It’s an unsolvable problem.  You can’t “look into” someone’s brain years after the “ordination” took place to confirm if the minister 1) had the proper seminary training to understand the proper intention,....

Be careful.  This type of reasoning, that is whether a proper intention was understood at the time of taking one's vows, is what underlies the vast majority of annulments of marriage being granted today.  This is highly problematic, especially in instances when its 20 years and several children after the fact, whereupon it is decided that the couple did not understand what they were getting into, and as such, were never married to begin with.   

Conditional ordinations exist to remedy these kinds of problems and doubts.

Oh really? You don't trust superiors to do the right thing, and you don't trust them to understand sacramental theology as deeply as you do with your multiple doctorates in theology and canon law.

Yet if they would claim to have done a conditional ordination behind closed doors, you would believe them?

So the district priests and leadership look into the case of the "N.O." priest, do whatever they do, and eventually assign the priest to a priory where he offers mass publicly, and assigns him a chapel where he also offers mass.

On what basis would a layperson, not privy to any of the details of the case, doubt this priest isn't a priest?

some of us asked said priest if he was conditionally ordained post new rite.  Admitted he wasn't.  Doubt.  Again, what objectively couild be "investigated" other than what rite was used by any SSPX body?  they have about as much authority as the Ted Nugent fan club

If you think that the Novus Ordo Rite of Ordination of a priest is "less doubtful" than the Novus Ordo Episcopal Consecration Rite, you might want to consider the following:

Michael Davies: “… every prayer in the traditional rite [of Ordination] which stated specifically the essential role of a priest as a man ordained to offer propitiatory sacrifice for the living and dead has been removed [from the New Rite of Paul VI]. In most cases these were the precise prayers removed by the Protestant reformers, or if not precisely the same there are clear parallels.”[1]

In addition to having invalidating changes made to the Mass, the Devil knew that he had to tamper with the rite of ordination so that the priests of the New Church would be invalid as well.
The New Rite of Holy Orders (bishops, priests, deacons) was approved and imposed by Paul VI on June 18, 1968. The following information is crucial for all Catholics to know, since it concerns the validity of essentially every “priest” ordained within the diocesan structure since approximately 1968; and consequently, it concerns the validity of countless confessions, indult Masses, etc.
On Nov. 30, 1947, Pope Pius XII issued an apostolic Constitution called “Sacramentum Ordinis.” In this Constitution, Pope Pius XII declared, in virtue of his supreme apostolic authority, the words that are necessary for a valid ordination to the priesthood.

Pope Pius XII, Sacramentum Ordinis, Nov. 30, 1947: “But regarding the matter and form in the conferring of every order, by Our same supreme apostolic authority We decree and establish the following: … In the ordination of priests, the matter is the first imposition of the bishop’s hands which is done in silence… But the form [of Ordination] consists of the words of the preface of which the following are essential and so required for validity:
► “Grant, we beseech You, Almighty Father, to these Your servants, the dignity of the Priesthood (presbyterii dignitatem); renew the spirit of holiness within them, so that they may hold from You, O God, the office of the second rank in Your service and by the example of their behavior afford a pattern of holy living.”[2]

Here is the form of the New Rite of Ordination of Priests:

● “Grant, we beseech You, Almighty Father, to these Your servants, the dignity of the Priesthood; renew within them the spirit of holiness. May they hold from You, the office of the second rank in Your service and by the example of their behavior afford a pattern of holy living.”[3]

The difference between the two forms is that the Latin word “ut” (which means “so that”) has been omitted in the New Rite. This may seem insignificant, but in Sacramentum Ordinis Pius XII declared that this word was essential for validity. Further, the omission of “so that” gives rise to a relaxation of the naming of the sacramental effect (conferring the office of the second rank). In other words, removing “so that” presupposes an ordination which has already taken place, but is not taking place as the words are being pronounced.
Since the new rite purports to be the Roman Rite, this removal of “ut” (so that) renders the new rite of questionable validity. However, there is a much bigger problem which proves that the New Rite is invalid.
The change to the essential form is not the only problem with the New Rite of Ordination promulgated by Paul VI. The following points are just as significant because the Sacrament of Order, although instituted by Our Lord Jesus Christ, was not instituted by Our Lord with a specific sacramental form – unlike the Sacraments of the Eucharist and Baptism, which were instituted by Our Lord with a specific sacramental form – so that the form of words in Ordination is given its meaning and significance by the surrounding rite and ceremonies.
In his famous Bull, Apostolicae Curae, Sept. 13, 1896, Pope Leo XIII solemnly declared that Anglican Ordinations are invalid. This means that the Anglican sect doesn’t have valid priests or bishops.

