(Mishnah): Witnesses only become false witnesses when they themselves are proved to be false...

How is this? If they testified that Ploni murdered and a second set of witness say to them, "How can you testify, since the victim or the murderer was with us elsewhere on that day!" - they are not false witnesses.

But if they said, "How can you testify as you were with us elsewhere (at the time of the murder)" - they become false witnesses and are killed based on the testimony of the second set. If a third set came (and testified to the murder) and the second set disproved them; and then a fourth set came and again the second set disproved them; even if there were 100 such witnesses, they are all put to death.

(R. Yehuda): This is a conspiracy and we only kill the first set.

(Gemara - R. Ba bar Mamal): (If it is a conspiracy, why even kill the first set?) The ruling of R. Yehuda only applies when the first set were killed before the other sets came, but if they were not yet killed, you do not even kill that first set. This can be proven from the Mishnah that taught that, "they only kill the first set" - this shows that they had already killed them before the second set had been identified as conspiring; but if they had not yet killed the first set before they second had been shown to be conspiring, they are not believed to kill the first set.

Question (R. Bun bar Chiya to R. Zeira): If two people were testifying that Ploni killed someone in Lod on the 5th of the month; and a 2nd set came and said that they cannot testify since they were with them on that 5th of the month in Kisari (and it would be impossible to travel so quickly from Kisari to Lod unless they were on an incredibly swift camel). If a 3rd set came and said to the 2nd set that they cannot testify since they were with them on the 10th of the month in Tzipori (which cannot be reached from Kisari with regular travel)...

Do we say that the murderer is not killed as perhaps the witnesses are false and the witnesses are not killed as perhaps they were telling the truth? (Note: This question remains unanswered.)