The Mishnah (4:5) teaches that there are six sefiekot, cases of doubt involving tumah and terumah, that the Chachamim rule that the tumah should be burnt. There is a mitzvah to preserve terumah -- mishmeret terumati -- so the ruling of the Mishnah requires thought.
The Tifferet Yisrael notes that normally when considering rabbinic forms of tumah, the Chachamim rule that the terumah cannot be burnt, in order that it is clear that the tumah is rabbinic in origin. In this case however, it is different. For example, we will discuss the first case of tumat beit ha'pras. Recall that the beit ha'pras is a field in which a grave has been ploughed through. The concern is that a small bone from the corpse may have been dragged along by the plough a significant distance. The Chachamim therefore treated the area of concern within the field as being tameh. The first case in the Mishnah is if terumah entered a beit ha'pras. The Tifferet Yisrael explains that if the terumah was indeed located in a place that was tameh, it would have been tameh on a biblical level. The same can be said for the other cases listed in the Mishnah also. It is for this reason that the Chachimim treated these case differently and ruled that the terumah must be burnt. (See the Mishnah Achrona.)
The question may still be asked. Since these are cases of doubt, how can the Chachamim allow the terumah to be burnt?
The Sefer HaTerumah (Hilchot Eretz Yisrael 5) explains that the terumah we are discussing in the Mishnah is rabbinic terumah, e.g. produce that was grown in pot without a hole. Since the terumah is rabbinic, they were lenient in these cases of doubt to allow them to be burnt. If however the question was regarding terumah on a biblical level, unless we knew for certain that the terumah became tameh, it would be forbidden to burn it.
R' Efraim however disagrees. He understands that the Torah's requirement of mishmeret terumati only demands that one prevent the terumah from becoming tameh. It however does not prohibit one from burning terumah. His proof is from erev Pesach, where we allow one to burn chametz that is terumah, already from the time that chametz is prohibit only on a rabbinic level. If it is prohibited to burn terumah, then the Chachamim should not be allowed to require burning terumah early.
It is important to note that the Tosfot (Pesachim 13a) explains that there is no problem burning the chametz terumah at that time even if you consider burning a violation of mishmeret terumati. This is because since it would became assur a short while later anyway, mishmeret terumati would not apply.
The comment of the Tosfot leads us to an interesting third position brought in the Minchat Elazar. He explains, that since the Chachamim forbade the consumption of terumah in these six cases, even though on a biblical level the do not require burning, they can still be burnt since mishmeret terumati would not apply to this terumah that cannot be consumed.
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