I encountered a Math SO question about proofs, where the gist was that in order to get to a mathematical truth, you need to start from axioms, and work from them towards the thing you want to prove. If you need to prove a statement is true, and you start from it working towards some axiom, and your starting equation is not true, you'll basically end up proving anything is true. This is classic high-school stuff, but which I have somehow let slip.

Anyways, at work I encountered a situation where a system had a lot of requirements, some of which were conflicting. If all of these requirements are equally important, but some conflict, you can essentially build something that can conflict with any of the requirements; you're not going to be up to spec anyway, so now you have a choice which requirements you ignore.

Either the conflicts get resolved or the requirements have priorities, where a larger priority trumps lower, or the ensuing result will satisfy no one.