The High Priests didn't waste time once they had made up their mind, and they quickly escorted everyone out of the Cathedral and across the street, into what turned out to be one of the University's research labs.
Karl hadn't realized that the two were located adjacent to each other, as they both had vast green spaces around their main buildings, which made it look like the Cathedral was located in a city park.
There were armed security at the doors to the university lab, preventing anyone without a pass from entering, but the High Priests didn't seem bothered by the fact, and they simply waited for the supervisors to come down and let the group in after announcing their intentions to the guards.