= Solution
In this <first-order structure>, $R(x,z)\land R(y,z)$ says $x\leq z$ and $y\leq z$. Thus $z$ is an <upper bound> of $x,y$. The universally quantified clause says that if $w$ is any other <upper bound>, then $z\leq w$. Therefore $z$ is their <least upper bound>. In the usual <total order> on the <natural numbers>, this is their <maximum>:
$$
\boxed{\phi(x,y,z)\iff z=\max\{x,y\}.}
$$
This describes a condition on the values assigned to the free variables $x,y,z$; $\phi$ itself is not a closed <first-order sentence>.
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