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Answer for the clue "Irrelevance by virtue of being inapplicable to the matter at hand ", 15 letters:
inapplicability

Word definitions for inapplicability in dictionaries

The Collaborative International Dictionary Word definitions in The Collaborative International Dictionary
Inapplicability \In*ap`pli*ca*bil"i*ty\, n. [Cf. F. inapplicabilit['e].] The quality of being inapplicable; unfitness; inapplicableness.

WordNet Word definitions in WordNet
n. irrelevance by virtue of being inapplicable to the matter at hand [ant: applicability ]

Wiktionary Word definitions in Wiktionary
n. 1 (context uncountable English) The state of being inapplicable 2 (context countable English) Something inapplicable

Usage examples of inapplicability.

Her attorney's plea at the preliminary hearing that afternoon was double jeopardy and the inapplicability of retroactive legislation.

All emphasize the inapplicability of empirical determinations to the Absolute, and employ the language of negation.