Cost-Efficient Theorem Proving via Agent Orchestration in Program Verification
This study addresses the challenges of large-scale proof obligations and the difficulty of balancing success rates against computational overhead in program verification by proposing the CoCo-Prover framework. This method formulates formal proving as cost-aware meta-level decision-making, employing a bi-level AND/OR hypergraph proof structure and lemma dependency graphs to enable symbolic topological selection. Furthermore, it treats expensive expert invocations as priced services for dynamic agent orchestration and routing. Evaluated in the Lean 4 environment across five benchmarks, CoCo-Prover achieves state-of-the-art solve rates—reaching up to 100%—while reducing computational costs by 30.9% compared to the strongest baseline. Ultimately, this work effectively unifies efficiency and economy in automated theorem proving.