What Was Probably True
Modal Verbs of Probability - Past
Modal verbs of probability express an opinion based on what a speaker knows about a situation at the moment of speaking. The following forms are used to speak about past situations.
Example:
Their full-service suites can't have been operational at that time.
Their kitchen must have been abiding by sanitation standards.
Tim must have been a veteran of stage shows.
'Must' plus the perfect form (must have done) expresses the idea that you are almost 100% sure of your opinion about a given situation which took place in the past.
Subject + must + have + past participle + objects
Example:
Their kitchen must have been abiding by sanitation standards.
Management must have been unaware of our guests' needs.
'Might' or 'could' plus the perfect form of the verb (could / might have done) expresses an opinion that you think was probably true at a past moment in time.
Subject + might / could + have + past participle + objects
Example:
The manufacturers might have been responsible for the defect.
The tavern might have been offering a low priced beer.
'Can't' plus the perfect form of the verb (can't have done) expresses the idea that you are almost 100% sure that something was not true at a past moment in time. Note that the form is 'can't have done' NOT 'couldn't have done'.
Subject + can't + have + past participle + objects
Example:
The hotel can't have been offering employees benefits.
Their lateness can't have been caused by a high volume of orders.