Etymology
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inexpugnable (adj.)

late 15c., from Old French inexpugnable (14c.) or directly from Latin inexpugnabilis "not to be taken by assault, not to be rooted out, invincible," from in- "not" (see in- (1)) + expugnabilis "assailable," from expugnare (see expugn). Figurative sense, in reference to arguments, etc., is from 1530s.

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Definitions of inexpugnable

inexpugnable (adj.)
incapable of being overcome, challenged or refuted;
Synonyms: impregnable
From wordnet.princeton.edu