Can an all knowing, all powerful god exist while Godel Theorem is true?

Isn't any god that is all knowing a violation of Godel's theorem?

An all powerful God has the power to prove all theorems of mathematics. He can make a formal system that is both complete and consistent.

So therefore if God, Godel's theorem has a contradiction. If Godel's theorem is true, then no God.

Seems to me your definition of God is the dude that can violate the laws of logic and Godel's theorem.

So all you've proven is that it is irrational and illogical to have the concept of God in your mind.