  Q-resolution is a proof system for quantified Boolean formulas (QBFs) in
prenex conjunctive normal form (PCNF) which underlies search-based QBF solvers
with clause and cube learning (QCDCL). With the aim to derive and learn
stronger clauses and cubes earlier in the search, we generalize the axioms of
the Q-resolution calculus resulting in an exponentially more powerful proof
system. The generalized axioms introduce an interface of Q-resolution to any
other QBF proof system allowing for the direct combination of orthogonal
solving techniques. We implemented a variant of the Q-resolution calculus with
generalized axioms in the QBF solver DepQBF. As two case studies, we apply
integrated SAT solving and resource-bounded QBF preprocessing during the search
to heuristically detect potential axiom applications. Experiments with
application benchmarks indicate a substantial performance improvement.
