Establish the validity of the following sentence: if [[if P_1 then (P_2 or P_3) else (P_3 or P_4)] and [[if P_3 then (not P_6) else (if P_4 then P_1)] and [not (P_2 and P_5) and (if P_2 then P_5)]]] then not (if P_3 then P_6). Establish the validity of the following sentence: if [[if P_1 then (P_2 or P_3) else (P_3 or P_4)] and [[if P_3 then (not P_6) else (if P_4 then P_1)] and [not (P_2 and P_5) and (if P_2 then P_5)]]] then not (if P_3 then P_6)