This sounds like an incredibly stupid question but none of the relevant Wikipedia pages seem to answer it. So... if the runtime of an algorithm to solve 3SAT has running time $O(f(n))$ for some function $f$, what is $n$?
If $n$ is the number of variables appearing in the SAT-instance it seems quite easy to prove that $NP \neq P$: just note that merely reading the instance, without even dreaming about solving anything, will take exponential time in the worst case.
On the other hand, if the number $k$ of variables plays no role in $n$ we can reduce the 3SAT instance to $2^k$ 2SAT instances and solve these in polynomial time. (Polynomial from the perspective of the number $n$ that is.)
So what is going on here? Do the number of clauses and the number of variables both contribute to $n$ in some way?