Paired resolution and $\mathsf{NP}$ vs. $\mathsf{coNP}$?
It is known that some formulas require exponentially long Resolution proofs. Therefore Resolution cannot be used (directly) to prove that $\mathsf{NP}=\mathsf{coNP}$.

Note that the details of your procedure are completely irrelevant. The lower bounds show that whatever algorithm you use to create your Resolution refutations, there will be some formulas on which it will take exponential time, simply because every Resolution refutation of these formulas is exponentially long.