| $(M\ v\ N)\ \&\ K$ |
| $[M\ v\ N)\ v\ L] \rightarrow H$ |
| $[( M\ v\ N)\ \&\ H] \rightarrow Z$ |
| $\therefore Z$ |
| $(1)\ (M\ v\ N)\ \&\ K$ | $P$ |
| $(2)\ [(M\ v\ N)\ v\ L] \rightarrow H$ | $P$ |
| $(3)\ [( M\ v\ N)\ \&\ H] \rightarrow Z$ | $P/\therefore Z$ |
| $(4)\ M\ v\ N$ | $1,$ Simp. |
| $(5)\ (M\ v\ N)\ v\ L$ | $4,$ Add. |
| $(6)\ H$ | $2, 5,$ MP$ |
| $(7)\ (M\ v\ N)\ \&\ H$ | $4, 6,$ Conj. |
| $(8)\ Z$ | $3, 7, MP$ |
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| $H \rightarrow (I \rightarrow J)$ |
| $K \rightarrow (I \rightarrow J)$ |
| $(\sim H\ \&\ \sim K) \rightarrow (\sim\ L\ v\ \sim M)$ |
| $(\sim L \rightarrow\ \sim N)\ \&\ (\sim M \rightarrow \sim Q)$ |
| $\sim (I \rightarrow J)$ |
| $\sim N\ v\ \sim Q$ |
| $(A\ v\ B)\ \rightarrow [D\ \rightarrow\ (P\ \&\ \sim \ Q)]$ |
| $(A\ \&\ J) \rightarrow [(P\ \&\ \sim\ Q)\ \rightarrow\ K]$ |
| $(A\ \&\ J)\ \&\ (\sim\ K\ v\ D)$ |
| $\therefore (D\rightarrow K)\ v\ \sim\ Q$ |
| $(P\ \&\ Q) \rightarrow R$ |
| $R \rightarrow (H \rightarrow G)$ |
| $H\ \&\ K$ |
| $P\ \&\ Q$ |
| $\therefore (G\ v\ I)\ \&\ H$ |
| $(A\ \rightarrow\ E)\ \&\ (D\ \rightarrow\ F)$ |
| $B\ \&\ (A\ v\ D)$ |
| $(E\ v\ F)\ \rightarrow\ (B\ v\ D)$ |
| $\sim\ B$ |
| $\therefore D$ |