This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

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adj. Not reconcilable.

Irreconcilable.

adj. impossible to reconcile

"But a senior U.S. diplomat in Kabul said "there is some thinking going on in Washington" now about being more open to reconciliation, even to Karzai's proposed outreach to Taliban leaders that the Pentagon has described as unreconcilable, including hard-line chief Mullah Mohammad Omar."

hostile    inconsistent   

unreconcilably