Enderton problem 4 in Section 2.5

Let $\displaystyle \Gamma = \{\neg \forall v_1 Pv_1, Pv_2, Pv_3, \ldots \}$. Is $\displaystyle \Gamma $consistent? Is $\displaystyle \Gamma$ satisfiable?

The completeness theorem says that any consistent set of formulas is satisfiable. Therefore, we only need to show that $\displaystyle \Gamma$ is consistent.

Suppose to the contrary, towards a contradiction, $\displaystyle \Gamma \vdash \bot$. Then, we have both $\displaystyle \Gamma \vdash \phi$ and $\displaystyle \Gamma \vdash \neg \phi$ for any wff $\displaystyle \phi$. I am looking for a counterexample $\displaystyle \phi$, which is either $\displaystyle \Gamma \vdash \phi$ or $\displaystyle \Gamma \vdash \neg \phi$, not both.

Any help will be appreciated.