conflict

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."

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."

To be at odds (with); to disagree or be incompatible

To overlap (with), as in a schedule.

"It appears that our schedules conflict."