In my opinion, the majority of useful work done by CERN is not in the domain of theoretical physics, but in that of engineering. A lot of really bizarre configurations are build (with respect to day-to-day engineering challenges), with extreme requirements that push materials and other forms of engineering forward. Personally I have discovered papers by CERN where they test things that are very useful to me, but if it wasn't for their massive budget, available tools and personnel, nobody else would be be able to, or bother testing and publishing.