# Automated Theorem Proving

38 papers with code • 8 benchmarks • 7 datasets

The goal of **Automated Theorem Proving** is to automatically generate a proof, given a conjecture (the target theorem) and a knowledge base of known facts, all expressed in a formal language. Automated Theorem Proving is useful in a wide range of applications, including the verification and synthesis of software and hardware systems.

Source: Learning to Prove Theorems by Learning to Generate Theorems

## Most implemented papers

# Holophrasm: a neural Automated Theorem Prover for higher-order logic

I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features.

# HOList: An Environment for Machine Learning of Higher-Order Theorem Proving

We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic.

# Proof Artifact Co-training for Theorem Proving with Language Models

Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built.

# DeepMath - Deep Sequence Models for Premise Selection

We study the effectiveness of neural sequence models for premise selection in automated theorem proving, one of the main bottlenecks in the formalization of mathematics.

# Measuring Systematic Generalization in Neural Proof Generation with Transformers

We observe that models that are not trained to generate proofs are better at generalizing to problems based on longer proofs.

# Lectures on Jacques Herbrand as a Logician

We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving.

# HOL(y)Hammer: Online ATP Service for HOL Light

HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable) mathematics encoded in the HOL Light system.

# HolStep: A Machine Learning Dataset for Higher-order Logic Theorem Proving

We propose various machine learning tasks that can be performed on this dataset, and discuss their significance for theorem proving.

# On-demand Injection of Lexical Knowledge for Recognising Textual Entailment

We approach the recognition of textual entailment using logical semantic representations and a theorem prover.