| $(R\ S) \rightarrow (F\ E)$ |
| $\sim (R\ S) \rightarrow J$ |
| $(F\ E) \rightarrow \sim H$ |
| $\sim\ \sim H$ |
| $\therefore \sim (J\ v\ G) \& \sim\ \sim H$ |
| $(1)\ (R\ S) \rightarrow (F\ E)$ | $P$ |
| $(2)\ \sim (R\ S ) \rightarrow J$ | $P$ |
| $(3)\ (F\ E) \rightarrow \sim H$ | $P$ |
| $(4)\ \sim\ \sim H$ | $P/ \therefore (J\ v\ G)\ \&\ \sim\ \sim\ H$ |
| $(5)\ (R\ S) \rightarrow \sim\ H$ | $1,3, HS$ |
| $(6)\ \sim\ ( R\ S)$ | $5,4, MT$ |
| $(7)\ J$ | $2,6, MP$ |
| $(8)\ J\ v\ G$ | $7,$ Add. |
| $(9)\ (J\ v\ G)\ \&\ \sim\ \sim\ H$ | $8, 4,$ Conj. |
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| $J\ v\ (J\ \&\ K)$ |
| $J \rightarrow D$ |
| $\sim\ D$ |
| $\therefore K\ v\ M$ |
| $B\ \&\ (A\ v\ D)$ |
| $(A \rightarrow E)\ \&\ (D \rightarrow F)$ |
| $(E\ v\ F) \rightarrow (B\ v\ D)$ |
| $\sim B$ |
| $D$ |
| $E\ v\ (E\ \&\ Q)$ |
| $E \rightarrow L$ |
| $\sim L$ |
| $Q\ v\ M$ |
| $K\rightarrow\ (W\ \rightarrow\ X)$ |
| $( \sim\ Q\ \&\ \sim\ K)\ \rightarrow\ (\sim\ Y\ v\ \sim\ M)$ |
| $(\sim\ Y\ \rightarrow\ \sim\ Z)\ \&\ (\sim\ M\ \rightarrow\ \sim\ P)$ |
| $(W\ \rightarrow\ X)$ |
| $\therefore \sim\ Z\ v\ \sim\ p$ |
| $A\ v\ B$ |
| $\sim\ A\ \&\ C$ |
| $\therefore (B\ v\ \sim\ D)\ \&\ C$ |
| $A \rightarrow B$ |
| $\sim B\ v\ D$ |
| $\sim D$ |
| $\therefore \sim A\ \&\ \sim D$ |
| $A \rightarrow B$ |
| $A\ v\ C$ |
| $E\ \&\ \sim F$ |
| $\sim B$ |
| $\therefore\ C\ \&\ \sim F$ |