This is the edited question:Suppose I have $(x_1 \vee y_1 \vee y_2)$. x is existential and y is universal. Then it should be like this in the quantifier string: $\forall y_1 \forall y_2 \exists x_1$   (WHY?)Now suppose I introduce a new variable z and convert the above clause to: $(x_1 \vee \neg z  \vee y_2 ) \land (z \vee x_2)$. My question is where should I insert z in the quantifier string and with which quantifier(exisential or universal)? Also, don't reply saying that you can place it anywhere...because the position of insertion does matter.Thank you  
Quantifier String Placement
algorithms;logic;satisfiability