It is known that there is sharp complexity jump between Horn 3-SAT and 3-SAT problems. The former is $P$-complete while the later is $NP$-complete. I would like to see a continuous spectrum of hardness variation between these two problems. I'm interested in finding the influence of the number Horn clauses in general 3-SAT problem. Suppose the number of Horn 3-SAT clauses in input 3-SAT formula is given as a function $f(n)$ in the number of variables $n$. What is known about the complexity of the 3-SAT(f) problem where $f(n)$ is one of the following cases:
1- $f(n)$ is $O(1)$
2- $f(n)$ is $O(\log n)$
3- $f(n)$ is $\Omega(n)$
4- $f(n)$ is $o(n)$
My intuition is that the first case is tractable while the third one is intractable. Also, I guess the second case is of intermediate complexity (NPI). What is known about the complexity of this problem? I'm looking for formal proofs of complexity?
EDIT: There is no restriction on the number of anti-Horn 3-SAT clauses. A 3-SAT clause must be either Horn or anti-Horn but not both.