Gemara

35b (Mishnah): If two oxen of Reuven damaged two of Levi's oxen, and Levi says that the big ox (or the Mu'ad) 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.

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

Question (Mishnah): If two oxen of Reuven, one big and one small...

(Inference): If Levi cannot bring proof, he collects like Reuven said.

Question: This is like wheat and barley (for which 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.

(Mishnah): If Reuven had two slaves (or fields), one big and one small, Shimon says, 'I bought the big one'; and Reuven says 'I sold the small one', Reuven swears that he sold the small one;

Question: Why does Reuven swear? He did not admit to (part of) what Shimon claimed, it is Heilach (he gives him the small slave (or land) he admits to at the time of the admission), and we do not swear about slaves (or land)!

Answer #1: They argue about the value of a big or small slave or field.

Answer #2 (Shmuel): They argue about (fabric to make) clothing of a big or small slave, or the piles of grain of a big or small field.

Rishonim

Rambam (Hilchos Nizkei Mamon 9:9): If Reuven's two oxen chased Levi's ox and we do not know which of them damaged it, and Levi says 'the big one (or Mu'ad) damaged', and Reuven says 'the small (Tam) one damaged', ha'Motzi mi'Chavero Alav ha'Re'ayah.

Magid Mishneh: If he cannot bring a proof, Reuven is totally exempt. The Rambam says so in Halachah 11, when each damaged one animal; it is like an admission of barley in response to a claim of wheat. Further, since Reuven admits about a Tam, it there are no witnesses he is exempt like one who admits to a fine. Our Sugya is like the opinion that half-damage is Mamon. The Halachah does not follow this.

Rambam (10): If there was no clear proof, but witnesses say that one of them damaged, Reuven pays according to what he said. If Levi says 'you know that this one damaged in front of you', Reuven swears mid'Oraisa and pays like he admitted, for he partially admitted.

Ra'avad: This refers to the case of a Tam and a Mu'ad.

Magid Mishneh: This is unlike wheat and barley, for here there are witnesses. The Rambam holds that when he claims that the Mu'ad damaged, his claim (is against all Reuven's money, and) includes the Tam. When both are Tam, this is like wheat and barley. Perhaps even in this case mid'Oraisa he must swear, for there are witnesses. This requires investigation.

Rebuttal (Shach CM 400:6): The Ra'avad said that one is Mu'ad, for if both are Tam he is exempt, for even if he would admit he does not pay the fine! Also, if when both are Tam the admission is not mi'Min ha'Ta'anah, even if there are witnesses he should be exempt! Rather, the Rambam requires witnesses so he cannot retract from his admission.

SMA (3): The Magid Mishneh says that the Rambam holds that since there are witnesses, it is like a partial admission. The Tur holds that since the witnesses do not know which gored, they do not change the law.

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.

Magid Mishneh: There were no witnesses at all. If not, Reuven would pay like he says, like above (Halachah 10). The Halachah is the same as above. The Ra'avad explained that half-damage is unlike other fines. If the victim seized, he need not return. When there are no witnesses at all, he is totally exempt. When there are witnesses but they do not know which damaged, Reuven pays like he says and swears mid'Oraisa about the rest. Above the Rambam discusses when there are witnesses. If there is only one damager he is liable, and all the more so here, when two damaged! Here the Rambam discusses when there are no witnesses. He exempts when there are two damagers, and all the more so he is exempt above, when only one damaged!

Rosh (3:15): Surely witnesses saw the goring, just they are unsure which ox gored. If not, he admits to a fine, and is exempt!

Poskim

Shulchan Aruch (CM 400:3): If Levi says 'your big (or Mu'ad) ox damaged', and Reuven says 'no, the small (Tam) one damaged', ha'Motzi mi'Chavero Alav ha'Re'ayah.

Rema: If there was no clear proof, but witnesses say that one of them damaged, Reuven pays according to what he said.

Shulchan Aruch (4): If Levi says 'your big (or Mu'ad) ox damaged my big ox, and the small ox (or the Tam) damaged the small ox, and Reuven says oppositely, ha'Motzi mi'Chavero Alav ha'Re'ayah. If there was no clear proof, Reuven is exempt. This is like a claim of wheat and admission of barley. He swears Heses and is exempt even from paying the barley.

Shach (10): The Mechaber and Rambam hold that when there are no witnesses he is exempt, even if one of the damagers was Mu'ad. The Nimukei Yosef disagrees. Bava Metzia 100a supports him.

Rema: This is like the opinion I brought in Sa'if 3. Some distinguish and say that if there were witnesses that one damaged but they do not know which, Reuven pays according to what he says. This is not like wheat and barley; rather, it is an admission, like the first opinion in the Mechaber.

Question (SMA 3 and Shach 12): Also this is like the Rambam, like the Magid Mishneh explained!

Answer (SMA 3): Perhaps the Rema held that since the Mechaber did not specify, he discusses even if there are witnesses but they do not know which damaged. 'Some distinguish' refers to the Magid Mishneh, who says that 'there is no clear proof' does not imply that there are witnesses.

Shach (12, citing Gedulei Terumah): How can the Rambam obligate when there are witnesses? The Mishnah discusses with witnesses. If not, he is exempt for admitting to a fine! Also, the Rambam exempts, because he is like one who admits that he does not owe barley. This is even if there are witnesses! Rather, the Rambam (Sa'if 3) obligates the damager when the victim is unsure.

Rebuttal (Shach 12): The Magid Mishneh said that the Mishnah is without witnesses, like the opinion that half-damage is not a fine. When there are witnesses, not claiming barley is not an admission. He did not need to claim, because he has witnesses!