GenesisGeo: Technical Report

2025-09-26

AI Summary

Automated theorem proving for Euclidean geometry remains challenging due to the combinatorial explosion of auxiliary constructions and the need for both geometric intuition and rigorous symbolic deduction. Method: This paper proposes GenesisGeo, a neuro-symbolic framework integrating large-scale geometric data learning with efficient symbolic reasoning. It introduces an open-source geometry dataset comprising 21.8 million problems—including over 3 million with human-provided auxiliary constructions—and develops DDARN, a symbolic engine accelerated 120× via theorem matching and low-level C++ optimization. The neural component is built upon Qwen3-0.6B-Base, supporting both single-model and dual-model ensemble inference. Contribution/Results: On the IMO-AG-30 benchmark, GenesisGeo solves 24 problems with the single model (achieving IMO Silver Medal level) and 26 with dual-model ensemble (reaching IMO Gold Medal level), substantially advancing automated solving capability for complex, competition-level Euclidean geometry theorems.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

We present GenesisGeo, an automated theorem prover in Euclidean geometry. We have open-sourced a large-scale geometry dataset of 21.8 million geometric problems, over 3 million of which contain auxiliary constructions. Specially, we significantly accelerate the symbolic deduction engine DDARN by 120x through theorem matching, combined with a C++ implementation of its core components. Furthermore, we build our neuro-symbolic prover, GenesisGeo, upon Qwen3-0.6B-Base, which solves 24 of 30 problems (IMO silver medal level) in the IMO-AG-30 benchmark using a single model, and achieves 26 problems (IMO gold medal level) with a dual-model ensemble.

Problem

• Automated theorem proving for Euclidean geometry problems
• Accelerating symbolic deduction engine by 120x
• Solving IMO-level geometry problems with neuro-symbolic approach

Innovation

• Automated theorem prover for Euclidean geometry
• Accelerated symbolic engine via theorem matching
• Neuro-symbolic approach using Qwen3-0.6B-Base model