Commentary for Bava Metzia 1:2
הָיוּ שְׁנַיִם רוֹכְבִין עַל גַּבֵּי בְהֵמָה, אוֹ שֶׁהָיָה אֶחָד רוֹכֵב וְאֶחָד מַנְהִיג, זֶה אוֹמֵר כֻּלָּהּ שֶׁלִּי, וְזֶה אוֹמֵר כֻּלָּהּ שֶׁלִּי, זֶה יִשָּׁבַע שֶׁאֵין לוֹ בָהּ פָּחוֹת מֵחֶצְיָהּ, וְזֶה יִשָּׁבַע שֶׁאֵין לוֹ בָהּ פָּחוֹת מֵחֶצְיָהּ, וְיַחֲלֹקוּ. בִּזְמַן שֶׁהֵם מוֹדִים אוֹ שֶׁיֵּשׁ לָהֶן עֵדִים, חוֹלְקִים בְּלֹא שְׁבוּעָה:
If both were riding on a beast [We are hereby apprised that riding acquires, even if he (the rider) does not lead, the beast not moving from its place], or if one were riding and the other leading [It is only when the rider moves his feet to make the animal go that the rider is equated with the leader; but if not, the leader acquires, and not the rider.], the first says: "It is all mine," and the second says: "It is all mine," the first swears that he has in it no less than a half, and the second swears that he has in it no less than a half, and they divide. When they concede, or when there are witnesses, they divide without an oath. [If they concede, or if witnesses come, even after it has been ruled that they are to divide with an oath, they divide without an oath.]
Bartenura on Mishnah Bava Metzia
English Explanation of Mishnah Bava Metzia
If after the case is settled, they both admit to the others claim, or if there are witnesses they can split the animal without an oath.
This mishnah is similar to the previous mishnah and just deals with a different disputed object. In the second clause the mishnah states that if they agree to the other party’s claim or if there are witnesses that the animal is owned by both parties, they split the animal without an oath. The function of the oath is to ensure that the person is telling the truth. When there is no dispute, or when there are witnesses who testify, there is no need for an oath. Since it is preferable to avoid oaths altogether the two may split the animal without an oath.