1. Prove using PROPOSITIONAL logic and Prover9 (departing from any of these two requirements will give you automatically 0 points) that the map that includes only Chile, Peru, Argentina and Bolivia (cf. Fig. 1) cannot be painted with 2 colors if adjacent countries must have different colors. To simplify, assume that the colors are blue and green. More precisely proceed as follows (and clearly include in your assignment report these three stages) 1. Prove using PROPOSITIONAL logic and Prover9 (departing from any of these two requirements will give you automatically 0 points) that the map that includes only Chile, Peru, Argentina and Bolivia (cf. Fig. 1) cannot be painted with 2 colors if adjacent countries must have different colors. To simplify, assume that the colors are blue and green. More precisely proceed as follows (and clearly include in your assignment report these three stages)