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Rewriting techniques based on reduction orderings generate "just enough" consequences to retain first-order completeness. This is ideal for superposition-based first-order theorem proving, but for at least one approach to inductive…
Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search…
Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large…
As AI-generated text enters the real-world at scale, institutions increasingly use commercial AI-text detectors, especially in education and academic-integrity workflows. We report a surprising empirical finding about such systems: when…
That the Haskell Compiler GHC is capable of proving non-trivial equalities between Haskell code, by virtue of its aggressive optimizer, in particular the term rewriting engine in the simplifier. We demonstrate this with a surprising little…
Explicit theory axioms are added by a saturation-based theorem prover as one of the techniques for supporting theory reasoning. While simple and effective, adding theory axioms can also pollute the search space with many irrelevant…
Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where…
We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), inspired by the recent success of AlphaZero. Our model learns from…
Techniques combining machine learning with translation to automated reasoning have recently become an important component of formal proof assistants. Such "hammer" tech- niques complement traditional proof assistant automation as…
Using reinforcement learning for automated theorem proving has recently received much attention. Current approaches use representations of logical statements that often rely on the names used in these statements and, as a result, the models…
This paper aims to improve the performance of large language models by addressing the variable computational demands in inference steps, where some tokens require more computational resources than others. We present HARP, a simple…
We present Isabellm, an LLM-powered theorem prover for Isabelle/HOL that performs fully automatic proof synthesis. Isabellm works with any local LLM on Ollama and APIs such as Gemini CLI, and it is designed to run on consumer grade…
Despite the recent progress in automatic theorem provers, proof engineers are still suffering from the lack of powerful proof automation. In this position paper we first report our proof strategy language based on a meta-tool approach.…
he cvc5 solver is today one of the strongest systems for solving first order problems with theories but also without them. In this work we equip its enumeration-based instantiation with a neural network that guides the choice of the…
We present an approach for testing student learning outcomes in a course on automated reasoning using the Isabelle proof assistant. The approach allows us to test both general understanding of formal proofs in various logical proof systems…
This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can…
Neural graphics primitives are faster and achieve higher quality when their neural networks are augmented by spatial data structures that hold trainable features arranged in a grid. However, existing feature grids either come with a large…
Many inductive logic programming (ILP) methods are incapable of learning programs from probabilistic background knowledge, e.g. coming from sensory data or neural networks with probabilities. We propose Propper, which handles flawed and…
As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless…
Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…