| $R\ \rightarrow\ (S\ v\ T)$ |
| $P\ v((S\ v\ T)\ \rightarrow\ W]$ |
| $M\ v\ \sim\ P$ |
| $(H\ \&\ N)\ \rightarrow\ \sim\ M$ |
| $H\ \&\ N$ |
| $(R\ \rightarrow\ W)\ v\ S$ |
| $(1)\ R\ \rightarrow\ (S\ v\ T)$ | $P$ |
| $(2)\ P\ v\ [(S\ v\ T)\ \rightarrow\ W)$ | $P$ |
| $(3)\ M\ v\ \sim\ P$ | $P$ |
| $(4)\ (H\ \&\ N)\ \rightarrow\ \sim\ M$ | $P$ |
| $(5)\ H\ \&\ N$ | $P/(R\ \rightarrow\ W)\ v\ S$ |
| $(6)\ \sim\ M$ | $4, 5, MP$ |
| $(7)\ \sim\ P$ | $3, 6, DS$ |
| $(8)\ (S\ v\ T) \rightarrow\ W$ | $2, 7, DS$ |
| $(9)\ R\ \rightarrow\ W$ | $1, 8, HS$ |
| $(10)\ (R\ \rightarrow\ W)\ v\ S$ | $9,$ Add. |
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| $(A\ v\ B)\ \rightarrow [D\ \rightarrow\ (P\ \&\ \sim \ Q)]$ |
| $(A\ \&\ J) \rightarrow [(P\ \&\ \sim\ Q)\ \rightarrow\ K]$ |
| $(A\ \&\ J)\ \&\ (\sim\ K\ v\ D)$ |
| $\therefore (D\rightarrow K)\ v\ \sim\ Q$ |
| $M \rightarrow \sim (S \ \&\ T)$ |
| $\sim (A \ \&\ B)\ v\ \sim D$ |
| $\sim D (S \ \&\ T)$ |
| $M$ |
| $[\sim (A \ \&\ B) \ \&\ M)\ v\ D$ |
| $P\ v\ Q$ |
| $R \rightarrow \sim P$ |
| $R\ \&\ S$ |
| $Q \rightarrow (R\ \&\ P)$ |
| $\therefore P\ v\ R$ |
| $E\rightarrow H$ |
| $F\rightarrow (I\ v\ P)$ |
| $(E\ v\ F)\ \&\ \sim G$ |
| $H \rightarrow G$ |
| $\therefore I\ v\ P$ |