Answer #2 (Rav Papa): They argue about whether Bnei Yisrael offered Nesachim in the Midbar.

(The Torah commands to bring Nesachim upon entering Eretz Yisrael. Chachamim hold that Nesachim were already brought in the Midbar. We must say that upon entering, Nesachim will be brought (also) on private Bamos (which will become permitted), i.e. without Klei Shares. Therefore, one is liable for Ha'alas Chutz of water, even without a Kli Shares. R. Elazar holds that Nesachim were not brought in the Midbar. The Torah commands to bring Nesachim in the Mikdash in Eretz Yisrael, i.e. in Klei Shares; therefore, there is no source to obligate for water (b'Chutz) unless it was Hukdash in a Kli Shares.)

Answer #3 (Ravina): (All agree that Nesachim (of wine) were brought in the Midbar, and on private Bamos in Eretz Yisrael without Klei Shares. Therefore, one is liable for Ha'alas Chutz of wine, even without a Kli Shares.) They argue about whether we learn Nisuch ha'Mayim from Nisuch of wine.

(Beraisa): One who is Menasech three Lugim of water outside is liable;

R. Elazar b'Rebbi Shimon says, this is only if they were Hukdeshu in a Kli Shares.

Question: What do they argue about?

Answer #1 (Rav Ada bar Rav Yitzchak): They argue about a heaping measure (above the rim. Chachamim say that the excess is Mekudash, and R. Elazar b'Rebbi Shimon says that it is not.)

Answer #2 (Rava brei d'Rabah): They argue about whether Nesachim are offered on a Bamah, like the following Tana'im argue:

(Beraisa - Rebbi): Nesachim are not needed on a private Bamah;

Chachamim say, they are required.

These Tana'im argue as the following Tana'im do;

(Beraisa - R. Yishmael): "Ki Savo'u (...v'Yayin la'Nesech)" teaches that Nesachim must be brought on a Bamas Tzibur;

Suggestion: Perhaps it rather teaches that they must be brought on a Bamas Yachid!

Rejection: "El Eretz Moshvoseichem Asher Ani Nosen Lachem" refers to a Bamah that is for everyone.

R. Akiva says, "Ki Savo'u" teaches that Nesachim must be brought on a Bamas Yachid;

Suggestion: Perhaps it rather teaches that they must be brought on a Bamas Tzibur!

Rejection: "El Eretz Moshvoseichem" refers to a Bamah that applies in all your dwellings, i.e. a Bamas Yachid.

R. Yishmael holds that Nesachim were not offered in the Midbar. R. Akiva holds (Panim Me'iros; Sefas Emes - could hold) that they were offered in the Midbar.

(Mishnah - R. Nechemyah): One who offers Shirayim of blood b'Chutz is liable.

(R. Yochanan): R. Nechemyah holds like the opinion that Shirayim are Me'akev.

Question (Beraisa - R. Nechemyah): One who offers Shirayim b'Chutz is liable;

R. Akiva: Shirayim are a remnant of the Mitzvah (they are not Me'akev)!

R. Nechemyah: One is liable for limbs (of an Olah) and Chelev, even though they are only remnants!

R. Akiva: No previous Avodah was done with limbs and Chelev, so you cannot bring a proof from them to Shirayim of blood!

Summation of question: According to R. Yochanan, R. Nechemyah could have answered that Shirayim are Me'akev!

(Seemingly,) R. Yochanan is refuted.

Answer: We can answer for R. Yochanan according to Rav Ada:

(Rav Ada bar Ahavah): They argue about inner Shirayim (e.g. of inner Chata'os), but all agree that outer Shirayim (of most Korbanos, of the outer Mizbe'ach) are not Me'akev.

R. Yochanan teaches that R. Nechemyah holds like the opinion that inner Shirayim are Me'akev. The Beraisa discusses outer Shirayim.

Question: If so, R. Nechemyah should have told R. Akiva 'I obligate only for inner Shirayim, but not for outer Shirayim!'

Answer: R. Nechemyah answered R. Akiva according to R. Akiva's reasoning (that no Shirayim are Me'akev).

(Mishnah): If one did Melikah inside (the Mikdash) and offered the bird outside, he is liable (for Ha'alas Chutz);

If Melikah and Ha'alah were b'Chutz, he is exempt (for both of these);

If Shechitah was inside and Ha'alah was b'Chutz, he is exempt for Ha'alas Chutz;

If Shechitah and Ha'alah were outside, he is liable (for both).

