# CNF-SAT time complexity and input processing

Boolean Satisfiability (CNF-SAT) problem in $$n$$ variables may contain a CNF formula with $$O(2^n)$$ clauses in the worst case.

My question is: Wouldn't a program reading a CNF formula have to asymptotically run $$O(2^n)$$ steps? Is the search for a sub-exponential CNF-SAT algorithm moot?

For instance, suppose we have CNF formulas with $$n$$ variables and only $$10n$$ clauses. No one knows how to solve this in time polynomial in $$n$$.