# Towards Ranking Geometric Automated Theorem Provers

## TL;DR

This paper discusses the development of a ranking system for geometric automated theorem provers, emphasizing the need for standardized testing, common problem descriptions, and quality measures to evaluate and compare their performance.

## Contribution

It proposes a framework for ranking geometric theorem provers through a common test bench, standardized problem descriptions, and quality metrics.

## Key findings

- Highlights the importance of evaluation criteria for geometric provers
- Identifies the need for a common test bench and problem repository
- Suggests potential improvements in prover performance and reliability

## Abstract

The field of geometric automated theorem provers has a long and rich history, from the early AI approaches of the 1960s, synthetic provers, to today algebraic and synthetic provers. The geometry automated deduction area differs from other areas by the strong connection between the axiomatic theories and its standard models. In many cases the geometric constructions are used to establish the theorems' statements, geometric constructions are, in some provers, used to conduct the proof, used as counter-examples to close some branches of the automatic proof. Synthetic geometry proofs are done using geometric properties, proofs that can have a visual counterpart in the supporting geometric construction. With the growing use of geometry automatic deduction tools as applications in other areas, e.g. in education, the need to evaluate them, using different criteria, is felt. Establishing a ranking among geometric automated theorem provers will be useful for the improvement of the current methods/implementations. Improvements could concern wider scope, better efficiency, proof readability and proof reliability. To achieve the goal of being able to compare geometric automated theorem provers a common test bench is needed: a common language to describe the geometric problems; a comprehensive repository of geometric problems and a set of quality measures.