Without a proof that the hierarchy theorem's machine-specific separations lift uniformly to relativization-resistant class separations, the proper subset claim outruns its formal justification.

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Hierarchy theorem(in computational complexity theory): A mathematical result showing that computational problems can be organized into strict levels of difficulty—solving harder problems requires more computing power or time than solving easier ones.
Machine-specific(in computational theory): Results or properties that depend on the particular type of computer or computational model being used, rather than being true for all possible computing devices.
Outruns its formal justification(in logical argumentation): Makes a claim that goes beyond what can actually be proven or supported by the available evidence and logical reasoning.
Proper subset(mathematical/computational): A collection that contains some, but not all, of the items in another collection. For example, all dogs are a proper subset of all animals, since there are animals that aren't dogs.

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