How to find "if Q then S" in this classic CSL derivation [closed]

Question

Here's the problem: I have to derive Q>S from:

1. (P^Q^R)>S
2. (~P^Q^~R)>S

I'm not allowed to use any derived rules or replacement rules (De Morgan's, implication, Modus Tolluns etc), only classic logic rules. I have tried everything I can think of and still cannot manage to get to the answer I need.

Answer 1

The reason that you cannot prove it is because it is not true.

Consider:

IF P and Q are true and R and S are false, 

THEN:      < T   T    F     F >
        1. ( P & Q &  R) -> S  is true     ( because "(False) -> False" is valid )
 and    2. (~P & Q & ~R) -> S  is true     ( also because "(False) -> False" )

BUT:             Q       -> S  is NOT true ( because "True -> False" is invalid )

Therefore it cannot be possible to (validly) derive Q->S from your statements 1 and 2, even if you could use all of the derived rules, replacement, etc.

Pretty hard to prove something that's not true. (In logic anyway :)