| $A \rightarrow J$ |
| $B \rightarrow R$ |
| $(A\ v\ B)\&\ \sim D$ |
| $J \rightarrow D$ |
| $\therefore (D\ v\ R)\ \&\ (B\ v\ K)$ |
| $(1)\ A \rightarrow J$ | $P$ |
| $(2)\ B \rightarrow R$ | $P$ |
| $(3)\ (A\ v\ B)\ \& \sim\ D$ | $P$ |
| $(4)\ J \rightarrow D$ | $P/ \therefore (D\ v\ R)\ \&\ (B\ v\ K)$ |
| $(5)\ A \rightarrow D$ | $1, 4, HS$ |
| $(6)\ A\ v\ B$ | $3,$ Simp. |
| $(7)\ D\ v\ R$ | $5, 2, 6, CD$ |
| $(8)\ \sim D$ | $3,$ Simp. |
| $(9)\ \sim A$ | $5, 8, MT$ |
| $(10)\ B$ | $6, 9, DS$ |
| $(11)\ B\ v\ K$ | $10,$ Add. |
| $(12)\ (D\ v\ R)\ \&\ (B\ V\ K)$ | $7, 11,$ Conj. |
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| $A \rightarrow B$ |
| $C \rightarrow D$ |
| $\sim B\ \&\ \sim D$ |
| $(\sim A\ \&\ \sim C)\ v\ P$ |
| $A \rightarrow B$ |
| $A\ v\ C$ |
| $E\ \&\ \sim F$ |
| $\sim B$ |
| $\therefore\ C\ \&\ \sim F$ |
| $(M\ v\ N)\ \&\ K$ |
| $[M\ v\ N)\ v\ L] \rightarrow H$ |
| $[( M\ v\ N)\ \&\ H] \rightarrow Z$ |
| $\therefore Z$ |
| $(A\ \&\ B) \rightarrow\ \sim\ R$ |
| $R\ v\ \sim \ D$ |
| $T \rightarrow B$ |
| $D\ v\ (B \rightarrow P)$ |
| $A\ \&\ B$ |
| $\therefore (T\ P)\ v\ L$ |
| $P \rightarrow Q$ |
| $R \rightarrow S$ |
| $( \sim\ Q\ \&\ A) \& (P\ v\ R)$ |
| $\therefore (S\ v\ Z) \& \sim\ Q$ |