Leanstral 1.5 open source AI model proves mathematical theorems and verifies code. Learn about formal verification with Lean 4 for reliable software.
The reliability of software and mathematical proofs has become a critical concern in an era of AI generated code. Traditional testing methods catch many bugs, but they cannot guarantee the absence of subtle logical errors in complex systems. The growing complexity of software and the increasing reliance on AI generated solutions demand more rigorous verification approaches.
Mistral AI has introduced Leanstral 1.5, an open source AI model designed specifically for Lean 4 formal proof engineering and code verification. The model writes and verifies mathematical proofs while also checking that code logic is actually correct, not just plausible. Leanstral 1.5 represents a practical solution for teams that need mathematically guaranteed correctness without the high costs traditionally associated with formal verification.
Leanstral 1.5 arrives as a specialized tool with a specific job. The model uses a sparse Mixture of Experts architecture with 119 billion total parameters but only 6 billion active during inference. This design keeps computational costs low while delivering state of the art performance on theorem proving benchmarks. The model is released under the Apache 2.0 license, allowing developers to use, modify, and deploy it without the licensing restrictions of many proprietary models.
Technical Architecture and Performance
Leanstral 1.5 uses a Mixture of Experts design that activates only 6 billion of its 119 billion total parameters for each token. This architectural choice enables efficient computation while scaling to handle complex mathematical reasoning and proof engineering tasks. The context length of 256,000 tokens allows the model to process lengthy proof files and related code together in a single session.
The model's training process involves a three stage pipeline: mid-training, supervised fine-tuning, and reinforcement learning with CISPO. Two reinforcement learning environments help the model master proof engineering workflows. In the multi-turn environment, the model receives a theorem statement and must prove or disprove it, submitting proof attempts and refining its approach based on Lean compiler feedback. In the code agent environment, Leanstral operates like a developer in a raw filesystem, editing files, running bash commands, and using the Lean language server to inspect goals, errors, and type information in real time.
Leanstral 1.5 is specifically optimized for Lean 4, a proof assistant used in mathematical research and software verification. The model understands Lean's type system, tactic language, and proof obligations from the ground up rather than treating Lean code as plain text. This native understanding enables the model to navigate existing formal repositories, diagnose proof failures, and suggest fixes based on actual compiler feedback.
Benchmark Results and Mathematical Capabilities
Leanstral 1.5 achieves perfect scores on some of the most challenging formal mathematics benchmarks. The model saturates miniF2F, a cross-system benchmark for formal mathematics ranging from elementary problems to IMO-level challenges, reaching 100 percent on both the validation and test sets. This demonstrates the model's ability to handle diverse proof abilities across algebra, combinatorics, and number theory.
On PutnamBench, consisting of 672 problems from the Putnam Mathematical Competition, Leanstral 1.5 successfully solves 587 problems. These problems require deep reasoning and long proof chains, testing the model's capacity for sustained logical deduction. The model edges out Seed-Prover 1.5 high by 7 problems at far lower cost, approximately $4 per problem compared to an estimated $300 or more for Seed-Prover.
The model sets new state of the art results on the FATE-H and FATE-X abstract algebra benchmarks. FATE-H tests graduate level problems in areas like group theory, ring theory, and module theory, where Leanstral achieves 87 percent completion. FATE-X tests doctoral level problems, where the model achieves 34 percent completion. These results demonstrate the model's ability to handle advanced mathematical reasoning that goes well beyond undergraduate competition problems.
Cost Effectiveness and Accessibility
Leanstral 1.5 offers exceptional cost effectiveness compared to competing approaches. On PutnamBench, the average cost to solve a problem is approximately $4, compared to over $300 for Seed-Prover 1.5 and $54 to $68 for Aleph Prover. This cost advantage of roughly 99 percent makes formal verification economically viable for a much wider range of applications.
The model's cost efficiency extends to practical proof engineering tasks. On the FLTEval benchmark, based on real pull requests from the Fermat's Last Theorem repository, Leanstral 1.5 achieves a pass@8 score of 43.2, surpassing Claude Opus 4.6's 39.6 at one seventh the cost. At pass@2, Leanstral achieves a score of 26.3 for approximately $36, compared to Claude Sonnet's equivalent at $549, representing a roughly 15x cost reduction.
