  A quantified Boolean formula (QBF) is a propositional formula extended with
universal and existential quantification over propositions. There are two
methodologies in CEGAR based QBF solving techniques, one that is based on a
refinement loop that builds partial expansions and a more recent one that is
based on the communication of satisfied clauses. Despite their algorithmic
similarity, their performance characteristics in experimental evaluations are
very different and in many cases orthogonal. We compare those CEGAR approaches
using proof theory developed around QBF solving and present a unified calculus
that combines the strength of both approaches. Lastly, we implement the new
calculus and confirm experimentally that the theoretical improvements lead to
improved performance.
