  We prove the depth formula, for homologically bounded complexes $X, Y$
provided that the complete intersection flat dimension of $X$ is finite and
$\sup(X\utp_RY)<\infty$. 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 $\Tor^R_i(M,N)=0$ for all $i\ge 1$.
