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The Collaborative International Dictionary
Inconvincible

Inconvincible \In`con*vin"ci*ble\, a. [L. inconvincibilis. See In- not, and Convince.] Not convincible; incapable of being convinced.

None are so inconvincible as your half-witted people.
--Gov. of the Tongue.

Wiktionary
inconvincible

a. Incapable of being convinced.