it's a philosophy, so no it doesn't have testable predictions - but neither does objectivism, its counterpart. But then, testable predictions don't tell you about the nature of reality so c'est la vie.

> is there a function from theorems of ZFC to {invented, not invented}?

Can you derive definitions of inventions versus discoveries from set theory? No, probably not. You can't derive the smell of a rose from set theory either though so it's probably not a very good theory of everything.