*incompossible*

a. [ Pref. in- not + compossible: cf. F. incompossible. ] Not capable of joint existence; incompatible; inconsistent. [ Obs. ] [ 1913 Webster ]

Ambition and faith . . . are . . . incompossible. Jer. Taylor.

-- In`com*pos`si*bil"i*ty n. [Obs.] [1913 Webster]