A good collegiate dictionary is probably the most useful book you can own. It will give you derivations of most words, and there is no better way to build your vocabulary than by learning the derivations of words and not just their meaning. Know where a word comes from enables you to use it properly in speech and writing. It is also the best way of choosing a word from among all the related words in the English language.
If you want to have a dictionary online, the Merriam-Webster Online Dictionary is easy to access and bookmark. It provides thorough explanations of words with etymologies, synonyms, and other information. Please use the reference link below to access this online dictionary.
This dictionary also has a lot of quizzes that are fun to take and help to build vocabulary as well as general knowledge.
I looked up "counterexample" in the Merriam-Webster Online Dictionary. Their definition is brief and does not include any derivations. Obviously a counterexample is an example offered in contradiction or opposition to a previous example. Therefore, it is necessary to refer to the word "example."
The word "example" is thoroughly explained in the online dictionary. In fact, they say that this word is among the top ten percent of the words that are looked up in their site. Part of this explanation is the following:
Origin of EXAMPLEMiddle English, from Anglo-French essample, example, from Latin exemplum, from eximere to take out, from ex- + emere to take — more at redeemFirst Known Use: 14th century
Related to EXAMPLE
case, exemplar, exemplification, illustration, instance, prototype, representative, sample, specimen, case in point
The definition given for "counterexample" is simply:
: an example that refutes or disproves a proposition or theory
You are very wise to be taking an interest in ontological derivations. It can provide rich learning experiences for your entire life. I suggest that you also look up "etymology."
I have owned a copy of The American Heritage Dictionary, Second College Edition, for many years. I still use it. It is like an old friend.