In a situation like this, you need to do two things -
you need to examine what you would like as a solution
and
you need to assess if your solution is within reasonable reach.
On the basis of what you have said, your solution is that people either admit that they have said and / or heard something negative and untruthful about you, or that they move on and stop making rumours an issue.
How manageable is that as a solution?
As a lifelong office worker, and student of human nature, i would suggest not very - because people do not like to admit that they indulge in hurtful gossip, even though they do.
Best practice here is to draw a line and move on.
People will say what they say, and think what they think, you have no control over that.
What you do control is your reaction to it - and that is what directly affects your life.
You need to see this for what it is - an incident of gossip which will be forgotten sooner than you think, and worrying about it is hurting you, and will not give you the soloution you see.
These people are colleagues who share a work space with you, nothing more. Absence of their friendship will not hurt you, absence of their hurtful attitude will help you.
So be polite, but no more - this is one office coven you do not need membership of.
Good luck.