diff --git a/src/ast.rs b/src/ast.rs
index 27e7883..2067cfe 100644
--- a/src/ast.rs
+++ b/src/ast.rs
@@ -501,8 +501,6 @@ impl Formula
 
 	pub fn exists(parameters: std::rc::Rc<VariableDeclarations>, argument: Box<Formula>) -> Self
 	{
-		assert!(!parameters.is_empty());
-
 		Self::Exists(Exists::new(parameters, argument))
 	}
 
@@ -518,8 +516,6 @@ impl Formula
 
 	pub fn for_all(parameters: std::rc::Rc<VariableDeclarations>, argument: Box<Formula>) -> Self
 	{
-		assert!(!parameters.is_empty());
-
 		Self::ForAll(ForAll::new(parameters, argument))
 	}
 
diff --git a/src/format/formulas.rs b/src/format/formulas.rs
index dcfe0cb..580b3a8 100644
--- a/src/format/formulas.rs
+++ b/src/format/formulas.rs
@@ -139,39 +139,51 @@ impl<'formula> std::fmt::Debug for FormulaDisplay<'formula>
 		{
 			crate::Formula::Exists(exists) =>
 			{
-				assert!(!exists.parameters.is_empty());
-
-				write!(format, "exists")?;
-
-				let mut separator = " ";
-
-				for parameter in exists.parameters.iter()
+				if exists.parameters.is_empty()
 				{
-					write!(format, "{}{:?}", separator, parameter)?;
-
-					separator = ", "
+					write!(format, "{:?}", display_formula(&exists.argument, self.parent_formula,
+						self.position))?;
 				}
+				else
+				{
+					write!(format, "exists")?;
 
-				write!(format, " {:?}",
-					display_formula(&exists.argument, Some(self.formula), ChildPosition::Any))?;
+					let mut separator = " ";
+
+					for parameter in exists.parameters.iter()
+					{
+						write!(format, "{}{:?}", separator, parameter)?;
+
+						separator = ", "
+					}
+
+					write!(format, " {:?}", display_formula(&exists.argument, Some(self.formula),
+						ChildPosition::Any))?;
+				}
 			},
 			crate::Formula::ForAll(for_all) =>
 			{
-				assert!(!for_all.parameters.is_empty());
-
-				write!(format, "forall")?;
-
-				let mut separator = " ";
-
-				for parameter in for_all.parameters.iter()
+				if for_all.parameters.is_empty()
 				{
-					write!(format, "{}{:?}", separator, parameter)?;
-
-					separator = ", "
+					write!(format, "{:?}", display_formula(&for_all.argument, self.parent_formula,
+						self.position))?;
 				}
+				else
+				{
+					write!(format, "forall")?;
 
-				write!(format, " {:?}",
-					display_formula(&for_all.argument, Some(self.formula), ChildPosition::Any))?;
+					let mut separator = " ";
+
+					for parameter in for_all.parameters.iter()
+					{
+						write!(format, "{}{:?}", separator, parameter)?;
+
+						separator = ", "
+					}
+
+					write!(format, " {:?}", display_formula(&for_all.argument, Some(self.formula),
+						ChildPosition::Any))?;
+				}
 			},
 			crate::Formula::Not(argument) => write!(format, "not {:?}",
 				display_formula(argument, Some(self.formula), ChildPosition::Any))?,
@@ -386,6 +398,12 @@ mod tests
 			let $intermediate = |f: Box<Formula>| f;
 			assert!($formula, $output);
 
+			let $intermediate = |f: Box<Formula>| exists(vec![], f);
+			assert!($formula, $output);
+
+			let $intermediate = |f: Box<Formula>| for_all(vec![], f);
+			assert!($formula, $output);
+
 			let $intermediate = |f: Box<Formula>| and(vec![f]);
 			assert!($formula, $output);
 
@@ -661,6 +679,7 @@ mod tests
 	#[test]
 	fn format_exists()
 	{
+		assert!(exists(vec![], p()), "p");
 		assert!(exists(vec![x()], p()), "exists X p");
 		assert!(exists(xyz(), p()), "exists X, Y, Z p");
 	}
@@ -668,6 +687,7 @@ mod tests
 	#[test]
 	fn format_for_all()
 	{
+		assert!(for_all(vec![], p()), "p");
 		assert!(for_all(vec![x()], p()), "forall X p");
 		assert!(for_all(xyz(), p()), "forall X, Y, Z p");
 	}
@@ -718,10 +738,14 @@ mod tests
 		assert!(not(false_()), "not false");
 
