AI Generates Millions of Proof Lines
Anthropic's model has produced formal proofs for a large batch of open-source code, finding bugs in the process.
By Amy Swan ·
On October 23, 2026, Anthropic reported that its Claude model can now automatically generate formal proofs to verify the safety of existing software code. This new capability aims to address a significant challenge in software development: the high cost and difficulty of ensuring that programs are free from errors. The company is working with partner Theorem on this project, using Claude to mathematically verify the correctness of software code and create proofs of its safety.
Traditionally, proving that software runs without error under all conditions has been extremely resource-intensive. For example, verifying the seL4 operating system kernel required a team of specialists to work for 20 person-years. Such a method was therefore reserved for high-stakes applications like Airbus avionics software. Anthropic's Frontier Red Team, in partnership with Theorem, is now using AI to take on this proof work. Claude generated approximately 180 million lines of mathematical proof code within a few weeks. This effort involved analyzing test programs from 123 open-source libraries in Google's OSS-Fuzz security project.
Claude's work involved translating crash tests into mathematical problems and analyzing the compiled machine code to produce extensive proofs. An independent verification program called Rocq checks these proofs. According to Anthropic, this process requires almost no human reviewers, making the proof generation fully autonomous. The models and formal foundations were created by humans at Theorem.
As Claude generated these proofs, it uncovered hundreds of bugs that conventional testing had missed. Many of these issues only appear under specific conditions, such as with unusually large input files or a particular sequence of accesses. For instance, while verifying a widely used PDF reader, the team found as many security bugs in one week as are typically reported for that software in an entire year. In another case, Claude identified a logical error that had remained undetected for over a decade. Anthropic states that even when a proof attempt fails, it can still surface real bugs.
Anthropic acknowledges that a 'formally verified' program is not necessarily 'error-free.' The proofs are valid only under strict conditions, including a specific processor architecture, single-threaded programs, and inputs under 64 MB. In practice, these libraries operate on various hardware and in different configurations. The computational cost is also significant, with individual proofs running up hundreds of millions of tokens, and Anthropic does not report the total project costs. However, if AI can verify its own code, developers can trust AI-generated software more and spend less time on review, which reduces costs across the coding process. Anthropic also noted that newer models are becoming more efficient at this task; Opus 5.5 can solve half the proofs with about 40 percent fewer tokens than Opus 5.
The project strengthens the case for greater software automation. If an AI can write code and guarantee its correctness under defined conditions, the central question shifts from whether AI can program to whether it can prove that the code it writes is safe. Anthropic expects that formal verification with AI will soon become as routine as standard testing. Theorem's roadmap already targets critical infrastructure components like glibc, OpenSSL, and cURL for this process.
Source: The Decoder
