conflict
Definitions
noun
A clash or disagreement, often violent, between two or more opposing groups or individuals.
The conflict between the government and the rebels began three years ago.
One particularly damaging, but often ignored, effect of conflict on education is the proliferation of attacks on schools[…]as children, teachers or school buildings become the targets of attacks. Parents fear sending their children to school. Girls are particularly vulnerable to sexual violence.
An incompatibility, as of two things that cannot be simultaneously fulfilled.
I wanted to attend the meeting but there's a conflict in my schedule that day.
verb
To be at odds (with); to disagree or be incompatible
[T. E.] Lawrence said that in the end he felt himself to be fighting not for the imperial British but for the rebellious Arabs. All too often he conflicted with British bureaucratic fustiness.
To overlap (with), as in a schedule.
Your conference call conflicts with my older one: please reschedule.
It appears that our schedules conflict.