Rava quoted a Beraisa which permits rubbing grain on Yom Tov to remove the kernels. Abayye quoted a different Beraisa which seems to forbid rubbing the grain on Yom Tov since it mentions the law of one who rubbed grain “before Yom Tov” rather than “on Yom Tov”.
Resolution: It is actually permitted even on Yom Tov, but since the Beraisa begins with the law of grain rubbed before Shabbos, it continues with grain rubbed before Yom Tov.
Challenge: If so, there’s a case of Terumah which can be separated on Yom Tov! The Mishnah (056) states that there is no such case [since terumah must be separated before threshing and threshing is not permitted on Yom Tov]?
Resolution: It is not difficult. The Mishnah follows Rebbi while the Beraisa follows Rabbi Yosi b’Rebbi Yehuda [not that it’s permitted to separate Terumah on Yom Tov, but that Terumah must not be separated from grains].
Beraisa: If he brought in ears of grain in order to process it for dough, he may eat from it in a casual manner and he need not separate Terumah, but if he brought them in with the intention of rubbing them and eating them in that manner, Rebbi requires Terumah to be separated [since it is brought in with that purpose] and Rabbi Yosi b’Rebbi Yehuda does not.
Challenge: Even according to Rabbi Yosi b’Rebbi Yehuda there is a case where he will have to separate Terumah on Yom Tov; if he originally brought the grain in with the intention of making dough, he cannot use it for rubbing grain without separating Terumah? 
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