(Baraisa): Payments for Terumah - one may not pay other payments of principal and the extra fifth from them, nor does one pay the principal and extra fifth for them. They are not obligated in Challah and hands do not cause them impurity even though the Chachamim decreed that if a Tevul Yom touches actual Terumah, he renders it impure. And even R. Shimon and R. Yosi agree to this (even though they say that if a Chulin dough became mixed with Terumah sourdough, it can become impure from a Tevul Yom).

If the Kohen wishes to waive the payment, he may not do so before the Yisrael separates the payment; but once he separated it, and before the Kohen had acquired it, if the Kohen waived the payment, the Yisrael ate it - it is a dispute between Rebbi and R. Elazar b'R. Shimon, as the Baraisa taught...

(Baraisa) (Rebbe): The pasuk states (Vayikra 22:14), "...and give the Kohen the holy item'' - its giving (to the Kohen) sanctifies it (and prohibits it to a non-Kohen) but not it's separation, to obligate one who eats it to pay the extra fifth.

(R. Elazar b'R. Shimon): Even its separation sanctifies it to obligate one who eats it to pay the principal and the extra fifth.

If he waived the payment and the Yisrael then ate it, it is a dispute between R. Yochanan and R. Shimon ben Lakish, as they disagreed in the following case - if a Yisrael stole Terumah from his mother's father who is a Kohen - R. Yochanan said that he must pay back the tribe; Reish Lakish said that he can pay himself.

(R. Yona): R. Shimon ben Lakish asked R. Yochanan - Doesn't the Mishnah (later in the Perek) teach that if he stole Terumah of Hekdesh and ate it, he pays two fifths and the principal..? But according to you, he should also pay the Kohen the principal?! (According to you, that it must be given (to the Kohen) rather than just separated, it's not enough just to pay Hekdesh, as through that, he has only fulfilled his obligated for the theft, but not for the required Terumah payment, which must be paid to the tribe.)

Answer (R. Yasa citing R. Yochanan): The Torah said that he fulfils his obligation of Terumah payment by paying the theft.

(R. Zeira to R. Isi): Two things were said in the name of R. Yochanan and where they were said and their sources were not said...

R. Yochanan said that he fulfils his obligation of Terumah payment by paying the theft; but you didn't say his source.

What's the source? The pasuk states (Vayikra 22:14), "...and give the Kohen the holy item'' - once he gives it to the Kohen, he has fulfilled his obligation for the theft.

R. Yochanan said that they must burn the Parah Adumah (Red Heifer) where it was slaughtered; but you didn't say his source.

What's the source? R. Elazar citing R. Hoshiya said, the pasuk states (Bamidbar 19:5), "(The cow shall then be burned in his presence; its skin, its flesh, its blood), with its dung (lit. separated things) he shall burn it''. How is it learned from here?

(R. Yirmiyah citing R. Imi): In the place that 'it was separated' from life, it must be burned.

Question: Do R. Yochanan and Reish Lakish disagree over the same dispute as Rebbi and R. Elazar b'R. Shimon? (R. Yochanan who required actually giving the Terumah to the Kohen would be like Rebbi, that it is the giving that sanctifies, rather than just separating. And Reish Lakish who said that separating is enough, would reason like R. Elazar b'R. Shimon, that its separating sanctifies it.)

Answer (R. Bun bar Chiya): According to Reish Lakish, Rebbi only says this when he is paying back the Kohen because of a theft from the tribe); but if not (such as if he inherited it from his Kohen grandfather), even Rebbi agrees that its separation sanctifies. It's like the Mishnah (in Maseches Bechoros) that teaches that when a person separated a sheep for Pidyon Peter Chamor (redeeming the firstborn donkey) and the lamb died, R. Eliezer says that he must replace it (as his responsibility continues until it gets to the hands of the Kohen). The Chachamim exempt him as they compare it to redeeming Maaser Sheni. (Once a person has separated the money and transferred the sanctity of the Maaser Sheni onto it, he is no longer responsible to replace it.)

R. Eliezer agrees concerning firstborn donkeys inherited from a Kohen's mother's father who was a Yisrael. (Since it was already obligated in the grandfather's house, the Kohen must separate a lamb, which he can then keep for himself. (Here also, according to Rebbi, when it is not given for stealing from the tribe,, he agrees that his separation sanctifies it.

If a person ate the Terumah of a Chaver, he must pay the Chaver. If he stole Terumah from an Am HaAretz, he must pay the Am HaAretz. But how can he give his Taharos to an Am HaAretz? What should he do? Give them both to a Kohen Chaver, who should then takes the value of one of them and give it to a Kohen Am HaAretz.

Question (R. Bun bar Chiya to R. Shimon ben Lakish): It's fine according to the opinion that the payments become Terumah through merely separating; but according to the opinion that the payment becomes Terumah when it is given to the Kohen from whom he ate, he is not atoned until he gives it to the Kohen Am HaAretz?

Answer (R. Shimon ben Lakish): He has someone else acquire it on behalf of the Kohen Am HaAretz.

Question: (The Mishnah (earlier Chulin 87(c)) taught that if the daughter of a Yisrael ate Terumah and then married a Kohen, if she ate Terumah that had not yet been acquired by another Kohen, she pays the principal and extra fifth to herself.) If before she had separated the Terumah, she was divorced, what's the law?

Objection: What's the question? If she had Terumos and Ma'asros when she was divorced, they were already hers; here also, she acquired the principal and the extra fifth!

Rebuttal of objection: There, they are a specific pile of produce, but here, she hadn't yet separated the Terumah payment. To what is it comparable?

Answer: To the case of the firstborn donkey - if a Yisrael inherited firstborn donkeys from his mother's father, who was a Kohen, he does not need to give them to a Kohen. The same is true for Terumah that she acquired when she was still married.