Gemara

74b (Mishnah - R. Meir): If one slaughters an animal and finds inside a live nine month fetus, it must be slaughtered. The Isur of slaughtering a mother and her child on the same day applies to the child;

Chachamim say, Shechitah of the mother is Metaher (permits) the child;

R. Shimon Shezuri says, even if the child is five years old and plowing in the field, Shechitah of the mother was Metaher it.

If one tore open the mother and found a live nine month fetus in it, the fetus must be slaughtered, for its mother was not slaughtered.

(R. Ami): If one slaughters a Treifah and finds a full term fetus inside:

In our Mishnah, R. Meir forbids (a Ben Peku'ah until it is slaughtered. Therefore), he permits this fetus through Shechitah;

Chachamim, who permit in our Mishnah, forbid this fetus, even if it is slaughtered.

(Rava): All permit this fetus through its own Shechitah. The Torah permits a fetus through Shechitah of its mother (if she is Kosher) or through its own Shechitah.

75b - Question: R. Shimon Shezuri says just like Chachamim!

Answer (Rav Kahana): They argue about a Ben Peku'ah that stepped on the floor. (Chachamim decree that it must be slaughtered.)

(Rav Mesharshiya): According to Chananya (who says that the father partially influences status of the child), if a Ben Peku'ah mates with a normal female, even Shechitah does not permit the child.

Version #1 (Abaye): Chachamim agree that a Ben Peku'ah Kalut (its hooves are not split) does not need Shechitah, even if it stepped on the ground;

This is because people remember bizarre things. (They will remember that it was a Ben Peku'ah. They will not think that animals do not need Shechitah.)

Version #2 (Abaye): If a Kalut fetus was found inside a Kalutah mother, a Peku'ah, Chachamim agree that the child does not need Shechitah, even if it stepped on the ground;

People remember doubly bizarre things. (end of Version #2)

(Ze'iri): The Halachah follows R. Shimon Shezuri. He permits all offspring of a Ben Peku'ah (without Shechitah) for all generations;

(R. Yochanan): It is permitted. Its child is forbidden.

Ada bar Chabo had a Ben Peku'ah that was clawed by a wolf.

Rav Ashi: Go slaughter it.

Ada bar Chabo: Ze'iri said that the Halachah follows R. Shimon Shezuri! (Even the offspring do not need Shechitah.) Also R. Yochanan does not require slaughtering a Ben Peku'ah!

Rav Ashi: R. Yochanan said that only according to R. Shimon Shezuri. (The Halachah follows Chachamim.)

Ada bar Chabo: Ravin said that the Halachah follows R. Shimon Shezuri wherever he appears in the Mishnayos!

Rav Ashi: I hold like R. Yonason, who disagrees.

Rishonim

Rif (25a): The Halachah follows Chachamim. It requires Shechitah only if it stepped on the ground. The Halachah follows Rava, for he is Basra.

Rambam (Hilchos Shechitah 12:11): If we know the father of an animal, we do not slaughter both of them on the same day. If one did, he is not lashed, for it is a Safek whether Oso v'Es Beno applies to males (i.e. fathers).

Rosh (4:5): Rashi explains that Rav Mesharshiya disagrees with Rava, who say that a fetus has four Simanim. I say that he agrees with Rava when the mother was not permitted through Shechitah, e.g. she is Tereifah. Her Shechitah did not permit the child, so its own Simanim permit it. When Shechitah permitted the mother, the child is already slaughtered. Chachamim require Shechitah only due to Mar'is Ayin (lest onlookers think that he transgresses). Its child has only two half-Simanim.

Ran (25a DH v'Garsinan Tu): Rashi explains that Rav Mesharshiya says that there is no Heter because it is as if the child has only one Siman of Shechitah. The other Siman was already slaughtered, for Shechitah does not apply to a Ben Peku'ah. We must slaughter two Simanim. We cannot join them, for this is the ultimate delay in Shechitah. The first Siman was slaughtered from birth! Rav Mesharshiya argues with what was said above that there are four Simanim (its two, and its mother's two).

Rebuttal (Ran): If so, there is a contradiction in the Halachah, for we hold that the Torah gave four Simanim of Shechitah! The Gemara connotes that the Halachah follows Rav Mesharshiya, for no one argues with him! Above (69a) the Gemara asked from Rav Mesharshiya. Rather, there are four Simanim of Shechitah regarding a Tereifah mother. Since her Simanim were not Metaher the fetus, he has his own Simanim. However, when her Simanim permitted him, it is as if his Simanim were slaughtered. A proof is that above (68b) we say that if a limb left the womb at the time of Shechitah, it is permanently forbidden. We cannot slaughter the child to permit the limb.

