When one approaches the matter this first way, the halakha that forbidden fat is pure applies specifically to kosher animals, but when one approaches the matter that second way, the halakha applies specifically to non-kosher animals. To decide the matter, the verse states: “The fat of a tereifa may be used for any other service” (Leviticus 7:24), indicating that only the forbidden fat of those animals to whose species the halakha of tereifa applies, i.e., kosher animals, is ritually pure. The status of tereifa is immaterial to a non-kosher animal as its consumption is prohibited in any event.

The baraita concludes: One might still assume that I will exclude from this halakha only the forbidden fat of a carcass of a non-kosher animal, as the halakha of tereifa does not apply to its species, but I will not exclude the fat of a carcass of an undomesticated kosher animal, as the halakha of tereifa applies to its species. Therefore, the verse states in conclusion: “But you shall in no way eat of it,” indicating that the reference is only to animals whose fat is forbidden for consumption if slaughtered but whose meat is permitted, i.e., kosher domesticated animals. Excluded are kosher undomesticated animals, whose fat and meat are both permitted for consumption.

Rav Ya’akov bar Abba said to Rava: If that is so, it appears from the baraita that the carcass of a kosher animal imparts impurity, but the carcass of a non-kosher animal does not impart impurity. Rava said to him: How many elders have you caused to err in the interpretation of this baraita? In the latter clause we come to discuss only the carcass of a non-kosher bird, which does not impart impurity. By contrast, carcasses of non-kosher animals are impure.

§ In the mishna, Rabbi Meir states that a bird offering whose nape was pinched and was found to be a tereifa does not impart impurity as would a carcass. Rabbi Yoḥanan says: Rabbi Meir deemed pure only unblemished birds whose napes were pinched, as they are fit to be sacrificed, but he did not deem pure blemished birds, which are not fit to be sacrificed. And Rabbi Elazar says: Rabbi Meir deemed even blemished birds pure and did not distinguish between the two. It was also stated that Rav Beivai says that Rabbi Elazar says: Rabbi Meir would deem pure blemished birds, and this was his opinion even concerning geese and chickens, species that may not be brought as offerings and as such are never supposed to be pinched.

Rabbi Yirmeya raises a dilemma: According to Rabbi Elazar’s understanding of Rabbi Meir’s opinion, what is the halakha with regard to one who broke the neck of a goat? Does the impurity of animal carcasses apply? The breaking of the neck is considered the proper procedure in certain cases, as the Torah commands that a heifer’s neck be broken if a murdered body is found between two cities and the identity of the murderer is unknown (see Deuteronomy 21:4).

One could claim: What is the reason that geese and chickens are pure if their napes are pinched? It is because they are species of birds and the napes of some birds are pinched; but a goat is not of the same species as a heifer, as goats are considered small livestock whereas cattle are large livestock. Or perhaps one could claim: Since a goat is still a species of domesticated animal, it is similar enough to a heifer that the breaking of its neck prevents it from imparting impurity as a carcass.

Rav Dimi was sitting and saying this halakha, i.e., this dilemma. Abaye said to him: By inference from this dilemma, it seems that you assume that a heifer whose neck is broken is itself pure and does not impart impurity as would a carcass. Rav Dimi said to him: Indeed, as the Sages of the school of Rabbi Yannai say: Since the language of atonement is written with regard to the heifer whose neck is broken, in the verse: “Forgive, Lord, Your people Israel” (Deuteronomy 21:8), just as atonement is written with regard to sacrificial animals, the breaking of the heifer’s neck is equivalent to the pinching of the nape of a bird offering, and breaking its neck prevents the heifer from imparting ritual impurity.

Rav Natan, father of Rav Huna bar Natan, raises an objection based on a baraita concerning the purity of the forbidden fat of a kosher animal, mentioned in the verse: “And the fat of a carcass, and the fat of a tereifa, may be used for any other service; but you shall in no way eat of it” (Leviticus 7:24). I have derived from the verse only that forbidden fat that is forbidden for consumption but from which deriving benefit is permitted is pure. From where is it derived that this halakha also applies to the forbidden fat of an ox that is stoned by the court or the forbidden fat of a heifer whose neck is broken, from both of which one is prohibited from deriving benefit?

The verse states: “You shall eat no fat nor blood” (Leviticus 3:17). The generalization “no fat” indicates that the same halakhot apply to the forbidden fats of all domesticated kosher animals, including those from which one is prohibited from deriving benefit.

Rav Natan concludes his objection: And if it enters your mind that the meat of a heifer whose neck is broken is pure, why must the verse teach that its forbidden fat is pure? Could one entertain the possibility that its meat is pure but its forbidden fat is impure?

The Gemara responds: The derivation in the baraita was not necessary for a case where one broke the neck of the heifer. It was necessary for the verse to teach that the forbidden fat is pure even in a case where one slaughtered a heifer whose neck was designated to be broken.

The Gemara asks: But the slaughter itself should be effective in purifying the forbidden fat, as slaughter prevents an animal from assuming the impure status of a carcass, and the derivation is still superfluous. The Gemara responds: No, it is necessary to teach that the forbidden fat of a heifer that died before its neck could be broken is pure even though the heifer itself assumes that status of a carcass.

The Gemara asks: If the baraita is referring only to a heifer that died before its neck could be broken, and it describes benefitting from it as being prohibited, by inference, is it prohibited to derive benefit from the heifer while it is still alive? The Gemara responds: Indeed, as Rabbi Yannai says: I heard the boundary, i.e., stage, beyond which it is forbidden, but I have forgotten what it is, and yet the members of the group of scholars were inclined to say that its descent to a hard valley (see Deuteronomy 21:4), where its neck was broken, is the action that renders it forbidden.

MISHNA: All the offerings that were intermingled with animals from which deriving benefit is forbidden, e.g., sin offerings left to die, or with an ox that was sentenced to be stoned, even if the ratio is one in ten thousand, deriving benefit from them all is prohibited and they all must die. If the offerings were intermingled with animals whose sacrifice is forbidden but deriving benefit from them is not, the halakha is different. Examples of this are an ox with which a transgression was performed, which disqualifies it from being sacrificed as an offering, or