Gemara

35b (Mishnah): If one of Reuven's oxen damaged Levi's ox, they are liable. If Levi says 'the big (or Mu'ad) ox damaged', and Reuven says 'no, the small (Tam) one damaged', ha'Motzi mi'Chavero Alav ha'Re'ayah.

If two oxen of Reuven damaged two of Levi's oxen, and Levi says that the big (or Mu'ad) ox damaged the big ox, and the small (or Tam) ox damaged the small ox, and Reuven says oppositely, ha'Motzi mi'Chavero Alav ha'Re'ayah.

(Rabah bar Noson): If David claimed that Shimon owes him wheat, and Shimon admitted that he owes barley, Shimon is exempt.

Question: The Mishnah connotes that if Levi cannot bring proof, he collects like Reuven said. This is like wheat and barley (and R. Noson totally exempts)!

Answer: Rather, if Levi cannot bring proof, he should collect like Reuven says, but does not collect at all.

Question (Beraisa): Levi collects for the small ox from the big ox, and for the big ox from the small ox.

Answer: That is when Levi seized the damager.

74b (Beraisa): Once, R. Gamliel once blinded the eye of his slave Tavi. R. Yehoshua said 'your words have no effect, for there are no witnesses.'

Rishonim

Rambam (Hilchos Nizkei Mamon 9:11): Rambam (11): If two oxen of Reuven damaged two of Levi's oxen, and Levi says that the big (or Mu'ad) ox damaged the big ox, and the small (Tam) ox damaged the small ox, and Reuven says oppositely, ha'Motzi mi'Chavero Alav ha'Re'ayah. If there was no clear proof, Reuven swears Heses and is totally exempt. If Levi seized, he is paid for the small animal from the big and for the big from the small, like Reuven said.

Magid Mishneh: There are no witnesses at all. If not, Reuven would pay like he says, like above (Halachah 10, in which one ox of Reuven gored Levi's ox). The Ra'avad explained that half-damage is unlike other fines. If the victim seized, he need not return it.

Rebuttal (Gra CM 400, Hashmatos on Sa'if 4): The Rambam says 'if there was no clear proof', i.e. witnesses know about the goring, but they do not know which. If there were no witnesses, why would Tefisah help?! The Rambam holds that the Sugya holds that half-damage is a fine. He holds that when there are witnesses on the basis of the matter (even if we need his admission in some respects), this is not considered admission to a fine.

Shach (CM 400:13): The Nimukei Yosef holds that according to the opinion that half-damage is a fine, it is like all fines. If there were no witnesses, Tefisah does not help. There are supports for this. R. Gamliel blinded his slave's eye. Even though a slave is the ultimate Tefisah (in himself), it did not help in a case of admission to a fine.

Rosh (3:15): The Mishnah did not say 'exempt', rather, ha'Motzi mi'Chavero Alav ha'Re'ayah. This teaches that if he seized, he keeps it. Since he has a claim against both animals, now the damager is ha'Motzi mi'Chavero (to take back his animal), and he must bring a proof! Tefisah does not help in the Reisha, when he has a claim only against one animal, or in the case of wheat and barley. Even if he seized, we take it from him. The Rif said that Tefisah of barley helps. Some answer for the Rif that Tefisah of the small animal does not help because his claim is only for the big animal, which pays only mi'Gufo, and he admitted that the small one did not damage. Tefisah of barley helps, for he can say 'you admitted that you owe me barley. If I do not merit through this, I seize for my claim of wheat.' According to this, seizure of a Tam helps when his claim was against a Mu'ad. Nevertheless, in the Reisha the Mishnah could not say 'ha'Motzi mi'Chavero Alav ha'Re'ayah', for seizure does not help when both were Tam and he seized the small one.

Pilpulei Charifta (5): (The Reisha says ha'Motzi mi'Chavero Alav ha'Re'ayah!) The Rosh means that in the Reisha we could not answer that he should collect like Reuven says, but does not (and the Mishnah says ha'Motzi mi'Chavero Alav ha'Re'ayah to teach that Tefisah helps) for Tefisah does not help when both are Tam.

Rebuttal (Rosh): These are different. When witnesses are unsure which damaged and he seized the small one in front of witnesses, it does not help, for he admits that he has no claim against it. All the more so Tefisah of barley does not help for a claim of wheat. He cannot hold it for its value for his claim of wheat, since Shimon denied the claim. He is exempt; R. Gamliel and Chachamim argue about whether or not he must swear. Tefisah helps only when there are two damagers and he has a claim against both of them. In this case his Tefisah helps, but only like the damager says, for he seized in front of witnesses.

Nimukei Yosef (17a DH Lo Tzericha): Even though admission without denial does not obligate paying, if the Levi seized before Reuven retracted, it is considered as if he had permission to seize.

Mordechai (40): The Rif says that Tefisah helps, like we say here, and regarding wheat and barley. R. Tam says that Tefisah helps only here, for he has a claim against both of them. R. Baruch holds like R. Tam regarding Keren paid mi'Gufo, and like the Rif regarding payments from the Aliyah.

Mordechai (42): The Riva explains that Levi seized the value of the small one before the admission. Therefore, the admission helps, even though it was not for what was claimed.

Poskim

Shulchan Aruch (CM 400:3): If Levi says 'your big (or Mu'ad) ox damaged', and Reuven says 'the small (Tam) one damaged', ha'Motzi mi'Chavero Alav ha'Re'ayah.

Rema: Some say that there is no oath here at all, like a claim of wheat and admission of barley. He is totally exempt. If he seized, we make him return it.

Shach (8): I proved (88:16,22) that the Halachah does not follow this opinion, Whenever there are witnesses, he pays the smaller, and Tefisah helps.

Shulchan Aruch (4): If Levi says 'your big (or Mu'ad) ox damaged my big ox, and the small (Tam) ox damaged the small ox, and Reuven says oppositely, ha'Motzi mi'Chavero Alav ha'Re'ayah. If there was no clear proof, Reuven is totally exempt. If Levi seized, he keeps like Reuven said, but not like Levi said. This is even if he seized in front of witnesses. This is if he seized before coming to Beis Din. After this, Tefisah does not help even to receive like Reuven says.

Question (Beis Yosef DH uv'Zeh): Why does the Tur attribute this opinion to the Rosh? The Gemara explicitly says so! The Rosh's Chidush is that we do not learn from here that Tefisah helps also when only one animal damaged.

Answer (Drishah 5): The Tur refers also to what he said above when there is only one damager. Alternatively, the Rosh holds that Tefisah helps only before coming to Beis Din, unlike the Ra'avad who does not distinguish.

SMA (9): The Shulchan Aruch holds that if Levi seized without witnesses, he keeps like he said, like the Rema said (399:3). This is like the Rosh and Tur.