Pope Leo XIII, Apostolicae Curae, Sept. 13, 1896: “… of Our own motion and certain knowledge We pronounce and declare that Ordinations carried out according to the Anglican rite have been and are absolutely null and utterly void.”[4]

In making this solemn pronouncement, it must be understood that Pope Leo XIII was not making Anglican Ordinations invalid, but rather he was declaring that they were invalid due to defects in the rite. But what were those defects or problems which Leo XIII saw with the Anglican Rite, which contributed to its invalidity?

Pope Leo XIII, Apostolicae Curae, Sept. 13, 1896: “When anyone has rightly and seriously made use of the due form and the matter requisite for effecting or conferring the sacrament he is considered by that very fact to do what the Church does. On this principle rests the doctrine that a sacrament is truly conferred by the ministry of one who is a heretic or unbaptized, provided the Catholic rite be employed. On the other hand, if the rite be changed, with the manifest intention of introducing another rite not approved by the Church, and of rejecting what the Church does, and what by the institution of Christ belongs to the nature of the sacrament, then it is clear that not only is the necessary intention wanting to the sacrament, but that the intention is adverse to and destructive of the sacrament.”[5]

Here we see Pope Leo XIII teaching that if a minister uses the Catholic rite in conferring the Sacrament of Order, with the correct matter and form, he is considered for that very reason to have intended to do what the Church does – intending to do what the Church does is necessary for the validity of any sacrament. On the other hand, he tells us, if the rite is changed with the manifest intention of introducing a new rite not approved by the Church, and of rejecting what the Church does, then the intention is not only insufficient, but is destructive of the Sacrament.
And what were the things that Pope Leo XIII described as showing the destructive intention of the Anglican rite of Ordination?

Pope Leo XIII, Apostolicae Curae, Sept. 13, 1896: “For, to put aside other reasons which show this to be insufficient for the purpose in the Anglican rite, let this argument suffice for all: from them has been deliberately removed whatever sets forth the dignity and office of the priesthood in the Catholic rite. That form consequently cannot be considered apt or sufficient for the sacrament which omits what it ought essentially to signify.”[6]
Pope Leo XIII, Apostolicae Curae, Sept. 13, 1896: “So it comes to pass that, as the Sacrament of Orders and the true sacerdotium [sacrificing priesthood] of Christ were utterly eliminated from the Anglican rite, and hence the sacerdotium [priesthood] is in no wise conferred truly and validly in the Episcopal consecration of the same rite, for the like reason, therefore, the Episcopate can in no wise be truly and validly conferred by it; and this the more so because among the first duties of the Episcopate is that of ordaining ministers for the Holy Eucharist and sacrifice.”[7]
Pope Leo XIII, Apostolicae Curae, Sept. 13, 1896: “Being fully cognizant of the necessary connection between faith and worship, between ‘the law of believing and the law of praying,’ under a pretext of returning to the primitive form, they corrupted the liturgical order in many ways to suit the errors of the reformers. For this reason in the whole Ordinal not only is there no clear mention of the sacrifice, of consecration, of the sacerdotium [sacrificing priesthood], but, as we have just stated, every trace of these things, which had been in such prayers of the Catholic rite as they had not entirely rejected, was deliberately removed and struck out. In this way the native character – or spirit as it is called – of the Ordinal clearly manifests itself. Hence, if vitiated in its origin it was wholly insufficient to confer Orders, it was impossible that in the course of time it could become sufficient since no change had taken place.”[8]

Dear reader, these things described above by Pope Leo XIII as the downfall of the Anglican Rite of Ordination – the systematic removal of every reference to the sacrifice of the Mass, consecration and the true sacrificing priesthood – are exactly the things that occurred in the New Rite of Ordination promulgated by Paul VI! In his book The Order of Melchisedech, despite his false conclusions on this and other matters, Michael Davies is forced to admit the following stunning facts:

