Premises:
a)~p v q -> r
b) s v ~q
c)~t
d)p -> t
e)~p (and) r -> ~s
Therefore, ~q

This is my attempt:

1) ~t (from c)

2) p-> t
~t
therefore, ~p (Modus Tollens)

3)~p v q-> r
~p
therefore, r (Whats is this called? elimination?)

4)~p (and) r-> ~s
~p (and) r (<---from 2, 3)
therefore, ~s (<--Modus Ponens)

5) s v ~q
~s (from 4)
therefore, ~q (elimination)

Did I do good? Is there anything I should add/ change?

2. Also, If I am working on a demonstration and the conclusion is an 'or statement' such as: ~p OR q

and I have proven that ~p, then does that means that I have completed my proof...? How would I write that as a step in the demonstration? b/c I am not suppose to use the conclusion as part of my proof. So once I reach the part of the proof where ~p, that is part of my conclusion, since (conclusion: ~p OR q). So am I done once I reach either ~p or q?

For example (conclusion: ~p OR t):
p OR q
~q
therefore, ~p
(would I add a separate step for the conclusion, or add another line here and write therefore AGAIN and then write ~p or t, since the conclusion is reached...??)