Leanstral 1.5, a free Apache-2.0 licensed model with 6 billion active parameters out of 119 billion total, was released to improve formal verification performance. The model solves 587 of 672 PutnamBench problems and achieves 87 % on FATE‑H and 34 % on FATE‑X, saturating the miniF2F benchmark at 100 % on validation and test sets.

Leanstral was created to make formal proof engineering practical in Lean 4. Since the initial release, the project has offered an open approach to verifying mathematical statements and code properties.

Training proceeds through three stages: mid‑training, supervised fine‑tuning, and reinforcement learning using the CISPO algorithm. The model was evaluated on miniF2F, PutnamBench, FATE‑H/X, and FLTEval, which tests proof engineering on real pull requests. In the multiturn environment, Leanstral iteratively submits proofs, receives compiler feedback, and refines attempts until compilation succeeds or the token budget is exhausted. In the code‑agent environment, it edits files, runs shell commands, and queries the Lean language server to manage long‑horizon tasks. Test‑time scaling shows a monotonic increase in Pass@8 as the token budget per attempt rises from 50 k to 4 M tokens, reaching 587 solved problems at the highest budget.

Leanstral achieves a new state‑of‑the‑art on FATE‑H and FATE‑X while costing roughly $4 per solved PutnamBench problem, compared with estimated costs of $300 or more for competing provers such as Seed‑Prover. Other provers that rank higher either require natural‑language guidance or incur substantially higher per‑problem expenses.

In a verification of AVL‑tree time‑complexity, Leanstral produced proofs spanning over 2.7 million tokens across 22 compactions, establishing an O(log n) bound for insertion and deletion. A separate bug‑discovery pipeline used Leanstral to infer correctness properties from Rust code translated to Lean, flagging 47 property violations and identifying 11 genuine bugs, including five previously unreported issues in the zigzag decoding library of the datrs/varinteger project.

The model is released under an Apache‑2.0 license, with weights hosted on Hugging Face and a free API endpoint at leanstral‑1‑5. Users are encouraged to access the model through Mistral Vibe, set up an API key, and install the accompanying tools as described in the project documentation. The release illustrates that rigorous formal methods can be both effective and affordable for real‑world software verification. Its long‑term impact on industry and research adoption remains to be measured.