SorryDB: Can AI Provers Complete Real-World Lean Theorems?
This work addresses the problem of evaluating AI theorem provers on realistic tasks for mathematicians and formal verification communities, though it is incremental in benchmarking methodology.
The authors introduced SorryDB, a dynamic benchmark of open Lean tasks from real-world formalization projects, to align AI provers with community needs and mitigate test-set contamination. They evaluated various approaches on 1000 tasks, finding that an agentic approach based on Gemini Flash performed best but was not strictly superior to other methods.
We present SorryDB, a dynamically-updating benchmark of open Lean tasks drawn from 78 real world formalization projects on GitHub. Unlike existing static benchmarks, often composed of competition problems, hillclimbing the SorryDB benchmark will yield tools that are aligned to the community needs, more usable by mathematicians, and more capable of understanding complex dependencies. Moreover, by providing a continuously updated stream of tasks, SorryDB mitigates test-set contamination and offers a robust metric for an agent's ability to contribute to novel formal mathematics projects. We evaluate a collection of approaches, including generalist large language models, agentic approaches, and specialized symbolic provers, over a selected snapshot of 1000 tasks from SorryDB. We show that current approaches are complementary: even though an agentic approach based on Gemini Flash is the most performant, it is not strictly better than other off-the-shelf large-language models, specialized provers, or even a curated list of Lean tactics.