Kimina-Prover hits 92.2% on math benchmark by learning to reuse its own lemmas

The team at Numina and Kimi just pushed automated theorem proving past a major milestone. Their new Kimina-Prover-72B scored a 92.2% pass rate on the miniF2F benchmark, a widely used testbed for formal mathematical reasoning. That’s a substantial leap, and it didn’t come from simply scaling up a model and throwing more samples at the problem.

The engine underneath is a test-time reinforcement learning search framework they’re calling TTRL. The core insight is letting the model act as an agent that can autonomously discover a useful lemma, prove it, and then call on that same lemma later in a more complex proof. This structured reuse of intermediate results is what breaks the model out of single-step generation, enabling the kind of long-horizon reasoning that genuinely hard problems demand. It’s a shift from generating a proof monolithically to composing it from subcomponents the model itself validates.

They also baked in a practical error-fixing loop. Instead of discarding a failed proof attempt and starting from zero, Kimina-Prover reads Lean’s compiler errors and proposes targeted fixes. This alone bumped the pass@32 score from 84% to 86.4%, a non-trivial efficiency gain. Anyone who has battled a proof assistant’s unforgiving feedback knows how valuable a non-stubborn model really is.

The scaling curve tells an interesting story too. Earlier versions of the prover got linearly better with more compute. This one plateaus. The team notes diminishing returns beyond pass@1024, meaning brute-force sampling is no longer the bottleneck. The real ceiling now is search strategy—knowing which lemmas are worth proving in the first place. A lot of the current compute budget is wasted on dead-end intermediate steps, which the authors flag as a clear target for optimization. The release also includes distilled 8B and 1.7B variants based on Qwen3, hinting that this lemma-driven approach could trickle down to much smaller, more practical models.