Is there an inference rule with premise neg X with neg X OR Y and conclusion Y?

Question

Is there an inference rule with a premise of $$\neg X,\neg X \lor Y $$ with the conclusion $$Y$$

How do I apply resultion as inference rule on the following for proposition logic formulas: $$\neg X,\neg X \lor Y, \neg Y$$

Thanks a lot in advance!

Answer 1

No, that would not be valid.   $\neg X, \neg X\vee Y\nvdash Y$.   The premises just say assume: "$X$ is definitely false, $Y$ may also be true."   So they don't infer that $Y$ is true.

However $\neg X,\neg X\wedge Y \vdash Y$ is valid . Under the assumption that $\neg X$ and $Y$ are true, then of course $Y$ is true.

Which did you actually mean?