What is the integer programming complexity of this sentence?
$\exists x\in\mathcal P\quad\forall y\in\mathcal P\quad\phi(x)\leq\phi(y)$ where $\mathcal P$ is a bounded convex polytope in $\mathbb Z^{t}\times\mathbb R^{t'}$ and $\phi(x),\phi(y)$ are linear conditions.