Depth formula via complete intersection flat dimension

We prove the depth formula, for homologically bounded complexes $X,Y$ provided that the complete intersection flat dimension of $X$ is finite and $\sup (X{\text{utp}}_{R}Y)<\mathrm{\infty }$. In particular, let $M$ and $N$ are two $R$-modules and the complete intersection flat dimension of $M$ is finite. Then $M$ and $N$ satisfies the depth formula, provided ${\text{Tor}}_i^R(M,N)=0$ for all $i\ge 1$.