Functional Number Theoretic Function

Let \(f (x)\) be a function on \(x\) which satisfies following conditions:

\[\begin{cases} f (\phi (x)+3) \leq f (x+3) +7 \\ f (x+1) \geq f (\phi (x)) \\ f (2)=7 \end{cases} \]

Find the value of \(f (4)+f (5)+15\).

Notation: \(\phi(\cdot) \) denotes the Euler's totient function.

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