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Portfolio theorem proving and prover runtime prediction for geometry

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Abstract

In recent years, portfolio problem solving found many applications in automated reasoning, primarily in SAT solving and in automated and interactive theorem proving. Portfolio problem solving is an approach in which for an individual instance of a specific problem, one particular, hopefully most appropriate, solving technique is automatically selected among several available ones and used. The selection usually employs machine learning methods. To our knowledge, this approach has not been used in automated theorem proving in geometry so far and it poses a number of new challenges. In this paper we propose a set of features which characterize a specific geometric theorem, so that machine learning techniques can be used in geometry. Relying on these features and using different machine learning techniques, we constructed several portfolios for theorem proving in geometry and also runtime prediction models for provers involved. The evaluation was performed on two corpora of geometric theorems: one coming from geometric construction problems and one from a benchmark set of the GeoGebra tool. The obtained results show that machine learning techniques can be useful in automated theorem proving in geometry, while there is still room for further progress.

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Acknowledgements

We thank the anonymous reviewers for their very detailed and helpful comments on earlier versions of this paper.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000, Belgrade, Serbia

    Mladen Nikolić, Vesna Marinković & Predrag Janičić

  2. The Priv. Univ. College of Educ. of the Diocese of Linz, Salesianumweg 3, 4020, Linz, Austria

    Zoltán Kovács

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  1. Mladen Nikolić
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  2. Vesna Marinković
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  4. Predrag Janičić
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Correspondence to Mladen Nikolić.

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The first, the second, and the fourth author have been partly supported by the grant 174021 of the Ministry of Science of Serbia.

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Nikolić, M., Marinković, V., Kovács, Z. et al. Portfolio theorem proving and prover runtime prediction for geometry. Ann Math Artif Intell 85, 119–146 (2019). https://doi.org/10.1007/s10472-018-9598-6

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