Answer #3 (Rav Papa): Rather, the Kal va'Chomer is from one witness, who obligates an oath of Gilgul (once a defendant must swear to contradict a witness, the claimant can make him include other matters in the oath).

Question: One witness obligates an oath about what he testifies about. Then, the law of Gilgul obligates swearing about other matters;

We have no source that two witnesses obligate any oath!

Answer: We learn from admission. It obligates one to swear about a claim not supported by an admission or testimony!

Question: Admission cannot be contradicted. We cannot learn to witnesses!

Answer: We learn from one witness, who can be contradicted, yet he obligates him to swear.

Question: One witness makes him swear about what the witness testifies about. We cannot learn that two witnesses make him swear about what they do not testify about!

Answer: We learn from admission. It makes him swear about a claim not supported by an admission or testimony!

The stringencies of admission and one witness are different. The Tzad ha'Shavah (common side) is that through claim and denial he must swear. The same applies to witnesses!

Question: In both sources (of the Tzad ha'Shavah), the defendant was not established to be a liar. We cannot learn to two witnesses, who establish him to be a liar (perhaps we do not believe his oath)!

Answer: Two witnesses do not establish him like a liar;

(Rav Idi bar Avin): One who (falsely) denies a loan is not disqualified from testifying. (Perhaps he intends to repay it, and he merely stalls until he can do so.) One who denies a deposit is disqualified from testifying. (If he intended to return it, he would do so now!)

Question: In both sources, there is no law of Hazamah (to pay for false testimony). We cannot learn to two witnesses, who pay if they are Huzmu!

Answer: R. Chiya does not consider this a refutation of the Tzad ha'Shavah (since Hazamah applies to one witness to invalidate his testimony).

Objection: How can R. Chiya support himself from our Mishnah? It is unlike his case!

In his case, only the lender is supported by witnesses. If witnesses supported the borrower, R. Chiya would not obligate him to swear!

In the Mishnah, we are witnesses for both sides (that each owns half)!

Retraction: Rather, R. Chiya brought our Mishnah to support a different law.

(R. Chiya): If Reuven told Shimon 'you owe me 100', and Shimon said 'I owe only 50. Heilach (Rashi - take back your loan, I never spent it; Ran - we discuss a deposit)' and returned 50, he must swear about the other 50.

Question: What is the reason? (We should say that they argue only about the other 50, and he totally denies it!)

Answer: Even when he says 'Heilach', he admits to part of the claim.

Support (Mishnah): If Reuven and Shimon are holding a garment...

We are witnesses that each owns half (and he must give up the other half. This is like Heilach), and still they swear!

(Rav Sheshes): One who partially admits to a claim and says 'Heilach' is exempt from swearing.

Question: The Mishnah shows that he must swear!

Answer: The Mishnah is only an enactment mid'Rabanan (lest people grab others' garments and claim them).

R. Chiya admits that the Mishnah is an enactment mid'Rabanan. However, Chachamim enact only what is similar to Torah law;

If Heilach were exempt, they would not enact an oath unlike Torah oaths.

(Beraisa - R. Shimon ben Elazar): A loan document says 'Dinarim', without specifying an amount. The lender says that he lent five and the borrower admits to three. Since he admitted to part of the claim, he swears;

R. Akiva says, he is like a Meshiv Aveidah (one who returns a lost object, i.e. he could have said two easily), and he is exempt.

Version #1 - Question (against R. Chiya): R. Shimon ben Elazar obligates an oath when he admits to three. Had he admitted to only two, he would be exempt (since clearly, the document means at least two, and there is a lien on his land to pay two). This is like Heilach, therefore he is exempt!

Answer #1: No, R. Shimon obligates even when he admits to two;

He taught about three to teach that he argues with R. Akiva, and does not exempt him like a Meshiv Aveidah.

Objection: If so, why did he say 'since he admitted to part of the claim, he swears'? He should say 'even in this case he swears!'

Answer #2: Really, R. Shimon exempts him when he admits to two, even though Heilach is liable;

Explanation #1: When he admits to two, the document supports him, therefore he is exempt.

Explanation #2: When he admits to two, there is a lien on his land to pay the entire admission;

Just like we do not swear about denial of debts that have a lien on land, also we do not swear due to admission of such debts.

Version #2 - Question (against Rav Sheshes): R. Akiva exempts him only because he is like a Meshiv Aveidah. Had he only admitted to two, he would be liable, even though (there is a lien on land to pay two, and) it is like Heilach!

Answer: Even if he admitted to two he would be exempt. The Beraisa discusses three to teach the argument about three;

R. Shimon obligates because he partially admits, and R. Akiva exempts like a Meshiv Aveidah.

Support: This must be correct. If R. Akiva obligated an oath regarding two, why would he exempt him when he says three? He will scheme to say three to avoid swearing!

Question: Since we must say that R. Akiva exempts regarding two, this refutes R. Chiya! (He is not a Meshiv Aveidah. The exemption must be due to Heilach!)

Answer #1: When he admits to two he is exempt because the document supports him.

Answer #2: When he admits to two there is a lien on his land to pay this, and we do not swear due to such admissions.

Question (Mar Zutra brei d'Rav Nachman - Mishnah #1): If Reuven claimed Kelim and land from Shimon and Shimon admitted to either one and denied the other, he is exempt from swearing;

If he partially admitted to the claim of land (and denied all the Kelim), he is exempt;

If he partially admitted to the claim of Kelim, he must swear.

Inference: He is exempt (in the first two clauses, in particular, when he admitted to land and denied Kelim) only because we do not swear about land;

In a corresponding case of two claims of Kelim (the Kelim he admits to are in front of him, like land) he would be liable.

Suggestion: Even though he says Heilach, he is liable!

Answer: No. In a corresponding case of two claims of Kelim, he is exempt;

The Mishnah discusses Kelim and land to teach that when he partially admits to the Kelim, he must also swear about the land.

Question: Another Mishnah teaches this!

(Mishnah #2): (Land has Achrayus, i.e. one may collect a loan document from land that the borrower sold after the loan. Metaltelim (movable objects) have no Achrayus. An obligation to swear about) property without Achrayus forces one to swear also about property with Achrayus.

Answer: Mishnah #1 is the primary place the law is taught. Mishnah #2, which teaches laws of (acquisitions of) land and Metaltelim, merely taught the law in passing.