Convert the following set of English statements into a set of predicate logic statements.

1) Every tree that is an oak contains some grackle.

2) If anyone walks under any tree that contains any grackle, then he hates every grackle.

3) For every building, there is some tree that is beside it.

4) Taylor Hall is a building.

5) Every CS student visits Taylor Hall.

6) If anyone visits any building, then he walks under every tree that is beside that building.

Show that the following conclusion is true:

If some CS student does not hate some grackle, then there is some tree beside Taylor Hall that is not an oak.