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 $s=12$.