arXiv:2607. 21191v1 Announce Type: cross Abstract: Event-B is a formal method rooted in predicate logic and set theory.
arXiv:2607. 21192v1 Announce Type: cross Abstract: ProB is a Prolog-based model checker, animator and constraint solver for high-level formal specifications.
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:2605. 20531v2 Announce Type: replace-cross Abstract: Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning.
Scratchy introduces a visual-scratchpad method for generating cryptographic proofs in EasyCrypt by converting natural-language security descriptions into a typed proof-relation graph and then into a visual proof state that guides multimodal language models. The approach exposes implicit proof-theoretic dependencies that LLMs struggle with, enabling clearer coordination of probability, adversarial games, invariants, assumptions, and bounds. Scratchy-eval, a 114-task dataset from official EasyCrypt files, demonstrates that classical LLMs achieve significant gains when using these structured visual proof states.
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.
arXiv:2608. 06399v1 Announce Type: cross Abstract: Datalog rules are often used to define ontologies over Knowledge Graphs.
arXiv:2607. 11307v1 Announce Type: new Abstract: Full-proof autoformalization bridges extensive mathematical proofs in natural language with formally validated reasoning, offering a pathway to elevate the ceiling of verifiable mathematical reasoning.
arXiv:2606. 15258v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly capable of mathematical problem solving and can even assist with research-level proofs, yet we still lack a scalable and reproducible way to measure step-level reasoning in long proofs across diverse sources.
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.
arXiv:2606. 09450v1 Announce Type: new Abstract: LLMs have recently achieved strong results on formal proving benchmarks.
arXiv:2607. 16372v1 Announce Type: cross Abstract: Interactive theorem proving (ITP) underpins program verification and formalized mathematics, but its manual effort limits scalability.
Stellar Colosseum is a model‑agnostic harness designed to improve long‑horizon research in mathematics and theoretical computer science by allocating inference across multiple agents. It explores alternative strategies before constructing proofs, uses a readiness gate to decide when a route is mature enough to decompose, represents proof plans as interdependent subproblems, and routes verifier findings back to the relevant part of the argument. The workflow generates candidates in parallel, attacks them with targeted falsification, and combines candidates and critiques into a single research artifact through overlapping random‑sample tree aggregation, and has been integrated into Google Antigravity's Teamwork framework as the Long Proof pattern. Demonstrations show that, when paired with Gemini 3.1 Pro, Stellar Colosseum achieves 71.0% accuracy on the TCS‑Bench theorem‑proving benchmark and solves 218 of 222 Codeforces problems.