| $H \rightarrow ( I\ \&\ \sim J)$ |
| $( I\ v\ G) \rightarrow K$ |
| $H$ |
| $\sim K\ \&\ I$ |
| $(1)\ H \rightarrow(I\ \&\ \sim J)$ | $P$ |
| $(2)\ (I\ v\ G) \rightarrow K$ | $P$ |
| $(3)\ H$ | $P/ K\ \&\ I$ |
| $(4)\ I\ \& \sim\ J$ | $1, 3, MP$ |
| $(5)\ I$ | $4,$ Simp. |
| $(6)\ I\ v\ G$ | $5,$ Add. |
| $(7)\ K$ | $2, 6, MP$ |
| $(8)\ K\ \&\ I$ | $7, 5,$ Conj. |
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| $(T\ \&\ P) \rightarrow \sim Q$ |
| $\sim (T\ \&\ P) \rightarrow (R \rightarrow \sim Q)$ |
| $(\sim S\ v\ R)\rightarrow\ \sim\ \sim Q$ |
| $\sim S$ |
| $\therefore \sim R\ \&\ \sim S$ |
| $A \rightarrow B$ |
| $\sim B\ v\ D$ |
| $\sim D$ |
| $\therefore \sim A\ \&\ \sim D$ |
| $(Q\ \&\ B)\ v\ \sim D$ |
| $(Q\ \&\ B) \rightarrow \sim E$ |
| $F \rightarrow \sim\ \sim E$ |
| $\sim D \rightarrow (L\ \&\ N)$ |
| $F$ |
| $L\ v\ (B\ \&\ D)$ |
| $N \ \&\ M$ |
| $\sim S\ (T \ \&\ W)$ |
| $(P \ \&\ R)\ v\ \sim S$ |
| $(N \ \&\ M) \rightarrow \sim (T \ \&\ W)$ |
| $(R \ \&\ N)\ v\ S$ |