Michael Davies: “As the previous section made clear, every prayer in the traditional rite [of Ordination] which stated specifically the essential role of a priest as a man ordained to offer propitiatory sacrifice for the living and dead has been removed [from the New Rite of Paul VI]. In most cases these were the precise prayers removed by the Protestant reformers, or if not precisely the same there are clear parallels.”[9]
Michael Davies: “… there is not one mandatory prayer in the new rite of ordination itself which makes clear that the essence of the Catholic priesthood is the conferral of the powers to offer the sacrifice of the Mass and to absolve men of their sins, and that the sacrament imparts a character which differentiates a priest not simply in degree but in essence from a layman… There is not a word in it that is incompatible with Protestant belief.”[10]

Here are some of the specific prayers and ceremonies which set forth the true nature of the priesthood in the Traditional Rite which have been specifically eliminated from the New Rite of Ordination of Paul VI. The following information is found in Michael Davies, The Order of Melchisedech, pp. 79 and following.
In the Traditional Rite, the bishop addresses the ordinands and says:

► “For it is a priest’s duty to offer sacrifice, to bless, to lead, to preach and to baptize.”

This admonition has been abolished.
The Litany of the Saints then follows in the Traditional Rite. It has been cut short in the New Rite. The New Rite abolishes the following unecuмenical assertion:

► “That Thou wouldst recall all who have wandered from the unity of the Church, and lead all believers to the light of the Gospel.”

Later on in the Traditional Rite, after pronouncing the essential form, which has been changed in the New Rite (see above), the bishop says another prayer, which includes the following:

► “Theirs be the task to change with blessing undefiled, for the service of thy people, bread and wine into the Body and Blood of Thy Son.”

This prayer has been abolished.
In the Traditional Rite, the bishop then intones the Veni Creator Spiritus. While anointing each priest he says:

► “Be pleased, Lord, to consecrate and sanctify these hands by this anointing, and our blessing. That whatsoever they bless may be blessed, and whatsoever they consecrate may be consecrated and sanctified in the name of Our Lord Jesus Christ.”

This prayer has been abolished. And this prayer was so significant that it was even mentioned by Pius XII in Mediator Dei #43:

Pope Pius XII, Mediator Dei (# 43), Nov. 20, 1947: “… they alone [priests] have been marked with the indelible sign ‘conforming’ them to Christ the Priest, and that their hands alone have been consecrated, ‘in order that whatever they bless may be blessed, whatever they consecrate may become sacred and holy, in the name of Our Lord Jesus Christ.’”[11]

Notice that Pius XII, in speaking of how the priests have been marked in ordination, makes reference to this very important prayer which was specifically abolished by Paul VI’s new 1968 Rite.
Shortly after this prayer in the Traditional Rite, the bishop says to each ordinand:

► “Receive the power to offer sacrifice to God, and to celebrate Mass, both for the living and the dead, in the name of the Lord.”

This exceptionally important prayer has been abolished in the New Rite.
In the Traditional Rite, the new priests then concelebrate Mass with the bishop. At the end, each new priest kneels before the bishop who lays both hands upon the head of each and says:

► “Receive the Holy Ghost. Whose sins you shall forgive, they are forgiven them; and whose sins you shall retain, they are retained.”

This ceremony and prayer has been abolished.
In the Traditional Rite:

► “…the new priests then promise obedience to their bishop who ‘charges’ them to bear in mind that offering Holy Mass is not free from risk and that they should learn everything necessary from diligent priests before undertaking so fearful a responsibility.”

This admonition has been abolished.
Finally, before completing the Mass, the bishop imparts a blessing:

► “The blessing of God Almighty, the Father, the Son, and the Holy Ghost, come down upon you, and make you blessed in the priestly Order, enabling you to offer propitiatory sacrifices for the sins of the people to Almighty God.”

This blessing has been abolished.

Conclusion: It is totally obvious from these facts that there is no intention in the New Rite of ordaining a true sacrificing priest. Every single mandatory reference to the true sacrificing priesthood was deliberately removed, just like in the Anglican Rite – which was declared invalid for that very reason by Pope Leo XIII.

Thus, the following words declared by Pope Leo XIII apply exactly to the New Rite of Paul VI.

