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

Word definitions for infeasibility in dictionaries

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

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

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.

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

Usage examples of infeasibility.

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