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The paradox assumes a much more substantive understanding of philosophy in its axioms.
Right back at you.
How is that an counterargument? Epicurus says: Those axioms create a paradox, they must be wrong. You're saying: Yeah well your axioms are too substantive. You are agreeing that the three premises can't be true. Everything else you've talked about was simply missing the point.
The Epicurean paradox does nothing else than to discuss if the premises as phrased can be true. If you talk about an idea outside those premises you've already missed the mark.
The Epicurian rebuttal to the Bronze Age understanding of omniscience can be resolved by asserting "God is less omniscient than we thought". That's it. And there are plenty of readings of Old Testament that imply the Abrahamic God isn't perfectly omniscient. Hell, the Garden of Eden myth asserts God isn't perfectly omniscient.
It asserts a paradox of infinities, rather than a non-existence of God.
It never attempted to prove non-existence. This is what you misunderstood from the beginning.