And this translation, since the promulgation of the Gospel, cannot be effected, without the laver of regeneration, or the desire thereof, as it is written; unless a man be born again of water and the Holy Ghost, he cannot enter into the Kingdom of God.

And this translation, since the promulgation of the Gospel, cannot be effected, without the sacrament of baptism actually conferred, or the desire thereof, as it is written; unless a man be born again of water and the Holy Ghost, he cannot enter into the Kingdom of God.

Canon 737

§ 1. Baptism, the gateway and foundation of the Sacraments, actually or at least in desire is necessary for all for salvation and is not validly conferred except by washing with true and natural water along with the prescribed formula of words.

Can. 849 Baptism, the gateway to the sacraments and necessary for salvation by actual reception or at least by desire, is validly conferred only by a washing of true water with the proper form of words. Through baptism men and women are freed from sin, are reborn as children of God, and, configured to Christ by an indelible character, are incorporated into the Church.

22. Actually only those are to be included as members of the Church who have been baptized and profess the true faith, and who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed

In Ecclesiae autem membris reapse ii soli annumerandi sunt, qui regenerationis lavacrum receperunt veramque fidem profitentur, neque a Corporis compage semet ipsos misere separarunt, vel ob gravissima admissa a legitima auctoritate seiuncti sunt.

If someone claims that Trent teaches ONE OR THE OTHER, then he is in error, given that Trent actually condemns those that say that water alone (without the will or desire) is sufficient to justify.

You in fact claim that water alone without the will or desire is sufficient to justify, which was condemned as heresy in the canons.

When speaking of adults (because the referenced canon is concerning the baptism of the impious), if either the water or desire separate from each other is enough to save, making desire alone enough to save, then necessarily water alone saves despite the will.

And this translation, since the promulgation of the Gospel, cannot be effected, without the laver of regeneration, or the desire thereof, as it is written; unless a man be born again of water and the Holy Ghost, he cannot enter into the Kingdom of God.

And this translation, since the promulgation of the Gospel, cannot be effected, without the baptismal water, or the desire thereof, as it is written; unless a man be born again of water and the Holy Ghost, he cannot enter into the Kingdom of God.

And this translation, since the promulgation of the Gospel, cannot be effected, without the sacrament of baptism, or the desire thereof, as it is written; unless a man be born again of water and the Holy Ghost, he cannot enter into the Kingdom of God.

"Laver of Regeneration" refers to the sacramental act provided by the Church, i.e. matter/form, i.e. water + prayers of the Church.  The "desire/disposition" of the person involved is separate which is why Trent spent so much time on explaining the manner of preparation for adults. 

Reply to Objection 2. If an adult lack the intention of receiving the sacrament, he must be rebaptized. But if there be doubt about this, the form to be used should be: "If thou art not baptized, I baptize thee."

The belief/disposition of the individual is beyond the Church's/God's control so it can't be implicit in the sacrament.

Trent was saying, no, a forced baptism doesn't work.  If a person receives a valid baptism formula, but has no desire, then the sacrament is invalid.

1. We should not posit any proposition from which an untenable conclusion follows. But, if we claim that explicit belief is necessary for salvation, an untenable conclusion follows. For it is possible for someone to be brought up in the forest or among wolves, and such a one cannot have explicit knowledge of any matter of faith. Thus, there will be a man who will inevitably be damned. But this is untenable. Hence, explicit belief in something does not seem necessary.

Answers to Difficulties

1. Granted that everyone is bound to believe something explicitly, no untenable conclusion follows even if someone is brought up in the forest or among wild beasts. For it pertains to divine providence to furnish everyone with what is necessary for salvation, provided that on his part there is no hindrance. Thus, if someone so brought up followed the direction of natural reason in seeking good and avoiding evil, we must most certainly hold that God would either reveal to him through internal inspiration what had to be believed, or would send some preacher of the faith to him as he sent Peter to Cornelius (Acts 10:20).

Whosoever will be saved, before all things it is necessary that he hold the Catholic Faith. Which Faith except everyone do keep whole and undefiled, without doubt he shall perish everlastingly.

10. In particular, ensure that the faithful are deeply and thoroughly convinced of the truth of the doctrine that the Catholic faith is necessary for attaining salvation.

