What is this PVC pipe for and do I need it?

[Mahorelee]

This PVC pipe runs from the basement drain to the attic vent. I found it opening a wall on the first floor and it is in the way. There's also a hot cold water line that runs with it. However the hot is not connected to anything in the basement, but the cold is. I can't seem to find where it goes to either, it's not in the attic I don't think.

Pictures of the PVC pipe from the basement and attic below.

 

[CT-18]

Someone did some shady stuff over there. What are those pipes on the right. To me it looks like someone tried to vent something off the sanitary stack.