Rejection (and Answer #3 - Reish Lakish): No, the Mishnah discusses an Av and a Vlad mid'Oraisa;

R. Meir learns from the words of R. Eliezer and R. Yehoshua.

Question: From which words of R. Yehoshua does he learn (see (f) below)?

Answer #1 (Mishnah - R. Eliezer): If a barrel of Terumah is Safek Tamei:

If it was in an open place (it is prone to become Vadai Tamei), we put it in a hidden place; if it was exposed, we cover it [to guard it from Tum'ah];

R. Yehoshua says, if it was in a hidden place, we put it in an open place; if it was covered, we expose it. (Rashi - one may do so; R. Chananel - one should help it to become Vadai Tamei, for then a Kohen may use it, e.g. he may burn oil or spray wine on the floor to give a nice aroma.)

Rejection: R. Yehoshua permits only Gerama (causation) - he does not permit to overtly Metamei!

Answer #2 (Mishnah): If a barrel of Terumah wine broke in the upper winepress and it is about to fall into Tamei Chulin below, R. Eliezer and R. Yehoshua agree that if one can save a Revi'is in Taharah, he must do so;

If he cannot - R. Eliezer says, he must allow the Terumah to fall [even though it will mix with the Chulin, become Tamei and forbid it all even to a Kohen]; he may not actively Metamei it (e.g. catch it in a Tamei vessel);

R. Yehoshua says, [in order to save the Chulin] he may actively Metamei the Terumah.

Question: If so, R. Meir learns only from R. Yehoshua - he should have said 'We learn from his words' (instead of 'from their words)!

Answer: He means, we learn from their argument (the rule is that the Halachah does not follow R. Eliezer).

Support (Mishnah - R. Yosi): R. Eliezer and R. Yehoshua agree [that each is burned by itself... - this shows that R. Meir learned from them.]

Rav Nachman also answered like Reish Lakish.

Question (Rava - Beraisa - R. Yosi): What you seek to learn is unlike your source!

Our teachers testified about burning meat [or oil] that was Nitma [or Nifsal] through a Vlad ha'Tum'ah [or a Tevul Yom] with meat [or oil] that was Nitma through an Av ha'Tum'ah - I agree that we may burn Terumah that was Nitma through a Vlad ha'Tum'ah with Terumah that was Nitma through an Av!

But how can we burn even Taluy Terumah with Tamei - perhaps Eliyahu will come and tell us that it was Tahor!

Beis Shamai say, [Kodshim that are] Pigul (an Avodah was done with intent to eat the meat or throw the blood after the allowed time), Nosar and Tamei may not be burned together;

Beis Hillel permit burning them together.

Summation of question: If R. Meir learns from R. Yehoshua, why does R. Yosi challenge him from R. Chanina?!

Answer (Rav Nachman): R. Yosi originally thought that R. Meir learns from R. Chanina [and challenged him] - when R. Meir answered that he learns from R. Yehoshua [regarding wine falling into the winepress], R. Yosi challenged also this, for R. Yehoshua and R. Eliezer agree that each is burned by itself.

Question: Why can't we learn from R. Yehoshua - it is just like burning Tahor and Tamei together!

Answer: It is different - R. Yehoshua permits to avoid a loss of Chulin.

Question (R. Yirmeyah): Also in our Mishnah, R. Yehoshua requires burning separately even though this entails a loss, i.e. extra wood is required!

Answer (an elder): Chachamim were concerned for a large loss, but not for a small loss.

(Rav Asi citing R. Yochanan): They (R. Meir and R. Yosi) argue about during the sixth hour [on Erev Pesach], but all permit burning together from the start of the seventh hour [when Chametz is forbidden mid'Oraisa].

Question (R. Zeira): Does R. Yochanan hold that the Mishnah discusses an Av ha'Tum'ah mid'Oraisa and a Vlad mid'Rabanan, and that R. Meir learns from R. Chanina?

Rav Asi: Yes!

(R. Yochanan): The Mishnah discusses an Av mid'Oraisa and a Vlad mid'Rabanan; R. Meir learns from R. Chanina;

They argue about during the sixth hour, but all permit burning together from the start of the seventh.

Support (Beraisa - Beis Shamai): Pigul, Nosar and Tamei may not be burned together;

Beis Hillel permit burning them together [because all are forbidden mid'Oraisa].

Rejection: There is different, for all of them are Tamei mid'Rabanan (but Chametz is not Tamei even when it is forbidden):

(Mishnah): Pigul, Nosar and Tamei are Metamei the hands.

Support (Beraisa): If bread became moldy and is not fit for people to eat but dogs can eat it, it has Tum'as Ochlim if it is k'Beitzah (the size of an egg; Rishonim argue about whether this Shi'ur is needed for solid food to Metamei or to Mekabel Hechsher or to Mekabel Tum'ah), and [even if it is Terumah] it may be burned with Tamei [Chametz] on [Erev] Pesach.

Rejection: There is different - [since it is not fit for people to eat], it is like dirt (it lost Kedushas Terumah).

Question: If R. Meir learns from R. Chanina, why does it say 'R. Eliezer and R. Yehoshua agree...'?

Answer: R. Yosi says, even R. Yehoshua is lenient only about Tahor and Taluy - he does not allow Tahor and Tamei together.

Question: If R. Meir learns from R. Chanina, why does R. Yosi say 'We may not learn this' - we should be able to learn [regarding the sixth hour, when also Chametz is forbidden mid'Rabanan - since R. Yosi agrees about the seventh hour, this shows that he does not distinguish Tum'ah from Isur]!

Answer (R. Yirmeyah): The case is, the meat was Nitma through a liquid that was Nitma by a (Rashi - Keli that touched a) Sheretz:

R. Meir holds like he taught elsewhere, that liquids Metamei other things only mid'Rabanan [therefore, Chametz is just like R. Chanina's case];

R. Yosi holds like he taught elsewhere, that liquids Metamei other things mid'Oraisa [therefore, Chametz is unlike R. Chanina's case].