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As Bruce already mentioned this was dealt with by Saint Augustine of Hippo. Augustine held that baptism was valid if:
1. The right words are used, "I baptize you in the name of the Father, and of the Son, and of the Holy Ghost."
2. Water is used, either dipping in, or pouring or sprinkling on the candidate for baptism.
3. The cleric performing the baptism has Trinitarian intent.
Augustine held that Arian baptism would not be valid, no matter what words they used; because of lack of Trinitarian intent. The same would apply today to Jehovah's Witnesses and Latter Day Saints. Jesus only Pentecostal baptism would not be valid because the right words are not used.
Schismatic baptism would be valid, according to Saint Augustine, because the Donatists and Novations used water, the right words, and had Trinitarian intent. Thus baptisms performed by clerics of the Church of Rome would be valid even though the Church of Rome schismed from the one Holy Catholic and Apostolic Church by her dogmatic decrees at the Council of Trent.