Some of the folks that run Mini-Splits here recommend that you run the unit during the day on low--Rather than running (for example) when home from work on high to cool the home down.
Next, based on your solar power system. Say fixed array near Jacksonville Florida:
The above is fairly conservative--If you run the A/C system during the day (don't discharge the battery bank), you can get (roughly) 1/0.80 more hours per day (1.25x) because you are not cycling the battery bank (typical around 80% worst case efficiency for flooded cell lead acid battery banks).
On the other hand, it is difficult to run 100% of harvested energy from an off grid system... So, you might (on average) run 75% of daily harvested energy (unless you really manage your power usage closely).
Anyway--Some estimates and ways to look at the question--Your actual mileage may vary.
Perfect Bill. Thanks so much for your time. Is your 6,539 Wh per day from the array and average for the summer season or for the year?