Question
All artisans are diligent.
Some engineers are craftsmen.
Some engineers are diligent.
Some engineers are craftsmen.
Some engineers are diligent.

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| $(H\ \&\ K)\ \rightarrow\ (J\ v\ K)$ |
| $\sim\ E\ \&\ \sim\ F$ |
| $F\ v\ \sim\ (J\ v\ K)$ |
| $\sim\ (H\ \&\ K)\ \rightarrow\ H$ |
| $H\ \&\ \sim\ E$ |
| $(A\ \&\ D) \rightarrow C$ |
| $E\rightarrow (B\ v\ D)$ |
| $F \rightarrow (A\ \&\ D)$ |
| $F\ \&\ G$ |
| $C\ v\ (B\ v\ D)$ |
| $(A \rightarrow B) \rightarrow R$ |
| $R \rightarrow S$ |
| $(A \rightarrow B)\ \&\ T$ |
| $S\ \&\ T$ |
| $(X \rightarrow Y)\ v\ D$ |
| $A \rightarrow [(X \rightarrow Y) \rightarrow R]$ |
| $D \rightarrow E$ |
| $(E\ v\ F) \rightarrow A$ |
| $E\ v\ F$ |
| $\therefore (R\ v\ E)\ \&\ A$ |
| $(A\ v\ B)\ v\ Q$ |
| $(J\ v\ K)\ v\ R$ |
| $\sim\ R\ \&\ \sim\ Q$ |
| $\therefore\ (A\ v\ B)\ \&\ (J\ v\ K)$ |