| $(Q\ \&\ B)\ v\ \sim D$ |
| $(Q\ \&\ B) \rightarrow \sim E$ |
| $F \rightarrow \sim\ \sim E$ |
| $\sim D \rightarrow (L\ \&\ N)$ |
| $F$ |
| $L\ v\ (B\ \&\ D)$ |
| $(1)\ (Q\ \&\ B)\ v\ \sim D$ | $P$ |
| $(2)\ (Q\ \&\ B) \rightarrow \sim E$ | $P$ |
| $(3)\ F \rightarrow \sim\ \sim E$ | $P$ |
| $(4)\ \sim D \rightarrow (L\ \&\ N)$ | $P$ |
| $(5)\ F$ | $P/ L\ v\ ( B\ \&\ D)$ |
| $(6)\ \sim\ \sim E$ | $3, 5, MP$ |
| $(7)\ \sim (Q\ \&\ B)$ | $2, 6, MT$ |
| $(8)\ \sim D$ | $1, 7. DS$ |
| $(9)\ L\ \&\ N$ | $4, 8 MP$ |
| $(10)\ L$ | $9,$ Simp. |
| $(11)\ L\ v(B\ \&\ D)$ | $10,$ Add. |
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| $(A\ \rightarrow\ B)\ v\ D$ |
| $H\ \rightarrow\ [(A \ \rightarrow\ B)\ \rightarrow\ R]$ |
| $D\ \rightarrow\ E$ |
| $(E\ v\ F)\ \rightarrow\ H$ |
| $E\ v\ F$ |
| $(R\ v\ E)\ \&\ H$ |
| (P$\rightarrow$Q) & (R v S) |
| (R v S) $\rightarrow$ ~ L |
| L v (M & N) |
| $\therefore$ [(P $\rightarrow$ Q) & M] & ~ L |