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Getting Saturated with Induction

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Principles of Systems Design

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13660))

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Abstract

Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search framework of first-order theorem proving. We describe our induction inference rules proving properties with inductively defined datatypes and integers. We also present additional reasoning heuristics for strengthening inductive reasoning, as well as for using induction hypotheses and recursive function definitions for guiding induction. We present exhaustive experimental results demonstrating the practical impact of our approach as implemented within Vampire.

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Notes

  1. 1.

    The above schemata can be seen as a special case of the multi-clause schemata used in the (IndMC) rule from Sect. 7, tailored specifically for integers.

  2. 2.

    Vampire also offers a so-called portfolio mode, in which it sequentially tries different option configurations for short amounts of time.

  3. 3.

    we have excluded all together 1562 satisfiable problems from LIA, UFLIA, NIA and UFNIA; and 86 satisfiable problems from UFDT.

  4. 4.

    New rules change proof search organization and Vampire * might solve a problem without using induction, while this problem was not solved by Vampire. We do not consider such problems to be newly solved.

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Acknowledgements

We thank Johannes Schoisswohl for joint work related on experimenting with inductive theorem provers. This work was partially funded by the ERC CoG ARTIST 101002685, the EPSRC grant EP/P03408X/1, the FWF grant LogiCS W1255-N23, the Amazon ARA 2020 award FOREST and the TU Wien SecInt DK.

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Authors and Affiliations

  1. TU Wien, Vienna, Austria

    Márton Hajdu, Petra Hozzová, Laura Kovács & Andrei Voronkov

  2. University of Manchester, Manchester, UK

    Giles Reger & Andrei Voronkov

  3. EasyChair, Manchester, UK

    Andrei Voronkov

Authors
  1. Márton Hajdu
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  2. Petra Hozzová
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  3. Laura Kovács
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  4. Giles Reger
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  5. Andrei Voronkov
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Corresponding author

Correspondence to Petra Hozzová .

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Editors and Affiliations

  1. Université Libre de Bruxelles, Brussels, Belgium

    Jean-François Raskin

  2. Institute of Science and Technology Austria, Klosterneuburg, Austria

    Krishnendu Chatterjee

  3. École Normale Supérieure Paris-Saclay, Gif-sur-Yvette, France

    Laurent Doyen

  4. MPI for Software Systems, Kaiserslautern, Germany

    Rupak Majumdar

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Hajdu, M., Hozzová, P., Kovács, L., Reger, G., Voronkov, A. (2022). Getting Saturated with Induction. In: Raskin, JF., Chatterjee, K., Doyen, L., Majumdar, R. (eds) Principles of Systems Design. Lecture Notes in Computer Science, vol 13660. Springer, Cham. https://doi.org/10.1007/978-3-031-22337-2_15

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