Proof-system domination by conservative extensions conjecture

Let $Q$ be a propositional proof system. A theory $\mathcal{T}$ is a conservative extension of a base theory when it extends that theory without proving any new sentences in the base theory’s original language. Conservative-extension domination conjecture. For every propositional proof system $Q$, there is a conservative extension $\mathcal{T}$ of ZFC or PA that outperforms $Q$ in proving tautologies. Moreover, adjoining an undecidable statement as a new axiom to $\mathcal{T}$ to form a conservative extension $\mathcal{T}'$ further improves $\mathcal{T}$ in proving tautologies. The conjecture connects the nonexistence of optimal propositional proof systems with undecidability and the effect of adding axioms, but the source provides no resolution.