| $(A\ \&\ B) \rightarrow\ \sim\ R$ |
| $R\ v\ \sim \ D$ |
| $T \rightarrow B$ |
| $D\ v\ (B \rightarrow P)$ |
| $A\ \&\ B$ |
| $\therefore (T\ P)\ v\ L$ |
| $(1)\ ( A\ \&\ B) \rightarrow\ \sim\ R$ | $P$ |
| $(2)\ R\ v\ \sim\ D$ | $P$ |
| $(3)\ T \rightarrow B$ | $P$ |
| $(4)\ D\ v\ (B \rightarrow P)$ | $P$ |
| $(5)\ A\ \&\ B$ | $P/ \therefore (T \rightarrow P) \ v\ L$ |
| $(6)\ \sim R$ | $1, 5, MP$ |
| $(7)\ \sim D$ | $2, 6, DS$ |
| $(8)\ B \rightarrow P$ | $4, 7, DS$ |
| $(9)\ T \rightarrow P$ | $3, 8, HS$ |
| $(10)\ (T \rightarrow P)\ v\ L$ | $9,$ Add. |
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| $(A\ \rightarrow\ E)\ \&\ (D\ \rightarrow\ F)$ |
| $B\ \&\ (A\ v\ D)$ |
| $(E\ v\ F)\ \rightarrow\ (B\ v\ D)$ |
| $\sim\ B$ |
| $\therefore D$ |
| $J \rightarrow K$ |
| $J\ v\ (K\ v\ \sim\ L)$ |
| $\sim K$ |
| $\therefore \sim L\ \&\ \sim K$ |
| $(A\ v\ B) \rightarrow D$ |
| $A$ |
| $\therefore (D\ \&\ A)\ v\ P$ |
| $(P\ \&\ Q) \rightarrow S$ |
| $S \rightarrow ( \sim L \rightarrow \sim N)$ |
| $\sim L\ \&\ \sim N$ |
| $P\ \&\ Q$ |
| $\therefore\sim N\ v\ F$ |