I'm doing some research on second order logic and I'd like to write down a proof for the following argument:
x is a first order variable and
Q are predicate symbols.
A plain english instance of the argument would be something like
All men are mortals, so the property of being human has the property of being mortal
This looks an invalid argument to me, but I'd like a formal proof of its invalidity. I'm looking, for example, for a way to extend the finite universe method to second order arguments, but any formal proof would be good, either semantic or syntactic.