That person is merely proving that his/her definition of God does not exist.
God has property A. A is observed. God exists.
But property ~A has also been observed. God doesn't exist!
Ooops, paradox.
The bible is full of contradictions, if that's what you're referring to. If we are to assume (I know, big assumption here) that the bible is, in itself, proof then we are left with the conclusion that it's just a big paradox.
God's omniscient, oh wait, no he's not. But he is. But he's not.
God is singular. No, wait, this next line uses the plural. But this one uses the singular.
The bible has a really sloppy editor. But the assumption we've made, that it is proof of anything, is more a logical leap than I'm willing to take. The idea that the bible is divine is taken from the bible itself. Basically the argument is.. well... invalid in form. The bible is true because it is the word of god. The bible is the word of God because the Bible says it is the word of god and is therefore true. I hate circular arguments like that.
Still, the idea that some unseen intelligent power created our universe is possible, just not probable. And having faith is just that, believing in the improbable.