| $(J \rightarrow K)\ \&\ R$ |
| $\sim P \rightarrow (A \rightarrow B)$ |
| $P\ v\ (J\ v\ A)$ |
| $\sim P$ |
| $\therefore K\ v\ B$ |
| $(1)\ (J \rightarrow K)\ \&\ R$ | $P$ |
| $(2)\ \sim P \rightarrow (A \rightarrow B)$ | $P$ |
| $(3)\ P\ v\ (J\ v\ A)$ | $P$ |
| $(4) \sim P$ | $P/ \therefore \ K\ v\ B$ |
| $(5)\ J \rightarrow K$ | $1,$ Simp. |
| $(6)\ A \rightarrow B$ | $2, 4, MP$ |
| $(7)\ J\ v\ A$ | $3, 4, DS$ |
| $(8)\ K\ v\ B$ | $5, 6, 7, CD$ |
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| $E\rightarrow (F\ \&\ \sim G)$ |
| $( F\ v\ G)\rightarrow H$ |
| $E$ |
| $\therefore H$ |
| $(A\ \rightarrow\ E)\ \&\ (D\ \rightarrow\ F)$ |
| $B\ \&\ (A\ v\ D)$ |
| $(E\ v\ F)\ \rightarrow\ (B\ v\ D)$ |
| $\sim\ B$ |
| $\therefore D$ |
| $(A\ v\ B)\ \rightarrow [D\ \rightarrow\ (P\ \&\ \sim \ Q)]$ |
| $(A\ \&\ J) \rightarrow [(P\ \&\ \sim\ Q)\ \rightarrow\ K]$ |
| $(A\ \&\ J)\ \&\ (\sim\ K\ v\ D)$ |
| $\therefore (D\rightarrow K)\ v\ \sim\ Q$ |
| $M \rightarrow \sim (S \ \&\ T)$ |
| $\sim (A \ \&\ B)\ v\ \sim D$ |
| $\sim D (S \ \&\ T)$ |
| $M$ |
| $[\sim (A \ \&\ B) \ \&\ M)\ v\ D$ |
| $P\ v\ Q$ |
| $R \rightarrow \sim P$ |
| $R\ \&\ S$ |
| $Q \rightarrow (R\ \&\ P)$ |
| $\therefore P\ v\ R$ |
| $(A\ v\ B)\ \rightarrow\ D$ |
| $E\ \rightarrow\ \sim\ D$ |
| $(G\ \leftrightarrow\ F)\ \rightarrow\ (E\ \&\ H)$ |
| $G\ \leftrightarrow\ F$ |
| $\sim\ (A\ v\ B)\ \&\ H$ |