Mishnah 5 in chapter 15 of Tractate Yevamos deals with two co-wives who went overseas together with their husband and returned without him, where their testimony about his death contradicts one another.
The first case - one says he died and one says he did not die:
A man had two wives and traveled with them overseas, and both of them returned without him: one testifies that the husband died, and the other testifies that he did not die. The Mishnah rules:
"Zo she'omeres meis - tinasei v'titol kesubasah" - the one who says he died may marry, and she even collects her kesubah. As we learned earlier in the name of Beis Shammai, and Beis Hillel agreed with them that she collects the kesubah as well.
"V'zo she'omeres lo meis - lo tinasei v'lo titol kesubasah" - the one who says he did not die may not marry, and she does not collect her kesubah either.
The one who says "he died" need not be concerned about her co-wife's denial, because, as we learned in the previous Mishnah, a co-wife is not believed to testify either way: just as she is not believed to testify that the husband died, so too she is not believed to testify that he did not die.
The Gemara adds that even if the one who said "he did not die" retracts and admits, "I only said that in order to distress my co-wife, but in truth he did die" - she is not believed. Once those words left her mouth, she is no longer trusted.
The second case - one says he died and one says he was killed:
"Achas omeres meis v'achas omeres neherag" - one testifies that he died a natural death and the other testifies that he was killed. Both of them thus agree that he is no longer alive, but they differ about the circumstances of his death. The Tannaim disagree about this case:
Rabbi Meir: "Ho'il u'machishos zu es zu - harei elu lo yinasu". Since their testimonies contradict each other on the facts, neither of them may marry.
Rabbi Yehudah and Rabbi Shimon: "Ho'il v'zu v'zu modos she'eino kayam - yinasu". Since both of them admit that he is no longer alive, even though they differ as to how it happened, they are permitted to marry.
The Gemara explains that Rabbi Meir, who forbids even where they differ only about the manner of death, disagrees with the opening clause as well: if they may not marry when they differ over a detail that is not essential, such as the way he died, all the more so when they differ over whether he died at all. The earlier Tannaim, for their part, disagree even in that case and hold that both are permitted to marry, since both admit that he died, and the dispute is only over how.
The third case - contradictory testimony of one witness against another:
"Ed omer meis v'ed omer lo meis, ishah omeres meis v'ishah omeres lo meis - harei zo lo tinasei" - one witness says he died and one witness says he did not die, one woman says he died and one woman says he did not die: she may not marry. The Mishnah is dealing with a case where both witnesses came at once, or even where the one who testified to the death came first, but the court had not yet ruled on the basis of his testimony and the woman had not been formally permitted to marry.
Since the permission had not yet been granted, and the second witness came and contradicted the first, we are faced with two contradictory testimonies before she was permitted, and therefore she may not marry. This differs from the situation in the previous Mishnayos: there, if she had already been permitted to marry on the strength of one witness, and afterward another witness came and contradicted him - once she was permitted, she remains permitted. Here, by contrast, the testimonies came together or in close succession, before permission was granted, and therefore she does not marry.