apollo, I gathered from my classes; at least the Socrates presented by Plato. (I'm not well-read enough in Xenophon or the Straussian esoteric interpretations to summarize their versions.) Most obviously, Delphi wasn't Zeus's; that'd be Dodonna or one of the other oracles. As well, the text of things like the Apology or The Republic are vague enough that one could - and many like medieval Christians have - make Socrates out to be a monotheist, which allows for disbelief in Zeus.