The method that is Machshir inside (i.e. Melikah), if it was done outside (it disqualifies the bird, therefore), it exempts (from Ha'alas Chutz);

The method that is Machshir outside (Shechitah), if it was done inside, exempts (from Ha'alas Chutz).

R. Shimon says, if one is liable for an act outside, he is liable for Ha'alas Chutz after the same act was done inside;

The only exception is Ha'alas Chutz after Shechitah inside.

(Gemara) Question: How can we say that Shechitah is Machshir outside? It disqualifies (Korbanos Of)!

Answer: Here, 'Machshir' means that it enables one to be liable (for Ha'alas Chutz).

(Mishnah - R. Shimon): (If one is liable...)

Question: Which law does R. Shimon argue about?

Answer #1: He argues about the first law. Chachamim obligate (for Ha'alas Chutz) when Melikah was inside, and they exempt when Melikah was outside;

Answer #1A: R. Shimon says, just like one is liable when Melikah was inside, also when it was outside.

Rejection: If so, R. Shimon should not have said 'if one is liable outside (...he is liable inside)', rather, 'if one is liable inside (...he is liable outside')!

Answer #1B: Rather, he says that just like one is exempt when Melikah was outside, also when it was inside.

Rejection: If so, R. Shimon should not have said 'if one is liable outside (...he is liable inside)', rather, 'if one is liable inside (...he is liable outside')!

Answer #2: Rather, he argues about the Seifa. Chachamim exempt (for Ha'alas Chutz) when Shechitah was inside and obligate when it was outside;

Answer #2A: R. Shimon says, just like one is exempt when Shechitah was inside, also when it was outside.

Rejection: If so, he should have said 'if one is exempt inside...'!

Answer #2B: Rather, he says, just like one is liable when Shechitah was outside, also when it was inside.

Rejection: R. Shimon concludes that the only exception is Ha'alas Chutz after Shechitah inside (he is exempt!)

Answer #3 (Ze'iri): They argue about a Behemah slaughtered at night;

The Mishnah means, if one slaughtered a Behemah at night inside and offered outside, he is exempt;

If it was slaughtered at night outside and offered outside, he is liable;

R. Shimon says, just like one is liable when Shechitah was outside, also when it was inside. The only exception is Ha'alas Chutz of a bird.

Answer #4 (Rava): They argue about Kabalah in a Chulin Kli;

The Mishnah means that similarly, if Kabalah was in a Chulin Kli in the Mikdash and the Korban was offered outside, he is exempt;

If Kabalah was in a Chulin Kli b'Chutz and it was offered outside, he is liable;

R. Shimon says, just like one is liable when it was done outside, also when it was inside. The only exception is Ha'alas Chutz of a bird slaughtered inside.

The following suggests another answer.

(Shmuel's father - Beraisa): If Melikah was done inside and the bird was offered outside, he is liable;

If Melikah and Ha'alah were b'Chutz, he is exempt;

R. Shimon obligates.

Answer #5: R. Shimon discusses this case. The text should say 'whenever one is liable (for Ha'alas Chutz) for an act done inside (e.g. Melikah), he is liable if the act was done outside.' (This suggests that when one is exempt for an act inside, he is exempt outside. Therefore, R. Shimon adds 'except for Ha'alas Chutz of a bird slaughtered inside', for which he is exempt, but if it was slaughtered outside, he is liable.)

(Mishnah): If the blood of a Chatas was received in one bucket:

If some of the blood was thrown outside and then some inside, or vice-versa, he is liable, for all of the blood is Kosher for Zerikah inside;

If the blood was received in two buckets -

If both were thrown inside, he is exempt;

If both were thrown outside, he is liable (for each one, e.g. if he remembered in between);

If one was thrown inside and then the other outside, he is exempt;

If one was thrown outside and then the other inside, he is liable for the former, and the latter is Mechaper. (The Korban is Kosher, and he was Yotzei.)

This is similar to one who was Makdish his Chatas, lost it, made another Hekdesh, and then found the first;

If he slaughtered both of them inside, he is exempt;

If he slaughtered both of them outside, he is liable (for each one);

If he slaughtered one inside and then the other outside, he is exempt;

If he slaughtered one outside and then the other inside, he is liable for the former, and the latter is Mechaper;

(When both were slaughtered inside,) just like Zerikah (of the first) exempts the meat of that animal (from Me'ilah), it exempts the meat of the other animal, too.