Rewrite this argument in PL form

Question

I need to rewrite this argument in propositional logic, or PL, form.

There are events in our world—innocent children being brutally beaten and sexually assaulted, burning to death, dying painfully from disease—such that allowing those events when one could prevent them would be immoral. Any being that was omniscient and omnipotent would be capable of preventing events of this character. Therefore, any omniscient and omnipotent being that allowed such things to happen would be immoral. Since ‘God’ is defined as a being that is omniscient, omnipotent, and omni-benevolent, God must not exist.

What I have so far is:
I = "There are events in our world—innocent children being brutally beaten and sexually assaulted, burning to death, dying painfully from disease—such that allowing those events when one could prevent them would be immoral."
O = "God is omniscient, omnipotent, and omni-benevolent"
E = "God exists"

And my representation of the argument is as follows:
I
O → ¬I
¬O → ¬E
Conclusion: ¬E

My professor said that I need more letters, because right now what i have is incorrect. If someone could point me in the right direction here I would really appreciate it!

Answer 1

It is foolish and cruel trying to teach propositional logic that way...

Having said that :

"Bad events" are occurring in our world.

Any being that is capable of preventing "bad events" to occur and do not do that is immoral.

Any being that was omniscient and omnipotent would be capable of preventing "bad events".

Therefore, any omniscient and omnipotent being that allowed "bad events" to happen would be immoral.

God is omniscient and omnipotent.

God does not exist.

Symbolization :

1) BE_Occur i.e. Not_Prev

2) If (Prev and Not_Acting), then Immoral

3) If Omni, then Prev

4) Therefore, if (Omni and Not_Acting), then Immoral.

2)-4) is valid :

2) $(P \land \lnot A) \to I$

3) $O \to P$

4) $(O \land \lnot A) \to I$.

IMO, in order to properly manage an individual ("God") and to assert its existence, we need quantifiers, but we can still try to continue with propositional logic :

5) If God_exists, then Omni.

Thus, from 5) and 3) :

5) $G \to O$

6) $G \to P$.

With :

1) $\lnot P$

we have :

7) $\lnot G$

that we may read as : "God does not exist".