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invalidity (n.)

"want of energy, force, or efficiency," 1540s, from French invalidité (16c.) or directly from Medieval Latin invaliditas "weakness, infirmity," from Latin invalidus "not strong, weak, feeble" (see invalid (adj.1)).

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Definitions of invalidity from WordNet

invalidity (n.)
illogicality as a consequence of having a conclusion that does not follow from the premisses;
Synonyms: invalidness
From wordnet.princeton.edu