This statement hasn't been objected so far.
OK - let me have a go at refutation...
Whether God exists or not, the universe still exists - we still have perception, etc.
Suppose a hypothetical p such that p is either true or false.
Define ~p such that if p is true, then ~p is false and vice versa.
Define p --> q such that (insert truth table)
This leads us to some axioms that are tautological (list axioms)
From these axioms, we can deduce (list a bunch of theorems)
Define more stuff <->, ^, v, etc. (list definitions)
All this stuff that has been listed is necessarily true or false - and it applies to all things, including God. I don't see how God can possibly be "above" logic at all.