I'd respond with "OK, thanks. I won't waste any more of your or my time here then..."

Even if there are no other competing coworking spaces to use locally there's bound to be other temporary/occasional desk space options if you look around hard enough, and _I_ would choose not to be contractually obligated to those sorts of arse-clowns. (Intellectual property in co-working space??? _Seriously??? Patent it or GTFO...)