It DOES answer the question. Father O’Reilly preemptively addressed your question nearly 150 years ago, you just don’t like the answer. He wrote this AFTER the Vatican Council, obviously he didn’t believe what he wrote contradicted the Council. What’s worse is that you hold the grave error that Church Councils approved by the pope are not infallible.
It DOES NOT answer the question. I don't care either way, all I want is a clear answer to a clear question - it is you who does not like the question so you keep referring me to Fr. Oreilly's opinion. If you do not know the answer, simply say that.
I do not know what you think he is saying, but one thing he is not answering is my question, he does not answer how long of an interregnum before the perpetual succession is broken. Nor does he mention anything about how many false successors can be elected until we can presume to pronounce without anathema that the Roman pontiff is not the successor of blessed Peter.
I do not know what you think he says, but this is what he says.....
Here is Father O’Reilly again READ IT:
“The great schism of the West suggests to me a reflection which I take the liberty of expressing here. If this schism had not occurred, the hypothesis of such a thing happening would appear to many chimerical. They would say it could not be; God would not permit the Church to come into so unhappy a situation. Heresies might spring up and spread and last painfully long, through the fault and to the perdition of their authors and abettors, to the great distress too of the faithful, increased by actual persecution in many places where the heretics were dominant. But that the true Church should remain between thirty and forty years without a thoroughly ascertained Head, and representative of Christ on earth, this would not be.
He is saying
("suggests to me a reflection which I take the liberty of expressing here") is that the GWS, something nobody thought could happen, lasted between 30 and 40 years and was when pretty much nobody knew who the real pope was.
That's all he is saying.
Yet it has been; and we have no guarantee that it will not be again, though we may fervently hope otherwise. What I would infer is, that we must not be too ready to pronounce on what God may permit. We know with absolute certainty that He will fulfill His promises; not allow anything to occur at variance with them; that He will sustain His Church and enable her to triumph over all enemies and difficulties; that He will give to each of the faithful those graces which are needed for each one’s service of Him and attainment of salvation, as He did during the great schism we have been considering, and in all the sufferings and trials which the Church has passed through from the beginning."
Here he says it could happen again, and he concludes
("what I would infer") that we should not presume
"to pronounce on what God may permit", and that like during the GWS, God will supply all necessary graces to save our souls as He did during the GWS.
How does this answer the OP regarding the issue of the divine law of perpetual successors from V1? - It doesn't.