Ran (DH v'Garsinan): Ada's Ben Peku'ah became Tereifah. Rashi explains that it could not live any more. Rav Ashi told him to slaughter it, like Chachamim, since it had stepped on the ground. Since letter of the law it is permitted without Shechitah, and Chachamim were stringent merely for Mar'is Ayin, Shechitah helps even though it is Tereifah. Mar'is Ayin does not apply to Tereifah, for not everyone knows the laws of Tereifah. The Rashba says that perhaps even if the Shechitah was invalid due to Chaladah (the knife was covered) or Drisah (pressing), it is permitted, for onlookers do not know of the Chaladah or Drisah. If one asks, we tell him the laws of Shechitah, just like we say about Tereifah. Others say that since we require Shechitah, all laws of invalid Shechitah disqualify. It seems that this is correct.

Poskim

Shulchan Aruch (YD 13:4): If one slaughtered a Kosher animal and inside was a live nine-month fetus, and it matured and mated with a regular animal, the resulting child cannot be permitted through Shechitah.

Beis Yosef (DH Ben): Also the Rashba rejected Rashi. He says that we should be concerned for the opinion that is concerned for the father. (Regarding Oso v'Es Beno) the Rambam was unsure whether we are concerned for the father. I do not know why he omitted Rav Mesharshiya's law.

Shach (12): Even though Shechitah permits a Ben Peku'ah taken from a Tereifah mother, here, since the father was a Ben Peku'ah, his Simanim are considered slaughtered. If so, if a Ben Peku'ah from a Tereifah mother mated with a regular animal, the child is normal, and Shechitah permits it. This is why the Shulchan Aruch said 'in a Kosher slaughtered animal.'

Taz (9): From the father's side, it was already slaughtered. Form the mother's side, it was not yet slaughtered, so it must be slaughtered. The same applies to a Bas Peku'ah that mated with a regular animal. If the mother was slaughtered with the child inside, even if the child later stepped on the ground, the child was already permitted. It requires Shechitah only for Mar'is Ayin. This is Version #2 of Abaye (if it is doubly bizarre, no Shechitah is needed).

Mishbetzos Zahav: Meforshim asked, when the mother was a Bas Peku'ah, why does it help if she was slaughtered with the child inside? She was slaughtered from birth! Granted, when the father was a Ben Peku'ah, the child is permitted through the mother's Shechitah, even though its own Shechitah would not help, just like Shechitah of the mother permits a dead fetus. The Pri To'ar (12) says that it is a Gezeras ha'Kasuv that whatever is found in an animal may be eaten, since it was not born. It seems that this is even if the mother was torn, and not slaughtered. Even if it grew (after the mother was torn), it is not a problem. All disagree with this.

Shach (14): The Tur and Shulchan Aruch mentioned that the child was born. It seems that if it was found in its mother after slaughter, it is permitted like a regular Ben Peku'ah. The Bach says that similarly, a fetus found in a slaughtered Bas Peku'ah is permitted. It requires Shechitah only for Mar'is Ayin. He learns from Version #2 of Abaye. He holds that it discusses this case. We do not say that since mid'Oraisa, the mother does not require Shechitah, but her fetus needs Shechitah if we are concerned for the father, her Shechitah does not permit her fetus. Rather, "Kol bi'Vhemah Tochlu" teaches that whenever we may eat the mother, we may eat what is inside her. This is astounding. Really, Version #2 discusses a Kalut Ben Peku'ah in a Kalutah, and the mother is not a Bas Peku'ah, rather, her stomach was torn and the Kalut was found inside. However, if a fetus was found inside a Bas Peku'ah that mated with a regular animal, since she does not need Shechitah, it would not permit her fetus. It is as if her fetus was born, and he has only one Siman. "Kol bi'Vhemah Tochlu" includes only when Shechitah permitted the mother.

Shulchan Aruch (ibid.): If the Ben Peku'ah mated with another Ben Peku'ah, the child and grandchild and all generations have the same status. Mid'Rabanan, all of them must be slaughtered. Tereifos do not disqualify them.

Shach (15): This is even if the children are born normally, just they mate with other Peku'os or Benei P. Gra (10): The Gemara (i.e. Ze'iri) said that R. Shimon Shezuri (permits all offspring without Shechitah, but R. Yochanan says that he permits only the Ben Paku'a itself, but the child must be slaughtered), and all the more so Rabanan (obligate Shechitah of the child). R. Yochanan taught this only according to R. Shimon Shezuri (but the Halachah follows Chachamim).