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