Pope Leo XIII, Apostolicae Curae, Sept. 13, 1896: “For this reason in the whole Ordinal not only is there no clear mention of the sacrifice, of consecration, of the sacerdotium [sacrificing priesthood], but, as we have just stated, every trace of these things, which had been in such prayers of the Catholic rite as they had not entirely rejected, was deliberately removed and struck out. In this way the native character – or spirit as it is called – of the Ordinal clearly manifests itself.”[12]

The New Rite fits this description precisely. Could anyone deny this fact? No, to do so one would have to bear false witness. The New Rite of Ordination specifically eliminated the sacrificing priesthood. The intention it manifests is therefore contrary to the intention of the Church and cannot suffice for validity.

Pope Leo XIII, Apostolicae Curae, Sept. 13, 1896: “For, to put aside other reasons which show this to be insufficient for the purpose in the Anglican rite, let this argument suffice for all: from them has been deliberately removed whatever sets forth the dignity and office of the priesthood in the Catholic rite. That form consequently cannot be considered apt or sufficient for the sacrament which omits what it ought essentially to signify.”[13]

Michael Davies proves the New Rite is invalid
In his book, The Order of Melchisedech, Michael Davies (a man who actually defended the validity of the New Rite of Ordination) is forced to make, in the face of the undeniable evidence, statement after statement which proves that the New Rite of Ordination must be considered invalid, just as the Anglican Rite. Here are a few:

Michael Davies, The Order of Melchisedech, p. 97: “If the new Catholic rite is considered satisfactory, then the entire case put by Apostolicae Curae [of Leo XIII] is undermined… If the new Catholic rite, shorn of any mandatory prayer signifying the essential powers of the priesthood, is valid, then there seems no reason why the 1662 Anglican rite should not be valid too, and still less can there be any possible objection to the 1977 Anglican Series III Ordinal.”
Michael Davies, The Order of Melchisedech, p. 99: “As a final comment on the new Catholic ordinal, I would like to quote a passage from Apostolicae Curae and to ask any reader to demonstrate to me how the words which Pope Leo XIII wrote of Cranmer’s rite cannot be said to apply to the new Catholic Ordinal, at least where mandatory prayers are concerned.”
Michael Davies, The Order of Melchisedech, p. 109: “… the differences between the 1968 Catholic rite and the new Anglican Ordinal are so minimal that it is hard to believe that they are not intended for the same purpose… It will be found that every imperative formula which could be interpreted as conferring any specifically sacerdotal power denied to the faithful at large has been carefully excluded from the new rite.”
Michael Davies, The Order of Melchisedech, pp. 94-95: “When the changes [to the Rite of Ordination] are considered as a whole it seems impossible to believe that any Catholic of integrity could deny that the parallel with Cranmer’s reform [the Anglican reform] is evident and alarming. It is quite obvious that there are powerful forces within the Catholic Church and the various Protestant denominations determined to achieve a common Ordinal at all costs… The sixteenth century Protestants changed the traditional Pontificals because they rejected the Catholic doctrine of the priesthood. Archbishop Bugnini and his Consilium changed the Roman Pontifical in a manner which makes it appear that there is little or no difference between Catholic and Protestant belief, thus undermining Apostolicae Curae [of Leo XIII].”[14]

