R' Yehudah tells us in the name of Shmuel (Sanhedrin 104b) that the Anshei Kenesses HaGedolah wanted to include Shlomo HaMelech on the list of kings who lost their portion of Olam Haba. An image of David HaMelech had prostrated itself before them, beseeching them not to include him in his merit, but they ignored it. A fire came out of the Kodesh Kadashim, presumably invoking Shlomo's merit of having built the Beis HaMikdash, but they ignored that as well. A Bas Kol rang out, invoking the merit that Shlomo built the Beis HaMikdash before his own palace, and was much more diligent in building the former than the latter, but they still ignored it. Finally, a Bas Kol rang out, telling them that Shlomo would be welcomed into Olam Haba regardless of what they would say - the Chachamim can only decide Halacha, not whether a person should be welcomed into Olam Haba. At that point, the Anshei Keneses HaGedolah conceded and left Shlomo's name out of the Mishnah.
What exactly is this back and forth? If the Chachamim can't determine whether a person should enter Olam Haba, why was that Bas Kol not the first proof? Why were Shlomo's merits not invoked before his father's? And why did the Chachamim reject each one?