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