| $(Q\ \&\ B)\ v\ \sim D$ |
| $(Q\ \&\ B) \rightarrow \sim E$ |
| $F \rightarrow \sim\ \sim E$ |
| $\sim D \rightarrow (L\ \&\ N)$ |
| $F$ |
| $L\ v\ (B\ \&\ D)$ |
| $(1)\ (Q\ \&\ B)\ v\ \sim D$ | $P$ |
| $(2)\ (Q\ \&\ B) \rightarrow \sim E$ | $P$ |
| $(3)\ F \rightarrow \sim\ \sim E$ | $P$ |
| $(4)\ \sim D \rightarrow (L\ \&\ N)$ | $P$ |
| $(5)\ F$ | $P/ L\ v\ ( B\ \&\ D)$ |
| $(6)\ \sim\ \sim E$ | $3, 5, MP$ |
| $(7)\ \sim (Q\ \&\ B)$ | $2, 6, MT$ |
| $(8)\ \sim D$ | $1, 7. DS$ |
| $(9)\ L\ \&\ N$ | $4, 8 MP$ |
| $(10)\ L$ | $9,$ Simp. |
| $(11)\ L\ v(B\ \&\ D)$ | $10,$ Add. |
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| $(R\ S) \rightarrow (F\ E)$ |
| $\sim (R\ S) \rightarrow J$ |
| $(F\ E) \rightarrow \sim H$ |
| $\sim\ \sim H$ |
| $\therefore \sim (J\ v\ G) \& \sim\ \sim H$ |
| $R\ \rightarrow\ (A\ \&\ B)$ |
| $P\ v\ \sim\ (S\ \&\ T)$ |
| $\sim\ T\ \&\ \sim\ P$ |
| $(A\ \&\ B)\ \rightarrow\ (S\ \&\ T)$ |
| $(\sim\ R\ \&\ \sim\ T)\ v\ D$ |
| $T \rightarrow W$ |
| $X \rightarrow Y$ |
| $Z \rightarrow W$ |
| $X \rightarrow A$ |
| $W \rightarrow X$ |
| $[(T \rightarrow Y)\ \&\ (Z \rightarrow A)] \rightarrow (T\ v\ Z)$ |
| $B\ \&\ (A\ v\ D)$ |
| $(A \rightarrow E)\ \&\ (D \rightarrow F)$ |
| $(E\ v\ F) \rightarrow (B\ v\ D)$ |
| $\sim B$ |
| $D$ |