| $(P\ v\ R)\ \rightarrow (S\ v\ T)$ |
| $\sim M\ \&\ \sim N$ |
| $N\ v \sim (S\ v\ T)$ |
| $H \rightarrow (P\ v\ R)$ |
| $[\sim H\ \&\ \sim (P\ v\ R)]\ v\ S$ |
| $(1)\ (P v R)\ \rightarrow (S\ v\ T)$ | $P$ |
| $(2)\ \sim M\ \&\ \sim N$ | $P$ |
| $(3)\ N\ v\ \sim (S\ v\ T)$ | $P$ |
| $(4)\ H \rightarrow (P\ v\ R)$ | $P/ [\sim H\ \&\ \sim (P\ v\ R) ]\ v \ S$ |
| $(5)\ \sim N$ | $2,$ 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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| $G \rightarrow H$ |
| $(A\ v\ B) \rightarrow D$ |
| $D \rightarrow [(S\ \&\ T) \rightarrow P]$ |
| $(S\ \&\ T)\ v\ G$ |
| $A\ v\ B$ |
| $(P\ v\ H)\ \&\ D$ |
| $A \rightarrow B$ |
| $C \rightarrow B$ |
| $(\sim\ A\ \&\ \sim \ C)\ \rightarrow\ (D\ \rightarrow\ E)$ |
| $(E\ \rightarrow\ G)\ \&\ (D\ v\ E)$ |
| $E\ v\ G$ |
| $J\ v\ (J\ \&\ K)$ |
| $J \rightarrow D$ |
| $\sim\ D$ |
| $\therefore K\ v\ M$ |