Which word refers to a condition of being impossible to overcome?

The term "insurmountable" specifically refers to a condition that is impossible to overcome or conquer. It originates from the idea of something being unable to be surpassed or dealt with successfully. In various contexts, this word might be used to describe challenges, obstacles, or barriers that appear too great to be resolved or navigated.

The other options have distinct meanings that do not align with the idea of being impossible to overcome. “Indomitable” suggests a spirit that cannot be subdued or crushed but does not inherently mean that an issue is insurmountable. “Inveterate” is used to describe habits or practices long-established and unlikely to change, lacking any direct implication of difficulty in overcoming a condition. “Indefatigable” refers to someone who is persistent and tireless, particularly in their efforts, but again does not capture the essence of a condition that cannot be surpassed. Therefore, "insurmountable" is the most fitting choice for the condition described in the question.