How is the law in a case of multiple edim zomemim justified by Chachomim?

Question

Mishna Makkos 1 (5) describes the case of witness who are zomemim.

The mishna according to Chachomim (with whom the halacha goes) says

If others [i.e. another pair of witnesses] come and are proven [a prior pair] to be zomemin, and [still] others come and prove them to be zomemin, even [if this occurs] one hundred [times], all of them are executed.

This means that Set 1 are shown to not have been present when the murder took place because Set 2 says that Set 1 were with them somewhere else. Set 1 are put to death.

Later Set 3 accuse Set 2 of not being present with Set 1 because they were present with them somewhere else. So Set 2 are are put to death.

Now we look back and see that Set 1 were put to death wrongly.

Rabbi Yehudah would only put to death Set 1 because (Bartenura) he holds that after the first group is categorised as zomemim, the testimony of a second group that comes is no longer accepted, and if [a second group does in fact] testify and is categorised as zomemim, they are not killed.

How can Chachomim justify that Set 1 were put to death wrongly?

Answer 1

You are interpreting the Mishna incorrectly.

As the Bartenua already teaches us:

ואפילו היו מאה. כתות שהעידו זו אחר זו בעדות אחת וכת אחת הזימה את כולן, כולן יהרגו:‏

Even if there were a hundred. pairs that testified one after the other with one testimony and one pair zommemizes all of them, all of them are killed.

The Rambam learns the Mishna the same way, as does Rashi in the Gemara.

I.e. Set 2 accuses Set 3 and Set 4 and all further sets of witnesses to all be Zomemim.

This should take care of your question.

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The question on this Mishna should be on Rabbi Yehuda:

רַבִּי יְהוּדָה אוֹמֵר, אִסְטָסִית הִיא זוֹ, וְאֵינָהּ נֶהֱרֶגֶת אֶלָּא כַת הָרִאשׁוֹנָה בִלְבָד:‏

Rabbi Yehuda says, this is a conspiracy, and only the first group [of witnesses] is executed.

What is Rabbi Yehuda's problem? Surely we don't simply put the zomemized sets of witnesses to death; surely Bet Din has to cross-examine both sets thoroughly, like any death sentence.

So why is Rabbi Yehuda worried? Why doesn't he rely on this Bet Din anymore?