How do you PROVE something that didn’t happen, didn’t happen??

This is so obnoxious and I’m really over it.

I work in a place where two coworkers do not like me. Haven’t liked me from day one. I’m generally good at what I do, I’m younger, I’m single and independent.

I also don’t really sugar coat emails to sound flowery, but they aren’t rude.

Anyway, I found out they have been accusing me of saying some pretty awful things. I have never said or even thought these things.

When I found out they were telling people this, I went to them in person and said “I have heard you’re telling other coworkers I said xyz and I want to clarify right now that I never said that.”

They didn’t believe me, said someone told them I said it, wouldn’t name their sources.

I thought it was over, but no. They called in higher ups to discuss me and continue their accusations. I was not included in the meeting. They are also contacting coworkers I have become friendly with outside of work and telling them they should be careful around me and to not trust me.

Apparently HR says we have to do a “mediation”. (I have not been told this, but someone else in the meeting said this is the next step.)

I will go to the mediation, but what can we mediate if I blatantly didn’t say the things they’re accusing me of? I feel like saying “unless you’re willing to bring in the person you claim told you this, this is a waste of my time.”

I’m not really worried about my job, because I didn’t do/say anything wrong. It’s just annoying.

I’m mid 30s and they are mid to late 40s.