This message was posted on behalf of Intel Corporation
Thank you for contacting Intel Communities.
In this case, as you mentioned, the Intel® HD Graphics 4000 does support the resolution in question, your inquiry is more related to the HDMI specifications other than the graphics controller capabilities.
Please check the following link with information regarding different HDMI revisions and their specifications:
Understanding the Different HDMI Versions (1.0 to 2.0)
It is important to mention that since you have an OEM product, you may want to contact the system manufacturer as the resolutions available on each video port are limited by the computer manufacturer.
You can also check the following thread for further information:
Can The HD 4000 support 3440*1440 resolution via dp 1.1 or HDMI 1.4?
Hope this information helps.
Please don't hesitate in replying to this post if you need further assistance.