Exercise 9.24

Let $\cal L$ be the first-order language with a single predicate $S(p,q)$, meaning “$p$ shaves  $q$.” Assume a domain of people.

1. Consider the sentence “There exists a person $P$ who shaves every one who does not shave themselves, and only people that do not shave themselves.” Express this in $\cal L$.

2. Convert the sentence in (a) to clausal form.

3. Construct a resolution proof to show that the clauses in (b) are inherently inconsistent. (Note: you do not need any additional axioms.)