The Collaborative International Dictionary of English v.0.48:

Incompossible \In`com*pos"si*ble\, 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]