ודאי רמאי (Bava Metzia 2a-3a)

The gemara on 3a applies the principle of ודאי רמאי to the idea of יחלוקו that if someone is definitely lying you would not say יחלוקו. The simple reading of the Gemara is that even the רבנן hold that you don't say יחלוקו if there is a ודאי רמאי because the Gemara asks on both ר' יוסי and the רבנן from חנוני על פנקסו that in that case there is a ודאי רמאי.

However, in fact, this is a מח' ראשונים. The last Rashi on 2a states that whenever you have a ודאי רמאי you say יהא מונח, implying that according to Rashi this is even according to the רבנן. Tosafos (2b ד"ה אי תנא מציאה) as well as the Rosh in סימן א both disagree and say that even in the case of זה אומר אני ארגתיה וזה אומר אני where there is a ודאי רמאי, you say יחלוקו. They hold that the סברה of ודאי רמאי was only said for ר' יוסי.

A נפקא מינה is the case of זה אומר אני ארגתיה וזה אומר אני ארגתיה. Rashi says the din is יהא מונח because there is a ודאי רמאי. However, Tosafos (2b ד"ה אי תנא מציאה) as well as the Rosh in סימן א both disagree and say that even in the case of זה אומר אני ארגתיה וזה אומר אני ארגתיה where there is a ודאי רמאי, you say יחלוקו. They bring a proof from the Gemara later (7a) from the case of שנים אדוקים בשטר where there is a ודאי רמאי and still the din is יחלוקו. Tosafos and the Rosh explain that according to the רבנן there is a different סברה, that the חלוקה יכולה להיות אמת. What this means is that we don't look at the 2 people to see if one is definitely lying but rather we look at the psak din, can the psak din be correct. In the case of זה אומר אני ארגתיה וזה אומר אני ארגתיה the answer is yes, it is possible that both of them own it and the correct psak is יחלוקו.

What do Tosafos and the Rosh do with the Gemara (3a) of חנוני על פנקסו where the Gemara seems to assume the סברה of ודאי רמאי even according to the רבנן? The answer is that although the Gemara uses the language of ודאי רמאי that is לפי ר' יוסי, according to the רבנן the question really is that by חנוני על פנקסו the psak din cannot be correct. Reuven owes his worker Levi $100 and tells him to collect from Shimon. Both Levi and Shimon now come to collect from Reuven. Reuven only owes $100 yet the psak din is to make him pay $200, $100 to Levi and $100 to Shimon. Even according to the רבנן that is a problem because the חלוקה cannot be אמת.