 		// Quantified formula + Boolean
+		assert!(exists(vec![], true_()), "true");
+		assert!(exists(vec![], false_()), "false");
 		assert!(exists(vec![x()], true_()), "exists X true");
 		assert!(exists(vec![x()], false_()), "exists X false");
 		assert!(exists(xyz(), true_()), "exists X, Y, Z true");
 		assert!(exists(xyz(), false_()), "exists X, Y, Z false");
+		assert!(for_all(vec![], true_()), "true");
+		assert!(for_all(vec![], false_()), "false");
 		assert!(for_all(vec![x()], true_()), "forall X true");
 		assert!(for_all(vec![x()], false_()), "forall X false");
 		assert!(for_all(xyz(), true_()), "forall X, Y, Z true");
@@ -769,6 +793,18 @@ mod tests
 		assert!(not(not_equal(term_1(), term_2())), "not (a + b) * c != |d - e|");
 
 		// Quantified formula + compare
+		assert!(exists(vec![], greater(term_1(), term_2())), "(a + b) * c > |d - e|");
+		assert!(exists(vec![], less(term_1(), term_2())), "(a + b) * c < |d - e|");
+		assert!(exists(vec![], less_or_equal(term_1(), term_2())), "(a + b) * c <= |d - e|");
+		assert!(exists(vec![], greater_or_equal(term_1(), term_2())), "(a + b) * c >= |d - e|");
+		assert!(exists(vec![], equal(term_1(), term_2())), "(a + b) * c = |d - e|");
+		assert!(exists(vec![], not_equal(term_1(), term_2())), "(a + b) * c != |d - e|");
+		assert!(for_all(vec![], greater(term_1(), term_2())), "(a + b) * c > |d - e|");
+		assert!(for_all(vec![], less(term_1(), term_2())), "(a + b) * c < |d - e|");
+		assert!(for_all(vec![], less_or_equal(term_1(), term_2())), "(a + b) * c <= |d - e|");
+		assert!(for_all(vec![], greater_or_equal(term_1(), term_2())), "(a + b) * c >= |d - e|");
+		assert!(for_all(vec![], equal(term_1(), term_2())), "(a + b) * c = |d - e|");
+		assert!(for_all(vec![], not_equal(term_1(), term_2())), "(a + b) * c != |d - e|");
 		assert!(exists(vec![x()], greater(term_1(), term_2())), "exists X (a + b) * c > |d - e|");
 		assert!(exists(vec![x()], less(term_1(), term_2())), "exists X (a + b) * c < |d - e|");
 		assert!(exists(vec![x()], less_or_equal(term_1(), term_2())),
@@ -787,6 +823,25 @@ mod tests
 		assert!(for_all(vec![x()], equal(term_1(), term_2())), "forall X (a + b) * c = |d - e|");
 		assert!(for_all(vec![x()], not_equal(term_1(), term_2())),
 			"forall X (a + b) * c != |d - e|");
+		assert!(exists(xyz(), greater(term_1(), term_2())), "exists X, Y, Z (a + b) * c > |d - e|");
+		assert!(exists(xyz(), less(term_1(), term_2())), "exists X, Y, Z (a + b) * c < |d - e|");
+		assert!(exists(xyz(), less_or_equal(term_1(), term_2())),
+			"exists X, Y, Z (a + b) * c <= |d - e|");
+		assert!(exists(xyz(), greater_or_equal(term_1(), term_2())),
+			"exists X, Y, Z (a + b) * c >= |d - e|");
+		assert!(exists(xyz(), equal(term_1(), term_2())), "exists X, Y, Z (a + b) * c = |d - e|");
+		assert!(exists(xyz(), not_equal(term_1(), term_2())),
+			"exists X, Y, Z (a + b) * c != |d - e|");
+		assert!(for_all(xyz(), greater(term_1(), term_2())),
+			"forall X, Y, Z (a + b) * c > |d - e|");
+		assert!(for_all(xyz(), less(term_1(), term_2())), "forall X, Y, Z (a + b) * c < |d - e|");
+		assert!(for_all(xyz(), less_or_equal(term_1(), term_2())),
+			"forall X, Y, Z (a + b) * c <= |d - e|");
+		assert!(for_all(xyz(), greater_or_equal(term_1(), term_2())),
+			"forall X, Y, Z (a + b) * c >= |d - e|");
+		assert!(for_all(xyz(), equal(term_1(), term_2())), "forall X, Y, Z (a + b) * c = |d - e|");
+		assert!(for_all(xyz(), not_equal(term_1(), term_2())),
+			"forall X, Y, Z (a + b) * c != |d - e|");
 
 		// And + compare
 		assert!(and(vec![greater(term_1(), term_2()), greater(term_3(), term_4()),
@@ -884,6 +939,8 @@ mod tests
 		assert!(not(not(p())), "not not p");
 
 		// Quantified formulas + not
+		assert_all!(i, exists(vec![x()], i(not(p()))), "exists X not p");
+		assert_all!(i, for_all(vec![x()], i(not(p()))), "forall X not p");
 		assert_all!(i, exists(xyz(), i(not(p()))), "exists X, Y, Z not p");
 		assert_all!(i, for_all(xyz(), i(not(p()))), "forall X, Y, Z not p");
 
