"We desire also that this docuмent of Ours be read in the presence of all in the first Congregations
usually held after the death of the Pontiff, as above (no. 12 a); again after entry into the
Conclave, as above (no. 51); likewise when anyone is raised to the dignity of the purple, after
having pledged a solemn oath to scrupulously preserve the things that have been decreed in the
present Constitution.

Notwithstanding any whatsoever Apostolic Constitutions and Orders to the contrary issued by
Our Predecessor Roman Pontiffs, which, to the extent it is necessary, We declare each and every
one to be abrogated, as above, and even other matters worthy of individual and special mention
and derogation.

Therefore, let it be permitted to no man to weaken this page of Our constitution, ordinance,
abrogation, commandment, binding order, warning, prohibition, precept, and will, or to go
against it by a rash undertaking. Moreover, if any one presumes to attempt this, let him know that
he will incur for it the anger of Almighty God and of the blessed Apostles Peter and Paul.
Given in Rome, at St. Peter’s, A.D. 1945, on the eighth day of December, on the feast of the
Immaculate Conception of the Blessed Virgin Mary, in the seventh year of Our Pontificate." - Pope Pius XII, Vacantis Apostolicae Sedis

If he is the legitimate Pope, then he has the full power of his office ...

I disagree.  Distinctions between different aspects of the papal authority are not "bifurcations".  That's not what Vatican I was talking about.  It was talking about the error of distinguishing between the person of the pope and his papal authority.

This distinction of the material vs. formal aspects of the papal office can be found in St. Robert Bellarmine.

One good illustration is this.  Let's say a layman were elected pope, and he accepts.  He has the designation to office but he cannot exercise aspects of that office.  Not being a cleric, he cannot have jurisdiction over the the Church (e.g. tell bishops, priests, and other clerics what to do).  So the next day he's ordained to the priesthood.  That then allows him to exercise certain aspects of the papal authority, such as making appointments or other decisions.  But he's still not fully pope at that point, since one must be a BISHOP.  Nor can he exercise TEACHING authority, which is the most crucial aspect of the papacy, because only bishops are part of the Ecclesia Docens (the teaching Church).  Let's say this priest-pope refused to be consecrated a bishop.  That would, according to theologians, constitute a tacit resignation from office, because the essence of the papacy requires being a bishop, and this would signal intent not to accept the papal office.

Papacy is absolutely unique in the Church.  Bishops and priests all derive their authority from the pope.  But the pope receives his authority directly from God.  All the Church does is to DESIGNATE the person they have chosen to receive said authority, but their election does not formally imbue him with authority (whereas a papal appointment DOES imbue the bishops with their authority).  So the election is the material aspect of the papacy, whereas the granting of authority in response to this election or designation by the Church is the FORMAL aspect of his authority.  For bishops and lower, the two are inseparable.  Bishops receive authority directly through their designation and selection by the Pope.  But the papacy is the one office where the material aspect of election is clearly separate from the formal aspect of their receiving authority.

This question was raised in the Councils of Trent and Vatican I, but it was not decided. Several authors with Victoria and Vazquez have held that the jurisdiction is given immediately by God to the individual Bishops; but generally Catholic authors with St. Thomas , St. Bonaventure, St. Robert Bellarmine and Suarez hold that jurisdiction is given to the bishops not immediately by God but mediated through the Roman Pontiff. Pius XII teaches this opinion positively in the Encyclical, Mystici Corporis, when he says: "But the Bishops so far as their own diocese is concerned . . . are not completely independent but are subject to the proper authority of the Roman Pontiff, although they enjoy ordinary power of jurisdiction received directly from the Sovereign Pontiff himself." We think that his opinion is to be preferred.

Father Joachim Salverri's Sacrae Theologiae Summa,  Volume 1B, On the Church of Christ/On Holy Scripture. Section 374, Scholium 2, ("On the mediate or immediate origin from God of the jurisdiction of Bishops")

I'm going to keep saying it.  Those of you who articulate R&R the way it's being done here on its thread [asserting that it's possible for the Catholic Magisterium and Catholic public worship to go corrupt, to become non-Catholic, and to lead souls to hell], you promote heresy and blaspheme Holy Mother Church.  I'm not going to mince any words about your impious filth.  You are enemies of the faith, not its defenders, and you are little better than Protestants, Old Catholics, and Eastern Orthodox.

You can keep quibbling about the limits of infallibility-in-the-strict sense or about papa haereticus ipso facto depositus this or ab ecclesia deponendus that, but I care little about that debate.  Those are merely details that may offer explanations for HOW this happened.  I care only about your grave error (heresy) and blasphemy.

It doesn't meet the criteria for an ex cathedra teaching, no. But that doesn't necessarily mean its liable to any kind of error. Soteriological error is just about (if not actually) the worst kind of error imaginable, since it pertains directly to what is necessary for the salvation of souls, and the salvation of souls is THE telos of the Church. 

https://www.cathinfo.com/baptism-of-desire-and-feeneyism/singulari-quidem-66223/msg806416/#msg806416

I've pointed out your inconsistency on a number of issues, and you often avoid them ...

I read it, the whole refutation is based off the very first item, which is itself error.... "As we’ve already shown, it’s a dogma that 1) heretics are not members of the Church;"