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.
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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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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