Fx: x is a logic student
Gx: x is ambitious
Hx: x studies hard
Jx: x is an exercise
Kx: x is easy
Fxy: x does y
a: Bob
b: Carol

10. Some logic students do not do any exercises. Only someone doing some of the exercises can be said to be studying hard, so some logic students must not be studying hard.

FxJyFNxyCA, HxJyFxyAC |- FHNE

1. FxJyFxyCA
2. HxJyFxyAC |- show FHNE
3. FaJyFNayCA.....1 x inst the new name rule applies
3. FaJbFNabCA.....3 y inst
4. HaJyFayAC.....2 x inst
5. HaJbFabAC.....4 y inst
6. JbFabANHNaC....5 C subs
7. JNbFNabCHNaC...6 AN subs
8. JbFNabCHNaC...7 CO subs
9. JbFNabC.......3 A elim
10. HNa............8,9 C elim
11. Fa.............3 A elim
12. FaHNaA.........10,11 A int
13. FHNE...........12 E int