The first two perakim of Shevuot []{dir="rtl"}discuss the prohibition of tumat Mikdash ve'kodashav. In other words, the prohibition of entering the Beit HaMikdash or partaking in korbanot in a state of tumah. The Mishnah also discusses how the atonement is achieved when the prohibition is violated. Much of the focus however is when the violation requires the korban olah ve'ored to be offered. This would be when there is yediah (knowledge) both prior and after the violation, but at the time he entered, the person forgot that he was either tameh or that the location he entered, was prohibited to enter while tameh.
The Mishnah (2:3) however discusses a case where the individual became tameh in the azara (courtyard of the Beit HaMikdash) and then forgot one of the two details above. The question the Mishnah addresses is how long he would then have to be there before being liable to bringing the korban olah ve'yored. The Mishnah explains that if he bowed or delayed for the time it would take to prostrate fully, he would be liable. The Gemara (16b) explains that this would be the time it would take to recite the pasuk from Divrei HaYamim (II 7:3), from "and they bowed" till the end of the pasuk. The Mishnah adds that if he took the most direct path out, he would be exempt. If he however took the long way, he would be liable.
The Gemara explains that the length of the exit is not a matter of speed. If the individual took the shortest path, but took very small steps, heal-to-toe, such that it took the whole day to exit, he would still be exempt.
The Mikdash David (38:1) notes that there are two reasons why one would be exempt when leaving by the shortest path. The first is that it is ones -- what else can he do to leave? The second is that since he is engaged in leaving, it is not considered as shehiya -- staying in the Beit HaMikdash whilst tameh. From the Gemara cites above, it would seem that it is the latter of the two explanations. The individual can certainly do more than walking heal-to-toe, yet he is exempt since he is continually engaged in leaving.
The Yerushalmi (2:3) however explains that one would be liable for taking the longer path if it was longer by ten amot. That is because the Yerushalmi explains that this is the distance one could walk in time it would take someone to bow.
The Mikdash David explains that the Yerushalmi and Bavli have different understandings of why one is liable if took the longer exit path. He understands that since the Yerushalmi provides that distance of ten amot which is associated with the time it takes to bow, the issue is one of shehiya. One is not liable for the short distance, but any excess is considered sheyia and liable provided it is ten amot.
Based on this, we can understand the discussion in Yerushalmi. According to the Ridbaz the question is if someone took the long path, is he liable for the excess in the beginning or the end. On the one hand, from the beginning he was given the time it takes to leave on the quickest path. Consequently, he should be liable for the time beyond that. R' Yossi however argues that he is obligated to leave for that final stretch, so how can he liable then. It must therefore be the time in the beginning of his exit for which he is liable. R' Chaim Kanievsky (Yoma 5:1) however explains that the question is regarding one that delayed the time it takes to bow and then exited the fasted way. The considerations are nonetheless the same. Either way, it is clear from this discussion that sheyiha is the issue. The question is when or whether the walking is itself considered shehiya.
Returning to the Mikdash David, he explains that according to the Bavli however the issue is not shehiya. As explained above, the time it takes to leave is not important provided it is the shortest path. Instead, one is liable for the (excessive) steps taken in the Beit HaMikdash whilst tameh -- even a single step. He explains that accordingly, even if he walked rapidly on the longer path in the time it would take to go on the short path, he would still be liable.
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