Recently, large pre-trained language models (LLMs) have demonstrated superior language understanding abilities, including zero-shot causal reasoning. However, it is unclear to what extent their capabilities are similar to human ones. We here study the processing of an event B in a script-based story, which causally depends on a previous event A. In our manipulation, event A is stated, negated, or omitted in an earlier section of the text. We first conducted a self-paced reading experiment, which showed that humans exhibit significantly longer reading times when causal conflicts exist (¬ A → B) than under logical conditions (A → B). However, reading times remain similar when cause A is not explicitly mentioned, indicating that humans can easily infer event B from their script knowledge. We then tested a variety of LLMs on the same data to check to what extent the models replicate human behavior. Our experiments show that 1) only recent LLMs, like GPT-3 or Vicuna, correlate with human behavior in the ¬ A → B condition. 2) Despite this correlation, all models still fail to predict that nil → B is less surprising than ¬ A → B, indicating that LLMs still have difficulties integrating script knowledge.