Question 1179972
In this proof I use the Natural Deduction Rules. The kind that uses introduction rules and elimination rules.  See illustration.
*[illustration proof]



For those who may not be familiar what -->I means the I here stands for Introduction. The arrow is the symbol (called a connective) for a IF . . . THEN statement --also called a CONDITIONAL STATEMENT.  So when you see the connective --> you expect to see something like If Al is a Man, then Al is a Human. 
A Conditional Proof also goes by the name --> Introduction. Some sources will write --->I at the end of a proof. Others my show the same proof and write Conditional Proof as a justification instead of -->I. They are the same concept.

***Well the instruction clearly say do not use Conditional proof!  Well then you may be not using Natural Deduction Rules.  You are using what is called Copi rules with rules like disjunctive syllogism, modus tollens, material implication and so on. 
Okay that can also be done.
<pre>

1. O ⊃ (Q • N)
2. (N Ú E) ⊃ S     /   O ⊃ S
----------------------------------
3. ~O v (Q & N)               1    Implication
4. (~O v Q) & (~O v N)        3    Distribution
5. (~O v N) & (~O v Q)        4    Commutation
6. (~O v N)                   5    Simplification
7. ~O v (N v E)               6    Addition
8. ~O --> (N v E)             7    Implication
9.  O --> S                  2,8   Hypothetical Syllogism
                                                              QED.
</pre>