| (~ 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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| (A & B) $\rightarrow$ [A $\rightarrow$ (D & E)] |
| (A & B) & C |
| $\therefore$E v G |
| $A \rightarrow J$ |
| $B \rightarrow R$ |
| $(A\ v\ B)\&\ \sim D$ |
| $J \rightarrow D$ |
| $\therefore (D\ v\ R)\ \&\ (B\ v\ K)$ |
| $P \rightarrow Q$ |
| $R \rightarrow S$ |
| $( \sim\ Q\ \&\ A) \& (P\ v\ R)$ |
| $\therefore (S\ v\ Z) \& \sim\ Q$ |
| $(M \leftrightarrow N) \rightarrow O$ |
| $\sim A\ v\ (B\ \&\ D)$ |
| $B \rightarrow (O \rightarrow P)$ |
| $\sim \sim A$ |
| $\therefore (M \leftrightarrow N) \rightarrow P$ |
| $R\ \rightarrow\ (S\ v\ T)$ |
| $P\ v((S\ v\ T)\ \rightarrow\ W]$ |
| $M\ v\ \sim\ P$ |
| $(H\ \&\ N)\ \rightarrow\ \sim\ M$ |
| $H\ \&\ N$ |
| $(R\ \rightarrow\ W)\ v\ S$ |
| $H \rightarrow I$ |
| $H\ \&\ J$ |
| $I \rightarrow G$ |
| $G\ \&\ J$ |
| $K\rightarrow\ (W\ \rightarrow\ X)$ |
| $( \sim\ Q\ \&\ \sim\ K)\ \rightarrow\ (\sim\ Y\ v\ \sim\ M)$ |
| $(\sim\ Y\ \rightarrow\ \sim\ Z)\ \&\ (\sim\ M\ \rightarrow\ \sim\ P)$ |
| $(W\ \rightarrow\ X)$ |
| $\therefore \sim\ Z\ v\ \sim\ p$ |