There are several synonyms that can be used for the phrase "not intelligent." One common synonym is "unintelligent," which refers to a lack of intellectual ability. Another synonym is "dim-witted," which suggests a lack of quickness or mental agility. "Slow-witted" can also be used to describe someone who is not very intelligent. "Stupid," a more colloquial term, implies a lower level of intelligence or mental capacity. "Ignorant" can also be considered a synonym for not intelligent, as it suggests a lack of knowledge or education. Finally, "foolish" can be used to describe someone who's not intelligent and tends to make poor decisions or show a lack of good judgement.