Gemara

(Rava): If a Treifah killed someone in front of Beis Din, he is liable, due to "u'Vi'arta ha'Ra mi'Kirbecha" (you will eradicate the evil from your midst).

If he killed not in front of Beis Din he is exempt, because the testimony cannot be Huzam.

(Rava): One who is Rove'a (has Mishkav Zachar with) a Treifah is liable. If a Treifah is Rove'a in front of Beis Din, he is liable due to "u'Viarta ha'Ra." If a Treifah is Rove'a not in front of Beis Din he is exempt because the testimony cannot be Huzam.

We already know this from Rava's previous teaching! The Chidush is one who is Rove'a a Treifah. Do not say that it is like Bi'ah with a dead person (which is exempt). Rather, since he enjoys the act, he is liable.

(Rava): If witnesses testified about a Treifah and they were Huzmu, they are exempt. If Treifah witnesses were Huzmu, they are killed.

Rebuttal (Rav Ashi): Also Treifah witnesses that were Huzmu are not killed, because the testimony of the Mezimim (who said that the witnesses were somewhere else) cannot be Huzam (we could not kill them for trying to kill Treifos).

Bava Kama 75b (Beraisa): If two witnesses testified that Reuven stole, and two others testified that he slaughtered or sold, and the witnesses about the slaughter or sale were Huzmu, Reuven pays Kefel, and the Edim Zomemim pay two or three;

Sumchus says, the Edim Zomemim pay Kefel, and Reuven pays two for a Seh or three for an ox.

(Rav Acha brei d'Rav Ika): The case is, two witnesses said 'you stole', and Reuven answered, I stole and slaughtered or sold, but I did not steal in front of you, rather, in front of Ploni and Almoni, and Ploni and Almoni testified that he stole and slaughtered or sold. Chachamim hold that since Ploni and Almoni cannot be Huzmu (for Reuven admitted that they witnessed it), their testimony is invalid. Sumchus says that, even so, their testimony is valid.

88a - Question: R. Yehudah holds that "his brother" excludes slaves. If so, Edim Zomemim who tried to kill a slave should not be killed, for it says "like he plotted to do to his brother"!

Answer (Rava): "U'Vi'arta ha'Ra" includes this case.

Chulin 11b (Rav Kahana): The Torah says that we kill a murderer. We are not concerned lest the victim was a Treifah, and the murderer is exempt! This shows that we rely on the majority (most people are not Treifah).

Rishonim

Rambam (Hilchos Edus 20:7): If witnesses testified that a Tereifah (Levi) murdered and they were Huzmu, they are not killed. Even had they physically killed Levi, they would not be killed, for he is a Tereifah. Similarly, if Tereifah witnesses testified about a capital case and they were Huzmu, they are not killed, for if the witnesses who were Mezim them would be Huzmu, they could not be killed, for they were Mezim Tereifos.

Question: Bava Kama 88a suggested that we cannot kill Edim Zomemim who tried to kill a slave, and hence we cannot execute a slave. It answered that "u'Vi'arta ha'Ra" includes a slave. Why don't we say that it includes only a slave who killed in front of Beis Din, like we say about a Tereifah?

Answer #1 (Ohr Some'ach): Beis Din punishes for what was done, and also so the murderer will not kill again, similar to Ben Sorer u'Moreh. We should kill a murderer even if we know that he will not kill again. Beis Din need not kill a Tereifah for what he did, since in any case he will die from his defect. We kill him lest he kill others, like we kill beasts. This is only if he killed in front of Beis Din. Witnesses cannot testify clearly, for it is Iy Efshar Lehazimah. If a slave killed, even if he is not called the brother of the witnesses, they must kill him for what he did, due to "u'Vi'arta ha'Ra." It is unreasonable that a slave not be punished for what he did.

NOTE: Rava taught that Beis Din kills a Tereifah due to "u'Vi'arta ha'Ra" also for Mishkav Zachar, not only for murder, and said that this is no Chidush. Perhaps this is only because we would kill a man who seeks to be Rove'a a man, but Beis Din would not kill one who served Avodah Zarah or was Mechalel Shabbos in front of them. This same verse obligates killing a slave for any capital Aveirah, for it is unreasonable that he not be punished for what he did.

Answer #2 (Ohr Some'ach): "U'Vi'arta ha'Ra" discusses only in front of Beis Din. It applies also to Edim Zomemim who tried to convict a slave. We cannot kill them for "Ka'asher Zomam La'asos l'Achiv", but "u'Vi'arta ha'Ra" applies because they sinned in front of Beis Din. Therefore, it is Efshar Lehazimah. This does not apply to Edim Zomemim who tried to convict a Tereifah, for even if they would kill him in front of Beis Din, they would not be killed.

Rambam (Hilchos Rotze'ach 2:9): If a Tereifah person killed someone, he is killed. This is if he killed in front of Beis Din. If he killed in front of witnesses he is exempt, lest they be Huzmu, and if they are Huzmu they cannot be killed, for they plotted to kill only a Tereifah. Any testimony she'Iy Efshar Lehazimah is invalid for capital cases.

Tosfos (Chulin 11b DH v'Chi): Rav Kahana did not learn that we follow the majority from the murderer himself (we are not concerned lest he is Tereifah), because the reason we do not kill a Tereifah murderer is because the testimony is Iy Efshar Lehazimah. If we kill Edim Zomemim, we do not kill properly. If so, his proof would be from that we kill the Edim Zomemim. This is Ravina's proof (in Chulin)!

Teshuvas R. Akiva Eiger (2:129 DH v'Zehu): The word 'not' in Tosfos is a printing mistake, or it is incredulous (do we not kill the murderer properly?!) I.e. even if Hash-m knows that the murderer is Tereifah, since we do not, we would kill Edim Zomemim who plotted against him, so it is Efshar Lehazimah.

Question (Tosfos Rid Bava Kama 84a DH Tereifah): If Edim Zomemim testified that a Tereifah murdered, since their testimony is Iy Efshar Lehazimah, it is Batel. We should say the same about testimony about a Ben Gerushah!

Answer (Tosfos Rid): Testimony that a Tereifah killed is Iy Efshar Lehazimah due to the Tereifah, for one who kills a Tereifah is not killed. Testimony about a Ben Gerushah cannot be Huzam because we cannot make a witness a Ben Gerushah. It is not due to the one they testified about!

Margoliyas ha'Yam (78a 9, citing Beis Yitzchak CM 2): According to the answer in Tosfos (Makos 2a) that lashes fulfill Ka'asher Zomam except for when "Nefesh b'Nefesh" applies, we should be able to kill a Tereifah, for this is not a Nefesh! Perhaps they are not lashed because Lo Sa'aneh has no action, and here we do not learn from "v'Hitzdiku Es ha'Tzadik."