One day, Alice, Betty, Cathy, David, and Edward were at home playing hide and seek. Unfortunately, one of them accidentally collided into a flower vase. When their mother came back home and saw the broken vase, she asked them who did it.
Alice: "Betty broke it!"
Betty: "Alice is not telling the truth."
Cathy: "I did it!"
David: "I did not break it and Betty is lying!"
Edward: "David is telling the truth!"
Given that at least three children are telling the truth, who broke the vase?