How to exclude values from output in SPARQL query for Wikidata?

Question

I'm trying to write a SPARQL query using Wikidata Query Service to retrieve all prime ministers of the Netherlands from 1970. However, I want to filter the output by checking if a prime minister worked for a university. If a minister worked for a university, it should not be in the output.

I think I must use the FILTER NOT EXISTS expression, but do not know how to properly write this line. Can someone please help me out?

See below for my query and output:

SELECT ?pmLabel ?start ?companyLabel
WHERE
{   
  ?pm wdt:P39 wd:Q3058109.
  ?pm p:P39 ?posHeld.
  ?pm wdt:P108 ?company.
  ?posHeld ps:P39 wd:Q3058109.
  ?posHeld pq:P580 ?start.
    
  FILTER(year(?start) > 1970) 
  # FILTER NOT EXISTS(?company (something) "Universit") 
  SERVICE wikibase:label { bd:serviceParam wikibase:language "en". } # labels

 } 
ORDER BY DESC(?start)

+----------------------+------------------+------------------------------+
|  primeMinisterLabel  |      start       |         companyLabel         |
+----------------------+------------------+------------------------------+
| Mark Rutte           | 14 October 2010  | Unilever                     |
| Mark Rutte           | 14 October 2010  | Calvé                        |
| Jan Peter Balkenende | 22 July 2002     | Erasmus University Rotterdam |
| Jan Peter Balkenende | 22 July 2002     | Vrije Universiteit Amsterdam |
| Ruud Lubbers         | 4 November 1982  | United Nations               |
| Ruud Lubbers         | 4 November 1982  | Harvard University           |
| Ruud Lubbers         | 4 November 1982  | Tilburg University           |
| Ruud Lubbers         | 4 November 1982  | Hollandia                    |
| Dries van Agt        | 19 December 1977 | Kyoto University             |
| Dries van Agt        | 19 December 1977 | Radboud University Nijmegen  |
| Dries van Agt        | 19 December 1977 | Kwansei Gakuin University    |
| Dries van Agt        | 19 December 1977 | Ritsumeikan University       |
+----------------------+------------------+------------------------------+