| $G \rightarrow J$ |
| $J \rightarrow K$ |
| $(G \rightarrow K) v (J \rightarrow L)$ |
| $L \rightarrow M$ |
| $\therefore (J \rightarrow M) v\ Q$ |
| $(1)\ G\ \rightarrow\ J$ | $P$ |
| $(2)\ J\ \rightarrow\ K$ | $P$ |
| $(3)\ (G \rightarrow K) \rightarrow (J \rightarrow L)$ | $P$ |
| $(4)\ L \rightarrow M$ | $P/\therefore (J \rightarrow \ M)\ v\ Q$ |
| $(5)\ G \rightarrow K$ | $1, 2, HS$ |
| $(6)\ J \rightarrow L$ | $3, 5, MP$ |
| $(7)\ J\rightarrow M$ | $6, 4, HS$ |
| $(8)\ (J \rightarrow M)\ v\ Q$ | $7,$ Add. |
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| $M \rightarrow \sim (S \ \&\ T)$ |
| $\sim (A \ \&\ B)\ v\ \sim D$ |
| $\sim D (S \ \&\ T)$ |
| $M$ |
| $[\sim (A \ \&\ B) \ \&\ M)\ v\ D$ |
| $\sim\ L\ \rightarrow\ \sim\ N$ |
| $(A\ v\ B)\ \rightarrow\ Q$ |
| $Q\ \rightarrow\ [(S\ \&\ T) \rightarrow\ P]$ |
| $(S\ \&\ T)\ v\ \sim\ L$ |
| $A\ v\ B$ |
| $\therefore\ (P\ v\ \sim\ N)\ \&\ Q$ |
| $(P \rightarrow\ Q)\ \&\ R$ |
| $E\ \&\ F$ |
| $\therefore [(F\ \&\ G)\ \&\ R ]\ \&\ E$ |
| (A & B) $\rightarrow$ [A $\rightarrow$ (D & E)] |
| (A & B) & C |
| $\therefore$E v G |
| $R\ \rightarrow\ (A\ \&\ B)$ |
| $P\ v\ \sim\ (S\ \&\ T)$ |
| $\sim\ T\ \&\ \sim\ P$ |
| $(A\ \&\ B)\ \rightarrow\ (S\ \&\ T)$ |
| $(\sim\ R\ \&\ \sim\ T)\ v\ D$ |
| $A \rightarrow B$ |
| $C \rightarrow D$ |
| $(\sim\ B\ \&\ P)\ \&\ (A\ v\ C)$ |
| $(D\ v\ Z)\ \&\ \sim B$ |