Shevuos, Chapter 8, Mishnah 2. This mishnah deals with cases in which, even though a person swore falsely and made a claim that was untrue, he is still exempt from bringing an offering for a shevuas hapikadon (an oath concerning a deposit). The reason: even though he spoke words that were not true, the situation as it actually happened would have exempted him even had he told the truth. Let us go through the examples listed in the mishnah.
The cases in the mishnah:
The mishnah deals with someone who handed over his ox to an unpaid watchman - a watchman who receives no payment for guarding it. The owner asks him: "heichan shori?" - "Where is my ox?" - and the watchman gives an answer that is untrue:
"amar lo meis" - he claimed the ox died, when in fact it was injured, or was taken captive, or was stolen, or was lost.
"nishbar" - he claimed the ox was injured, when in fact it died, or was taken captive, or was stolen, or was lost.
"nishbah" - he claimed the ox was taken captive, when in fact it died, or was injured, or was stolen, or was lost.
"nignav" - he claimed the ox was stolen, when in fact it died, or was injured, or was taken captive, or was lost.
"avad" - he claimed the ox was lost, when in fact it died, or was injured, or was taken captive, or was stolen.
In each of these cases the owner says to him: "mashbi'acha ani" - meaning, I want you to swear to me, "ve'amar amen" - and the watchman answers amen. The ruling is that the watchman is exempt, even though what he said was false.
The reason for the exemption: had he told the truth, he would have been exempt then as well. An unpaid watchman is not liable in any of these cases - not for death, not for injury, not for capture, not for theft and not for loss. It turns out that the oath did not serve to exempt him from a payment he owed, and therefore there is no obligation here to bring an offering for a shevuas hapikadon.
But there is something he is liable for: shevuas bitui:
Shevuas bitui, which we mentioned at the beginning of the tractate, is when a person swears about something that is not true: he says that such and such happened, and it is not so. For this oath he is liable:
If done intentionally: he is liable to lashes.
If done unintentionally: he is liable to bring a korban oleh v'yored (a sliding-scale offering).
In summary: in this mishnah we learned that an unpaid watchman who made a false claim about his ox - that it died, that it was injured, that it was taken captive, that it was stolen or that it was lost - and swore to it, is exempt from the offering of shevuas hapikadon, since even according to the truth he would not have owed any payment. Nevertheless, he does not come away entirely clean, for he did lie under oath, and therefore shevuas bitui applies to him: lashes if he did so intentionally, and a korban oleh v'yored if he did so unintentionally.