Property Directed Reachability (Pdr), also known as IC3, is a state-of-the-art model checking algorithm widely used for verifying safety properties. While Pdr is effective in finding inductive invariants, its underlying proof system, Resolution, limits its ability to construct short proofs for certain verification problems.
In this talk we present PdrER, a generalization of Pdr that uses Extended Resolution (ER), a proof system exponentially stronger than Resolution. Using a strong proof system is not straight forward: the stronger a proof system is, the harder it is to implement an *efficient* proof-search algorithm for it. While strong proof systems, such as Extended Resolution, have been used in the context of Boolean Satisfiability (SAT), it has had very limited success.
PdrER is the first model checking algorithm to use ER. This allows PdrER to construct safety proofs more efficiently, and to overall outperform Pdr on standard benchmarks. Achieving this result required careful engineering of the algorithm in order to overcome the overhead of the increased search-space associated with ER. We will delve into the details of this effort in this talk.
We implemented PdrER in a new open-source verification framework and evaluated it on the Hardware Model Checking Competition benchmarks from 2019, 2020 and 2024. Our experimental evaluation demonstrates that PdrER outperforms Pdr, solving more instances in less time and uniquely solving problems that Pdr cannot solve within a given time limit. We argue that this work represents a significant step toward making strong proof systems practically usable in model checking.