Masechet Bava Kama, Perek Dalet, Mishnah Gimel. The Mishnah says that if the ox of a Jew gores the ox of Hekdesh, the property of the temple treasury of the Beit HaMikdash, an animal that was sanctified to be brought as a korban (offering), or, conversely, if the ox of Hekdesh that was sanctified to the Beit HaMikdash gores the ox of Israel, the owner in both cases would be patur, would not be obligated to pay for the damages. As the Pasuk (verse) says, “If an ox of a man strikes the ox of his friend, then he has to pay.” But we see from here that this applies only if it is an ox of his friend, which implies an ox that belongs to an ordinary Jew, but not an ox owned by the Beit HaMikdash; damages would not be paid in that situation.
It does not matter whether it is a tam (unforewarned) or mu'ad (forewarned) goring. It does not matter who the damager or the victim was. It has to be apples to apples, an ox that was on the same level. Those are the types of oxen that could damage each other and then result in an obligation to pay damages, but not if one side was owned by the Beit HaMikdash. That would not be a situation, because the word Re'ehu, your friend, shows that the oxen have to be on the same level. If the ox of a Jew gores the ox of an idolater, an idol worshiper, a non-Jew, it does not matter whether it is tam or mu'ad; he is not obligated to pay for the damages. The reason is that the goyim (non-Jews) themselves did not obligate a person to pay for the damages that animals did. So, when it comes to the nezek that we caused them, damage that we caused them, there would be no obligation. There would be no obligation to go beyond their law and pay them.
If you have the ox of a non-Jew that gores the ox of a Jew, ben tam, ben mu'ad, whether that ox that gored was tam or mu'ad, meshalem nezek shalem, that non-Jew has to pay full damages, even if it was a tam; he has to pay full damages to the Jew. This was a penalty that the Chachamim (the sages) instituted. The goyim were not careful with their animals. They were not safe with their animals. They did not hold them back from doing damage. Therefore, Chachamim said that, in order to put the responsibility on them and put the pressure on, they made them responsible for their animal, even if it was a tam, for full damages, nezek shalem. The Meiri points out here that, of course, all of these halachot (laws) only apply when dealing with nations who are uncivilized. But in today's day and era, when we have a code of law and there is civility between Jews and non-Jews, for the most part, these halachot, these penalties of Chachamim, Chazal (the Sages), would not apply.