Solution of a symbolic logic problem with Separation of Cases inference rule

Question

$$(( S \land \lnot P ) \lor ( Q \land R )) ∴ ( \lnot P \lor Q )$$

I am trying to solve this symbolic logic problem ^^ with the separation of cases inferences rule but I am having trouble.

Answer 1

1) $( S \land \lnot P ) \lor ( Q \land R )$ --- premise

2) $( S \land \lnot P )$ --- assumed [a]

3) $\lnot P$ --- from 2) by Conjunction elimination (or simplification)

4) $(\lnot P \lor Q)$ --- from 3) by Disjunction introduction

5) $( S \land \lnot P ) \rightarrow (\lnot P \lor Q)$ --- from 2) and 4) by Conditional introduction, discharging [a]

6) $( Q \land R )$ --- assumed [b]

7) $Q$ --- from 6) by Conjunction elimination

8) $(\lnot P \lor Q)$ --- from 7) by Disjunction introduction

9) $( Q \land R ) \rightarrow (\lnot P \lor Q)$ --- from 6) and 8) by Conditional introduction, discharging [b]

7) $(\lnot P \lor Q)$ --- from 1), 5) and 9) by Disjunction elimination (or Separation of Cases).