Consider these four claims taken together: P ≥ Q, Q > R, R ≥ S, and S > P. Which statement about them is correct?

The four claims form a closed loop, so compose them right round: P ≥ Q, Q > R, R ≥ S, S > P give P ≥ Q > R ≥ S > P. Every link points the same way and two of them are strict, so the composite is strict and reads P > P, which no value satisfies. The claims cannot all hold. 'Consistent, for example when P = Q = R = S' fails immediately on the second claim, since Q > R is false when Q = R. 'Consistent only if all four variables are equal' describes what a loop of purely non-strict links would force, but this loop contains two strict links. 'Contradictory only if P ≥ Q is replaced by P > Q' gets it backwards: strengthening that link is unnecessary, because Q > R and S > P already make the loop strict.