diff --git a/examples/example-0.spec b/examples/example-0.spec
index a4da9b4..b2b6232 100644
--- a/examples/example-0.spec
+++ b/examples/example-0.spec
@@ -1,3 +1,3 @@
 input: p/2.
 
-assert: exists X, Y p(X, Y) <-> exists X q(X).
+spec: exists X, Y p(X, Y) <-> exists X q(X).
diff --git a/examples/example-1.spec b/examples/example-1.spec
index 6c9f890..c3857bc 100644
--- a/examples/example-1.spec
+++ b/examples/example-1.spec
@@ -1,6 +1,6 @@
 input: p/1.
 
-assert:
+spec:
 	forall N
 	(
 		forall X (p(X) -> exists I exists M (I = M and I = X and I <= N))
diff --git a/examples/example-2.spec b/examples/example-2.spec
index cae8461..389b946 100644
--- a/examples/example-2.spec
+++ b/examples/example-2.spec
@@ -10,7 +10,7 @@ axiom: forall N1, N2, N3 (N1 > N2 and N3 > 0 -> N1 * N3 > N2 * N3).
 # This axiom is necessary because we use Vampire without higher-order reasoning
 axiom: (p(0) and forall N (N >= 0 and p(N) -> p(N + 1))) -> (forall N p(N)).
 
-assert: exists N (forall X (q(X) <-> X = N) and N >= 0 and N * N <= n and (N + 1) * (N + 1) > n).
+spec: exists N (forall X (q(X) <-> X = N) and N >= 0 and N * N <= n and (N + 1) * (N + 1) > n).
 
 
 
diff --git a/examples/example-exact-cover.spec b/examples/example-exact-cover.spec
index 9bbf4b4..73f175c 100644
--- a/examples/example-exact-cover.spec
+++ b/examples/example-exact-cover.spec
@@ -18,8 +18,8 @@ output: in/1.
 assume: forall X, Y (s(X, Y) -> is_int(Y)).
 
 # Only valid sets can be included in the solution
-assert: forall X (in(X) -> X >= 1 and X <= n).
+spec: forall X (in(X) -> X >= 1 and X <= n).
 # If an element is contained in an input set, it must be covered by all solutions
-assert: forall X (exists I s(X, I) -> exists I (in(I) and s(X, I))).
+spec: forall X (exists I s(X, I) -> exists I (in(I) and s(X, I))).
 # Elements may not be covered by two input sets
-assert: forall I, J (exists X (s(X, I) and s(X, J)) and in(I) and in(J) -> I = J).
+spec: forall I, J (exists X (s(X, I) and s(X, J)) and in(I) and in(J) -> I = J).
diff --git a/examples/example-prime.spec b/examples/example-prime.spec
index b863d9e..c02a101 100644
--- a/examples/example-prime.spec
+++ b/examples/example-prime.spec
@@ -13,7 +13,7 @@ lemma(backward): forall N (composite(N) -> (exists N10 (1 <= N and N <= n and 2
 
 lemma: forall X1 (composite(X1) <-> (exists N1, N10 (X1 = N1 and 1 <= N1 and N1 <= n and 2 <= N10 and N10 <= N1 - 1 and exists N11 (N1 = (N10 * N11) and 0 < N11)))).
 
-assert: forall X (composite(X) -> p__is_integer__(X)).
-assert: forall N (composite(N) <-> N > 1 and N <= n and exists I, J (I > 1 and J > 1 and I * J = N)).
-assert: forall X (prime(X) -> p__is_integer__(X)).
-assert: forall N (prime(N) <-> N > 1 and N <= n and not exists I, J (I > 1 and J > 1 and I * J = N)).
+#spec: forall X (composite(X) -> p__is_integer__(X)).
+#spec: forall N (composite(N) <-> N > 1 and N <= n and exists I, J (I > 1 and J > 1 and I * J = N)).
+spec: forall X (prime(X) -> p__is_integer__(X)).
+spec: forall N (prime(N) <-> N > 1 and N <= n and not exists I, J (I > 1 and J > 1 and I * J = N)).
diff --git a/src/input/specification.rs b/src/input/specification.rs
index ecd8ead..d46fe2e 100644
--- a/src/input/specification.rs
+++ b/src/input/specification.rs
@@ -364,16 +364,16 @@ pub(crate) fn parse_specification(mut input: &str, problem: &crate::Problem)
 
 				continue;
 			},
-			"assert" =>
+			"spec" =>
 			{
 				let (formula, remaining_input) = formula_statement_body(input, problem)?;
 
 				input = remaining_input;
 
 				let statement = crate::problem::Statement::new(
-					crate::problem::StatementKind::Assertion, formula);
+					crate::problem::StatementKind::Spec, formula);
 
