Human logic can be only one of these 3:
1) Circular
2) Based on premises which are accepted as truth without asking for reason for the premises
3) Infinite reasoning
All 3 of these forms of logic are flawed.
1) is a logical fallacy.
2) is based on no proof.
3) cannot be proven at all, since infinity cannot be demonstrated.
However, if we accept any of these as basis for our logic, we end up proving God.
1) Circular logic: God exists because Bible says so. Bible is true because it is the word of God.
2-1) Unquestionable premise: God exists because it says so in the Bible. Bible is unquestionable.
(Awkward moment for people who think feelings are unquestionable).
2-2) If feelings are unquestionable, that means God exists because many people feel the presence of God.
3) Infinite reasoning: God exists because of infinite amount of reasons, such as God1, God2, God3...
So therefore, no matter what logic we use, God exists.