  We present the solution of a century-old problem known as Schur Number Five:
What is the largest (natural) number $n$ such that there exists a five-coloring
of the positive numbers up to $n$ without a monochromatic solution of the
equation $a + b = c$? We obtained the solution, $n = 160$, by encoding the
problem into propositional logic and applying massively parallel satisfiability
solving techniques on the resulting formula. We constructed and validated a
proof of the solution to increase trust in the correctness of the
multi-CPU-year computations. The proof is two petabytes in size and was
certified using a formally verified proof checker, demonstrating that any
result by satisfiability solvers---no matter how large---can now be validated
using highly trustworthy systems.
