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