\item \self In the following text fill the blanks with the missing word(s).

The Ackermann's reduction is used to reduce a formula $\phi_{in}$ in \rule{4cm}{.4pt} \rule{6cm}{.4pt} to a formula in \rule{5.5cm}{.4pt} \rule{4.5cm}{.4pt} that is equisatisfiable. Two formulas are equisatisfiable if \rule{10cm}{.4pt}.
The algorithm adds explicit constraints to the formula $\phi_{in}$ to enforce \rule{7cm}{.4pt}. These constraints say, that $\forall \bar{x} \forall \bar{y} \; (\bigwedge_i x_i = y_i) \imp $ \rule{2.5cm}{.4pt} $ ) $.
The resulting equisatisfiable formula consists of two parts and is of the form: $\phi_{out}  := \phi_C \wedge \hat{\phi_{in}}$.
The right part of the formula $\hat{\phi_{in}}$ describes the flattening original formula in which we replace \rule{7cm}{.4pt} with \rule{5.5cm}{.4pt}.