But even if you are only interested in satisfiability, it sometimes happened that OBDD-based solvers are more efficient than CDCL SAT-solver. Indeed, for some application, you need to have richer constraints than the clauses used in CNF formulas. For example, for circuit synthesis, you often need to represent parity constraints (parity(x1...xn) is true iff there are an even number of values set to 1). CNF encoding of such constraints are expensive and kill most of the clever stuff that CDCL solvers do, while representing a parity constraint is actually quite easy with an OBDD of size 2n.