Eidim Zommemin (first set) on Eidim Zommemin (second set)?

Question

Eidim Zommemin are conspiring witnesses, which have a whole Perek of Gemara that talk about them: the first perek in Makkot.

My question is: the first set says edut. The second one claims they are conspiring witnesses and with them on that date in a certain location. What happens if the first set then says that the second was with them at the incident?

i.e. the second set claims they were in Chevron, and the first one claims they were in Los Angeles, and that the second set was with them in Los Angeles.

If this were possible, it would create a huge problem for the halacha of eidim zommemin - the first set could just say that the second was with them in a different place.

So, is this possible?

Answer 1

No, this is not possible.

Once the second set of witnesses testifies that the first pair is lying, the first witnesses become invalid witnesses and cannot testify anymore.

Sanhedrin 27a:

עד זומם אביי אמר למפרע הוא נפסל ורבא אמר מיכן ולהבא הוא נפסל

Concerning a conspiring witness: Abaye says: He is disqualified retroactively, from when he provided his testimony. Any testimony he may have provided after that point in time is retroactively nullified. And Rava says: He is disqualified only from that point forward, i.e., from when he was established to be a conspiring witness, but not retroactively from when he provided his testimony.

Thus, once the second set testifies, the first set cannot simply add the location of the second witnesses to their testimony, as they are no longer believed in court.