The Posthumous trial of Pope Formosus known as
the Cadaver Synod
Basically what the Council was saying was that priests, bishops, and deacons (as well as subdeacons and the minor orders in use at the time) ordained by these three false claimants to the papacy were invalidly ordained to their respective Orders. Why? Were they ordained according to a defective rite? No, the rite was the same rite used by the Bishops of Rome in ordinations. Did the candidates or the ordaining prelates have faulty intention? No, the ordaining bishops intended to ordain the men according to the mind of the Church regarding the sacraments and the men being ordained presumably had sound intentions as well. The only reason for declaring the rival ordination as null and void was to challenge the authority of the papal rivals. You can be sure that these various antipopes had challenged the validity of the ordinations of Alexander III who is today recognized as having been the legitimate claimant to the papal throne but who, in his own time, was initially recognized by only a minority of bishops while Victor and his successors, Pascal and Callixtus, were thought by many of their contemporaries to have the most authentic claim to the Chair of Peter. You may remember the papal imbroglio at the time of Pope Formosus (reigned 891-896) when the dead Pope was exhumed by his successor but one, Stephen VI, who convoked a synod, had Formosus posthumously deposed, and declared that the ordinations he had performed were null and void. Stephen’s successor but one, Theodore II, (reigned for twenty days in December 897), declared the ordinations of Formosus to have been valid and those of Stephen to have been null and void. The next two popes, John IX and Benedict IV, upheld the ordinations of Formosus—in fact John had been ordained priest by Formosus—but then Sergius III came along (904-911) and declared the ordinations of Formosus to have been null and void. What is going on??? It has nothing to do with sacramental theology but with claims of legitimacy and political power.
The undermining of opposition within the Church by declaring the ordinations of the opposition leaders was not new to the tenth century any more than it was to the Church at the time of Lateran III. In the debates of the second through the sixth centuries with the various factions such as the Montanists and the Donatists claimed exclusive validity of the sacraments and denied the validity of the ordinations in the “Great Church” (the mainline Church in which both Orthodoxy and Catholicism have their roots) and these splinter groups in turn had their ordinations condemned as invalid by the bishops who clung to the Apostolic faith.
All this is by way of saying that at the time of the Protestant Reformation, the papacy pulled out this canard once again in declaring “invalid” the ordinations of the various "Protestant” Churches. By this point they had to do more than declare; they needed to give a rationale and the development of scholastic theology with its breakdown of matter, form, and intention gave them a theological apparatus by which they could rationalize this but it was still basically a political and not a theological decision. It was only by devising a theological justification robbing the Churches of the Reformers of sacramental character that they could undermine the confidence of the believers in the Reformed Churches. Now, I am not going to say that all “Protestant” Churches have maintained a continuity of apostolic succession in their clergy. For many—especially in the second and later waves of the Reformation—this was not even a concern, but the case of the Scandinavian (Lutheran) and Anglican Churches merits very close study. Furthermore, while the Council of Trent taught that only a bishop possesses the “fullness of the priesthood” and thus only a bishop can ordain priests, there are historical instances of presbyteral ordination (ordination of priests by priests), recognized by Rome, at least up to the thirteenth century. I seem to recall an instance as late as the sixteenth century of a Bull authorizing presbyteral ordinations in the Spanish missions of Mexico, but it may have been authorizing a priest to ordain deacons which would be a somewhat different question. If presbyteral ordination can be shown to have a legitimate place in the history of the Church, that also opens the door to German Lutheran as well as Reformed Church orders. Again, I only write from a historical perspective and make no claims to theology but perhaps in future entries we will look more closely at Catholic objections to Anglican and Lutheran Orders and even the very concept of Sacramental Validity—from a historical perspective.