-				problem.add_statement(crate::problem::SectionKind::Assertions, statement);
+				problem.add_statement(crate::problem::SectionKind::Specs, statement);
 
 				continue;
 			},
diff --git a/src/problem.rs b/src/problem.rs
index 310a15c..5c89e83 100644
--- a/src/problem.rs
+++ b/src/problem.rs
@@ -190,7 +190,8 @@ impl Problem
 		{
 			self.print_step_title("Started",
 				termcolor::ColorSpec::new().set_bold(true).set_fg(Some(termcolor::Color::Green)))?;
-			self.shell.borrow_mut().println(&"verification of assertions from translated program",
+			self.shell.borrow_mut().println(
+				&"verification of specification from translated program",
 				&termcolor::ColorSpec::new())?;
 
 			let mut statements = self.statements.borrow_mut();
@@ -229,7 +230,7 @@ impl Problem
 			};
 
 			self.print_step_title("Finished", &step_title_color)?;
-			println!("verification of assertions from translated program");
+			println!("verification of specification from translated program");
 		}
 
 		if proof_direction == ProofDirection::Both
@@ -242,7 +243,8 @@ impl Problem
 		{
 			self.print_step_title("Started",
 				termcolor::ColorSpec::new().set_bold(true).set_fg(Some(termcolor::Color::Green)))?;
-			self.shell.borrow_mut().println(&"verification of translated program from assertions",
+			self.shell.borrow_mut().println(
+				&"verification of translated program from specification",
 				&termcolor::ColorSpec::new())?;
 
 			let mut statements = self.statements.borrow_mut();
@@ -256,7 +258,7 @@ impl Problem
 					{
 						StatementKind::Axiom
 						| StatementKind::Assumption
-						| StatementKind::Assertion =>
+						| StatementKind::Spec =>
 							statement.proof_status = ProofStatus::AssumedProven,
 						StatementKind::Lemma(ProofDirection::Forward) =>
 							statement.proof_status = ProofStatus::Ignored,
@@ -280,7 +282,7 @@ impl Problem
 			};
 
 			self.print_step_title("Finished", &step_title_color)?;
-			println!("verification of translated program from assertions");
+			println!("verification of translated program from specification");
 		}
 
 		Ok(())
@@ -537,6 +539,7 @@ impl<'p> std::fmt::Display for ProblemTPTPDisplay<'p>
 				continue;
 			}
 
+			// TODO: refactor
 			let title = match section_kind
 			{
 				SectionKind::CompletedDefinitions => "completed definitions",
@@ -544,7 +547,7 @@ impl<'p> std::fmt::Display for ProblemTPTPDisplay<'p>
 				SectionKind::Axioms => "axioms",
 				SectionKind::Assumptions => "assumptions",
 				SectionKind::Lemmas => "lemmas",
-				SectionKind::Assertions => "assertions",
+				SectionKind::Specs => "specs",
 			};
 
 			write_title(formatter, title, section_separator)?;
diff --git a/src/problem/section_kind.rs b/src/problem/section_kind.rs
index 65b925f..faf362b 100644
--- a/src/problem/section_kind.rs
+++ b/src/problem/section_kind.rs
@@ -7,7 +7,7 @@ pub enum SectionKind
 	Lemmas,
 	CompletedDefinitions,
 	IntegrityConstraints,
-	Assertions,
+	Specs,
 }
 
 impl std::fmt::Debug for SectionKind
@@ -21,7 +21,7 @@ impl std::fmt::Debug for SectionKind
 			Self::Axioms => write!(formatter, "axiom"),
 			Self::Assumptions => write!(formatter, "assumption"),
 			Self::Lemmas => write!(formatter, "lemma"),
-			Self::Assertions => write!(formatter, "assertion"),
+			Self::Specs => write!(formatter, "spec"),
 		}
 	}
 }
diff --git a/src/problem/statement.rs b/src/problem/statement.rs
index 14d72e6..8afea10 100644
--- a/src/problem/statement.rs
+++ b/src/problem/statement.rs
@@ -8,7 +8,7 @@ pub(crate) enum StatementKind
 	CompletedDefinition(std::rc::Rc<crate::PredicateDeclaration>),
 	IntegrityConstraint,
 	Lemma(ProofDirection),
-	Assertion,
+	Spec,
 }
 
 impl std::fmt::Debug for StatementKind
@@ -23,7 +23,7 @@ impl std::fmt::Debug for StatementKind
 				write!(formatter, "completed definition of {}", predicate_declaration.declaration),
 			Self::IntegrityConstraint => write!(formatter, "integrity constraint"),
 			Self::Lemma(_) => write!(formatter, "lemma"),
-			Self::Assertion => write!(formatter, "assertion"),
+			Self::Spec => write!(formatter, "spec"),
 		}
 	}
 }