Solution
= Solution
Every pair of <natural numbers> has a <maximum>, itself a <natural number>. Given arbitrary $x,y$, choose $z=\max\{x,y\}$. Then $x,y\leq z$, and any $w$ satisfying $x,y\leq w$ also satisfies $z\leq w$. All three clauses of $\phi$ hold. Thus
$$
\boxed{\mathbf N\models\psi.}
$$
This explicitly supplies the witness required by the <existential quantifier> for every pair chosen by the two <universal quantifiers>.