| $(R\ \&\ S)\ v\ P$ |
| $P\ \rightarrow\ Q$ |
| $T\ v\ (R\ \&\ S)\ \rightarrow\ W ]$ |
| $S\ \&\ \sim\ T$ |
| $[S\ \&\ (W\ v\ Q)]\ v\ \sim\ P$ |
| $(1)\ (R\ \&\ S)$ | $P$ |
| $(2)\ P\ \rightarrow\ Q$ | $P$ |
| $(3)\ T\ v\ [(R\ \&\ S)\ \rightarrow\ W$ | $P$ |
| $(4)\ \sim\ T$ | $P/ [S\ \&\ (W\ v\ Q)]\ v\ \sim\ P$ |
| $(5)\ \sim\ T$ | $4,$ Simp. |
| $(6)\ (R\ \&\ S)\ \rightarrow \ W$ | $3, 5, DS$ |
| $(7)\ W\ v\ Q$ | $6, 2, 1, CD$ |
| $(8)\ S$ | $4,$ Simp. |
| $(9)\ S\ \&\ (W\ v\ Q)$ | $8, 7,$ Conj. |
| $(10)\ [S\ \&\ (W\ v\ Q)\ v\ \sim\ P$ | $9,$ Add. |
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| $M \rightarrow N$ |
| $N \rightarrow O$ |
| $(M \rightarrow O) \rightarrow (N \rightarrow P)$ |
| $(N \rightarrow P) \rightarrow Q$ |
| $(Q\ v\ Z)\ \&\ Q$ |
| $(P\ \&\ Q) \rightarrow S$ |
| $S \rightarrow ( \sim L \rightarrow \sim N)$ |
| $\sim L\ \&\ \sim N$ |
| $P\ \&\ Q$ |
| $\therefore\sim N\ v\ F$ |
| (~ X v ~ Y) $\rightarrow$ [A $\rightarrow$ (P & ~ Q)] |
| (~ X & ~R) $\rightarrow$ [(P & ~Q) $\rightarrow$ Z) |
| (~ X & ~R) & (~ Z v A) |
| $\therefore$ (A $\rightarrow$ Z) v ~ R |
| $A \rightarrow B$ |
| $\sim B\ v\ D$ |
| $\sim D$ |
| $\therefore \sim A\ \&\ \sim D$ |