6/1/18 5:10 PM PT -- It looks like the puppet wars are over -- Sesame Street just dismissed its lawsuit against producers of "The Happytime Murders" ... according to new legal docs.

Melissa McCarthy and her cast of raunchy puppets are free to keep using their "Sesame Street"-inspired tagline -- 'cause a judge says the 2 ideas are clearly not the same thing.

A judge in NYC handed down a ruling Wedenesday in favor of STX Productions -- which is producing McCarthy's "The Happytime Murders" -- saying the film's catchphrase, "No Sesame. All Street.," makes a blatant distinction to fans that this is NOT "Sesame Street."

As we reported ... Sesame Workshop is suing STX for allegedly infringing on their company name, and trashing their kid-friendly reputation with a not-so-kid-friendly flick.

Lawyers for "Sesame Street" reportedly tried saying that an older court case about a 1970s porn movie named "Debbie Does Dallas" being found to infringe on the Dallas Cowboys' good name supported their argument now ... but the judge shot that down, saying that flick's X-rated ... this one's R ... and there's a difference.

STX issued a statement through their pupper lawyer, Fred, Esq., saying ... "We fluffing love Sesame Street and we're obviously very pleased that the ruling reinforced what STX's intention was from the very beginning — to honor the heritage of The Jim Henson Company's previous award-winning creations while drawing a clear distinction between any Muppets or Sesame Street characters and the new world Brian Henson and team created."

Long story short ... ejaculating puppets walked away with a win on the street.