Clarification: Rashi explains that this a Machlokes in Perek ha'Techeiles (Menachos, 39a & 39b).

Refutation: This is not correct however, since the Gemara concludes there that the top knot is d'Oraysa!

Explanation #1: Rashi explains 'If Beis-Din in Lishkas ha'Gazis were asked; they answered them and he returned to his town where he remained until the Sanhedrei Gedolah were exiled.

Question: The question remains however, how they could then wait until Yom-Tov and carry out the death-penalty, seeing as Sanhedrin was in exile, and we have learned in Perek Hayu Bodkin (earlier on Daf 41a) that as long as Beis-Din are in exile, they cannot judge Dinei Nefashos?

Suggested Answer: And if you will say that on Yom-Tov Beis-Din ha'Gadol would return to the Lishkas ha'Gazis and issue the death-sentence, even after having already gone into exile ...

Refutation #1: ... Firstly, that would mean that Raban Yochanan ben Zakai actually sat on the Sanhedrin, whereas the Gemara in Perek Hayu Bodkin (ibid.) implies that this was not the case.

Refutation #2: Secondly, where is then the 'Inuy ha'Din', which is only applicable if they waited after the final death-sentence has been issued ...

Proof: ... as is evident in Perek Echad Dinei Mamonos (Daf 35.) where the Gemara asks 'Let them conclude his Din on Shabbos and kill him ... '? Then after answering 'Atah Me'aneh es Dino!', it asks 'Let them judge him on Erev Shabbos ... ?'

Refutation #3: Thirdly, why does the Gemara then state specifically Zakein Mamrei, since it will apply equally to other sinners too?

Refutation #4: And fourthly, why specifically Yavneh, why not the Beis-Din in the 'shop' (the first of Beis-Din's ten exiles - see Rosh Hashanah 31a & b)?

Pushed Answer: And to say that regarding a sin that was performed before Beis-Din went into exile they judged even whilst in exile is a Dochek, and we don't say that it is the location that auses it.

Explanation #2: Rabeinu Tam therefore explains that the Gemara speaks where the death-sentence was issued already before the Sanhedrin went into exile.

Implied Question #1: Firstly, this sin does not constitute a La'av ...

Implied Question #2: Secondly, no act was performed (So how can he receive Malkos)?

Answer: The Din therefore is that Beis-Din beat him until he submits, like somebody who refuses to build a Succah.

Explanation #1: This implies that he was prophesying in the Name of Hakadosh-Baruch-Hu, and that, since he was an established Navi, he was believed even though he did not produce a sign.

Source: In Perek ha'Ishah Rabah (Yevamos, 90b & 91a) we learn from the Pasuk "Eilav Tishme'un" that one must obey him even if the Chachamim tell you to go and contravene one of the Mitzvos of the Torah, just like Eliyahu did on Har ha'Carmel.

Question #1: How can the Geara there then ask that we should learn from there? Since, as we just explained, his prophesy was from Hash-m, how can we learn from there to transgress, when it is based on a Takanah de'Rabbanan which is not by Divine command?

Question #2: Furthermore, why do we need to come on to the fact that Eliyahu was an established Navi, since even if he was not a Navi, Beis-Din have a mandate to permit transgression in order to strengthen the law (to protect it against laxness)?

Answer: The Gemara there extrapolates from the Lashon of the Beraisa, which says 'Everything goes according to the time', implying that it all depends according to the current needs of that time'. Now if it was referring to a Divine Decree, of what significance would the current need be? Necessary or not, one would need to fulfill the command of Hash-m?

Explanation #2: The Beraisa must therefore maintain that the Pasuk is speaking about a Navi who acted of his own accord.

Clarification: And the reason that our Gemara requires Eliyahu to have been an established Navi is so that the people could rely that he would indeed bring down fire, to go ahead and Shecht Kodshim outside the Beis-Hamikdash based on his promise, that through his merit and his Tefilah fire would descend from Heaven, and that this would indeed strengthen the law, to publicly sanctify Hash-m's Name and bring Yisrael back into the fold.

Implied Question: The Pesukim however, imply that he acted under Divine instructions, as Eliyahu himself said "And it is through Your word that I did this ... ", and Rashi Me'or ha'Golah explains in his commentary tqo Nevi'im 'And I acted according to Your word, to sacrifice at a time when Bamos were forbidden'?

Answer: We must therefore say that, since through the Divine command it is permitted (to transgress) due to the needs of the moment, it is also permitted even without the Divine command, since, as the Gemara states in the first Perek of Megilah, 2b 'A Navi is not permitted to present anything new'.

Explanation #3: One can also answer that, when Eliyahu said that what he did, he did by the command of Hash-m, he did not mean that Hash-m commanded him to do it, but rather, he was referring to Hash-m's words to Ya'akov "a nation and an assembly of nations will descend from you", which Chazal interpret to mean that his children would act like the Nochri nations to Shecht outside the Beis-Hamikdash and that He (Hash-m) would give His stamp of approval. And because he (Eliyahu) was an established Navi, they relied on him when he told them that that Pasuk referred to him.