Leanstral 1.5 is available under the Apache 2.0 license, allowing global developers to download and use it for commercial purposes without additional fees. The model weights can be accessed through Hugging Face, with a free API endpoint also available. The model integrates with Mistral Vibe, where users can install Leanstral as an agent with a single command.
Real World Code Verification
Leanstral 1.5 demonstrates practical value beyond mathematical competitions. The model proved time complexity guarantees for AVL tree implementations, a task that required structural induction, careful handling of monadic time tracking, and exhaustive case analysis for rebalancing paths. The proof ran for over 2.7 million tokens across 22 compactions, establishing that insertion and deletion operations are indeed O(log n).
The model also excels at bug detection in real world codebases. Mistral built an automated pipeline where Aeneas translates Rust code to Lean, Leanstral infers user intent and generates correctness properties, and then attempts to prove each property. Across 57 tested repositories, this process flagged 47 violated properties, with 11 pointing to genuine bugs, and 5 of them had not been previously reported on GitHub.
One discovered bug involved an overflow in the sign function for zigzag decoding of a varinteger library. On the maximum input value, the expression (value + 1) overflowed, causing crashes in debug mode and silent corruption in release mode. This edge case would typically be missed by testing and fuzzing, demonstrating that formal verification can catch bugs that traditional methods overlook.
Agentic Proof Engineering Workflow
Leanstral 1.5 operates as an agentic assistant that actively participates in the proof engineering process. The model edits files, evaluates compiler feedback, and improves its solutions step by step. This agentic approach enables the model to handle long-horizon tasks like completing partial proofs in a repository, building auxiliary lemmas, and persisting through multiple rounds of context compaction.
The model demonstrates strong test-time scaling, with performance improving monotonically as the token budget increases. On PutnamBench, performance climbs from 44 problems solved at 50,000 tokens to 244 at 200,000, 493 at 1 million, and 587 at 4 million tokens. Rather than giving up when a proof runs long, Leanstral keeps reasoning, editing files, and revising across millions of tokens.
The model supports configurable reasoning modes and handles complex tool calling scenarios with reliability. Sensitive commands, file changes, and high-permission actions go through confirmation before execution. The environment's ability to pause for clarification on ambiguous requirements represents an important reliability feature.
Competitive Positioning
Leanstral 1.5 competes in a specialized market for formal verification and automated theorem proving tools. The model outperforms open source models 3 to 10 times larger on proof engineering benchmarks. Against proprietary models, Leanstral offers a compelling cost-performance tradeoff, achieving competitive scores at a fraction of the cost.
The model's Apache 2.0 license removes legal barriers to adoption and integration, allowing teams to incorporate Leanstral into their commercial products without complex licensing negotiations. The open source approach enables customization and self-hosting for organizations with high compliance requirements.
Leanstral 1.5 expands Mistral's portfolio of specialized AI tools, following the earlier release of Mistral OCR 4 for document analysis. The model's success suggests a growing trend toward specialized, cost effective AI tools for specific technical workflows rather than general purpose solutions.
Future Development and Roadmap
Mistral has indicated that Leanstral 1.5 represents a continuing development effort. The team plans to accelerate technical iteration and focus on real world application capabilities. The model's strong performance on both academic benchmarks and practical code verification suggests significant potential for future improvements.
The fully open source FLTEval benchmark suite provides a foundation for ongoing evaluation and comparison of formal proof models. This transparency supports the broader research community and enables continuous improvement of automated theorem proving technology.
The focus on making formal verification accessible at scale reflects a long term vision beyond individual model releases. As the technology continues to evolve, users can expect further enhancements that make mathematical proof and code verification more practical and cost effective for diverse applications.
Conclusion
Leanstral 1.5 delivers a compelling combination of theorem proving capability, code verification, and cost effectiveness for formal proof engineering. The model writes and verifies mathematical proofs in Lean 4 while also checking software correctness with mathematical rigor. With 119 billion total parameters and only 6 billion active, it achieves state of the art results on miniF2F, PutnamBench, and FATE benchmarks at a fraction of the cost of competing approaches.
