Since it is strongly suspected that \(\textbf{NP} \neq \textbf{coNP}\) (see   Section 3.4.1), the current consensus is that polynomial proof systems do not exist. At present, however, the failure of polynomial boundedness has not been proven for most familiar proof systems, inclusive of \(\mathcal{P}_1\), \(\mathcal{P}_2\), and \(\mathcal{P}_3\).