But although the coincidence of \(\textbf{P}\) and \(\textbf{NP}\) would have intriguing consequences, it also seems likely that the discovery of a proof validating the consensus view that \(\textbf{P} \neq \textbf{NP}\) would be regarded as foundationally significant. As we have seen, the sort of evidence most often cited in favor of the proper inclusion of \(\textbf{P}\) in \(\textbf{NP}\) is the failure of protracted attempts to find polynomial time algorithms for problems in \(\textbf{NP}\) in which we have a strong practical interest either in deciding in practice or in proving to be intractable.[39] A proof that \(\textbf{P} \neq \textbf{NP}\) would thus not only have the effect of validating such inductive evidence, but it would provide additional evidence that the Cobham-Edmonds Thesis provides a correct analysis of the pre-theoretical notion of feasibility. In particular, it would allow us to unconditionally assert that \(\textbf{NP}\)-hard problems are intractable in the general case.