A SAT-based Resolution of Lam's Problem

In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lam's problem from projective geometry—the long-standing of determining if a plane order ten exists. Both the original search an independent verification in 2011 discovered no such plane. However, these were each performed using highly specialized custom-written code did not produce nonexistence certificates. this paper, we resolve translating into Boolean logic use satisfiability (SAT) solvers to certificates that can be verified third party. Our work uncovered consistency issues both previous searches—highlighting difficulty relying on special-purpose for results.