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