St. Thomas Aquinas, Summa Theologica, Pt. III, Q. 60, A. 8: “… intention is essential to the sacrament, as will be explained further on. Wherefore if he intends by such addition or suppression to perform a rite other than that which is recognized by the Church, it seems that the sacrament is invalid; because he seems not to intend to do what the Church does.”
It’s also worth noting that Cranmer, in creating the invalid Anglican Rite, abolished the subdiaconate and minor orders and replaced them with a ministry in three degrees – bishops, priests, and deacons. This is exactly what Paul VI did in changing the Catholic rites.
The New Rite does mention that the candidates for ordination are to be elevated to the “priesthood” – but so does the invalid Anglican. The fact is that Pope Leo XIII explained in Apostolicae Curae that if an ordination rite implies the exclusion of the power to offer propitiatory sacrifices, as the New Rite does, then it is necessarily invalid, although it may express or mention the word “priest.”
The Congregation for Divine Worship and the Discipline of the Sacraments admitted that the Catholic theology of the priesthood was not made explicit in the 1968 rite.[15]
The fact is that the New Rite of Paul VI is an entirely new rite, which rejects what the Church does, by rejecting what by the institution of Christ belongs to the nature of the sacrament [the sacrificing priesthood], so it is clear that the necessary intention manifested by this rite is insufficient, and even adverse to and destructive of the Sacrament of Holy Orders (Leo XIII). These facts prove that the New Rite of Ordination of Paul VI cannot be considered valid, but must be considered invalid.
Conclusion: This means that any Confessions made of grave sins to “priests” ordained in the New Rite must be made again to a validly ordained priest who was ordained in the Traditional Rite of Ordination by a bishop consecrated in the Traditional Rite of Episcopal Consecration. If one cannot remember which sins were confessed to New Rite “priests,” and which were forgiven by a priest ordained in the Traditional Rite, then a Catholic must make a general confession mentioning all grave sins (if there were any) that may have been confessed to a “priest” ordained in the rite of Paul VI (the New Rite).
Obviously, no Catholic may lawfully approach “priests” ordained in the New Rite of Paul VI for either “Communion” or confession or any other sacrament requiring a valid priesthood under pain of grave sin, since they are not valid priests.
As mentioned already, Pope Innocent XI, Decree of the Holy Office, March 4, 1679,[16] condemns the idea that Catholics can receive “probable” sacraments. In other words, even if one believed that the New Rite of Ordination is probably valid (which is clearly false, since it is clearly invalid), one is still forbidden to receive sacraments from those “ordained” in it under pain of mortal sin. Sacraments may only be received when matter and form are certainly valid.
These facts mean that all indult Masses celebrated by “priests” ordained in the New Rite of Paul VI (1968 Rite) are invalid and cannot be attended.
The Society of St. Pius X occasionally has men join their society who were “ordained” in the New Rite of Ordination, and they don’t always have them conditionally ordained – or at least they don’t publicly admit it. The “Masses” offered by such “priests” would be invalid.
Those priests who were “ordained” in this New Rite of Paul VI who are open to the truth must be re-ordained by a validly consecrated bishop in the Traditional Rite. This also necessarily means that the Novus Ordo Missae (the New Mass), without even considering its own problems which render it invalid, is of course invalid if celebrated by any “priest” ordained in the New Rite of Ordination.
Endnotes:
[1] Michael Davies, The Order of Melchisedech, hαɾɾιson, NY: Roman Catholic Books, 1993, p. 83.
[2] Denzinger, The Sources of Catholic Dogma, B. Herder Book. Co., Thirtieth Edition, 1957, no. 2301.
[3] The Oratory Catechism, Published by the Oratory of Divine Truth, 2000, p. 340; also The Rites of the Catholic
 Church, The Liturgical Press, Vol. 2, 1991, pp. 44-45.
[4] The Great Encyclical Letters of Pope Leo XIII, Rockford, IL: Tan Books, 1995, p. 405; Denzinger 1966.
[5] The Great Encyclical Letters of Pope Leo XIII, p. 404.
[6] The Great Encyclical Letters of Pope Leo XIII, p. 401.
[7] The Great Encyclical Letters of Pope Leo XIII, p. 402.
[8] The Great Encyclical Letters of Pope Leo XIII, pp. 402-403.
[9] Michael Davies, The Order of Melchisedech, hαɾɾιson, NY: Roman Catholic Books, 1993, p. 83.
[10] Michael Davies, The Order of Melchisedech, p. xix.
[11] The Papal Encyclicals, by Claudia Carlen, Raleigh: The Pierian Press, 1990, Vol. 4 (1939-1958), p. 127.
[12] The Great Encyclical Letters of Pope Leo XIII, pp. 402-403.
[13] The Great Encyclical Letters of Pope Leo XIII, p. 401.
[14] Michael Davies, The Order of Melchisedech, pp. 94-95.
[15] Michael Davies, The Order of Melchisedech, p. xxii.
[16] Denzinger 1151.

So, what about Fr. Chad Ripperger FSSP ? He is supposed to be an exorcists and to have performed a number of successful exorcisms, if he was not validity ordained how would he be able to perform exorcisms? I am just curious as I do not go to FSSP masses.