For developers building formal verification workflows with Leanstral 1.5, the model offers a practical solution for mathematically guaranteed software correctness. The model has already proven its real world value by finding five previously unknown bugs across 57 open source repositories. Availability under the Apache 2.0 license ensures accessibility for commercial and research applications.
The combination of low cost, open source licensing, and strong performance on both academic and practical tasks positions Leanstral 1.5 as a foundational tool for the future of formal verification. The model bridges the gap between theoretical proof assistance and practical software engineering, making rigorous verification accessible to a wider audience. As AI generated code becomes more prevalent, tools like Leanstral 1.5 will play an essential role in ensuring that code is not just plausible but provably correct.
Frequently Asked Questions
1. What is Leanstral 1.5 and what does it do?
Leanstral 1.5 is an open source AI model released by Mistral AI specifically designed for Lean 4 formal proof engineering and code verification. The model writes and verifies mathematical proofs while also checking that code logic is actually correct, not just plausible. It operates as an agentic assistant that edits files, evaluates compiler feedback, and improves its solutions step by step. The model uses a sparse Mixture of Experts architecture with 119 billion total parameters but only 6 billion active during inference, making it cost effective for high volume proof engineering workflows. Leanstral 1.5 is released under the Apache 2.0 license and can be downloaded from Hugging Face or accessed through a free API endpoint.
2. How does Leanstral 1.5 perform on mathematical proof benchmarks?
Leanstral 1.5 achieves state of the art results across multiple formal mathematics benchmarks. The model saturates miniF2F with 100 percent completion on both validation and test sets. On PutnamBench, consisting of 672 problems from the Putnam Mathematical Competition, Leanstral solves 587 problems. For abstract algebra, the model achieves 87 percent on FATE-H, which tests graduate level problems, and 34 percent on FATE-X, which tests doctoral level problems, both representing new state of the art results. The model also demonstrates strong test-time scaling, with performance improving from 44 problems solved at 50,000 tokens to 587 at 4 million tokens on PutnamBench.
3. How much does Leanstral 1.5 cost to use?
Leanstral 1.5 offers exceptional cost effectiveness compared to competing approaches. On PutnamBench, the average cost to solve a problem is approximately $4, compared to over $300 for Seed-Prover 1.5 and $54 to $68 for Aleph Prover. On the FLTEval benchmark for practical proof engineering, Leanstral achieves a pass@8 score of 43.2, surpassing Claude Opus 4.6's 39.6 at one seventh the cost. At pass@2, Leanstral achieves a score of 26.3 for approximately $36, compared to Claude Sonnet's equivalent at $549, representing a roughly 15x cost reduction. The model is available under Apache 2.0 license, with weights on Hugging Face and a free API endpoint.
4. Can Leanstral 1.5 find bugs in real code?
Yes, Leanstral 1.5 has demonstrated real world bug detection capabilities. In a test across 57 open source repositories, the model flagged 47 violated properties, with 11 pointing to genuine bugs, and 5 of these had not been previously reported on GitHub. The model operates through an automated pipeline where Aeneas translates Rust code to Lean, Leanstral infers user intent and generates correctness properties, and then attempts to prove each property. One discovered bug was an overflow in the sign function of a varinteger library that would have caused crashes in debug mode and silent corruption in release mode. This demonstrates that formal verification can catch bugs that traditional testing and fuzzing typically miss.
5. How is Leanstral 1.5 different from general purpose coding assistants?
Leanstral 1.5 is specifically designed for Lean 4 proof engineering rather than general purpose code generation. The model understands Lean's type system, tactic language, and proof obligations from the ground up, rather than treating Lean code as plain text. Unlike general purpose models that generate code that merely appears correct, Leanstral works with Lean's verification engine to mathematically prove correctness. The model operates with live awareness of the proof state, querying the Lean compiler for type information and error diagnostics in real time. It is trained specifically to work with the lean-lsp-mcp protocol, enabling it to navigate existing formal repositories, diagnose proof failures, and suggest fixes based on actual compiler feedback.
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