Question

What is the simple predicate in the sentence "They have destroyed some buildings"?

Answer 1

have destroyed

Explanation:

The predicate of a sentence tells what the subject is doing.

A complete predicate tells us everything - all the details available.
A simple predicate tells us only the simple verb.

In the sentence They have destroyed some buildings, the simple predicate is "have destroyed". If we want to know what they destroyed, then we look to the complete predicate of "have destroyed some buildings".