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In English, we often use the ‘must + have + p.p’ to draw a conclusion about a particular situation we are witnessing. For instance, arriving at the gate of an house which has been on sale for a while, I tell my wife, after seeing some trucks being unloaded and words of felicitations being exchanged between some people: “O love! We are late! The house must have already been bought/sold.” The must-pattern is used when there is high probability for the veracity of the speaker’s conclusion. Should we be less certain about the circumstances, we tend to dilute the certainty by using ‘might + have + p.p.’

Here is a summary of what I have learnt about the passive form in German, yet none seems to fit the example I have given above.

  • Present: „Das Haus wird gekauft.“ corresponding to “The house is being bought.”
    It must be noted that using werden+p.p emphasises the action rather than the result, i.e. to say “the house is bought” we should either say „Das Haus ist gekauft.“ or use the perfect form below.

  • Perfect: „Das Haus ist gekauft worden.“ corresponding to “The house has been bought.”
    I have also come to realise that this pattern is used when the speaker intends to break something new to his hearer the same way as in English.

  • Past: „Das Haus war wurde gekauft.“ corresponding to “The house was bought.”

  • Past Perfect: „Das Haus war gekauft worden.“ corresponding to “The house had been bought.”

  • Future: „Das Haus wird gekauft werden.“ corresponding to “The house will be bought.”

  • Future Perfect: „Das Haus wird gekauft werden worden sein.“ corresponding to “The house will have been bought.”
    This usage requires modification by time-adverbs of some sort: „Bis Freitag wird das Haus gekauft werden sein.“ “The house will have been bought by Friday.”

The last form in particular is interesting in as much as it differs, at least in the English form, from ‘must+have+p.p’ structure in only one element, i.e. will vs. must. So, considering all this, can we possibly translate the sentence in the question as follows?

Das Haus muss bereits gekauft worden sein. Wir hätten früher kommen sollen.“

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    Although gekauft ‘bought’ isn’t wrong, verkauft ‘sold’ would be more idiomatic to use here in German. To express less certainty you could use scheint or wird [wohl] instead of muss, but then you’ll need to add zu before sein, possibly replacing worden, which some people tend to hyper-correct to geworden.
    – Crissov
    Commented Jan 31, 2016 at 19:36
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    There is no difference between English and German grammar in this respect: The correct form in English is a past progressive passive with additional auxilliary must. German does not have a progressive form, so it is simply past passive with an auxiliary müssen. Because there is an auxilliary, the past tense must be perfect, cannot be preterite.
    – Jan
    Commented Jan 31, 2016 at 20:49

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Your translation is perfectly fine, although as Crissov notes, "verkauft" would be more idiomatic than "gekauft". Just be aware that the German construction can have two different, only tangentially related, meanings:

  1. High-probability supposition:

"Das Haus muß schon verkauft worden sein" = "I suppose it must have been sold already."

  1. Rule-based precondition:

"Damit die Hypothek gewährt werden kann, muß das Haus bereits verkauft worden sein." = "A mortgage can only be approved if the house has already been sold."

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    To add to this - I think this is one of the typical cases, where modal particles are used in German. Adding "wohl" ("Das Haus muss wohl schon verkauft worden sein") will state a bit less certainty, but I think it is a bit more idiomatic, at least in spoken German. And after all, one is not sure, otherwise one would have said "Das Haus ist schon verkauft worden". You could also say "Das Haus ist wohl schon verkauft worden", which is less complex, and roughly on the same uncertainty scale as your English suggestion.
    – Gerhard
    Commented Feb 1, 2016 at 8:54
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    @Gerhard That's true, "wohl" is often used to disambiguate in favor of (1), and in fact it's so decisive that it can do the job alone, without usung "muß" at all. Commented Feb 1, 2016 at 9:03
  • With “Zustandspassiv” instead of “Vorgangspassiv” your suggestion would become das Haus ist wohl schon verkauft _ without the _worden.
    – Crissov
    Commented Feb 1, 2016 at 10:22

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