$14\mathrm{.}2$: A Logically Defined Language

Let D be the language of all strings, over the language $\backslash$Sigma $=\{$a$,$ b$\},$ that satisfy the logical formula:

exists x: for all y: exists z: Ca$($x$)$ and Cb$($y$)-->($Ca$($z$)$ and $($x $<$ y$)$ and $($y $<$ z$))$

Then there are exactly eight strings of length $<=4$ in D

true or false