The tree looks like a Norway Maple to me, though that hasn't been verified. The small section of the root I found (there may be others close by) varies from 2-4 inches wide. While I'm not certain it's coming from the Norway Maple outside, it's the leading suspect given the sizes of the other trees. I'm attaching photos of the root, the Norway Maple and the other nearby trees (all in my neighbor's yard) along that side of my house.
The Norway Maple's trunk is about 3' in diameter and the root section under the basement floor is about 9' away, 5' under ground.
Am I right in assuming this root is from the Norway Maple? In this situation, would it be more prudent to cut down the tree before/after removing the offending roots?