"The three sons are not sleeping."
Translation:Tres filii non dormiunt.
The 'are' is a part of the translation for dormiunt.
dormiunt -> "(they) sleep", "(they) are sleeping", "(they) do sleep".
The 'are' in the English is used here for the present continuous, which Latin often best represents using the Latin present (which is also often used for the English simple present and present emphatic).