Nested quantifiers: Please give me a solution

Question

How can I express this proposition using predicates and quantifiers?

There are at least two paths connecting every two distinct endpoints on the network

Answer 1

There are at least two paths connecting every two distinct endpoints on the network.

For all $x,y$ (($x$ endpoint on network and $y$ endpoint on network and not-($x = y$)) implies exists $p,q$ with ($p$ path and $q$ path and not-($p = q$) and ($p$ connects $x$ and $y$) and ($q$ connects $x$ and $y$))).