Mishnah 2 of Maseches Eruvin. To understand this Mishnah we need one preliminary piece of information: a resident of a courtyard who did not join in an eruv chatzeiros - whether because he forgot or because he refrained for some other reason - is able, according to the way we rule, to declare on Shabbos itself that his ownership in the courtyard is nullified and handed over to the others, that he has no ownership in it at all and he renounces his share. This declaration is called 'bitul reshus', and it permits the other residents of the courtyard to carry there on Shabbos.
The missing words at the opening of the Mishnah:
Our Mishnah is missing several words at its beginning, because it comes to discuss the status of a Tzeduki - a member of the group that did not believe in the Oral Torah. The question arises from the previous Mishnah, which stated that we do not want a Jew living together with a non-Jew: does that same approach apply to a Tzeduki as well?
If the Tzeduki has the status of a non-Jew, two conclusions follow:
He cannot be included in the eruv.
He cannot perform bitul reshus if he forgot to join the eruv, and the only way to use the courtyard together with him is sechiras reshus - renting his ownership in the courtyard from him.
Accordingly, the opening of the Mishnah should read that a Tzeduki has the status of a non-Jew, followed by the words of the Tanna Kamma, who disagrees and holds that a Tzeduki is not like a non-Jew: he can take part in the eruv, and if he did not do so, he has the ability to perform the nullification that a Jew performs.
The incident with the Tzeduki in Jerusalem - Rabban Gamliel's testimony:
Here begin the words of our Mishnah, which were said in support of the position that a Tzeduki has the status of an ordinary Jew. Rabban Gamliel relates that there was an incident involving a certain Tzeduki who lived together with them and their family in Jerusalem, and who prohibited them from carrying because he had not joined their eruv. Their father said to them: "Maharu vehotzi'u es hakeilim" - hurry and take out your vessels, and show that you have taken possession of this courtyard after him, before he takes out his own belongings and causes the prohibition to fall upon you.
What is the concern? That the Tzeduki, even though he performed the nullification, can retract it by taking out his vessels. If he takes out his vessels on Shabbos, the nullification is void and carrying there becomes forbidden to them. But if they act first and take out their vessels, Rabban Gamliel holds that the Tzeduki can no longer retract. That is why the father said: hurry and take out your belongings, so that you get there first and he will not be able to retract his nullification.
From here Rabban Gamliel proves that the Tzeduki was capable of performing bitul reshus, and it is therefore clear that he did not have the status of a non-Jew.
Rabbi Yehudah's version:
Rabbi Yehudah says: "Belashon acher" - there is no proof from that incident, since his version of the events is different, and the father's words were something else. In his view the father said: hurry and attend to your needs in the alleyway "ad shelo yotzi veye'aser aleichem".
"Yotzi" here does not mean that the Tzeduki will take out his belongings; rather, it refers to the day: before the day goes out and comes to an end, before Shabbos enters - for if not, the Tzeduki will render carrying forbidden to you, since his status is that of a non-Jew.
And since, for whatever reason, no sechiras reshus was performed - whether because they did not rent from him or because he did not want to rent it out - it will not be possible to carry in this courtyard. The father therefore instructed them to see to their belongings before Shabbos: attend to your needs before Shabbos, because on Shabbos you will not be able to, since the Tzeduki has the status of a non-Jew and sechiras reshus is required, and bitul reshus is not an option.
In summary: This Mishnah discusses the status of a Tzeduki with regard to eruv chatzeiros. According to the Tanna Kamma, and according to Rabban Gamliel's proof, he does not have the status of a non-Jew: he can take part in the eruv, and if he did not join the eruv he can perform bitul reshus, as proven from the incident in Jerusalem, where the members of the family hurried to take out their vessels in order to prevent him from retracting his nullification. Rabbi Yehudah disagrees with the very version of the incident: in his view the father instructed them to finish attending to their needs before Shabbos began, because a Tzeduki has the status of a non-Jew, and the only permit is through sechiras reshus.