Reminds me of Gödel's incompleteness theorems. Also interesting that one of the predicates is "In the same universe" It seems that two beings that existed outside of the universe could know everything about our universe so long as the information only flowed in one direction. What they couldn't know about each other would be irrelevant. That said, it's difficult to see why we should pay any attention to a god (or gods) who know everything but can't or don't act in our universe. Unless maybe the gods are Yanny and Laurel deciding on which afterlife we are due to enter depending up whether we uphold the sacred truth of the White and Gold dress or the heretic Black and Blue interpretation.

"We refute it thus."

That is a good saying but, I don't know that that is not possible.