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The phrase "are mutually incompatible" is correct and usable in written English.
It can be used to describe two or more things that cannot coexist or function together without conflict.
Example: "The two theories are mutually incompatible, leading to confusion among researchers."
Alternatives: "cannot coexist" or "are fundamentally opposed".
Exact(35)
Most of the new theories suggested are mutually incompatible.
Suddenly, it's beginning to look as though the 10% growth rate and democracy are mutually incompatible.
"Now they will have to resolve that by explaining how they will balance the tradeoffs … between the different things they promised which are mutually incompatible.
What I wrote: "When you buy an e-reader, you're committing to that one company's catalog of books forever, because their book formats are mutually incompatible".
These apps are mutually incompatible, so you want to choose the most popular one, because you'll increase the odds that your contacts have the same app.
An important result from the analysis shows that the two potential treatment approaches are mutually incompatible.
Similar(24)
These two extras, however desirable, should never have been turned into outright aims not least because they may be mutually incompatible.
It seems clear that he did not consider revolution and evolution to be mutually incompatible.
This suggests that for NiAl-based substrates, hot corrosion resistance and exceptional scale spallation resistance may be mutually incompatible goals.
Then if \(p\cup r\sim q\cup r\) for some \(r\) that is mutually incompatible with both \(p\) and \ q\) and is such that \(\neg(r\sim p)\), then \(p\cup r\sim q\cup r\) for every such \(r\).
This is a significant shift in thinking from the past, where the environmental agenda has been pitted against the development agenda, as if the two were mutually incompatible.
More suggestions(3)
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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