Ex girlfriends

Okay, so my boyfriend of 3 years has an ex girlfriend who recently moved back into our town. He claims he hates her, never speaks good of her (she cheated on him). And it's 4+ years after they dated. She's tried to get us to break up before, a couple of times. Now she's claiming that they message and he vents crap about me to her. And that he's messaged girls in the past about wanting to be "fuck buddy's" while I wasn't really horny due to birth control. He absolutely denies it, we have lived together for the last year and a half, and are always together. It's turned into a "he said, she said" kind of situation. However, she is a constant lair, and it's hard to tell what's true or not.