Longman Dictionary of Contemporary English - dispute

~1 n 1 »SERIOUS DISAGREEMENT« a situation in which two countries or groups of people quarrel or disagree with each other  (a border dispute | A prolonged labor dispute disrupted rail services.) 2 be beyond dispute if something is beyond dispute, everyone agrees that it is true or that it really happened  (It is beyond dispute that advances in medicine have enabled people to live longer.) 3 be in/under dispute if facts are in or under dispute, people do not agree about them 4 be in dispute (with sb) to disagree publicly with another person or group  (The miners were in dispute with their employers over pay.) 5 be open to dispute if something is open to dispute, it is not completely certain and not everyone agrees about it  (His interpretation of the poem is open to dispute.) ~2 v 1 to say that you think something such as a fact or idea is not correct or true  (Few would dispute that travel broadens the mind.) 2 to argue or disagree with someone  (hotly disputed (=argued about with strong feelings or with anger)) 3 to argue with another country, group etc about who owns a piece of land  (The defending army disputed every inch of ground.)