Towards Combining Model Checking and Proof Checking

Model checking and automated theorem proving are two pillars of formal verification methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and the complete automaticity of model checking. It places the focus on the verification of temporal logic properties of Kripke models. The main contributions are (i) introducing an extended computation tree logic that allows polyadic predicate symbols; (ii) designing a proof system for this logic, taking Kripke models as parameters; (iii) developing a proof search algorithm for this system and a new automated theorem prover to implement it. The verification process of the new prover is completely automatic and produces either a counterexample when the property does not hold, or a certificate when it does. The experimental results compare well to existing state-of-the-art tools on some benchmarks, and the efficiency is illustrated by the application to an air traffic control problem.