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