On his way to look for Ivan, Alyosha notes that the lights are on at Katerina's, and figures Ivan must be visiting her. Sure enough, he meets Ivan just as he's leaving Katerina's. They both go up to see her.
Alyosha tells Katerina that Dmitri doesn't want her to testify, but Katerina scoffs at him. She reveals that she's been to visit Smerdyakov because Ivan has told her that Smerdyakov is the real killer, but she still seems unconvinced.
When Ivan leaves, Alyosha chases after him and gives him Lise's note. Ivan tears up the letter.
Ivan then tells Alyosha that he's only staying friendly with Katerina because he doesn't want her to ruin Dmitri's chances at the trial. Ivan claims he's no longer in love with Katerina, but he also believes that Katerina has a document that "mathematically" proves that Dmitri killed their father, an idea that Alyosha rejects.
When Ivan asks Alyosha who he thinks killed their father, Alyosha insists that he doesn't think it was Dmitri. Ivan is strangely disturbed, then accuses Alyosha of spying on him in his room when he was visited by an unnamed man.
Alyosha is completely mystified and denies spying on his brother.
Ivan tells Alyosha to leave him alone, and they go their separate ways.
Instead of going home, Ivan decides on impulse to go to Smerdyakov's.