From $P\subseteq \oplus P \subseteq PSPACE$ and $P\subseteq PP \subseteq PSPACE$ we infer $\oplus P\neq PP$ gives that $$P\neq PSPACE$$ $$P\neq PP \mbox{ }(PP^{PP}=PP^P=PP=P=CH\mbox{ and }\oplus P\subseteq CH\implies \oplus P=PP).$$

Are there any other consequences?

From $P\subseteq \oplus P \subseteq PSPACE$ and $P\subseteq PP \subseteq PSPACE$ we infer $\oplus P\neq PP$ gives that $$P\neq PSPACE.$$

Are there any other consequences?

From $P\subseteq \oplus P \subseteq PSPACE$ and $P\subseteq PP \subseteq PSPACE$ we infer that $$\oplus P\neq PP\implies P\neq PSPACE.$$

Are there any other consequences?

From $P\subseteq \oplus P \subseteq PSPACE$ and $P\subseteq PP \subseteq PSPACE$ we infer $\oplus P\neq PP$ gives that $$P\neq PSPACE$$ $$P\neq PP \mbox{ }(PP^{PP}=PP^P=PP=P=CH\mbox{ and }\oplus P\subseteq CH\implies \oplus P=PP).$$

Are there any other consequences?