5:19 PM PT -- We spoke with a co-CEO of F45 who tells us straight up, "Everything that's been lodged is a total fabrication of the truth."

F45 not only plans to fight the allegations -- but the co-CEO says they will countersue Owens adding, "He picked a fight with the wrong company."

F45 says the company respects Owens as one of the greatest athletes alive -- and thinks he should be in the Pro Football Hall of Fame -- but says he's lying through his teeth when it comes to his lawsuit.

The company notes they have great endorsement relationships with several high profile athletes including Joel Embiid and Harrison Barnes.

"We're not a company that doesn't pay our bills."

Want Terrell Owens to star in a promotional video for your business? It's gonna cost you.

TMZ Sports obtained a lawsuit T.O. filed against a massive gym company called F45 -- a bootcamp-style workout studio that offers high intensity, 45-minute workouts.

Owens is pissed because he says F45 approached him to essentially be a spokesperson for the gym -- in a deal that would pay $15k for a promo "hype" video to help get investors.

He made the video -- 53 seconds long and says he got paid his $15k.

The problem ... Terrell says the deal was supposed to pay him an additional $25,000 bonus for each of the first 25 F45 franchises that opened in the United States. After 25 locations, Owens says the bonus dropped to $5k per gym.

Owens claims F45 opened at least 45 locations in the U.S. -- but he didn't get paid a cent of his bonus money and now he's demanding at least $725k to make things right.

So far, no comment from F45.