Do URIs which are neither URLs nor URNs exist?

Can a URI be neither a URL nor a URN?

Over the Internet, there are a lot of Venn diagrams like this one:

According to those representation, in the gray space there are some URIs which are neither URLs nor URNs, but it sounds pretty weird to me.

In fact, according to this SO answer,

A URI can be further classified as a locator, a name, or both.

So it seems that the answer to my question is "absolutely no". But those kinds of Venn diagrams make me doubt.

According to the classical view ("early to mid 90s"), a URI was either a URL or a URN.¹ There were discussions about defining additional classes (e.g., URC), but it didn’t seem to catch on.

According to the contemporary view, it’s not relevant/useful to define such formal classes:

the view became that an individual scheme does not need to be cast into one of a discrete set of URI types such as "URL", "URN", "URC", etc.

So the answer is probably no. There could be additional classes, but back then none were defined (or to be more accurate, none found wide approval), and today we mostly don’t care anymore.

Now typically one term is used for all URIs: URI or URL.

¹ It doesn’t state that a URI could be both, a URL and a URN. But in RFC 2396, it says (bold emphasis mine): "A URI can be further classified as a locator, a name, or both."