A mental set generally refers to the human brain's tendency to persist with a familiar solution and stubbornly ignore alternatives. However, if a familiar solution is unable to solve a problem similar to a previous problem, does it continue to hinder alternative solutions, and if so, how and why? To answer these questions, a Chinese character decomposition task was adopted in this study. Participants were asked to perform a practice problem that could be solved by a familiar loose chunk decomposition (LCD) solution followed by a test problem that was similar to the practice problem but could only be solved by an unfamiliar tight chunk decomposition (TCD) solution or were asked to repeatedly perform 3-5 practice problems followed by a test problem; the former is the base-set condition, and the latter is the enhanced-set condition. The results showed that the test problem recruited more activation of the inferior frontal gyrus (IFG), middle occipital cortex (MOG), superior parietal lobule (SPL) and dorsal anterior cingulate cortex (dACC) than the practice problem in the latter operation and verification stage, but almost equal activation of the dACC occurred in the early exploration stage. This likely implied that people did not think that the familiar but currently invalid LCD solution could not be used to solve the test problem; thus, it continuously competed for attention with the unfamiliar TCD solution, which required more executive control to suppress. Moreover, compared with the base-set condition, the test problem in the enhanced-set condition recruited greater activations of the IFG, SPL and dACC in the latter verification stage but less activations of regions in the left IFG and MOG in the early exploration stage. These results revealed that people less actively explored and had to work harder to operate the unfamiliar TCD solution, particularly to resolve competition from the familiar but currently invalid LCD solution. In conclusion, people lost the ability to identify errors in the familiar but currently invalid solution, which in turn decreased the exploration efforts and increased the processing demands associated with alternative solutions in the form of attentional bias and competition. This finding broadly explains the dilemma of creative problem solving.