Abstract
Tarski raised the High School Problem, i.e., whether a set of 11 identities (denoted by HSI) serves as a basis for all the identities which hold for the natural numbers. It was answered by Wilkie in the negative, who gave an identity which holds for the natural numbers but cannot be derived from HSI. This paper describes some computer searching efforts which try to find a small model of HSI rejecting Wilkie’s identity. The experimental results show that such a model has at least 11 elements. Some experiences are reported, and some issues are discussed.
Supported by the National Science Fund for Distinguished Young Scholars of China (grant No. 60125207).
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Zhang, J. (2005). Computer Search for Counterexamples to Wilkie’s Identity. In: Nieuwenhuis, R. (eds) Automated Deduction – CADE-20. CADE 2005. Lecture Notes in Computer Science(), vol 3632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11532231_32
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DOI: https://doi.org/10.1007/11532231_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28005-7
Online ISBN: 978-3-540-31864-4
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