irreconcilable

ir|rec|on|cil|able /ɪr'ekəns'aɪləbəl/
1 [ADJ] oft ADJ with n
If two things such as opinions or proposals are irreconcilable, they are so different from each other that it is not possible to believe or have both of them. (FORMAL)
These old concepts are irreconcilable with modern life.
= incompatible
2 [ADJ]
An irreconcilable disagreement or conflict is so serious that it cannot be settled. (FORMAL)
...an irreconcilable clash of personalities.

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