PRocH: Proof Reconstruction for HOL Light. PRocH is a proof reconstruction tool that imports in HOL Light proofs produced by ATPs on the recently developed translation of HOL Light and Flyspeck problems to ATP formats. PRocH combines several reconstruction methods in parallel, but the core improvement over previous methods is obtained by re-playing in the HOL logic the detailed inference steps recorded in the ATP (TPTP) proofs, using several internal HOL Light inference methods. These methods range from fast variable matching and more involved rewriting, to full first-order theorem proving using the MESON tactic. The system is described and its performance is evaluated here on a large set of Flyspeck problems.