Complex sentence: However, the archdiocese does not dispute that the deed to the church property itself belongs not to the archdiocese but to the parish corporation; what is disputed is the membership of that corporation, and how they are to be chosen.
Split into simpler sentences: However, the archdiocese does not dispute that the deed to the church property itself belongs to the parish corporation and not to the archdiocese. What is disputed is the membership of that corporation, and how the members are to be chosen.