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'must have failed' is correct and usable in written English.
It is used to express a deduction based on past evidence or facts. Example: She missed the deadline for the assignment, so she must have failed it.
Exact(27)
One after another must have failed.
Such theorized brown dwarfs must have failed to reach stardom.
She also must have failed to persuade him that he was no businessman.
Q: But you must have "failed somewhere" to do what you should have done.
Then I was told we must have failed to protect our computer with Norton – but we had.
For the John S. McCain to have hit the Alnic MC, a handful of separate functions in the safety chain must have failed, the officer said.
Similar(33)
She must had failed Crafting 101 because she didn't know that spray paint eats away at foam!
They must also have failed all standard therapies and not be eligible for a heart transplant.
As W. Somerset Maugham – or was it Ally MacLeod? – said: it is not enough to achieve personal success, one's best friend must also have failed.
They would go and say, 'How terrible you must feel to have failed with this original child!' and then drive off with me in a huff".
For tests of some experimental cancer therapies, for example, volunteers must be terminal and have failed standard therapy.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com