We provide more information on AIPS' deductive engine and the training process for the value network. To highlight the reasoning ability and maintain readability of proofs, we avoid using brute-force methods such as augmentation-substitution and Wu's method Wu [1978].

Solving Olympiad-level mathematical problems represents a significant advancement in machine intelligence and automated reasoning.

Large Language Models (LLMs) with strong abilities in natural language processing tasks have emerged and have been applied in various kinds of areas such as science, finance and software engineering.

We have provided baseline models, comprehensive experimental observations, and analysis to accelerate future research.

In this paper, we present Rotating Features, a generalization of complex-valued features to higher dimensions, and a new evaluation procedure for extracting objects from distributed representations.