To correct my first sentence of the parent and expand the explanation a little:

Your line $doc->documentElement->setNamespace("http://www.crtp.it","p"); does not work, and the documentation of XML::LibXML::Element->setNamespace explains why:

The function fails if it is required to create a declaration associating the prefix with the namespace URI but the element already carries a declaration with the same prefix but different namespace URI.

Which means you can't re-use the "p" prefix as it's already in use on the element; you'd have to pick a different prefix, then the setNamespace call would work and you wouldn't need to do registerNs on two namespaces.

However, you would still need to make one XML::LibXML::XPathContext->registerNs set-up as shown in the parent.

So TIMTOWTDI; personally I wouldn't manipulate the XML, but adjust my XPath to fit the XML (this is the solution shown in the parent, and you could remove the setNamespace call from your code).