diff --git a/test/Project.toml b/test/Project.toml
index 25e3ead7..165b883d 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -6,4 +6,5 @@ InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Supposition = "5a0628fe-1738-4658-9b6d-0b7605a9755b"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/test/interval_tests/construction.jl b/test/interval_tests/construction.jl
index df57db64..d40d5d5f 100644
--- a/test/interval_tests/construction.jl
+++ b/test/interval_tests/construction.jl
@@ -9,6 +9,9 @@
     @test sup(IntervalArithmetic._unsafe_bareinterval(Float64, Inf, Inf)) == Inf
     @test isempty_interval(bareinterval(Inf, Inf))
     @test isnai(interval(Inf, Inf))
+    @test isnai(interval(1//0, 1//0))
+    @test isnai(interval(-1//0, -1//0))
+    @test isnai(interval(1//0, -1//0))
 end
 
 @testset "Basics" begin
@@ -70,6 +73,9 @@ end
     @test isnai(interval(1, NaN))
     @test isnai(interval(NaN))
 
+    @test isnai(interval(1//0))
+    @test isnai(interval(-1//0))
+
     # check no issue with `Integer` modular arithmetic
     @test bounds(interval(typemin(Int64), typemax(Int64))) == (float(typemin(Int64)), float(typemax(Int64)))
 
diff --git a/test/interval_tests/supposition/numeric.jl b/test/interval_tests/supposition/numeric.jl
new file mode 100644
index 00000000..42a60165
--- /dev/null
+++ b/test/interval_tests/supposition/numeric.jl
@@ -0,0 +1,30 @@
+using Test
+using IntervalArithmetic
+using Supposition, Supposition.Data
+
+# Define properties to be checked
+function degenerate_interval(a)
+    x = interval(a)
+    y = interval(a, a)
+    x === y
+end
+
+@testset "Float tests" begin
+    # Define number generators
+    floatgen = Data.Floats()
+
+    # Check properties
+    @check max_examples=1000 degenerate_interval(floatgen)
+end
+
+@testset "Rational tests" begin
+    # Define number generators
+    intgen = Data.Integers(typemin(Int)+1,typemax(Int)) # Don't allow typemin(Int) to avoid overflow
+    rationalgen = @composed function generate_rational(num=intgen, den=intgen)
+        assume!(!(iszero(num) && iszero(den)))
+        return num // den
+    end
+
+    # Check properties
+    @check max_examples = 1000 degenerate_interval(rationalgen)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 62d506da..d5a0fd1d 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -9,7 +9,14 @@ import IntervalSets as IS
 include("generate_ITF1788.jl")
 
 # interval tests
-for f ∈ readdir("interval_tests"; join = true)
+for f ∈ filter(isfile, readdir("interval_tests"; join = true))
+    @testset "$f" begin
+        include(f)
+    end
+end
+
+# interval tests using Supposition
+for f ∈ filter(isfile, readdir("interval_tests/supposition"; join = true))
     @testset "$f" begin
         include(f)
     end