KORBANOS THAT WERE OFFERED SHE'LO LISHMAN
(Mishnah): Any Zevach (animal Korban) that was slaughtered Lo Lishmah (to be a different Korban, e.g. an Olah was slaughtered to be a Shelamim; Tosfos - or with intent Lizrok (to throw on the Altar) the blood of Reuven's Zevach for Shimon) is Kosher, but the owner was not Yotzei;
The only exceptions are Pesach or Chatas. A Pesach (Lo Lishmah) is Pasul (disqualified) if slaughtered at the proper time to slaughter the Pesach (on Erev Pesach). A Chatas (Lo Lishmah) is always Pasul;
R. Eliezer says, also Asham is Pasul if slaughtered Lo Lishmah;
Pesach is Pasul (Lo Lishmah) at its proper time, and Chatas and Asham at any time.
Asham (usually) comes to atone for transgression, just like Chatas. Just like Chatas is Pasul Lo Lishmah, also Asham.
Yosi ben Choni says, any Zevach that was slaughtered l'Shem (to be a) Pesach or Chatas is Pasul;
Shimon Achi Azaryah says, any Zevach that was slaughtered l'Shem a Korban of higher Kedushah is Kosher. A Zevach slaughtered l'Shem a Korban of lower Kedushah is Pasul:
For example, if Kodshei Kodoshim were slaughtered l'Shem Kodshim Kalim, they are Pasul. (Kodshei Kodoshim must be slaughtered in the north. Only male Kohanim may eat them, in the Azarah, for a day and a night. Kodshim Kalim are permitted in all of Yerushalayim, even to Yisre'elim, and usually for two days and a night.) If Kodshim Kalim were slaughtered l'Shem Kodshei Kodoshim, they are Kosher;
If a Bechor or Ma'aser was slaughtered l'Shem Shelamim, it is Kosher. If a Shelamim was slaughtered l'Shem Bechor or Ma'aser, it is Pasul.
(Gemara) Question: Why did the Tana say but the owner was not Yotzei? (He could have omitted this word!)
Answer: He teaches that even though the owner was not Yotzei, the Zevach is still Kodesh. One may not do another Avodah (Kabalah (receiving the blood), Holachah (bringing it to the Altar) or Zerikah (throwing the blood on the Altar) Lo Lishmah.
(Rava): If an Olah was slaughtered Lo Lishmah, one may not throw the blood Lo Lishmah.
We can learn from reasoning or a verse.
Reasoning - because it was (improperly) slaughtered Lo Lishmah, should we do another Avodah Lo Lishmah?!
A verse - "...v'Asisa Ka'asher Nadarta... Nedavah." (Neder is a vow to bring a Korban with Acharayus, i.e. if the animal becomes lost, stolen or blemished, he must bring another. Nedavah has no Acharayus.)
Question: Why does the Torah call a Neder 'Nedavah'?
Answer: If you did like you Nadar (vowed, i.e. the Zevach was offered Lishmah), it is a Neder (you fulfilled your obligation). If not, it is a Nedavah (you did not fulfill your vow).
The Torah calls a Zevach slaughtered Lo Lishmah a Nedavah. A Nedavah may not be offered Lo Lishmah!
SHECHITAH WITHOUT SPECIFYING AN INTENT
Ravina: Rava asked contradictions, and answered them.
(Rava): Our Mishnah teaches that any Zevach slaughtered Lo Lishmah is Kosher, but the owner was not Yotzei;
Inference: If it was slaughtered Stam (without specifying), he was Yotzei. This teaches that Stam is like Lishmah.
Contradiction (Mishnah): A Get written Lo Lishmah (i.e. it was written for Leah and given to Rachel) is Pasul;
A Get written Stam (without intent for any particular woman) is also Pasul (we will explain the source of this law later), i.e. it is like Lo Lishmah!
Answer (Rava): We expect Zevachim to be offered Lishmah (so if it was slaughtered Stam, we consider this Lishmah);
There is no reason why a particular woman should be divorced (in any case, with a Get not written specifically for her), therefore it is Lo Lishmah.
Question: What is the Rava's source that we expect Zevachim to be offered Lishmah?
Suggestion: Our Mishnah teaches 'any Zevach slaughtered Lo Lishmah (i.e. with improper intent)...' It did not say 'it was not slaughtered Lishmah (i.e. Stam, for then he is Yotzei)'!
Rejection: Also regarding Get, the Mishnah says 'a Get written Lo Lishmah...' It does not say 'a Get not written for a woman'!
Answer #1 (Mishnah #1): What is the case of intent Lishmah followed by Lo Lishmah (Rashi - during Shechitah; Tosfos - in different Avodos), which is Pasul? (Regarding a Pesach), first he intended for Pesach, and then for Shelamim.
Inference: Had he first intended for Pesach, and then Stam, it would be Kosher. This shows that Stam is like Lishmah!
Rejection: Perhaps (normally,) Stam is not like Lishmah. Here it is Kosher, for we assume that he finished the Avodah with the same intent he started with.
Answer #2 (Seifa of Mishnah #1): A case of Lo Lishmah followed by Lishmah (which is Pasul) - first he intended for Shelamim, and then for Pesach.
Inference: Had he started Stam, and then intended for Pesach, it would be Kosher. This shows that Stam is like Lishmah!
Rejection #1: Stam is not like Lishmah. Here it is Kosher, for his final intent reveals what his initial intent was.
Rejection #2: The inference is wrong. Had he started Stam, and then intended for Pesach, it is also Pasul;
This clause was taught just for parallel structure to the Reisha.
Answer #3 (Mishnah): There are six intents in offering a Zevach: which Korban it is (e.g. Olah), for whom it atones, it is offered to Hash-m, the Chelev (if an Olah, also the limbs) will be burned (and consumed, not just roasted) on the Altar, it should be a pleasant aroma (the meat should not be roasted before it is put on the Altar), and it should be pleasing to Hash-m;
Additionally, a Chatas or Asham is offered for a particular transgression.
R. Yosi says, even if it was offered without any of these intents, it is Kosher. Beis Din enacted to offer Zevachim Stam, lest it be offered Lo Lishmah.
We cannot say that Stam (Tosfos - without verbal or mental intent) is Pasul. Beis Din would not make an enactment to disqualify Zevachim! (Tosfos - they would not enact to offer it silently, lest one forget to have mental intent)!
A GET WITHOUT A SPECIFIED INTENT
Question: What is Rava's source that a Get written Stam is Pasul?
Suggestion (Mishnah): If Reuven overheard a scribe reciting the text of a Get (while writing it), the names corresponded to him and his wife, he cannot divorce his wife with it.
Rejection: Perhaps the case is as Rav Papa explained;
(Rav Papa): The case is, the scribe was writing it to practice. He did not intend that it be used to divorce.