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## IMC 2012 Problem 4

Let ${f: \Bbb{R} \rightarrow \Bbb{R}}$ be a continuously differentiable function that satisfies ${f'(t)>f(f(t))}$ for all ${t \in \Bbb{R}}$. Prove that ${f(f(f(t))) \leq 0}$ for all ${t \geq 0}$.