Available statements
Initial premises
(p ∧ q) ∨ r
r → s
Inference rules
distribution
From (p ∧ q) ∨ r you may derive p ∨ r or q ∨ r.
implication-elim
From r → s you may derive ¬r ∨ s.
resolution
From (X ∨ r) and (¬r ∨ Y) derive (X ∨ Y).
Drop premises here (you can drop multiple)
Drop rule
Target conclusion: p ∨ s