1. If the Domain is All the animals.
No dogs are intelligent = $\sim \exists x (Dog(x) \wedge Int(x) ) $
Interpretation : There does not exists any animal which is Both Dog and intelligent.
Or
$\forall x(Dog(x) \rightarrow \,\,\sim Int(x))$
Interpretation : For all animals, If It is Dog then It is Not intelligent.
2. If the Domain is All Dogs :
(Just make the Dog(x) in the above formulas True(T)..)
Hence,
No dogs are intelligent = $\sim \exists x ( Int(x) ) $
Or $\forall x( \sim Int(x))$