Abstract. In this work (ArXiv: 1409.0048), we show that there is a Cantor set of initial conditions in a planar four-body problem such that all four bodies escape to infinity in finite time, avoiding collisions. This proves the Painlevé conjecture for the four-body case, and thus settles the conjecture completely. This work is a continuation of the work ArXiv: 1307.2645 jointly with D. Dolgopyat.