Conflict is serious disagreement and argument about something important. If two people or groups are in conflict, they have had a serious disagreement or argument and have not yet reached agreement.
A conflict is a serious difference between two or more beliefs, ideas, or interests. If two beliefs, ideas, or interests are in conflict, they are very different.
If ideas, beliefs, or accounts conflict, they are very different from each other and it seems impossible for them to exist together or to each be true.