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Combinatorics Difficulty 5.0 AIME, harder Find the answer United Kingdom

Let $S$ be a set of five different positive integers, the largest of which is $m$ . It is impossible to construct a quadrilateral with non-zero area, whose side-lengths are all distinct elements of $S$ . What is the smallest possible value of $m$ ?

(A) $2$ (B) $4$ (C) $9$ (D) $11$ (E) $12$

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