Problem 1: use resolution refutation in order to prove the propositional sentence Light5(Light7 & Light2)) from the given set of premises -Light2-> Lightl Light4 >Light3 Lights-> (Light 1 & Light4) -Light6> -Light2 Light7 =>-Light& Show all details of CNF conversion followed by resolution refutation (also with all details) For resolution refutation, each step of resolution should be displayed in a manner similar to the following hypothetical step 5. with 17. Remember that each clause can participate in any number of resolution steps. Each new resolvent is simply added with a new number for reference in future resolution steps Repeat this exercise for the same set of given premises, but this time, prove that Light3Light4 & -Light5) Problem 1: use resolution refutation in order to prove the propositional sentence Light5(Light7 & Light2)) from the given set of premises -Light2-> Lightl Light4 >Light3 Lights-> (Light 1 & Light4) -Light6> -Light2 Light7 =>-Light& Show all details of CNF conversion followed by resolution refutation (also with all details) For resolution refutation, each step of resolution should be displayed in a manner similar to the following hypothetical step 5. with 17. Remember that each clause can participate in any number of resolution steps. Each new resolvent is simply added with a new number for reference in future resolution steps Repeat this exercise for the same set of given premises, but this time, prove that Light3Light4 & -Light5)