| $R\ \rightarrow\ (A\ \&\ B)$ |
| $P\ v\ \sim\ (S\ \&\ T)$ |
| $\sim\ T\ \&\ \sim\ P$ |
| $(A\ \&\ B)\ \rightarrow\ (S\ \&\ T)$ |
| $(\sim\ R\ \&\ \sim\ T)\ v\ D$ |
| $(1)\ R\ \rightarrow\ (A\ \&\ B )$ | $P$ |
| $(2)\ P\ v\ \sim\ (S\ \&\ T)$ | $P$ |
| $(3)\ \sim\ T\ \&\ \sim\ P$ | $P$ |
| $(4)\ (A\ \&\ B)\ \rightarrow\ (S\ \&\ T)$ | $P/\ (\sim\ R\ \&\ \sim \ T)\ v\ D$ |
| $(5)\ \sim\ P$ | $3,$ Simp. |
| $(6)\ \sim\ (S\ \&\ T)$ | $2, 5, DS$ |
| $(7)\ \sim\ (A\ \&\ B)$ | $4, 6, MT$ |
| $(8)\ \sim\ R$ | $1, 7, MT$ |
| $(9)\ \sim\ T$ | $3,$ Simp. |
| $(10)\ \sim\ R\ \&\ \sim\ T$ | $8, 9,$ Conj. |
| $(11)\ (\sim\ R\ \&\ \sim\ T)\ v\ D$ | $10,$ Add. |
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| $P \rightarrow Q$ |
| $R \rightarrow S$ |
| $( \sim\ Q\ \&\ A) \& (P\ v\ R)$ |
| $\therefore (S\ v\ Z) \& \sim\ Q$ |
| $M \rightarrow N$ |
| $N \rightarrow O$ |
| $(M \rightarrow O) \rightarrow (N \rightarrow P)$ |
| $(N \rightarrow P) \rightarrow Q$ |
| $(Q\ v\ Z)\ \&\ Q$ |
| $(E\rightarrow F)\rightarrow H$ |
| $\sim J\ v (F\ \&\ G)$ |
| $F \rightarrow(H\rightarrow I)$ |
| $\sim\ \sim J$ |
| $G\ \&\ [(E\rightarrow F) \rightarrow I]$ |