On the Diophantine equation $F_{n_1}+F_{n_2}+F_{n_3} = p_1^{z_1} \cdots p_s^{z_s}$

Let $F_n$ denote the $n$-th Fibonacci number and $p_i$ the $i$-th prime number. In this paper we consider the Diophantine equation $F_{n_1}+F_{n_2}+F_{n_3} = p_1^{z_1} \cdots p_s^{z_s}$ in
non-negative integers $n_1 \geq n_2 \geq n_3 \geq 0$ and non-negative integers $z_i$ with $1\leq i \leq s$. In particular, we completely solve the case that $s = 12$.