Automated Geometry Theorem Proving for Human-Readable Proofs

Authors: Ke Wang, Zhendong Su

IJCAI 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental We have realized our approach as a new automated geometry theorem prover, i Geo Tutor and extensively evaluated it. Our problem corpus has 77 problems in total, including ones cited in prior work and from Math competitions. Evaluation results show that i Geo Tutor is very effective it solves all but two problems in under two minutes each. We have also performed a test pilot with 12 high school students, and found i Geo Tutor is effective in helping student to learn geometry proof.
Researcher Affiliation Academia Ke Wang Zhendong Su Department of Computer Science University of California, Davis {kbwang, su}@ucdavis.edu
Pseudocode Yes Algorithm 1: Construction search via template matching; Algorithm 2: Template matching procedure
Open Source Code No The paper provides links to a video demo, lists of predicates and axioms, problems and their descriptions, and the two tests for the pilot study, all hosted on a university domain (http://www.cs.ucdavis.edu/ su/igeotutor.html). However, it does not explicitly state that the source code for i Geo Tutor itself is open-source or available at any of these links.
Open Datasets Yes Our test corpus contains 77 problems in total (please refer to http://www.cs.ucdavis.edu/ su/igeotutor.html for the full list of problems and their descriptions). The problems have been gathered from various sources, including 22 from the work on GRAMY [Matsuda and Vanlehn, 2004]6 for comparison. The rest of the problems are from an archive of classical geometry proof problems online [Liu, 2011] and two Chinese textbooks [Shen, 2006; Zhou, 2004], both of which are popular practice materials for the Chinese Mathematics Olympiad.
Dataset Splits No The paper mentions a "test corpus" of 77 problems and a pilot study with pre-tests and post-tests. However, it does not describe specific training, validation, or testing splits for the problems used to evaluate the i Geo Tutor system in terms of percentages or sample counts, which is typical for machine learning models. The system is a theorem prover, not a model trained on data splits.
Hardware Specification Yes i Geo Tutor runs on a workstation with a third generation Intel Core i7-3770 processor and 16GB RAM.
Software Dependencies No In particular, we employ an off-the-shelf state-of-the-art SMT solver Z3 [De Moura and Bjørner, 2011; Microsoft Research, ] to resolve the arithmetic constraints when needed. The paper mentions the software Z3 but does not provide a specific version number.
Experiment Setup No The paper describes the system's architecture and logic, including its construction search procedure (Algorithm 1) with a 'depth' parameter, and a 'gain' heuristic for ranking non-minimum sufficient sets. However, it does not specify concrete numerical hyperparameters typically found in machine learning experimental setups, such as learning rates, batch sizes, or optimizer settings, as it is a symbolic reasoning system.