Property Directed Reachability with Extended Resolution

Abstract 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. This paper introduces PdrER , a novel generalization of Pdr that uses Extended Resolution (ER), a proof system exponentially stronger than Resolution, when constructing a proof of correctness. PdrER leverages ER to construct shorter bounded proofs of correctness, enabling it to discover more compact inductive invariants. While PdrER is based on Pdr , it includes algorithmic enhancements that had to be made in order to efficiently use ER in the context of model checking. 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 paper represents a significant step toward making strong proof systems practically usable in model checking.