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The phrase "contrary to the facts" is correct and usable in written English.
The phrase is often used to describe something that is not consistent with the known facts. For example, "The politician made a statement that was contrary to the facts, leading many to question his credibility."
Exact(16)
To surround Stalin with glory - contrary to the facts and contrary to historical truth.
General Gotovina's lawyer, Greg W. Kehoe, said by telephone from The Hague, "I am absolutely shocked — it is contrary to the facts and wrong in law".
The writer seems to assume that landlords are entitled to harass rent-regulated tenants, something clearly contrary to the law, although, unfortunately, not contrary to the facts.
"Contrary to the facts, the S*n published a front page story with the banner headline 'The Truth' which contained blatant lies".
Bill Jordan, a lawyer for Mr. Schlozman, called the report "inaccurate, incomplete, biased, unsupported by the law, and contrary to the facts".
Expert testimony is not admissible if it is "speculative, unsupported by sufficient facts, or contrary to the facts of the case". Marmo v. Tyson Fresh Meats, Inc., 457 F.3d 757, 757 (8th Cir. 2006).
Similar(44)
"Contrary-to-the-fact occurrences occur," Pynchon writes.
The suggestion implies, contrary to the fact, that the two decisions are contradictory.
The contention is contrary to the fact. 2 But the form of the order is without importance.
This runs contrary to the fact that the events themselves function for many as a jolly excuse for jingoism.
It is rather amazing that the complementary energy always attains minimum value at the equilibrium state irrespective of the stability of cable networks, contrary to the fact that only the stationary principles have been presented for elastic trusses and continua even in the case of stable equilibrium state.
More suggestions(18)
contrary to the conditions
opposition to the facts
contrary to the instructions
contrary to the estimates
contradiction to the facts
contrary to the information
contrary to the article
contrary to the intent
contrary to the aims
contrary to the interests
contrary to the requirements
contrary to the results
contrary to the allegations
contrary to the arguments
contrary to the provisions
contrary to the standards
contrary to the recommendations
contrary to the claims
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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