Predicate logic, is it the right solution?

Question

Mathematics

Prove justice using the method of resolutions:
No Republican or Democrat is a socialist. Norman Thomas is a socialist. Therefore, he is not a Republican.
I solved it like this:
P(x) = "x is a Republican"
Q(x) = "x is a Democrat"
S(x) = "x is a Socialist"
F1: ∀x∀y∀z ( (P(x) v Q(y)) → !S(z) ) = (CNF) = ( !S(z) v !P(x) ) ^ ( !S(z) v !Q(y) )
F2: S(Norman Thomas )
------------------------------------
R: !P(Norman Thomas)
Then many clauses:
{ !S(z) v !P(x), !S(z) v !Q(y), S(HT), P(HT) }
1) !S(z) v !P(x)
2) !S(z) v !Q(y)
3) S(HT)
4) P (HT)
-----------------
5) !P(HT) (connected 1 and 3)
6) F (connected 5 and 4)
since they came to a contradiction, then the original assumption was true.
Please tell me whether this decision is correct or not (and how then it should be decided)