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Douglas Harper's Etymology Dictionary
incongruency

c.1600, from incongruent + -cy.

Wiktionary
incongruency

n. incongruence

Usage examples of "incongruency".

This internal incongruency is sensed by others and contributes to an inauthentic communication that is superficial and boring—like small talk at parties.

The incongruency of my two versions of reality made me grapple for any kind of explanation.

I suddenly became angry and the incongruency of my feelings threw me into true panic.