Impossible to overcome or overthrow by force.(adjective)
Impossible to put aside or drive away: inexpugnable dislike. (adjective)
American Heritage(R) Dictionary of the English Language, Fifth Edition. Copyright (c) 2011 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Use "inexpugnable" in a sentence
"'Inertia' does not mean want of vigour, but may be metaphorically described as the inexpugnable resolve of everything to have its own way."
"Instinct never yet surrendered to arguments; it is their race-instinct, deep and strong and "inexpugnable," as Carlyle would say."
"I mean the inexpugnable belief that every detailed occurence can be correlated with its antecedents in a perfectly definite manner, exemplifying general principles."