Nothing proves anything in properties, because it would be trivial to fake.
For proof, you need digital signatures (signed with certificates from a public authority).
Open the PDf Document
and go to File-> properties
See the Application and PDF Producer and it will give you an idea about the it.
If it is blank then definately a third party application.
The "PDF Producer" field in the document metadata is a suggestion of what created it, but as TSN says it is absolutely not 'proof'. There is nothing to stop a program from putting whatever it wants in that field, and it's perfectly possible for an Adobe-created PDF to have blank fields if the PDF has been processed in an XMP editor after it was created.