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 .