∀x (Student(x) → MemberOf(x, university))
∀x (GraduateStudent(x) → Student(x))
∀x (PhDStudent(x) → GraduateStudent(x))
∃x (PhDStudent(x) ∧ TeachingFellow(x))
¬PhDStudent(john) → ¬MemberOf(john, university)
TeachingFellow(john) → PhDStudent(john) ⊕ GraduateStudent(john)
PhDStudent(john)