As bizarre as it sounds ... the sisters were hooked up to a polygraph machine and took turns grilling each other on their famous family's most intimate secrets -- including their own sex lives. A polygraph examiner sat at a table nearby to gauge the veracity of their answers in the 14-minute video published Thursday by Vanity Fair.

Khloe was grilled first by Kourtney, who peppered her sibling with questions about family fights, their children, weddings and social media posts. But, Kourt wasn't letting Khloe off that easy ... she asked a real zinger, setting it up this way ... "Is there anything you'd like me to ask you?" To clear up any rumors?"

Then she hit Khloe over the head ... "Oh, are you still sleeping with Tristan?"

Surprisingly, Khloe seemed amused ... "No, I am not. I'm really not." Of course, Khloe was referring to Tristan Thompson, her cheating ex-fiancé and father of their 2 young children.

Unconvinced, Kourt turned to the polygraph examiner, who confirmed Khloe was telling the truth. "Bravo!," Kourtney shouted.

The rolls were then reversed. Khloe questioned Kourtney ... partially about her kinky activities with husband Travis Barker, beginning with the couple getting caught having sex in public. "Do you regret doing that?" Khloe asked Kourt, who responded, "Nope."

It got weirder ... Khloe asked if the spouses dressed as animal characters known as "furries" in order "to bone one another." Kourt fired back, "No!" But then, she admitted to having sex with Travis in their Halloween costumes last year when they dressed as the lead characters in the 1993 romantic crime film, "True Romance."

The polygraph examiner gave Kourt the thumbs up ... she was truthful!!!