I'd have to agree with the other two comments. Good info.
Sibling rivalry can send parents bonkers.
Another point I'd like to add, is that you can't really "settle" the rivalry. As in, if you find yourself being in the judge role or the mediator role, its probably not going to end well no matter what you say or do.
If your kids and you have developed a habit of dragging you into the fight, then it's a good idea to have a discussion at a calm time when they're not at it and lay down some new guidelines.
Before you do that, you need to take a new perspective. Take a step back, and acknowledge that generally speaking, sibling rivalry to a certain extent has benefits. Kids learn negotiation skills. They also learn that people can hurl insults at them and they don't need to take it personally. It toughens them up.
But you want to have some rules so that you can have some peace. Decide what it is you want and don't want, and let them argue it out according to those guidelines. For example, some parents say you can argue as long as there is no name calling, foul language, or physical violence. Also, they might have to go to another room away from where you are so it doesn't bother you.
Also, while you're having your calm discussion about guidelines, you can mention that you trust that your kids are smart and creative and are able to come up with solutions to problems so that all the parties can be happy. Role play a couple of common scenarios to brainstorm possible solutions while they're not in the heat of the moment. Trust that they can figure it out themselves.
So that when they do have an argument, you can excuse yourself from being the mediator by reminding them that you know they are smart enough to come up with a happy solution.
Sometimes, they may be more motivated to come up with a happy solution if there is something to be lost or gained. For example, kids are arguing about who chooses the TV show. "You chose the last show." "You always get to choose." Yadda yadda yadda.
"Ok, kids. I know you can come up with a happy solution for everybody. The TV is going off until you can all resolve this."
Immediately the solutions are forthcoming.
Hope that helps :>