If you think that the Novus Ordo Rite of Ordination of a priest is "less doubtful" than the Novus Ordo Episcopal Consecration Rite, you might want to consider the following:
In addition to having invalidating changes made to the Mass, the Devil knew that he had to tamper with the rite of ordination so that the priests of the New Church would be invalid as well.
The New Rite of Holy Orders (bishops, priests, deacons) was approved and imposed by Paul VI on June 18, 1968. The following information is crucial for all Catholics to know, since it concerns the validity of essentially every “priest” ordained within the diocesan structure since approximately 1968; and consequently, it concerns the validity of countless confessions, indult Masses, etc.
On Nov. 30, 1947, Pope Pius XII issued an apostolic Constitution called “Sacramentum Ordinis.” In this Constitution, Pope Pius XII declared, in virtue of his supreme apostolic authority, the words that are necessary for a valid ordination to the priesthood.

TRADITIONAL FORM FOR ORDINATION OF PRIESTS

THE NEW FORM FOR ORDINATION OF PRIESTS

Here is the form of the New Rite of Ordination of Priests:The difference between the two forms is that the Latin word “ut” (which means “so that”) has been omitted in the New Rite. This may seem insignificant, but in Sacramentum Ordinis Pius XII declared that this word was essential for validity. Further, the omission of “so that” gives rise to a relaxation of the naming of the sacramental effect (conferring the office of the second rank). In other words, removing “so that” presupposes an ordination which has already taken place, but is not taking place as the words are being pronounced.
Since the new rite purports to be the Roman Rite, this removal of “ut” (so that) renders the new rite of questionable validity. However, there is a much bigger problem which proves that the New Rite is invalid.

THE BIGGEST PROBLEM WITH THE NEW RITE OF ORDINATION IS NOT THE FORM, BUT THE SURROUNDING CEREMONIES WHICH HAVE BEEN REMOVED

