Automated Theorem Proving with Neural Network Guidance

Abstract

Automated theorem proving (ATP) aims to develop systems capable of mechanically proving mathematical theorems. Despite significant advancements, ATP systems often struggle with complex reasoning tasks, largely due to the inherent difficulty in representing and executing logical deduction rules. This work proposes a novel approach to ATP that integrates neural networks to provide guidance during the proof process. The core idea is to train a neural network to suggest promising proof steps and identify relevant theorems, essentially acting as an "intelligent assistant" for the ATP system. This guidance mechanism is expected to improve the efficiency and effectiveness of ATP, particularly in tackling challenging mathematical problems. The presented framework utilizes a reinforcement learning approach, where the neural network learns to optimize the proof strategy based on the current state of the proof and the available theorems. The system is evaluated conceptually, outlining the architecture and training process, and highlighting potential improvements. Further research will focus on developing and refining the network architecture, exploring different training strategies, and integrating the guidance mechanism with existing ATP systems.