Related papers: Reconstructing veriT Proofs in Isabelle/HOL

We present a proof procedure for univariate real polynomial problems in Isabelle/HOL. The core mathematics of our procedure is based on univariate cylindrical algebraic decomposition. We follow the approach of untrusted certificates,…

Theorem proving is a fundamental task in mathematics. With the advent of large language models (LLMs) and interactive theorem provers (ITPs) like Lean, there has been growing interest in integrating LLMs and ITPs to automate theorem…

While large language models (LLMs) have demonstrated remarkable success on a broad range of tasks, math reasoning remains a challenging one. One of the approaches for improving math reasoning is self-correction, which designs self-improving…

Mission-time Linear Temporal Logic (MLTL), a widely used subset of popular specification logics like STL and MTL, is often used to model and verify real world systems in safety-critical contexts. As the results of formal verification are…

Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise…

The demand for synthetic data in mathematical reasoning has increased due to its potential to enhance the mathematical capabilities of large language models (LLMs). However, ensuring the validity of intermediate reasoning steps remains a…

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and…

The most promising recent methods for AI reasoning require applying variants of reinforcement learning (RL) either on rolled out trajectories from the LLMs, even for the step-wise rewards, or large quantities of human-annotated trajectory…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

In this paper we present the verification of an imperative implementation of the ubiquitous B+-tree data structure in the interactive theorem prover Isabelle/HOL. The implementation supports membership test, insertion and range queries with…

The application of automatic theorem provers to discharge proof obligations is necessary to apply formal methods in an efficient manner. Tools supporting formal methods, such as Atelier~B, generate proof obligations fully automatically.…

Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…

The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not…

A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…

We report on the development of an optimized and verified decision procedure for orthologic equalities and inequalities. This decision procedure is quadratic-time and is used as a sound, efficient and predictable approximation to classical…

The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…

In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…

Network administration is an inherently complex task, in particular with regard to security. Using the Isabelle interactive proof assistant, we develop two automated, formally verified tools which help uncovering and preventing bugs in…

To address the increasing size and complexity of modern software systems, compositional verification separates the verification of single components from the verification of their composition. In architecture-based verification, the former…

Formal methods (FM) are reliable but costly to apply, often requiring years of expert effort in industrial-scale projects such as seL4, especially for theorem proving. Recent advances in large language models (LLMs) have made automated…