Are the four schools of thought, which differ among themselves, included in the Hadith of the Prophet, peace and blessings be upon him, which states that his Ummah will divide into 73 sects, all of them in the Fire except one?

The well-known Hadith about the division of the Ummah into seventy-three sects, seventy-two of which are in Hellfire and one in Paradise, which is the Jama'ah (the main body of Muslims), was narrated by Mu'awiyah ibn Abi Sufyan, may Allah be pleased with him. In another narration, the saved sect is described as "that which I and my companions are upon." This division refers to disagreements in fundamental principles and beliefs, not in secondary matters. Thus, the Companions, the Four Imams, and their followers who adhered to the fundamental principles of Ahl al-Sunnah are the saved sect, whereas those who contradicted their principles and beliefs, such as the Mu'tazilah, the Shi'a, and the Murji'ah, are counted among the blameworthy sects.