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Answer for the clue "The quality of not being doable ", 13 letters:
infeasibility

Word definitions for infeasibility in dictionaries

Douglas Harper's Etymology Dictionary Word definitions in Douglas Harper's Etymology Dictionary
1650s, from infeasible + -ity .

Wiktionary Word definitions in Wiktionary
n. The state of being infeasible or impractical

WordNet Word definitions in WordNet
n. the quality of not being doable [syn: unfeasibility ] [ant: feasibility ]

The Collaborative International Dictionary Word definitions in The Collaborative International Dictionary
Infeasibility \In*fea`si*bil"i*ty\, n. The state of being infeasible; impracticability.

Usage examples of infeasibility.

This suggests the infeasibility of the use of military units for any aspect of the contrived situation.