  Software model checkers based on under-approximations and SMT solvers are
very successful at verifying safety (i.e. reachability) properties. They
combine two key ideas -- (a) "concreteness": a counterexample in an
under-approximation is a counterexample in the original program as well, and
(b) "generalization": a proof of safety of an under-approximation, produced by
an SMT solver, are generalizable to proofs of safety of the original program.
In this paper, we present a combination of "automatic abstraction" with the
under-approximation-driven framework. We explore two iterative approaches for
obtaining and refining abstractions -- "proof based" and "counterexample based"
-- and show how they can be combined into a unified algorithm. To the best of
our knowledge, this is the first application of Proof-Based Abstraction,
primarily used to verify hardware, to Software Verification. We have
implemented a prototype of the framework using Z3, and evaluate it on many
benchmarks from the Software Verification Competition. We show experimentally
that our combination is quite effective on hard instances.