The change to the essential form is not the only problem with the New Rite of Ordination promulgated by Paul VI. The following points are just as significant because the Sacrament of Order, although instituted by Our Lord Jesus Christ, was not instituted by Our Lord with a specific sacramental form – unlike the Sacraments of the Eucharist and Baptism, which were instituted by Our Lord with a specific sacramental form – so that the form of words in Ordination is given its meaning and significance by the surrounding rite and ceremonies.
In his famous Bull, Apostolicae Curae, Sept. 13, 1896, Pope Leo XIII solemnly declared that Anglican Ordinations are invalid. This means that the Anglican sect doesn’t have valid priests or bishops.In making this solemn pronouncement, it must be understood that Pope Leo XIII was not making Anglican Ordinations invalid, but rather he was declaring that they were invalid due to defects in the rite. But what were those defects or problems which Leo XIII saw with the Anglican Rite, which contributed to its invalidity?Here we see Pope Leo XIII teaching that if a minister uses the Catholic rite in conferring the Sacrament of Order, with the correct matter and form, he is considered for that very reason to have intended to do what the Church does – intending to do what the Church does is necessary for the validity of any sacrament. On the other hand, he tells us, if the rite is changed with the manifest intention of introducing a new rite not approved by the Church, and of rejecting what the Church does, then the intention is not only insufficient, but is destructive of the Sacrament.
And what were the things that Pope Leo XIII described as showing the destructive intention of the Anglican rite of Ordination?Dear reader, these things described above by Pope Leo XIII as the downfall of the Anglican Rite of Ordination – the systematic removal of every reference to the sacrifice of the Mass, consecration and the true sacrificing priesthood – are exactly the things that occurred in the New Rite of Ordination promulgated by Paul VI! In his book The Order of Melchisedech, despite his false conclusions on this and other matters, Michael Davies is forced to admit the following stunning facts:Here are some of the specific prayers and ceremonies which set forth the true nature of the priesthood in the Traditional Rite which have been specifically eliminated from the New Rite of Ordination of Paul VI. The following information is found in Michael Davies, The Order of Melchisedech, pp. 79 and following.
In the Traditional Rite, the bishop addresses the ordinands and says:This admonition has been abolished.
The Litany of the Saints then follows in the Traditional Rite. It has been cut short in the New Rite. The New Rite abolishes the following unecuмenical assertion:Later on in the Traditional Rite, after pronouncing the essential form, which has been changed in the New Rite (see above), the bishop says another prayer, which includes the following:This prayer has been abolished.
In the Traditional Rite, the bishop then intones the Veni Creator Spiritus. While anointing each priest he says:This prayer has been abolished. And this prayer was so significant that it was even mentioned by Pius XII in Mediator Dei #43:Notice that Pius XII, in speaking of how the priests have been marked in ordination, makes reference to this very important prayer which was specifically abolished by Paul VI’s new 1968 Rite.
Shortly after this prayer in the Traditional Rite, the bishop says to each ordinand:This exceptionally important prayer has been abolished in the New Rite.
In the Traditional Rite, the new priests then concelebrate Mass with the bishop. At the end, each new priest kneels before the bishop who lays both hands upon the head of each and says:This ceremony and prayer has been abolished.
In the Traditional Rite:This admonition has been abolished.
Finally, before completing the Mass, the bishop imparts a blessing:This blessing has been abolished.Thus, the following words declared by Pope Leo XIII apply exactly to the New Rite of Paul VI.The New Rite fits this description precisely. Could anyone deny this fact? No, to do so one would have to bear false witness. The New Rite of Ordination specifically eliminated the sacrificing priesthood. The intention it manifests is therefore contrary to the intention of the Church and cannot suffice for validity.Michael Davies proves the New Rite is invalid
In his book, The Order of Melchisedech, Michael Davies (a man who actually defended the validity of the New Rite of Ordination) is forced to make, in the face of the undeniable evidence, statement after statement which proves that the New Rite of Ordination must be considered invalid, just as the Anglican Rite. Here are a few:St. Thomas Aquinas, Summa Theologica, Pt. III, Q. 60, A. 8: “… intention is essential to the sacrament, as will be explained further on. Wherefore if he intends by such addition or suppression to perform a rite other than that which is recognized by the Church, it seems that the sacrament is invalid; because he seems not to intend to do what the Church does.”
It’s also worth noting that Cranmer, in creating the invalid Anglican Rite, abolished the subdiaconate and minor orders and replaced them with a ministry in three degrees – bishops, priests, and deacons. This is exactly what Paul VI did in changing the Catholic rites.
The New Rite does mention that the candidates for ordination are to be elevated to the “priesthood” – but so does the invalid Anglican. The fact is that Pope Leo XIII explained in Apostolicae Curae that if an ordination rite implies the exclusion of the power to offer propitiatory sacrifices, as the New Rite does, then it is necessarily invalid, although it may express or mention the word “priest.”
The Congregation for Divine Worship and the Discipline of the Sacraments admitted that the Catholic theology of the priesthood was not made explicit in the 1968 rite.[15]
The fact is that the New Rite of Paul VI is an entirely new rite, which rejects what the Church does, by rejecting what by the institution of Christ belongs to the nature of the sacrament [the sacrificing priesthood], so it is clear that the necessary intention manifested by this rite is insufficient, and even adverse to and destructive of the Sacrament of Holy Orders (Leo XIII). These facts prove that the New Rite of Ordination of Paul VI cannot be considered valid, but must be considered invalid.
Conclusion: This means that any Confessions made of grave sins to “priests” ordained in the New Rite must be made again to a validly ordained priest who was ordained in the Traditional Rite of Ordination by a bishop consecrated in the Traditional Rite of Episcopal Consecration. If one cannot remember which sins were confessed to New Rite “priests,” and which were forgiven by a priest ordained in the Traditional Rite, then a Catholic must make a general confession mentioning all grave sins (if there were any) that may have been confessed to a “priest” ordained in the rite of Paul VI (the New Rite).
Obviously, no Catholic may lawfully approach “priests” ordained in the New Rite of Paul VI for either “Communion” or confession or any other sacrament requiring a valid priesthood under pain of grave sin, since they are not valid priests.
As mentioned already, Pope Innocent XI, Decree of the Holy Office, March 4, 1679,[16] condemns the idea that Catholics can receive “probable” sacraments. In other words, even if one believed that the New Rite of Ordination is probably valid (which is clearly false, since it is clearly invalid), one is still forbidden to receive sacraments from those “ordained” in it under pain of mortal sin. Sacraments may only be received when matter and form are certainly valid.
These facts mean that all indult Masses celebrated by “priests” ordained in the New Rite of Paul VI (1968 Rite) are invalid and cannot be attended.
The Society of St. Pius X occasionally has men join their society who were “ordained” in the New Rite of Ordination, and they don’t always have them conditionally ordained – or at least they don’t publicly admit it. The “Masses” offered by such “priests” would be invalid.
Those priests who were “ordained” in this New Rite of Paul VI who are open to the truth must be re-ordained by a validly consecrated bishop in the Traditional Rite. This also necessarily means that the Novus Ordo Missae (the New Mass), without even considering its own problems which render it invalid, is of course invalid if celebrated by any “priest” ordained in the New Rite of Ordination.
Endnotes:
[1] Michael Davies, The Order of Melchisedech, hαɾɾιson, NY: Roman Catholic Books, 1993, p. 83.
[2] Denzinger, The Sources of Catholic Dogma, B. Herder Book. Co., Thirtieth Edition, 1957, no. 2301.
[3] The Oratory Catechism, Published by the Oratory of Divine Truth, 2000, p. 340; also The Rites of the Catholic
 Church, The Liturgical Press, Vol. 2, 1991, pp. 44-45.
[4] The Great Encyclical Letters of Pope Leo XIII, Rockford, IL: Tan Books, 1995, p. 405; Denzinger 1966.
[5] The Great Encyclical Letters of Pope Leo XIII, p. 404.
[6] The Great Encyclical Letters of Pope Leo XIII, p. 401.
[7] The Great Encyclical Letters of Pope Leo XIII, p. 402.
[8] The Great Encyclical Letters of Pope Leo XIII, pp. 402-403.
[9] Michael Davies, The Order of Melchisedech, hαɾɾιson, NY: Roman Catholic Books, 1993, p. 83.
[10] Michael Davies, The Order of Melchisedech, p. xix.
[11] The Papal Encyclicals, by Claudia Carlen, Raleigh: The Pierian Press, 1990, Vol. 4 (1939-1958), p. 127.
[12] The Great Encyclical Letters of Pope Leo XIII, pp. 402-403.
[13] The Great Encyclical Letters of Pope Leo XIII, p. 401.
[14] Michael Davies, The Order of Melchisedech, pp. 94-95.
[15] Michael Davies, The Order of Melchisedech, p. xxii.
[16] Denzinger 1151.

