(Mishnah): The children of five women got mixed up. These children grew up and married women. One of the men died [without children. There is a five-way doubt about who is his father.] Four [definite sons from different possible fathers] do Chalitzah, and one [a son of the fifth possible father] does Yibum (or Chalitzah).

[If another of the mixed-up men died,] the man who did Yibum and sons from three other (possible) fathers do Chalitzah, and a son from one father does Yibum;

It turns out that there are four Chalitzos and one Yibum (or a fifth Chalitzah) for every widow (whenever a man from the mixture dies).

(Gemara) Question: Everywhere, you say that there is no Chalitzah after Chalitzah, and here you say so?!

Answer: Here [there is no Chalitzah after Chalitzah] regarding Vadai. Here it is a Safek.

Question: Everywhere, you say that when we do not tell him to do Yibum, we do not tell [even another brother] to do Chalitzah, and here you say so?!

Answer: Here [when we do not tell him to do Yibum, we do not say to do Chalitzah] regarding Vadai. Here it is a Safek.

(Mishnah): Leah's son was mixed up with her daughter-in-law's son. The mixed-up children grew up and married women and died. A [Vadai] son of the daughter-in-law does Chalitzah, but not Yibum. It is a Safek whether [the widow] is his brother's wife, or the wife of his father's brother;

A son of Leah does Yibum or Chalitzah. The widow is either his brother's wife, or his nephew's wife (who is permitted).

If a Kosher (i.e. one who knows his lineage) died (without children) - to Leah's sons, each Safek (mixed-up child) does Chalitzah but not Yibum (this will be explained). It is a Safek whether [the widow] is his brother's wife, or his uncle's wife;

To the daughter-in-law's sons, one Safek does Chalitzah, and the other does Yibum (or Chalitzah. The widow is either his brother's wife, or his nephew's wife.)

(Gemara -R. Yochanan): [The Seifa of] our Mishnah means that [each Safek does Chalitzah, or sometimes Yibum] to the wives (widows) of the daughter-in-law or to the wives of Leah's sons.

(R. Chagai): [Our Mishnah] teaches that one may marry the wife of his brother's son. (We do not decree lest one come to marry his brother's wife.)

(Mishnah): If the son of a Kohen became mixed with his Shifchah's son, both of them may eat Terumah. They receive one share at the granaries;

They may not become Tamei Mes. They cannot marry Kosher or Pasul women.

(Gemara): They may eat Terumah, for slaves of Kohanim may eat Terumah.

(Mishnah): They receive one share at the granaries;

This supports R. Chiyah, who taught that women and slaves do not receive a share at the granaries, but we give to them Matanos Kehunah and Leviyah from the house.

(Mishnah): They cannot marry Kosher or Pasul women.

They cannot marry Kosher women, due to the Pasul (each is a Safek slave). They cannot marry Pasul women due to the Kosher (each is a Safek Kohen).

Question: May they bring one Minchah, [and stipulate that it is of the Kohen,] and it is offered Kalil (totally consumed on the Mizbe'ach)?

Answer (Beraisa): They may bring one Minchah, and stipulate about it, and it is offered Kalil.

Question: May they bring two Menachos, and one is offered Kalil, and Kemitzah is taken from the other, and it is eaten?

Answer (Beraisa): They may bring two Menachos, and one is offered Kalil, and the other is Nikmetezes, and it is eaten.

Question: May they testify one testimony, and it will count like one testimony (i.e. one witness)?

Or, is it like R. Ze'ira said citing Rav Yitzchak citing Rav Asi - since if they were found to be Edim Zomemin, they are not killed, the murderer [that they testified about] is not killed (for testimony must be Efshar Lehazimo). Also here, it is so (since we could not punish either of them, for we do not know whose testimony counted, the testimony is invalid. SHIREI KORBAN - surely it is invalid for capital cases. The question is for monetary cases. OTZAR HA'YERUSHALMI - Tosfos (Sanhedrin 31a DH she'Beis) says that 'if one of the witnesses was found to be Pasul, the entire testimony is Batel' applies only when we know who is Pasul.)