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The phrase "inconsistent with the facts" is correct and usable in written English.
You can use this phrase whenever you want to describe a statement or theory that does not align with existing evidence or is contradicted by that evidence. For example: "The defendant's alibi was inconsistent with the facts of the case, so the jury found him guilty of the crime."
Exact(25)
"Yet such a view is inconsistent with the facts.
A committee overturned the ruling, finding it inconsistent with the facts," Zhang said.
A spokesman described Gary Locke's remarks as "inconsistent with the facts".
Our understanding of the basic make-up of Britain is also inconsistent with the facts.
It's unfortunate if those perceptions are shaped not by the facts but by criticisms inconsistent with the facts.
"Comptroller Liu paints a picture of ARIS that is inconsistent with the facts and his own survey findings," he said.
Similar(35)
Such a conclusion, however, seems to be inconsistent with the fact that aesthetic judgment is a form of judgment.
"It would be contrary to the results I have found," said W. Kip Viscusi, a law and economics professor at Harvard Law School, "and it seems inconsistent with the fact that in the real world you see judges reducing punitive awards by juries".
However, one assumption of the GAB model for vapor sorption in glassy polymers is inconsistent with the fact that there are two species of sorption sites as the CDMS model assumes.
He does not seem to notice, moreover, that this wilful blindness is inconsistent with the fact that if video games make us better at anything, it is precisely at visual tasks.
If this statement appears to be inconsistent with the fact that we have just experienced the warmest decade on record and that sea levels continue to rise, ice sheets continue to melt and the oceans continue to build up heat, then that's because it is.
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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