The phrase 'facts exist' is correct and usable in written English.
You can use this phrase to emphasize the reality of a situation. For example, "The news reports may be subjective, but the facts exist regardless."
Few undisputed facts exist about the playwright's life, but he was baptised in Canterbury on 26 February 1564.
Mr. Hevesi's lawyers wrote that "one can only wonder what other facts exist that are contrary and unsupportive of your conclusions, but which remain unrevealed".
Few facts exist to illuminate Leo's actual life in Rome, but Davis fills us in on the scholars with whom he may have conversed and the social mores to which he would have had to adjust, arriving at a portrait of "a man with a double vision," straddling two warring cultures.
In a famous lecture at Harvard, Russell concluded that irreducibly negative facts exist.
"Of course, I think that if such facts exist they will be investigated [by anti-corruption committee]," he told Gazprom-owned Ekho Moskvy radio.
If, of course, he does in fact exist.
Or that Khaufpur does not, in fact, exist.
In fact, we often spot coincidences and call them patterns when none in fact exist.
A time exposure at twilight proves that the Magic Hour does in fact exist.
On one page, he writes, "The Factoids: Nobody knows whether they in fact exist".
