An upper bound of 61 for the Ramsey number $R(3,3,3,3)$

We improve the upper bound on the classical Ramsey number $R(3,3,3,3)$ from 62 to 61. The proof is based on a global incidence count, classifications of small neighborhoods and exhaustive SAT computations. We formalize the mathematical reductions in Lean and refute every resulting formula with two SAT solvers.