How can I ensure that two atoms in my query are not part of the same ring?

​To achieve this, you can use the ability in the ConQuest sketcher to specify that particular bonds are acyclic. This is done by right-clicking on the relevant bond (or atom), going to Cyclicity in the drop-down menu and then choosing Acyclic.

For example, if you are looking at ketones, you may want to ensure that the 1- and 3- carbons are part of rings, but not part of the same ring. In this case you would specify that the 1- and 3- carbons are cyclic, but the two C-C bonds to the 2- carbon are both acyclic.

Note that you can also access these Cyclicity options from the top-level Atoms and Bonds menus in the ConQuest sketcher.