Hepatocellular carcinoma is the primary malignancy (cancer) of the liver that ranks fifth in frequency among all malignancies in the world. In highly suspected patients, the best method of diagnosis involves a scan of the abdomen, but only at a high cost. A cheap and effective alternative consists in detecting small or subtle increases for serum enzymes levels. Consequently, based on a set of 14 significant enzymes, a group of 299 individuals and two outcomes (benign or malignant), we aim to tackle this practical classification task through a novel evolutionary learning framework which embodies two contradictory prototypes coming from the acknowledged field of coevolution and has previously proven to be a viable alternative to state-of-the-art classifiers. The solution is regarded as a set of if-then conjunctive rules in first order logic, with the condition part in the attributes space and the outcome as the conclusion. Learning is driven either by the cooperation between rules towards a complete and accurate rule set or by the competition between rules and training samples for extensive testing on each side. Within the cooperative alternative, a natural decomposition of the problem solution is to assign rules of the same outcome to a population. When the quality of an individual is measured, collaborators from all the other populations are selected with the aim of forming complete solution(s) that may be easily evaluated. The training accuracy represents the evaluation of the considered individual (rule). The competitive classifier considers the training data set as one fixed species and the potential rules of assessment as the other evolving one. The two species evolve together, through the inverse fitness interaction: As candidate rules fit certain samples descriptions, these records receive weaker evaluation scores and are therefore not selected for encounters any more. Consequently, other samples, more difficult to assess, will be more often selected for competitions and rules will have to evolve through adaptation to the new records that must be given a verdict. The individuals have lifetime evaluations which allow them to keep up with the changing rankings in the other species. The coevolutionary couple gives a high accuracy of prediction on the hepatic cancer problem and thus provides an efficient means of checking the consistency of decision making in its early detection at significantly low expense.