A consistent Formula Example

Question

I am asked to provide an example of a consistent Formula $\psi(x)$ with one free variable $x$ (meaning that the set {$\psi(x)$} is consistent) but $\forall x\psi(x)$ is not consistent. I'm at a loss here..

is this a good one? $\psi(x) = \exists y(x^2=y)$

Answer 1

Suppose you're working in a language with a constant symbol $c$. Then $x \neq c$ is clearly consistent, but $\forall x\ x \neq c$ is inconsistent.