It is less doubtful since all that was removed was "ut" while the new rite "essential form" could be used for the installment of a Christian emperor. There are only a few references to the episcopate in the new rite of episcopal consecration that might make it valid. There is also one mention to sacrifice in the NO rite of ordination but it is not necessarily propitiatory. However, the Chaldean rite does not explicitly mention propitiatory sacrifice but you can clearly see a priest is being ordained sacramentally to offer sacrifice by the rite.
Prayer for the bishop-elect
"The principal consecrator says, “Lord, be moved by our prayer. Anoint your servant with the fullness of priestly grace and blesshim with spiritual power in all its richness. We ask this through Christ our Lord.” R. Amen."

"Father, you know all hearts. You have chosen your servant for the office of bishop. May he be a shepherd to your holy flock, and a high priest blameless in your sight, ministering to you night and day; may he always gain the blessing of your favor and offer the gifts of your holy Church. Through the Spirit who gives the grace of high priesthood grant him the power to forgive sins as you have commanded, to assign ministries as you have decreed, and to loose every bond by the authority which you gave to your apostles.May he be pleasing to you by his gentleness and purity of heart, presenting a fragrant offering to you, through Jesus Christ, your Son, through whom glory and power and honor are yours with the Holy Spirit in your holy Church, now and for ever. R. Amen.”

If these were not in the rite I would probably condemn the new rite as straight up invalid and not just doubtful.

Stanley, you can quit asking “what do you do?”...you’ve asked that 5x on this thread.  Haha.  We’ve all told you what the theology is, you just ignore facts, and somehow think that sspx superiors (post +ABL) have some super-secret investigative process that we should all blindly trust.  ...Just because they’re sspx.
.
That’s how cults are formed.

We’ve all told you what the theology is, you just ignore facts,

You've said they must be conditionally ordained, but that's not answering my question .The priest might have been, but has no obligation to tell you. He may have even been ordained by someone you would consider a bishop, eg an older Roman bishop, or possibly an Eastern bishop (rare).  You don't have any of these facts.

What you seem to be saying is that you will not accept any priest unless the superiors demonstrate to your satisfaction that they have acted exactly as you've said they should act. Doesn't that seem backwards?