Automated theorem proving reveals a lengthy Andrews–Curtis trivialization for a Miller-Schupp trivial group presentation

• Published in: Examples and counterexamples Vol. 8; p. 100201
• Main Author: Lisitsa, Alexei
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2025; Elsevier
• Subjects: AC-trivializations; Andrews–Curtis conjecture; Automated theorem proving; Combinatorial group theory; Combinatorial group theory; AC-trivializations; Automated theorem proving; Andrews–Curtis conjecture
• ISSN: 2666-657X; 2666-657X
• DOI: 10.1016/j.exco.2025.100201

We present an independently discovered Andrews–Curtis trivialization of the balanced trivial group presentation MS9(w∗)=〈a,b∣a−1b9ab−10,a−1b−1aba−1〉 obtained through automated theorem proving. At the time of discovery, the AC-status of this case was unsettled; it has since been resolved by other methods. The resulting simplification sequence, consisting of 8,634 elementary moves, remains the longest AC-simplification sequence found by any computational method to date (as of January 2025). The sequence was generated by the Prover9 theorem prover, which required approximately 74 days and over 56 GB of memory to compute. •New example of Andrews–Curtis trivilaization is demonstrated for a Miller-Schupp trivial group presentation.•Demonstrated trivialization sequence has the length 8634 steps which is longest ever found by computational methods.•The strength of generic automated reasoning methods in experimental mathematics is demonstrated.