I'm a student learning first-order logic, so forgive me if this is elementary.
If I'm given an inconsistent set (that is, a set $\Sigma$ that can be used to show $\phi$ and $\lnot\phi$), is it possible to form a set $\Gamma$ of out of its elements such that $\Gamma$ is consistent?
$\Gamma$ need not be maximally-consistent, as I'm told that is impossible to prove. Just looking for a general algorithm to do this. I feel like it involves resolution (as we've been taught resolution), but I'm not sure.