Pyotr Ilyitch persisted in returning to this point, and though he found out nothing conclusive, yet he carried away a conviction that Dmitri Fyodorovitch could have gone nowhere but to his father’s house, and that therefore something must have happened there.
As to Perhotin, the people at the tavern, and at Plotnikov’s shop, as well as the witnesses at Mokroe, their evidence seemed conclusive.
This was the document of which Ivan spoke to Alyosha later on as a "conclusive proof" that Dmitri had killed his father.
Alas! its mathematical conclusiveness was recognized, and had it not been for that letter, Mitya might have escaped his doom or, at least, that doom would have been less terrible.
The proof of premeditation is conclusive; the crime must have been committed for the sake of the money, that is stated clearly, that is written and signed.
Every one, perhaps, felt from the first that the case was beyond dispute, that there was no doubt about it, that there could be really no discussion, and that the defense was only a matter of form, and that the prisoner was guilty, obviously and conclusively guilty.
The jealous man can forgive extraordinarily quickly (though, of course, after a violent scene), and he is able to forgive infidelity almost conclusively proved, the very kisses and embraces he has seen, if only he can somehow be convinced that it has all been "for the last time," and that his rival will vanish from that day forward, will depart to the ends of the earth, or that he himself will carry her away somewhere, where that dreaded rival will not get near her.
She’s got a document in her hands, in Mitya’s own writing, that proves conclusively that he did murder Fyodor Pavlovitch."
There are no more uses of "conclusive" in the book.