an argument between two people, groups or countries; discussion about a subject on which people disagree

to question whether something is true or legally or officially acceptable

to argue or disagree strongly with somebody about something, especially about who owns something

I tried to dispute the bill with the waiter.

The United Nations recognizes the area as a disputed territory.

The issue remains hotly disputed.

He taught and disputed with local poets.

to fight to get control of something or to win something

On the last lap three runners were disputing the lead.

LEARNit Dictionary