Must
can be used to express the future-in-the-past, and occurs in reported clauses
in formal contexts:
She had little appetite for the food on the tray, but she knew that she
must eat
something or else she would faint with hunger.
Deduction
The perfect form must have always refers to deduction, not obligation:
I
must have been on the phone.
(it is likely/probable that I was on the phone)
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