Is did not a simple predicate?

No, "did not" is not a simple predicate; it is a compound verb phrase. A simple predicate consists of the main verb or verb phrase without any auxiliary verbs or modifiers. In this case, "did" serves as an auxiliary verb, while "not" negates the action of the main verb that would follow. For example, in the sentence "She did not go," the simple predicate is "go."