Safar 10, 1330
Those who follow the Sunnah and consensus deny this will simply because of what alBukhari has narrated in his Sahih where he quotes alAswad saying, "It was said once to `Ayesha, may Allah be pleased with her, that the Prophet (pbuh) had made a will regarding `Ali, and she responded: `Who said so? I have seen the Prophet, while I was reclining him to my chest, when he ordered a washbowl to be brought to him; I hardly noticed how fast he collapsed and died; so, how could he have made a will to `Ali?" In the same reference, the author quotes other sources citing `Ayesha saying, "The Messenger of Allah breathed his last while being between my stomach and under my chin," and she is often quoted saying, "He died reclining on my chest," and she may have said: "He died while his head was on my thigh." So, had there been any will, she would have come to know about it. In Muslim's Sahih, in a treatise on the subject of wills on page 14, Vol. 2, the author quotes `Ayesha saying, "The Messenger of Allah (pbuh) left neither a dinar nor a dirham, nor a male nor a female camel, nor did he leave any will." In both sahihs, in a treatise on wills, Talhah ibn Masrif is quoted saying, "I asked `Abdullah ibn Abu `Awfah: `Did the Prophet leave any will at all?' He answered: `No.' I asked him: `How did he enjoin people to write their wills while he himself did not do so?' He answered: `His will is the Book of Allah.'" Since these ahadith are more authentic than the ones which you have cited, and are included in both sahihs, while the ones you have cited are not, they can be brought forth as irrefutable arguments, Wassalam.
 You probably already know that both shaykhs have intentionally narrated this hadith while discussing the Prophet's will to `Ali, for those who stated at that time that the Prophet had left a will to `Ali had not yet split from the ranks of the nation. They were either among the sahabah or the tabi`in who had the courage to reveal what would make the mother of believers unhappy and would oppose the politics of the time; for this reason, she, may Allah be pleased with her, was shaken a great deal when she heard their hadith. Such a reaction is seen in her own statement in response to it, a statement which is one of the most feeble of answers. Imam al-Sindi, in his comment on this hadith in al-Nisai's Sunan, as indicated on page 241, Vol. 6 (the Egyptian Press at al-Azhar), said: "It is quite obvious that such hadith [by the mother of the believers `Ayesha] does not rule out the existence of the will prior to her statement, nor does it prove that he (pbuh) had died suddenly without being able to leave a will or could have thought of doing so, since he came to know that his end was approaching even before falling sick, then he remained sick for days...," up to the conclusion of his statement. If you scrutinize this statement, you will find it quite strong.
 Her statements "He died on my chest," and "He died between my belly and chin," are recorded in a chapter dealing with his sickness and demise (pbuh) in Bukhari's Sahih. As regarding her statement "He died while his head was on my thigh," this exists in another chapter in which the author discusses his sickness and demise without an intervening chapter.