Polshing

Chapters/Chapter02.tex

@@ -760,13 +760,13 @@ its model $M$ and another call to the \QFBV solver is made to
 determine whether $M$ is also a~model of
 $\forall x_1, x_2, \dots, x_n \, (\psi)$. This is achieved by asking
 the solver whether the formula $\neg \widehat{\psi}$ is satisfiable,
-where $\widehat{\psi}$ is the formula $\psi$ after substituting values
-of all variables except for $x_1 \ldots x_n$ and uninterpreted
-functions replaced by their values in $M$. If $\neg \widehat{\psi}$ is
-not satisfiable, then the structure $M$ is indeed a model of the
-formula $\forall x_1, x_2, \dots, x_n\,(\psi)$, therefore the entire
-formula is satisfiable and $M$ is its model. If $\neg \widehat{\psi}$
-is satisfiable, we get values $v_1, \dots, v_n$ such that
+where $\widehat{\psi}$ is the formula $\psi$ after replacing all
+uninterpreted functions and all variables except for $x_1 \ldots x_n$
+and by their values in $M$. If $\neg \widehat{\psi}$ is not
+satisfiable, then the structure $M$ is indeed a model of the formula
+$\forall x_1, x_2, \dots, x_n\,(\psi)$, therefore the entire formula
+is satisfiable and $M$ is its model. If $\neg \widehat{\psi}$ is
+satisfiable, we get values $v_1, \dots, v_n$ such that
 $\neg\widehat{\psi}[v_1, \dots, v_n]$ holds. To rule out $M$ as a
 model of the input formula, the instance $\psi[v_1, \dots, v_n]$ of
 the quantified formula is added to the quantifier-free part, i.e.~the