The existence of life is a straightforward and definitive proof for the existence of God.
I don't see why "life exists and no god exists" should be a contradiction for formal or other reasons.
Furthermore: the existence of which god? As you know there and have been many religions with different gods.
And lastly: if it was straightforward, how come so many people fail to see it?
We can determine the truth of this statement empirically due to our understanding of information science, entropy, chemistry, and physics.