Proof Using Resolution

Prove: (P -> Q) & (Q -> R) => (P -> R)

Negate the conclusion:

(P -> Q) & (Q -> R) => ~(P -> R)

Obtain clause form:

~P v Q, ~Q v R, P, ~R.

Derive the null clause using resolution:

Q resolving P with ~P v Q.

R resolving Q with ~Q v R.

F resolving R with ~R.

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