Learn Farsi: سوپ باید سر رفته باشد.

To express past deduction—making a logical guess that something happened in the past—Farsi uses bâyad followed by the Present Perfect Subjunctive. Here, that's the past participle rafte plus the subjunctive form of "to be", bâshad. Together, bâyad ... rafte bâshad translates to "must have boiled over."

Why is it rafte bâshad instead of the normal present perfect rafte ast?

rafte ast is the standard indicative Present Perfect ("has boiled over"). However, the word bâyad (must) acts as a trigger that forces the following verb into the subjunctive mood. To keep the past meaning while obeying bâyad, we change the auxiliary verb ast into its subjunctive counterpart, bâshad.

What is the literal meaning of sar raftan, and is it only used for boiling liquids?

Literally, sar raftan translates to "head going" or "top going." For liquids, it means "to overflow" or "to boil over." However, it is also very commonly used metaphorically to talk about boredom or running out of patience. For example, howsele-am sar raft literally means "my patience overflowed," which is how you say "I got bored" in Farsi.

Could this sentence also mean "The soup SHOULD have boiled over"?

Yes! Farsi uses this exact same structure (bâyad + Present Perfect Subjunctive) for both logical deductions ("must have done") and past obligations ("should have done"). You have to rely on context. If you left a pot unattended on a high flame, it means "must have boiled over." If you are checking a recipe's timeline, it could mean "should have boiled over (by now)."