What is the consequence of $\oplus P\neq PP$?
Turns out, you are immediately able to separate $\mathrm{P}$ from $\mathrm{PP}$.

Assuming that $\oplus\mathrm{P\neq PP}$ but also assume to the contradiction that $\mathrm{P=PP}$, then $\mathrm{P^{PP}=P}$. But $\oplus\mathrm{P\subseteq P^{\#P[1]}=P^{PP}=P}$. So, $\oplus\mathrm{P=P=PP}$ violating our assumption and concluding our proof by contradiction.