Tristan Thompson is fed up with what he calls out-and-out lies about him fathering a child... so he's followed through with a lawsuit against his accuser.
Tristan just filed the suit against Kimberly Alexander ... the woman who's very publicly claimed the NBA star is the father of her 5-year-old son -- something he's repeatedly denied. In the lawsuit, Tristan says the paternity test he took back in January "definitively concluded that [he] is not the father." Paging, Maury Povich!
According to the suit, obtained by TMZ, after the test results came back .