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