DAP Agentic Framework Advances Hard Mode ATP in Lean 4 Toward Autonomous Math Discovery
DAP achieves SOTA on CombiBench (10 solved) and first 36 Putnam Hard Mode proofs, exposing >80% LLM informal accuracy vs <10% formal rate on identical problems.
The Discover And Prove (DAP) framework uses LLM natural-language reasoning with self-reflection to first discover solutions then rewrite Hard Mode statements into Easy Mode for existing provers (Liu et al., arXiv:2604.15839, 2026). It releases MiniF2F-Hard and FIMO-Hard expert-reannotated benchmarks. DAP lifts CombiBench solved problems from prior SOTA of 7 (Pass@16) to 10 and becomes first to prove 36 PutnamBench theorems in Hard Mode.
Original source focuses on benchmark results and the Easy/Hard Mode distinction but misses broader pattern of agentic autonomy seen in DeepMind AlphaProof solving four IMO problems via Lean formalization (DeepMind, 2024) and retrieval-augmented methods in LeanDojo (Yang et al., arXiv:2306.15626, 2023). Mainstream coverage rarely notes the 80%+ LLM informal answer accuracy versus under 10% formal prover success on Putnam, a gap Hard Mode uniquely quantifies.
Synthesizing these reveals DAP as incremental step in shifting AI from proof assistants to independent theorem generators, consistent with increasing use of reflection loops and tool integration that prior Easy Mode benchmarks obscured. This under-explored trajectory points to future systems capable of advancing open-ended mathematics and science beyond current verification limits.
AXIOM: DAP shows LLMs excel at informal mathematical discovery (>80% accuracy) yet formal Lean proofs remain under 10%; bridging this via agentic self-reflection may enable AI systems that independently propose and prove novel theorems.
Sources (2)
- [1]Discover and Prove: An Open-source Agentic Framework for Hard Mode Automated Theorem Proving in Lean 4(https://arxiv.org/abs/2604.15839)
- [2]AlphaProof: AI achieves silver-medal standard solving International Mathematical Olympiad problems(https://deepmind.google/discover/blog/ai-solves-imo-problems/)