Techniques to prove rather unobvious arguments

Question

I'm trying to prove this argument but I can't seem to find a way to prove it.

$a \to b$

$b \lor c$

$(c \land \sim a) \to (d \land \sim a)$

$\sim b$

$\therefore d$

EDIT: Attached below is the rules we are allowed to use. Rules

Answer 1

$1)$ $\overline{b}\to c$ (Given Premise).

$2)$ $\overline{b}$ (premise)

$3)$ $c$ (Modus ponens of 1,2)

$4)$ $\overline{b} \to \overline{a}$ (premise)

$5)$ $\overline{a}$ (Modus ponens of 2 ,4)

$6)$ $c$ $\wedge$ $\overline{a}$ (Conjunction of 3 ,5)

$7)$ $(c$ $\wedge$ $\overline{a})$ $\implies$ $(d$ $\wedge$ $\overline{a})$ (premise)

$8)$ $d$ $\wedge$ $\overline{a}$ (Modus ponens of 6,7)

$9)$ $d$ (From 8).