Translating a English Sentence to Predicate Logic

Let $C(a,b)$ be "$a$ and $b$ have communicated over the web," and the domain of discourse is all students in the class. What is the translation of "Everyone has communicated over the web with the same student" Note: the student hasn’t communicated with themselves.

Very stumped on this one. I am initially stating $forall a exists b ((a neq b) implies C(a,b)).$ Is this the correct way to show that someone is not themselves in this statement?