There is no evidence that Neanderthals were extant 20,000 years ago. Even 30,000 years is a stretch, with only scant and inconclusive evidence. The best estimate, based on solid evidence, is extinction around 40,000 years ago, and that the sharp cooling after the Campanian Ignimbrite, which lasted for at least a year, with acid rain being another adverse environmental factor for years afterwards, were quite likely pivotal in their extinction. I prefer to look things up before I post...