Putnam 2025 Problems in Rocq using Opus 4.6 and Rocq-MCP

2026-03-20

AI Summary

This work addresses the challenge of enabling AI systems to autonomously solve difficult mathematical competition problems—such as those from the Putnam 2025 exam—and generate formally verifiable proofs in a network-isolated environment. We propose a “compile-then-interact” methodology for constructing an MCP (Mathematical Coq Proof) toolchain, which leverages historical interaction logs to automatically build a Rocq proof toolkit tailored to large language models. Integrating Claude Opus 4.6 within a multi-agent collaborative architecture, our system autonomously proved 10 out of 12 target problems, requiring 17.7 hours of active computation and consuming approximately 1.9 billion tokens. All generated formal proofs are fully reproducible and machine-verifiable, substantially advancing the practicality and scalability of automated theorem proving.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Multiagent Systems: Adversarial Agents
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

We report on an experiment in which Claude Opus~4.6, equipped with a suite of Model Context Protocol (MCP) tools for the Rocq proof assistant, autonomously proved 10 of 12 problems from the 2025 Putnam Mathematical Competition. The MCP tools, designed with Claude by analyzing logs from a prior experiment on miniF2F-Rocq, encode a "compile-first, interactive-fallback" strategy. Running on an isolated VM with no internet access, the agent deployed 141 subagents over 17.7 hours of active compute (51.6h wall-clock), consuming approximately 1.9 billion tokens. All proofs are publicly available.

Problem

• Putnam Competition
• automated theorem proving
• autonomous reasoning
• mathematical problem solving
• AI agent

Innovation

• Model Context Protocol
• automated theorem proving
• large language models
• interactive fallback strategy
• multi-agent collaboration