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"it cannot be the case" is a correct and usable phrase in written English
You can use it to express a denial or disagreement, such as when you want to say something definitely is not true or cannot happen. For example: "It cannot be the case that she would forget her own birthday!"
Exact(39)
Finally, (15) states that for any argument to which we assign undecided, it cannot be the case that all its attackers are false or that one of them is true.
But it cannot be the case that every investor has both functions at once.
Equally, it cannot be the case that CO2 causes warming as well as cooling.
For another, it cannot be the case that 80% or 90% of all private activity becomes genuinely unproductive overnight.
However, we've already concluded that even in this setting it cannot be the case only to have doves in the population.
Surely it cannot be the case that whenever a controlling stockholder can vote against a sale the out voted minority can assert a coercion claim.
Similar(21)
It simply cannot be the case that Crossrail 2 is the highest priority for transport investment in our country.
"I refuse to believe there are only 19 brilliant African-Americans in the city; it simply cannot be the case," Mr. Hewitt said.
"It simply cannot be the case that a candidate must prove his or her claim in order to get access to the very evidence needed to prove that case," the brief said.
The court engaged in a perfectly ordinary exercise of statutory construction, and it surely cannot be the case that the law "changes" when a jurisdiction's highest court settles the meaning of state law.
"It simply cannot be the case that someone like Amri was able to move around Germany freely even though he was suspected of planning a terrorist attack," said Michael Ortmann, a terrorist expert for broadcaster RTL.
More suggestions(15)
it cannot exceed the case
it cannot resolve the case
it cannot be the reason
it cannot tag the case
it cannot be the material
it cannot withdraw the case
it cannot be the threat
it cannot exploit the case
it cannot distinguish the case
it cannot crush the case
it cannot be the guarantor
it cannot generate the case
it cannot evaluate the case
it cannot determine the case
it cannot infer the case
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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