Incompatible (adjective)

1. Not able to exist or function together in a harmonious way.
2. Not able to be used together or with something else.
3. Inconsistent or contradictory.

Origin:

From latin incompatibilis, from in- ("not") + compatibilis ("compatibl.e")

Examples:

1. The two chemicals are incompatible and should not be mixed.
2. The software is incompatible with the operating system.
3. The couple had incompatible schedules.
4. The ideas were incompatible with each other.
5. His values were incompatible with the company's.