Symbolize the following:

Although some mean elves will bite even though not provoked, neither Bruce nor Carrie will bite unless provoked.

Symbolization attempt:

$\displaystyle \exists x ((Gx \wedge Hx) \wedge (Ix \wedge \neg Jx)) \wedge (\neg (Ib \vee Ic) \vee (Jb \vee Jc)) $

Symbolization Key:

F{1} {1} is friendly.

G{1} {1} is mean.

H{1} {1} is an elf.

I{1} {1} will bite.

J{1} {1} is provoked.

b Bruce

c Carrie

Apparently my answer is wrong, but I don't know why. Any help would be appreciated.