Is every sorcerer considered a disbeliever?

A sorcerer is one who uses jinn and draws close to them through sacrificing, supplicating, and obeying them in acts of disobedience to Allah (such as fornication, drinking alcohol, abandoning prayer, and becoming defiled with impurities), so that they may help him harm those bewitched, sow discord between people, and inform him of some unseen matters. This act is considered major shirk (definition) (polytheism) and disbelief (kufr), as substantiated by the Almighty's saying: "And Solomon did not disbelieve, but the devils disbelieved, teaching people magic" and His saying: "And they [i.e., the two angels] would not teach anyone until they had said, 'We are only a trial, so do not disbelieve.'" Therefore, a sorcerer is a disbeliever, even if he prays and fasts, because shirk nullifies good deeds.