13. Now We consider another abundant source of the evils with which the Church is afflicted at present: indifferentism. This perverse opinion is spread on all sides by the fraud of the wicked who claim that it is possible to obtain the eternal salvation of the soul by the profession of any kind of religion, as long as morality is maintained.

Surely, in so clear a matter, you will drive this deadly error far from the people committed to your care. With the admonition of the apostle that “there is one God, one faith, one baptism”[16] may those fear who contrive the notion that the safe harbor of salvation is open to persons of any religion whatever.

They should consider the testimony of Christ Himself that “those who are not with Christ are against Him,”[17] and that they disperse unhappily who do not gather with Him. Therefore “without a doubt, they will perish forever, unless they hold the Catholic faith whole and inviolate.”

2. Therefore, guided by the example of Our predecessors, We are grieved to hear reports from your dioceses which indicate that some of the people committed to your care freely encourage mixed marriages. Furthermore, they are promoting opinions contrary to the Catholic faith:

[. . .]

Finally some of these misguided people attempt to persuade themselves and others that men are not saved only in the Catholic religion, but that even heretics may attain eternal life.

7. Here, too, our beloved sons and venerable brothers, it is again necessary to mention and censure a very grave error entrapping some Catholics who believe that it is possible to arrive at eternal salvation although living in error and alienated from the true faith and Catholic unity. Such belief is certainly opposed to Catholic teaching. There are, of course, those who are struggling with invincible ignorance about our most holy religion. Sincerely observing the natural law and its precepts inscribed by God on all hearts and ready to obey God, they live honest lives and are able to attain eternal life by the efficacious virtue of divine light and grace. Because God knows, searches and clearly understands the minds, hearts, thoughts, and nature of all, his supreme kindness and clemency do not permit anyone at all who is not guilty of deliberate sin to suffer eternal punishments.


19.

(. . .)

Let us pray that the errant be flooded with the light of his divine grace, may turn back from the path of error into the way of truth and justice and, experiencing the worthy fruit of repentance, may possess perpetual love and fear of his holy name.

6.

[ . . . ]

Do men like these pour forth their prayers to God that in His mercy he may bring to the Divine light of the Gospel by His victorious grace the people sitting in the darkness?

It is assuredly not unknown to you, venerable brethren, that in our times many of the enemies of the Catholic faith especially direct their efforts toward placing every monstrous opinion on the same level with the doctrine of Christ, or of confounding it therewith, and so they try more and more to propagate that impious system of the indifference of religions.


But quite recently, we shudder to say it, men have appeared who have thrown such reproaches upon our name and apostolic dignity, that they do not hesitate to slander us, as if we shared in their folly and favored the aforesaid most wicked system. [. . .] as to suppose that not only the sons of the Church, but that the rest also, however alienated from Catholic unity they may remain, are alike in the way of salvation, and may arrive at everlasting life." We are at a loss from horror to find words to express our detestation of this new and atrocious injustice that is done us.

13.

[ . . . ]

We desire that Our children should also know, not only those who belong to the Catholic community, but also those who are separated from Us: if these latter humbly beg light from heaven, there is no doubt but that they will recognize the one true Church of Jesus Christ and will, at last, enter it, being united with us in perfect charity.

Trent could have simply said "justification cannot be effected without the laver of regeneration" and stopped right there because after saying that, no matter what else they could have said, no matter what other conditions one can imagine, the thing they communicated clearly is that there can be no justification without the sacrament. 

But because among the heresies of the day was the heresy of "salvation through faith alone," it is for this reason that they included "or the desire thereof" and "as it is written..." so as to explicitly condemn the idea that justification can be effected through faith alone, or by any other means except the sacrament exclusively. This remains true even if Trent would have said "or without the desire thereof" instead of "or the desire thereof."

If a BOD / BOB is anything, it's salvation through faith alone.

The 5 conditions needed for the laver of regeneration

1. The one administering the sacrament
2. The one receiving the sacrament
3. The words
4. The water
5. The intention of both the one administering and the one receiving


These conditions are implicit in the term laver of regeneration.

Take away even one condition and there is no laver of regeneration.

Not by the works of justice, which we have done, but according to his mercy, he saved us, by the laver of regeneration, AND renovation of the Holy Ghost;