Boolean satisfiability problem
For instance, the Boolean satisfiability problem is NP-complete by the Cook–Levin theorem, so "any" instance of "any" problem in NP can be transformed mechanically into an instance of the Boolean satisfiability problem in polynomial time. The Boolean satisfiability problem is one of many such NP-complete problems. If any NP-complete problem is in P, then it would follow that P = NP. However, many important problems have been shown to be NP-complete, and no fast algorithm for any of them is known.