Gittin 81B

דבית שמאי סברי: אדם עושה בעילתו בעילת זנות;

as Beit Shammai hold: A person does engage in licentious sex. Although they were seen having sex, one cannot assume that he intended to betroth her, since they were recently divorced. The assumption is that they were simply engaging in licentious sex. Consequently, he is not required to give her a second bill of divorce.

ובית הלל סברי: אין אדם עושה בעילתו בעילת זנות. אבל לא ראוה שנבעלה ⁠– דברי הכל אינה צריכה הימנו גט שני.

And Beit Hillel hold: A person does not engage in licentious sex. Therefore, he had the intention to betroth her, and he must give her another bill of divorce. But if they did not see that she had sex, even though they spent the night together at an inn, everyone agrees that she does not require a second bill of divorce from him, as there is no concern that perhaps they had sex.

תנן: ומודים בנתגרשה מן האירוסין ⁠– שאינה צריכה הימנו גט שני, שאין לבו גס בה. ואי בשראוה שנבעלה, מה לי מן האירוסין ומה לי מן הנשואין?

The Talmud challenges this understanding of the Mishnah: We learned in the Mishnah that Beit Hillel concede that when she was divorced following the state of betrothal, she does not require a second bill of divorce from him because he is not accustomed to her. And if the Mishnah is referring to a case in which they saw that she had sex, what is the difference to me if it was following the state of betrothal and what is the difference to me if it was following the state of marriage? In either case, they saw that she had sex.

אלא מתניתין ⁠– בשלא ראוה שנבעלה; ורבי יוחנן דאמר ⁠– כי האי תנא, דתניא: אמר רבי שמעון בן אלעזר: לא נחלקו בית שמאי ובית הלל על שלא ראוה שנבעלה, שאינה צריכה הימנו גט שני,

Rather it can be explained that the Mishnah is actually speaking about a case in which they did not see that she had sex. R' Yoḥanan stated his opinion in accordance with the statement of that tanna. As it is taught in a baraita that R' Shimon ben Elazar said: Beit Hillel and Beit Shammai did not disagree about a case where they did not see that she had sex. Everyone agrees that in such a scenario, she does not require a second bill of divorce from him.