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The Collaborative International Dictionary
Incompossible

Incompossible \In`com*pos"si*ble\, a. [Pref. in- not + compossible: cf. F. incompossible.] Not capable of joint existence; incompatible; inconsistent.

Ambition and faith . . . are . . . incompossible.
--Jer. Taylor. -- In`com*pos`si*bil"i*ty, n. [Obs.]

Wiktionary
incompossible

a. (context rare English) Not capable of joint existence; incompatible; inconsistent.

Usage examples of "incompossible".

Under this remarkable confluence of pressures, serial traumas, provocations, and incompossible yearnings, Tony Donuts Junior accomplished something painful and for him almost unprecedented.