Intel 4000 HD Graphics with 2560×1440 on HDMI

First, see what’s your monitor connection.

$ xrandr --listmonitors
Monitors: 1
0: +HDMI-2 1920/697x1080/392+0+0  HDMI-2
$ xrandr --newmode "2560x1440" 220.812 2560 2608 2640 2720 1440 1443 1448 1478 -hsync -vsync
$ xrandr --addmode HDMI-2 "2560x1440"

After this you may have to bring up the “Display” control panel and choose newly added 2560×1440 resolution. This will be 55 Hz with reduced blanking