Quantified Invariant Generation Using an Interpolating Saturation Prover

Interpolating provers have a variety of applications in verification, including invariant generation and abstraction refinement. Here, we extended these methods to produce universally quantified interpolants and invariants, allowing the verification of programs manipulating arrays and heap data structures. We show how a paramodulation-based saturation prover, such as SPASS, can be modified in a simple way to produce a first-order interpolating prover that is complete for universally quantified interpolants. Using a partial axiomatization of the theory of arrays with transitive closure, we show that the method can verify properties of simple programs manipulating arrays and linked lists.