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Many real-world phenomena exhibit both relational structure and uncertainty. Probabilistic Inductive Logic Programming (PILP) uses Inductive Logic Programming (ILP) extended with probabilistic facts to produce meaningful and interpretable models for real-world phenomena. This merge between First Order Logic (FOL) theories and uncertainty makes PILP a very adequate tool for knowledge representation and extraction. However, this flexibility is coupled with a problem (inherited from ILP) of exponential search space growth and so, often, only a subset of all possible models is explored due to limited resources. Furthermore, the probabilistic evaluation of FOL theories, coming from the underlying probabilistic logic language and its solver, is also computationally demanding. This work introduces a prediction-based pruning strategy, which can reduce the search space based on the probabilistic evaluation of models, and a safe pruning criterion, which guarantees that the optimal model is not pruned away, as well as two alternative more aggressive criteria that do not provide this guarantee. Experiments performed using three benchmarks from different areas show that prediction pruning is effective in (i) maintaining predictive accuracy for all criteria and experimental settings; (ii) reducing the execution time when using some of the more aggressive criteria, compared to using no pruning; and (iii) selecting better candidate models in limited resource settings, also when compared to using no pruning.