The gemara concludes that the kal va’chomer from which Rabbi Chiya derived that two witnesses who testify to half a claim can obligate the defendant to swear about the rest t was referring to was learned out jointly (by a b’meh hatzad) from both one who admits to part of a claim (modeh bemiktzat) and from one witness who both need to swear. The gemara questions the proof for this halacha that Rabbi Chiya brought from our mishna and concludes that our mishna was brought for proof for a different halacha – one where one admits to half a claim and then says “heilach“. Rabbi Chiya hold that in that case one is still obligated to swear and that halacha can be proven from our mishna. An opposing opinion is brought by Rav Sheshet. Then the gemara brings a braita to first disprove Rabbi Chiya but reconciles it. Then brings the same braita to prove Rabbi Chiya (or question Rav Sheshet) but rejects it. Then brings another question on Rav Sheshet;s opinion from a mishna but also rejects it.