Unless you use an extremely narrow definition of "thinking" (yours is not commonly accepted among animal researchers, and is IMO too tautological to be useful), this is clearly disproven by decades of animal cognition research.
Animals can form future-oriented plans, engage in risk management activities, can remember inventories of items stored in safekeeping locations, develop "cultural" dialects to their vocalization patterns, and much more. You can find a good start on the current state of the research here