GamePad: A learning environment for theorem proving

Generative language modeling for automated theorem proving

Discovering New Theorems via LLMs with In-Context Proof Learning in Lean

arXiv:2509. 14274v3 Announce Type: replace Abstract: Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving.

Self-Supervised Theorem Discovery in a Formal Axiomatic System

arXiv:2606. 28747v1 Announce Type: new Abstract: Recent artificial intelligence (AI) systems have shown remarkable progress in mathematical reasoning.

ProofEvolve: Neuro-Symbolic Evolution for Formal Automated Theorem Proving

ProofEvolve is a neuro‑symbolic framework that evolves formally verified symbolic proof structures alongside neural models to expand the knowledge boundary in automated theorem proving. The neural component proposes variation operators such as decompositions, repairs, and schema recombinations, while the Lean kernel verifies every proof transition, ensuring formal soundness. Across three competition‑level Lean benchmarks, ProofEvolve achieves the highest average solve rate among evaluated proof systems.

MathCoPilot: An Interactive System for Human-AI Symbiotic Paradigm of Mathematical Research

arXiv:2607. 14582v1 Announce Type: new Abstract: Existing LLM-based theorem provers have achieved impressive results on formal mathematics benchmarks, yet they remain confined to acting as autonomous agents that prove a stated proposition.

MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize

MathAdv is a diagnostic benchmark for formal theorem proving that covers 13 undergraduate- and graduate-level mathematics domains. It includes Lean 4 proofs and up to three auxiliary tasks—multiple-choice questions, fill-in-the-blank problems, and expert-crafted transformations—to probe knowledge, informal reasoning, and robustness to problem presentation. Evaluation of current theorem provers shows formalization is a major bottleneck, performance varies by domain, natural-language guidance can help or hinder models, and equivalent reformulations reveal significant robustness gaps.

OpenProver: Agentic and Interactive Theorem Proving with Lean 4

arXiv:2607. 09217v1 Announce Type: new Abstract: In this system paper, we present OpenProver, an open-source system for LLM-driven automated theorem proving (ATP) with integrated Lean 4 formal verification.

LAMP: Lean-based Agentic framework with MCP and Proof Repair

arXiv:2606. 28841v1 Announce Type: cross Abstract: Large language models are increasingly capable of mathematical reasoning, but the proofs they generate are often unreliable and hard to verify.

LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks

arXiv:2606. 03303v1 Announce Type: new Abstract: Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean.

Imitation Learning for Connection-Tableau Construction

The paper presents an approach to automated theorem proving by framing the construction of clausal connection tableaux as a policy in a transition system. It introduces a graph neural network that scores proof edits based on structure, trained via imitation learning from existing proofs. Experiments on M2k, MPTP2078-bushy, and TPTP v9.2.1 show that the learned policies solve up to 46% more problems than leanCoP and find proofs in an order of magnitude fewer steps.

TheoremBench: Evaluating LLMs on Theorem Proving in Formal Mathematics

LLMs have recently achieved strong results on formal proving benchmarks. However, existing evaluations remain heavily concentrated on competition-style problems and often fail to capture how models behave on longer, more dependency-rich mathematical developments.

A Theoretical Framework for Self-Play Theorem Proving Algorithms

arXiv:2606. 01861v1 Announce Type: new Abstract: Self-play, a type of training algorithm that enables a model to self-improve, has recently shown promising empirical results in the context of formal theorem proving using Large Language Models (LLMs).