R. Ishmael’s Rule No. 9 – “shehu kheinyano” – presumably has as its fourth premise:
Some P1 are P2 and some P1 are not P2, and
some P2 are P1 and some P2 are not P1
This situation, where P1 and P2 only partly overlap, may be graphically represented as follows:
The conclusions we can formally draw are obvious enough. Since “Some S1 are P2”, as well as, “All S2 are P1” and “some P1 are not S2”, are general conclusions possible from the first three premises, without resort to the predicatal premise – the only formal conclusion specific to the current predicatal premise is “Some P2 are not S1”.
It is not clear (to me so far, at least) what R. Ishmael proposes to conclude in such cases.