@@ -914,6 +971,10 @@ mod tests
 		assert_all!(i, not(for_all(xyz(), i(p()))), "not forall X, Y, Z p");
 
 		// Quantified formula + quantified formula
+		assert_all!(i, exists(vec![x()], i(exists(vec![y()], p()))), "exists X exists Y p");
+		assert_all!(i, exists(vec![x()], i(for_all(vec![y()], p()))), "exists X forall Y p");
+		assert_all!(i, for_all(vec![x()], i(exists(vec![y()], p()))), "forall X exists Y p");
+		assert_all!(i, for_all(vec![x()], i(for_all(vec![y()], p()))), "forall X forall Y p");
 		assert_all!(i, exists(x1y1z1(), i(exists(x2y2z2(), p()))),
 			"exists X1, Y1, Z1 exists X2, Y2, Z2 p");
 		assert_all!(i, exists(x1y1z1(), i(for_all(x2y2z2(), p()))),
@@ -972,6 +1033,10 @@ mod tests
 		assert_all!(i, not(i(and(pqr()))), "not (p and q and r)");
 
 		// Quantified formula + and
+		assert_all!(i, exists(vec![x()], i(and(vec![p()]))), "exists X p");
+		assert_all!(i, for_all(vec![x()], i(and(vec![p()]))), "forall X p");
+		assert_all!(i, exists(vec![x()], i(and(pqr()))), "exists X (p and q and r)");
+		assert_all!(i, for_all(vec![x()], i(and(pqr()))), "forall X (p and q and r)");
 		assert_all!(i, exists(xyz(), i(and(vec![p()]))), "exists X, Y, Z p");
 		assert_all!(i, for_all(xyz(), i(and(vec![p()]))), "forall X, Y, Z p");
 		assert_all!(i, exists(xyz(), i(and(pqr()))), "exists X, Y, Z (p and q and r)");
@@ -1019,6 +1084,10 @@ mod tests
 		assert_all!(i, not(i(or(pqr()))), "not (p or q or r)");
 
 		// Quantified formula + or
+		assert_all!(i, exists(vec![x()], i(or(vec![p()]))), "exists X p");
+		assert_all!(i, for_all(vec![x()], i(or(vec![p()]))), "forall X p");
+		assert_all!(i, exists(vec![x()], i(or(pqr()))), "exists X (p or q or r)");
+		assert_all!(i, for_all(vec![x()], i(or(pqr()))), "forall X (p or q or r)");
 		assert_all!(i, exists(xyz(), i(or(vec![p()]))), "exists X, Y, Z p");
 		assert_all!(i, for_all(xyz(), i(or(vec![p()]))), "forall X, Y, Z p");
 		assert_all!(i, exists(xyz(), i(or(pqr()))), "exists X, Y, Z (p or q or r)");
@@ -1065,6 +1134,10 @@ mod tests
 		assert_all!(i, not(i(implies_left(p(), q()))), "not (q <- p)");
 
 		// Quantified formula + implies
+		assert_all!(i, exists(vec![x()], i(implies_right(p(), q()))), "exists X (p -> q)");
+		assert_all!(i, exists(vec![x()], i(implies_left(p(), q()))), "exists X (q <- p)");
+		assert_all!(i, for_all(vec![x()], i(implies_right(p(), q()))), "forall X (p -> q)");
+		assert_all!(i, for_all(vec![x()], i(implies_left(p(), q()))), "forall X (q <- p)");
 		assert_all!(i, exists(xyz(), i(implies_right(p(), q()))), "exists X, Y, Z (p -> q)");
 		assert_all!(i, exists(xyz(), i(implies_left(p(), q()))), "exists X, Y, Z (q <- p)");
 		assert_all!(i, for_all(xyz(), i(implies_right(p(), q()))), "forall X, Y, Z (p -> q)");
@@ -1119,6 +1192,10 @@ mod tests
 		assert_all!(i, not(i(if_and_only_if(pqr()))), "not (p <-> q <-> r)");
 
 		// Quantified formula + if and only if
+		assert_all!(i, exists(vec![x()], i(if_and_only_if(vec![p()]))), "exists X p");
+		assert_all!(i, for_all(vec![x()], i(if_and_only_if(vec![p()]))), "forall X p");
+		assert_all!(i, exists(vec![x()], i(if_and_only_if(pqr()))), "exists X (p <-> q <-> r)");
+		assert_all!(i, for_all(vec![x()], i(if_and_only_if(pqr()))), "forall X (p <-> q <-> r)");
 		assert_all!(i, exists(xyz(), i(if_and_only_if(vec![p()]))), "exists X, Y, Z p");
 		assert_all!(i, for_all(xyz(), i(if_and_only_if(vec![p()]))), "forall X, Y, Z p");
 		assert_all!(i, exists(xyz(), i(if_and_only_if(pqr()))), "exists X, Y, Z (p <-> q <-> r)");