As I mentioned on the other thread, and perhaps Praeter accidentally responded to the wrong thread there, but a thing cannot be ESSENTIALLY (or FORMALLY) two things at the same time. An animal cannot both be a horse and a pig at the same time. It is EITHER one OR the other. Let's say the horse is the Catholic Church, and the pig is the Conciliar Church. Catholics saw a horse in the same stall day after day. But one day they come in and there's a pig there in the same stall. Are they to conclude that this pig is really a horse? Or did the horse just one day start looking like a pig? No, the obvious conclusion is that someone swapped out the horse and replaced it with a pig.
Or, is the thing in the stall that looks like a pig merely a really sick horse?
Now, what's really at issue is whether this Conciliar Church is essentially different from the Catholic Church. Is what we see here still a horse but is so badly diseased and deformed that it kindof looks like a pig?