either the catholic church has contradicted itself, or unbaptized dead infants cannot enter heaven

In order to win this debate I do not need to prove the position held by the Church is true. All I have to do is show that the statements cited by Paul do not necessarily contradict infallible teaching. The Catechism states: 1257 The Lord himself affirms that Baptism is necessary for salvation. (...) The Church does notknow of any means other than Baptism that assures entry into eternal beatitude; this is why she takes care not to neglect the mission she has received from the Lord to see that all who can be baptized are "reborn of water and the Spirit." God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments.Decree for the Jacobites at the Council of Florence in 1442: "There is no other way to come to the aid [of little children] than the sacrament of Baptism (...)".There is no other way (for us) to come to the aid of the Children than the sacrament of Baptism. We are bound to the sacrament, this is exactly what the Catechism teaches.Pope Gregory X, Council of Lyons II, 1274: We define also that the souls of those who depart this life in actual mortal sin, or in original sin alone, go straightaway to hell, but to undergo punishments of different kinds. (Denz. 464)Those who die in original or mortal sin go to hell. This is indeed the general rule, however the Church has always recognized the Holy Infants (those killed by Herod) as Saints (with their own feast day no less) and so says nothing about there being exceptions to this rule.Pope Martin V, Council of Constance, Session 15, July 6, 1415 - Condemning the articles of John Wyclif - Proposition 6: Those who claim that the children of the faithful dying without sacramental baptism will not be saved, are stupid and presumptuous in saying this. - CondemnedThe Church gives no assurance as to the eternal fate of the infants, we merely pray God will have mercy on them and save them apart from his sacramental framework.Pope St. Innocent I, in 417, Synod of Milevis : "The idea that infants can be granted (...) eternal life even without the grace of baptism is utterly foolish" (DS 219).The grace of baptism (sanctifying Grace) is necessary, whether it is given through baptism or some other way we are not aware of.Pope Innocent III (...) those dying with only original sin on their souls will (...) [be] deprived forever of the vision of God" (Corp. Juris, Decret. l. III, tit. xlii, c. iii -- Majores). (Denzinger 410)We've covered thisThe provincial Council of Cologne: "Faith teaches us that infants, since they are not capable of this desire (Baptism of Desire), are excluded from the kingdom of heaven if they die [unbaptized]." (Collectio Lacensis, V. 320)Provincial Councils do not constitute infallible teaching, and are therefore cannot be included in the premise of this debate.Pope Gregory the Great (-604) taught the eternal torment of infants in his Moralia on the Book of Job. "(...) With what sort of visitation does the strict Judge mercilessly slay those, whom the guilt of their own deeds condemns, if He smites for all eternity even those, whom the guilt of deliberate choice does not impeach?" (Moralia 9)Not everything popes teach constitute infallible teaching, however this is also consistent with what the Catechism currently states. We know of no other way than baptism to ensure salvation, and so it is a perfectly orthodox position to take as it does not say that God cannot save outside of baptism.Pope St. Innocent, 414 A.D.: But that which Your Fraternity asserts the Pelagians preach, (...) is quite idiotic. (...) when they preach that infants already have what is believed to be conferred on them only through Baptism. (Jurgens, The Faith of the Early Fathers, Vol. 3: 2016.)Once again, we affirm Baptism is necessary for salvation, and infants do not already have saving grace. We merely acknowledge God can work outside of His Sacraments and pray he does so in His Mercy.Pope St. Zosimus, The Council of Carthage, Canon on Sin and Grace, 417 A.D.- It has been decided likewise that if anyone says that (...) there will be (...) place anywhere where the blessed infants live who departed from this life without baptism, without which they cannot enter into the kingdom of heaven, which is life eternal, let him be anathema. (...) (Denz. 102, authentic addition to canon 2.)Completely coherent with current understanding. We know of no salvation outside of baptism and no one can point to any source (scriptural or otherwise) which would indicate there is a place reserved for unbaptized infants. This Canon does not, however, limit God's freedom in any way.St. Augustine, A.D. 415: Anyone who would say that infants who pass from this life without participation in the Sacrament [of Baptism] shall be made alive in Christ truly goes counter to the preaching of the Apostle (...). (Jurgens, The Faith of the Early Fathers, Vol. 3: 2016.)Saint Augustine is not infallible teaching, but in any case this is consistent with what the Catechism currently teaches. We have no assurances of the salvation of unbaptized infants.St Aquinas, Summa Theologica Question 68, Article 3 "I answer that, In this matter we must make a distinction and see whether those who are to be baptized are children or adults. For if they be children, Baptism should not be deferred. First, because in them we do not look for better instruction or fuller conversion. Secondly, because of the danger of death, for no other remedy is available for them besides the sacrament of Baptism. On the other hand, adults have a remedy in the mere desire for Baptism, as stated aboveWe've covered this.Pope Eugene IV, Council of Florence, Session 11, Feb. 4, 1442: "Regarding children, indeed, because of danger of death, (...)holy baptism ought not be deferred for forty or eighty days, or any time (...)."Once again, we know of no other way and so it would indeed be inadvisable to defer baptism for infants.Pius XII-Allocution to midwives, October 29, 1951. "An act of love is sufficient for the adult to obtain sanctifying grace and to supply the lack of baptism; to the still unborn or newly born this way is not open."This is neither here nor there. Babies are incapable of certain actions which adults are capable which would supply the lack of baptism. This does not mean that there are not other ways, unknown to us, which can likewise supply the lack of baptism.Pope Pius VI, Auctorem fidei, Aug. 28, 1794: The doctrine which rejects as a Pelagian fable, that place (...) in which the souls of those departing with the sole guilt of original sin are punished with the punishment of the condemned, exclusive of the punishment of fire, just as if, by this very fact, that these who remove the punishment of fire introduced that middle place and state free of guilt and of punishment between the kingdom of God and eternal damnation, such as that about which the Pelagians idly talk. Condemned as false, rash, injurious to Catholic schools. (Denz. 1526)"Babies dead without baptism go to Limbo, where they do not enjoy God, but neither do they suffer, because, having original sin alone, they do not deserve paradise, but neither do they merit hell or purgatory." ~1905 Catechism of Pope Pius X,I put these two together as both refer to limbo, which was never in any sense infallible dogmatic teaching. It is theological speculation which has been given more or less credence at different times. It is not as popular amongst theologians today as it has been in the past, but in any case it does not constitute a contradiction of infallible teaching. In conclusion, we have seen no contradiction in the quotes presented thus far. All we have seen is an unnuanced presentation of Catholic quotes (many of which do not constitute infallible dogmatic teaching) set forth in the hopes that an uncritical examination will lead someone to come to the conclusion that there is a contradiction where there is none.