Vatican I directly blows away Benedict XVI

The quote you bring forward from Vatican I directly blows away Benedict XVI, who has rejected the dogma you quote by questioning whether the Bishop of Rome even possesses supreme jurisdiction in the Church! 

“Cardinal” Ratzinger, Principles of Catholic Theology (1982), pp. 216-217: “Patriarch Athenagoras [the non-Catholic, schismatic Patriarch] spoke even more strongly when he greeted the Pope [Paul VI] in Phanar: ‘Against all expectation, the bishop of Rome is among us, the first among us in honor, ‘he who presides in love’.  It is clear that, in saying this, the Patriarch [the non-Catholic, schismatic Patriarch] did not abandon the claims of the Eastern Churches or acknowledge the primacy of the west.  Rather, he stated plainly what the East understood as the order, the rank and title, of the equal bishops in the Church – and it would be worth our while to consider whether this archaic confession, which has nothing to do with the ‘primacy of jurisdiction’ but confesses a primacy of ‘honor’ and agape, might not be recognized as a formula that adequately reflects the position that Rome occupies in the Church – ‘holy courage’ requires that prudence be combined with ‘audacity’: ‘The kingdom of God suffers violence.’”

We would say that indirectly the quote from Vatican I also refutes the SSPX’s position.  We say only indirectly because they would claim that they are not denying the supreme jurisdiction of the Popes.  Nevertheless, they profess communion with a man who does.  What directly blows away the SSPX’s schismatic position is the definition of schism and the dogmatic definition on Papal Infallibility:

Canon 1325.2, 1917 Code of Canon Law: “One who after baptism… rejects the authority of the Supreme Pontiff or refuses communion with the members of the Church who are subject to him, he is a schismatic.”

They obstinately refuse working communion with the people and Bishops they consider to be the Catholic Church.  This is schismatic.  They also deny Papal Infallibility by asserting that Canonizations and a solemnly approved universal Council of their “Church” contains errors on faith and morals.  They also recognize apostates and heretics as Catholics, which is heretical.  And they believe that souls can be saved in other religions, but that’s a separate issue. Related: Who is the SSPX? Why is the SSPX heretical?