A certain Professor, who shall remain nameless, was at a dance. He did what he always does at dances - he thought about combinatorics. He noticed that every woman present danced with at least one man, and that no man danced with every woman. He wondered if there were any theorems he could prove about such a situation. He conjectured that there would always be two men, call them M1 and M2, and two women, call them W1 and W2, with the following properties: M1 danced with W1 and M2 danced with W2, but M1 did not dance with W2 and M2 did not dance with W1. Prove that his conjecture is correct.