It won't disappear. It could be split, close some sites, change leadership again, etc. but it won't simply cease to exist. The existing infrastructure itself is worth too much.

What would you say are HP's top 5 most valuable pieces of infrastructure?

Just guessing but: lab machines, buildings, purpose-built networks/processing centres, etc. I don't know how the production is organised, but assembly lines may be included.

Even if HP doesn't the technology for this will probably survive.