There are slight differences between have pp vs. having pp, but mainly because there are other grammar rules coming into play. For example:
Having eaten already, I was not hungry during the movie.
The having clause is a subordinate gerund DC. That much is true but there is also an element of time.
Notice that the main clause is “I WAS not hungry”... it’s in the past tense. The important thing is that the having clause happened before the main clause. You can also say,
Having eaten already, I am not hungry right now. “I am not” is in the present tense but it is still after the “having” clause.
In number 4, correct me if I’m wrong, but is the answer choice c, the one you didn’t write? (I just don’t have the answers with me now.)
The remains provide evidence of giants having existed on earth...
First, in terms of time, giants existing happens before remains providing, so that part works.
Second, there’s also a gerund vs. infinitive rule. The idiom “evidence of...” needs a gerund, so that’s also why “having” is in the gerund:
I don’t see any evidence of Michael LYING to us.
In this s tenderloin the LYING is the direct object. You know that gerunds can act like nouns.
If the issue was about a lie that Michael may or may not have told in the past, then the sentence with the same direct object would be:
I don’t see any evidence of Michael having lied to us.
This sentence is very close grammatically to your original question #4.
