| $(H\ \&\ K)\ \rightarrow\ (J\ v\ K)$ |
| $\sim\ E\ \&\ \sim\ F$ |
| $F\ v\ \sim\ (J\ v\ K)$ |
| $\sim\ (H\ \&\ K)\ \rightarrow\ H$ |
| $H\ \&\ \sim\ E$ |
| $(1)\ (H\ \&\ K)\ \rightarrow\ (J\ v\ K)$ | $P$ |
| $(2)\ \sim\ E\ \&\ \sim\ F$ | $P$ |
| $(3)\ F\ v\ \sim\ (J\ v\ k)$ | $P$ |
| $(4)\ \sim\ (H\ \&\ K)\ \rightarrow\ H$ | $P/ H\ \&\ \sim\ E$ |
| $(5)\ \sim\ F$ | $2,$ Simp. |
| $(6)\ \sim\ (J\ v\ k)$ | $3, 5, DS$ |
| $(7)\ \sim\ (H\ K)$ | $1, 6, MT$ |
| $(8)\ H$ | $4, 7, MP$ |
| $(9)\ \sim\ E$ | $2,$ Simp. |
| $(10)\ H\ \&\ \sim\ E$ | $8, 9,$ Conj. |
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| $K\rightarrow\ (W\ \rightarrow\ X)$ |
| $( \sim\ Q\ \&\ \sim\ K)\ \rightarrow\ (\sim\ Y\ v\ \sim\ M)$ |
| $(\sim\ Y\ \rightarrow\ \sim\ Z)\ \&\ (\sim\ M\ \rightarrow\ \sim\ P)$ |
| $(W\ \rightarrow\ X)$ |
| $\therefore \sim\ Z\ v\ \sim\ p$ |
| $A \rightarrow B$ |
| $C \rightarrow D$ |
| $(\sim\ B\ \&\ P)\ \&\ (A\ v\ C)$ |
| $(D\ v\ Z)\ \&\ \sim B$ |
| $P \rightarrow Q$ |
| $\sim Q\ v\ R$ |
| $\sim R$ |
| $\therefore (\sim P \& \sim R)\ v\ S$ |
| $(R\ \&\ S)\ v\ P$ |
| $P\ \rightarrow\ Q$ |
| $T\ v\ (R\ \&\ S)\ \rightarrow\ W ]$ |
| $S\ \&\ \sim\ T$ |
| $[S\ \&\ (W\ v\ Q)]\ v\ \sim\ P$ |