Let $(R,m)$ be a complete intersection ring with characteristic $p$. If $M$ is a finitely generated $R$-module with finite length i.e. $l(M)<\infty$. It follows that $l(F(M))\geq p^nl(M)$, where $n=\dim R$. $(\text{Here $F$ is the Frobenius functor})$. 

Now under the same assumption of $R$, let $M$ and $N$ be two finitely generated $R$-modules. If $l(M\otimes N)<\infty$ and $\dim M+\dim N=n$. Is it true that $l(\text{Tor}_i^R(F(M),N)\geq p^nl(\text{Tor}_i^R(M,N))$?