  In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved
Lam's problem from projective geometry$\unicode{x2014}$the long-standing
problem of determining if a projective plane of order ten exists. Both the
original search and an independent verification in 2011 discovered no such
projective plane. However, these searches were each performed using highly
specialized custom-written code and did not produce nonexistence certificates.
In this paper, we resolve Lam's problem by translating the problem into Boolean
logic and use satisfiability (SAT) solvers to produce nonexistence certificates
that can be verified by a third party. Our work uncovered consistency issues in
both previous searches$\unicode{x2014}$highlighting the difficulty of relying
on special-purpose search code for nonexistence results.
