| (~ X v ~ Y) $\rightarrow$ [A $\rightarrow$ (P & ~ Q)] |
| (~ X & ~R) $\rightarrow$ [(P & ~Q) $\rightarrow$ Z) |
| (~ X & ~R) & (~ Z v A) |
| $\therefore$ (A $\rightarrow$ Z) v ~ R |
| (1) ( ~ X v ~ Y)$\rightarrow$ (P& ~Q)] | P |
| (2) (~ X & ~ R) $\rightarrow$ (P & ~Q)$\rightarrow$ Z] | P |
| (3)(~ X &~R) & (~ Z v A) | P/$\therefore$ (A$\rightarrow$Z) V ~R |
| (4)( ~X &~R) | 3, Simp. |
| (5) ~X | 4, Simp. |
| (6) ~X v ~Y | 5, Add. |
| (7) A $\rightarrow$ (P & ~Q) | 1, 6, MP. |
| (8) (P &~Q) $\rightarrow$Z | 2,4, MP |
| (9) A$\rightarrow$Z | 7,8 HS |
| (10) (A$\rightarrow$Z) v ~R | 9, Add |
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| $(P\ \&\ Q) \rightarrow R$ |
| $R \rightarrow (H \rightarrow G)$ |
| $H\ \&\ K$ |
| $P\ \&\ Q$ |
| $\therefore (G\ v\ I)\ \&\ H$ |
| $(P \rightarrow\ Q)\ \&\ R$ |
| $E\ \&\ F$ |
| $\therefore [(F\ \&\ G)\ \&\ R ]\ \&\ E$ |
| $(P\ \&\ R)\ \&\ \sim T$ |
| $T\ v\ (F\ \&\ G)$ |
| $(F\ \&\ G )\ \rightarrow\ H$ |
| $\therefore (H\ \&\ P)\ v\ F$ |
| (P$\rightarrow$Q) & (R v S) |
| (R v S) $\rightarrow$ ~ L |
| L v (M & N) |
| $\therefore$ [(P $\rightarrow$ Q) & M] & ~ L |