What is the complexity of determining whether or not conjunction of positive CNF and negative CNF is satisfiable?
Given a CNF, which is a conjunction of positive CNF and negative CNF, what is the complexity of the problem to determine that this special case of CNF is satisfiable?


The problem is provably NP-complete by reduction from CNF satisfiability.

Each negative literal $\lnot{x}$ in a CNF SAT instance can be converted to a positive literal by replacing all occurrences of it with a new variable $z$ plus the following two CNF clauses: $x \lor z$ and $\lnot{x} \lor \lnot{z}$.  The clauses force $z$ to act as the same constraint as $\lnot{x}$.  Once all the original negated literals have been replaced, you are left with clauses that contain either all positive or all negative literals.  Since any CNF SAT instance can be reduced to this form and since CNF SAT is NP-complete and since your problem is trivially in NP, your problem must be NP-complete.