[umanwizard]

A decision problem (i.e., determining whether a string is a member of some set) is in NP if there is a program and polynomials p and q such that for every string x in the set, there is some proof of that fact of size at most q(|x|), which the program can verify is correct in time at most p(|x|).

This implies that there exists an exponential-time deterministic algorithm to solve any NP problem: just check all the possible proofs, reporting "yes" if you find one that works, or "no" when you've generated all the proofs size q(|x|) and found that they fail.