I saw the Prophet of Allah ﷺ sleep until he was breathing audibly, then he got up and prayed without performing ablution.
حدثنا معتمر بن سليمان التيمي قال أخبرنا حميد عن عبد الله بن عبيد
رأيت نبي الله ﷺ نام حتى نفخ ثم قام فصلى ولم يتوضأ
Its isnad is sahih. Humayd is Ibn Abu Humayd al-Tawil, and Abdullah bin Ubayd, its correct form is Ibn Ubayd bin Abu Mulaykah al-Taymi al-Madani, one of the senior trustworthy Followers.The hadith that the Prophet ﷺ slept after tahajjud until he snored, then got up and prayed without performing wudu, was narrated by Bukhari 1/238, no. 138, in Fath, in the Book of Wudu, chapter on lightening wudu, and by Muslim 1/527, no. 763, in the Book of Travelers, chapter on supplication in the night prayer, and by Tirmidhi 1/111, no. 77, in the Book of Purification, chapter on what has been said about wudu after sleep, and by Nasai 2/218, no. 1121, in the Book of Tatbiq, chapter on supplication in sujud, and by Ibn Majah 1/160, no. 474, in the Book of Purification, chapter on wudu after sleep.