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.