| $R\rightarrow (S\ \&\ T)$ |
| $P\ v\ \sim (S\ \&\ T)$ |
| $Q\ \&\ \sim P$ |
| $\sim R\rightarrow (X\ \&\ Y)$ |
| $Q\ \&\ X$ |
| $(1)\ R\rightarrow (S\ \&\ T)$ | $P$ |
| $(2)\ P\ v\ \sim (S\ \&\ T)$ | $P$ |
| $(3)\ Q\ \&\ \sim\ P$ | $P$ |
| $(4)\ \sim R \rightarrow (X\ \&\ Y)$ | $P/ Q\ \&\ x$ |
| $(5)\ \sim P$ | $3,$ Simp. |
| $(6)\ \sim (S\ \&\ T)$ | $2, 5, DS$ |
| $(7)\ \sim R$ | $1, 6, MT$ |
| $(8)\ X$ | $4, 7, MP$ |
| $(9)\ X$ | $8,$ Simp. |
| $(10)\ Q$ | $3,$ Simp. |
| $(11)\ Q\ \&\ X$ | $10, 9,$ Conj. |
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| $(P\ \&\ R)\ \&\ \sim T$ |
| $T\ v\ (F\ \&\ G)$ |
| $(F\ \&\ G )\ \rightarrow\ H$ |
| $\therefore (H\ \&\ P)\ v\ F$ |
| $H \rightarrow (I \rightarrow J)$ |
| $K \rightarrow (I \rightarrow J)$ |
| $(\sim H\ \&\ \sim K) \rightarrow (\sim\ L\ v\ \sim M)$ |
| $(\sim L \rightarrow\ \sim N)\ \&\ (\sim M \rightarrow \sim Q)$ |
| $\sim (I \rightarrow J)$ |
| $\sim N\ v\ \sim Q$ |
| $(A\ v\ D) \rightarrow (R\ \&\ S)$ |
| $E\ v\ (A\ v\ D)$ |
| $F\ \&\ \sim E$ |
| $(R\ \&\ F)\ v\ K$ |