diff --git a/test/test_dynamic_shapes.py b/test/test_dynamic_shapes.py
index ba8818da42981..68ec33d863301 100644
--- a/test/test_dynamic_shapes.py
+++ b/test/test_dynamic_shapes.py
@@ -500,13 +500,15 @@ def test_expect_true_with_s0(self):
         shape_env = ShapeEnv()
         s0 = create_symint(shape_env, 5)
         i0 = shape_env.create_unbacked_symint()
-        self.assertTrue(expect_true(i0 <= s0))
+        self.assertTrue(expect_true(i0 < s0))
         self.assertExpectedInline(
             str([ra.expr for ra in shape_env.deferred_runtime_asserts[i0.node.expr]]),
-            """[-s0 + u0 <= 0]"""
+            """[-s0 + u0 < 0]"""
         )
-        self.assertTrue(i0 <= s0)
+        self.assertTrue(i0 < s0)
+        self.assertTrue(i0 != s0)
         self.assertFalse(i0 > s0)
+        self.assertFalse(i0 >= s0)
 
     def test_expect_true_prefer_later(self):
         shape_env = ShapeEnv()
diff --git a/torch/fx/experimental/symbolic_shapes.py b/torch/fx/experimental/symbolic_shapes.py
index 34c8f14379416..e9b7f56f97488 100644
--- a/torch/fx/experimental/symbolic_shapes.py
+++ b/torch/fx/experimental/symbolic_shapes.py
@@ -1927,7 +1927,7 @@ def _init(
         self.var_to_stack: Dict[sympy.Symbol, CapturedTraceback] = {}
         # Maps from sympy ints to expressions representing them
         # Populated from equality guards (i.e. a.shape[0] == b.shape[0])
-        self.replacements: Dict[sympy.Symbol, sympy.Expr] = {}  #
+        self.replacements: Dict[sympy.Symbol, sympy.Expr] = {}
         # Set holds a % b expressions that evaluate to 0.
         self.divisible: Set[sympy.Expr] = set()
         # Set that holds "size-like" symbols.  When we perform
@@ -3486,20 +3486,31 @@ def _maybe_evaluate_static(
             # Unbacked symints only
             if s in self.var_to_val:
                 continue
+
             subst = {}
-            for ra in self.deferred_runtime_asserts.get(s, ()):
+
+            def add_expr(expr):
+                # Expr and negation
+                subst[canonicalize_bool_expr(expr)] = sympy.true
+                subst[canonicalize_bool_expr(sympy.Not(expr))] = sympy.false
+                if isinstance(expr, sympy.Rel):
+                    # multiplying by -1 changes the direction of the inequality
+                    dual = type(expr)(-expr.rhs, -expr.lhs)
+                    subst[canonicalize_bool_expr(dual)] = sympy.true
+                    subst[canonicalize_bool_expr(sympy.Not(dual))] = sympy.false
+
+            for e in itertools.chain(self.guards, self.deferred_runtime_asserts.get(s, ())):
+                e = e.expr
                 if compute_hint:
-                    e = canonicalize_bool_expr(ra.expr.xreplace(self.var_to_val))
-                else:
-                    e = ra.expr
-                # e is already canonical
-                subst[e] = sympy.true
-                subst[canonicalize_bool_expr(sympy.Not(e))] = sympy.false
+                    e = canonicalize_bool_expr(e.xreplace(self.var_to_val))
+                add_expr(e)
+                # Other relational expressions this expression implies
                 if isinstance(e, sympy.Eq):
-                    subst[sympy.Le(e.lhs, e.rhs)] = sympy.true
-                    subst[sympy.Le(-e.lhs, -e.rhs)] = sympy.true
-                    subst[sympy.Lt(e.lhs, e.rhs)] = sympy.false
-                    subst[sympy.Lt(-e.lhs, -e.rhs)] = sympy.false
+                    add_expr(sympy.Le(e.lhs, e.rhs))
+                    add_expr(sympy.Ge(e.lhs, e.rhs))
+                elif isinstance(e, sympy.Lt):
+                    add_expr(sympy.Le(e.lhs, e.rhs))
+                    add_expr(sympy.Ne(e.lhs, e.rhs))
 
             # NB: this helps us deal with And/Or connectives
             expr = expr.subs(subst)