Rif Brachot 33b

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33b

{Brachot 45b continued}
Rav Papa said: Amen.

And they do not argue. {It depends at what point he enters.} This was where he found them saying Baruch, and this is where he found them saying Nevarech.

For if he found them saying Nevarech, he says Baruch UMvorach. If he found them saying Baruch, he says Amen.

One brayta taught: One who answers Amen after his own blessing {of Birchat HaMazon} is to be commended, and another brayta taught: is reprehensible.
It is not a contradiction.
This is where he answers Amen after every blessing; That is where he answers Amen after Bone Yerushalayim. {the third blessing}

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Yerushalmi perek Ain Omdin LeHitpallel {Brachhot 5th perek}:
Tnei {a brayta}: One who is pores on {Rif: Al; Our girsa: Et} Shema {Rashi: 1/2 of the blessings of Shema - that is, the devarim sheBeKedusha; alternatively, Rambam: prepare, spread out; Geonim: begin; Meiri: bless}, and one who passes before the ark {to lead prayers} and one who raises his hands {for the priestly blessing}, and one who reads the Torah, and one who says the Maftir from Navi, and one who blesses on any of the mitzvot mentioned in the Torah, should not answer after himself Amen. And if he answers he is a boor. There is another version that learns: he is a Chacham {wise man}.

Rav Chisda said: The one that says that he is a boor refers to one who answers after each blessing {of Birchat HaMazon}. And the one who says he is a Chacham refers to one who answers at the end {that is, of Birchat HaMazon}. {The Rif, BTW, has the reverse order of Chacham and boor than we have in our girsa.}

{Brachot 46a}
Rabbi Yochanan cited Rabbi Shimon ben Yochai: The host breaks the bread so that he should do so generously, and the guest says grace so that he should bless the host.
What should he bless?
May it be Your Will that the host is not shamed, not in this world, nor in the next world.

Rabbi added some items to it: and he should succeed greatly in terms of all his possessions, and his possessions {estate} should be successful and near to the city, and there should not come before him or us any sinful or iniquitous thoughts, and the Satan should not rule in any of our handiwork, from now until eternity.

Until when is the blessing of the zimmun?
{Rashi: When three, as opposed to two or one say it, how much do they say? -- but then there will be a problem in Rav Sheshet's statement. Tosafot says: Until when does one who broke off in order to answer with the other two have to wait before resuming his meal? We will see this Rif says similar to Tosafot.}
Rav Nachman said: Until Nevarech.
Rav Sheshet said: Until Hazan.

That is to say, that if three people ate together, and one of them needs to leave, that he sits until they say Baruch SheAchalnu MiShelo Uvtuvo Chayinu, and then leaves, for this is the Birchat HaZimmun. And Rav Sheshet said: Until HaZan Et HaKol.

And we say {in the gemara}: Let us say this is like a Tanaitic dispute.
For one brayta taught: Two or three (*who ate, they bless Birchat HaMazon)
{The starred section should be removed - there are variant girsaot in play, and this would correspond to Tosafot. Our gemara speaks of two or three blessings}
And the other brayta taught: Three or four.
Is it not that all agree that HaTov VeHaMeitiv {the fourth blessing} is not Biblical, and they argue in this - that the one who said Two or Three holds until HaZan {is the Birchat HaZimmun}, and the one who said Three or Four holds until Nevarech.