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Herbrand sentences

Show that the following sets of sentences are inconsistent by producing a set of inconsistent Herbrand sentences:

  1. $ \forall$x[x smokes  $ \rightarrow$ $ \neg$ x is wise],
    $ \exists$x[x smokes $ \wedge$ x is wise].
  2. $ \exists$x$ \exists$y[x hates y],
    $ \neg$$ \exists$y$ \exists$x[x hates y],
  3. $ \exists$x$ \forall$y[x hates y],
    $ \exists$y$ \forall$x[$ \neg$ x hates y],



Sandy Berkovski