Defining class equivalent to negation of object property

Question

I'm trying to create an OWL ontology with following entities:

Classes:

• Design
• Requirement
• UnsatisfiedRequirement

Object properties:

• hasDesign(domain=Requirement, range=Design)

I want to define UnsatisfiedRequirementto be equivalent to Requirement which aren't related with any Design and use reasoner to classify individuals of type Requirement as UnsatisfiedRequirement.

Initially I tried defining UnsatisfiedRequirement as equivalent to Requirement and not(hasDesign some Design) which didn't work because of open world assumption of OWL.

I also tried defining SatisfiedRequirement class equivalent to Requirement and (hasDesign some Design) which gives me expected results (Requirements with hasDesign object property are correctly identified.). UnsatisfiedRequirement was updated to be disjoint with SatisfiedRequirement, even after this I'm not getting expected result.

I've also tried to write SWRL rule as Requirement(?requirement) ^ not(hasDesign(?requirement, ?design)) -> UnsatisfiedRequirement(?requirement) but in protege not is not a supported keyword.