inexpugnable (adj.) Look up inexpugnable at Dictionary.com
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.