Kaptain Kidd, Agent Pavel's image just illustrates what one should be looking at. This progress bar is not of your discovery. Log files are a bunch of text lines, not images.
What he tried to explain here is that the time given as "(at )" is the (local) time when the discovery finishes, which is useful when boosting to finish before the end of some tournament. In his example, I'm guessing from his own test account or something similar, the discovery that he was upgrading would finish on Wed (likely yesterday, not 27th, as the screenshot was done by him on 2nd for the purpose of this topic) at 6:32:06 local time.
Unless you're deleting your reports, you should have one with Tinker, telling you when the discovery has finished upgrading (although, I don't remember when the tournament finished).