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