Even more surprisingly, when we have complex systems of "$~$A$~$ is true if $~$B$~$ is provable and $~$C$~$ is not provable" plus "$~$C$~$ is true if it's provable that the consistency of $~$\\mathcal T$~$ implies $~$B$~$ and $~$D$~$" etcetera, we can compute exactly what is and isn't provable in polynomial time\.
I can't figure out what this paragraph means -- I have no idea what the "et cetera" could be. I'm wondering if "when we have complex systems of…" should be "when we have complex systems such as…"