Which word best represents something that cannot be attacked or disputed?

The word "indomitable" is the best choice because it conveys the idea of being impossible to overcome or defeat, often used to describe a person's spirit or resolve that remains strong despite challenges. In the context of something that cannot be attacked or disputed, "indomitable" signifies a quality of resilience and strength that makes it impervious to external challenges or criticisms.

When considering the other options, "inveterate" refers to something habitual or long-established, often with a negative connotation, but does not specifically denote the inability to be disputed. "Insurmountable" describes obstacles that cannot be overcome, but it typically refers to challenges rather than the qualities of an argument or position. "Impugnable," on the other hand, means something that can be disputed or attacked, which directly contradicts the essence of what is meant by something that cannot be attacked or disputed. Thus, "indomitable" provides the most suitable representation for that concept.