Although some think of omnipotence as unbounded power, as you here assume for your argument, I and most theist philosophers would define it as maximal power—thus, limited by that which is possible, as well as by God’s own nature.

By this definition, your argument doesn’t at all refute God’s existence.

See “Omnipotence” in the Stanford Encyclopedia of Philosophy.

While we’re on it, I must demand epistemic justification for the law of non-contradiction. I contend that a theistic externalism (a priori knowledge is given to us by God) is necessary for such knowledge to be counted trustworthy. Else you’re left with the conclusions of John Stuart Mill, that logical and mathematical axioms could be overturned by experiment, and may not be true in some distant part of the universe.