AGENTIC-SYSTEMSApril 20, 20261 min read7 views

Discover and Prove: An Open-source Agentic Framework for Hard Mode Automated Theorem Proving in Lean 4

Researchers introduce Discover and Prove (DAP), an agentic framework that enables AI to independently discover answers and construct formal proofs in a realistic 'Hard Mode' setting, setting new benchmarks in automated theorem proving.

Computer Science > Artificial Intelligence

Title:Discover and Prove: An Open-source Agentic Framework for Hard Mode Automated Theorem Proving in Lean 4

Abstract:Most ATP benchmarks embed the final answer within the formal statement -- a convention we call "Easy Mode" -- a design that simplifies the task relative to what human competitors face and may lead to optimistic estimates of model capability. We call the stricter, more realistic setting "Hard Mode": the system must independently discover the answer before constructing a formal proof. To enable Hard Mode research, we make two contributions. First, we release MiniF2F-Hard and FIMO-Hard, expert-reannotated Hard Mode variants of two widely-used ATP benchmarks. Second, we introduce Discover And Prove (DAP), an agentic framework that uses LLM natural-language reasoning with explicit self-reflection to discover answers, then rewrites Hard Mode statements into Easy Mode ones for existing ATP provers. DAP sets the state of the art: on CombiBench it raises solved problems from 7 (previous SOTA, Pass@16) to 10; on PutnamBench it is the first system to formally prove 36 theorems in Hard Mode -- while simultaneously revealing that state-of-the-art LLMs exceed 80% answer accuracy on the same problems where formal provers manage under 10%, exposing a substantial gap that Hard Mode benchmarks are uniquely suited to measure.

Source: arXiv cs.AI Recent

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