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Induction with Generalization in Superposition Reasoning

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Abstract

We describe an extension of automating induction in superposition-based reasoning by strengthening inductive properties and generalizing terms over which induction should be applied. We implemented our approach in the first-order theorem prover Vampire and evaluated our work against state-of-the-art reasoners automating induction. We demonstrate the strength of our technique by showing that many interesting mathematical properties of natural numbers and lists can be proved automatically using this extension.

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Notes

  1. 1.

    These clauses are instances of \(C_2\) and \(C_3\) from Fig. 2.

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Acknowledgements

We thank Giles Reger for discussions related to the work. We acknowledge funding supporting this work, in particular the ERC starting grant 2014 SYMCAR 639270, the EPSRC grant EP/P03408X/1, the ERC proof of concept grant 2018 SYMELS 842066, the Wallenberg Academy fellowship 2014 TheProSE, the Austrian FWF research project W1255-N23, and the Hungarian-Austrian project 101öu8.

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Authors and Affiliations

  1. TU Wien, Vienna, Austria

    Márton Hajdú, Petra Hozzová, Laura Kovács & Johannes Schoisswohl

  2. Chalmers University of Technology, Gothenburg, Sweden

    Laura Kovács

  3. University of Manchester, Manchester, UK

    Johannes Schoisswohl & Andrei Voronkov

  4. EasyChair, Manchester, UK

    Andrei Voronkov

Authors
  1. Márton Hajdú
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  2. Petra Hozzová
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  3. Laura Kovács
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  4. Johannes Schoisswohl
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  5. Andrei Voronkov
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Corresponding author

Correspondence to Laura Kovács .

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Editors and Affiliations

  1. Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany

    Christoph Benzmüller

  2. National Institute of Standards and Technology, Gaithersburg, MD, USA

    Bruce Miller

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Hajdú, M., Hozzová, P., Kovács, L., Schoisswohl, J., Voronkov, A. (2020). Induction with Generalization in Superposition Reasoning. In: Benzmüller, C., Miller, B. (eds) Intelligent Computer Mathematics. CICM 2020. Lecture Notes in Computer Science(), vol 12236. Springer, Cham. https://doi.org/10.1007/978-3-030-53518-6_8

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  • DOI: https://doi.org/10.1007/978-3-030-53518-6_8

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