Symbolize the following: Given that some mean elf will bite and some friendly one will too, the mean ones will bite whether or not provoked but the friendly ones will bite only if provoked.

Attempt:

$\displaystyle (\exists x((Gx \wedge Hx) \wedge Ix) \wedge \exists x((Fx \wedge Hx) \wedge Ix)) \rightarrow \forall x ((((Gx \wedge Hx) \wedge Ix) \rightarrow (Jx \vee \neg Jx)) \wedge ((Fx \wedge Hx) \wedge Ix) \rightarrow Jx) $

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

This is the last and unfortunately the hardest question in my problem set. I think my error lies within the second part of my attempt, though I'm not sure.