arXiv AI
Jul 24
Case study: solving P-99 with LPTP and an LLM
arXiv:2607. 21196v1 Announce Type: cross Abstract: Ninety-Nine Prolog Problems (P-99) is a famous set of Prolog exercises.
Case study: proving sqrt(2) irrational with LPTP and an LLM
arXiv:2607. 21187v1 Announce Type: cross Abstract: We present the interactions with an LLM (Large Language Model) aiming at proving that the square root of 2 is not a rational number in an LP (Logic Programming) context.
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arXiv AI
Jul 21
AoA: Theorem Proving Agent over Abstract Syntax Tree of Redesigned Language
arXiv:2607. 16372v1 Announce Type: cross Abstract: Interactive theorem proving (ITP) underpins program verification and formalized mathematics, but its manual effort limits scalability.
arXiv Machine Learning
Jun 19
Pseudo-Formalization for Automatic Proof Verification
arXiv:2605. 20531v2 Announce Type: replace-cross Abstract: Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning.
arXiv AI
Jul 24
Towards a Certifying Grounder
arXiv:2607. 21199v1 Announce Type: cross Abstract: Grounding, the translation of high-level theories into equivalent quantifier-free formulas, is a crucial step in declarative solving, yet it has so far escaped the proof-logging revolution.
Hugging Face Blog
Jul 10, 2025
Kimina-Prover: Applying Test-time RL Search on Large Formal Reasoning Models
arXiv AI
Jul 24
Autonomous disproofs of the sum-product conjecture over $\mathbb R$ with GPT-5.5 Pro
arXiv:2607. 20525v1 Announce Type: new Abstract: OpenAI's recent disproof of the Erd\H{o}s unit distance conjecture marked a milestone for AI in mathematics.
Hugging Face Trending Papers
Jul 23
Towards a Certifying Grounder
Grounding, the translation of high-level theories into equivalent quantifier-free formulas, is a crucial step in declarative solving, yet it has so far escaped the proof-logging revolution. When this grounding step is not certifying, there is no way of knowing that the obtained solutions actually correspond to the original problem specification, resulting in a trust gap.
arXiv AI
Jun 4
Abduction Prover in Isabelle/HOL
arXiv:2606. 04877v1 Announce Type: cross Abstract: Proof assistants based on expressive logics suffer limited automation for proof search, raising the cost of formal verification based on proof assistants.
arXiv AI
Aug 28
HybridProver: Augmenting Theorem Proving with LLM-Driven Proof Synthesis and Refinement
HybridProver is a unified framework that combines whole-proof synthesis and tactic-based generation using proof sketches as an intermediate representation. Implemented in Isabelle/HOL, it employs two 7B-scale LLMs trained on optimized Isabelle datasets. On the miniF2F Isabelle benchmark, HybridProver achieved a 73.8% success rate, surpassing the previous state of the art of 61.9%, and ablation studies examined the effects of dataset quality, training settings, and sampling strategies.
arXiv AI
Jul 8
Harnessing Code Agents for Automatic Software Verification
arXiv:2607. 06341v1 Announce Type: cross Abstract: Formal verification offers the strongest guarantee of software correctness, but it does not scale: the proofs demanded by interactive theorem provers such as Coq require enormous expert effort.
arXiv AI
Jun 9
TheoremBench: Evaluating LLMs on Theorem Proving in Formal Mathematics
arXiv:2606. 09450v1 Announce Type: new Abstract: LLMs have recently achieved strong results on formal proving benchmarks.
arXiv Machine Learning
Jun 25
MINIF2F-DAFNY: LLM-Guided Mathematical Theorem Proving via Auto-Active Verification
arXiv:2512. 10187v3 Announce Type: replace Abstract: LLMs excel at reasoning, but validating their steps remains challenging.