A Mathematical Benchmark for Inductive Theorem Provers

14 pages•Published: June 3, 2023

Thibault Gauthier, Chad Brown, Mikoláš Janota and Josef Urban

Abstract

We present a benchmark of 29687 problems derived from the On-Line Encyclopedia of Integer Sequences (OEIS). Each problem expresses the equivalence of two syntactically different programs generating the same OEIS sequence. Such programs were conjectured by a learning-guided synthesis system using a language with looping operators. The operators implement recursion, and thus many of the proofs require induction on natural numbers. The benchmark contains problems of varying difficulty from a wide area of mathematical domains. We believe that these characteristics will make it an effective judge for the progress of inductive theorem provers in this domain for years to come.

Keyphrases: arithmetic, automated theorem provers, benchmark, induction, inductive theorem provers, oeis

In: Ruzica Piskac and Andrei Voronkov (editors). Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 94, pages 224-237.

Links:	https://easychair.org/publications/paper/3hgH
	https://doi.org/10.29007/jr72

BibTeX entry

@inproceedings{LPAR2023:Mathematical_Benchmark_Inductive_Theorem,
  author    = {Thibault Gauthier and Chad Brown and Mikoláš Janota and Josef Urban},
  title     = {A Mathematical Benchmark for Inductive Theorem Provers},
  booktitle = {Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Ruzica Piskac and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {94},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/3hgH},
  doi       = {10.29007/jr72},
  pages     = {224-237},
  year      = {2023}}

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