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I'm kind of desperate at this point about this question.

A predicate-logic resolution derivation of a clause $C$ from a set of clauses $F$ is a sequence of clauses $C_1,\dots,C_m$, with $C_m = C$ such that each $C_i$ is either a clause of $F$ (possibly with the variables renamed) or follows by a resolution step from two preceding clauses $C_j ,C_k$, with $j, k < i$. We write $\operatorname{Res}^*(F)$ for the set of clauses $C$ such that there is a derivation of $C$ from $F$.

The question is to give an example of a finite set of clauses $F$ in first-order logic such that $\operatorname{Res}^*(F)$ is infinite.

Any help would be appreciated!

Yuval Filmus
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RnHdw
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1 Answers1

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This is Exercise 83 in Schöning's book "Logic for Computer Scientists". Similarly, the solution to this problem can be found in the original paper of Robinson. He gives an example with clauses $Q(a)$ and $\neg Q(x) \vee Q(f(x))$.

user1868607
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