'The old soldier is not fighting but sitting and resting' - this should also be considered as correct.
And, also, "The old soldier is not fighting but sitting down and having a rest."
sit ül, sit down leül?
Formally, "sitting down" isn't progressive while "ül" is. "sitting down" is more about the transitional moment when one puts themself into a sitting position.
What is the difference between "idős" and "öreg"?
"idős" is more like "elderly", considered more polite