diff --git a/src/cmd/compile/internal/ssa/prove.go b/src/cmd/compile/internal/ssa/prove.go
index 5195a48608..807f198787 100644
--- a/src/cmd/compile/internal/ssa/prove.go
+++ b/src/cmd/compile/internal/ssa/prove.go
@@ -1698,10 +1698,12 @@ func (ft *factsTable) flowLimit(v *Value) bool {
 		b := ft.limits[v.Args[1].ID]
 		return ft.unsignedMax(v, minU(a.umax, b.umax))
 	case OpOr64, OpOr32, OpOr16, OpOr8:
-		// OR can only make the value bigger.
+		// OR can only make the value bigger and can't flip bits proved to be zero in both inputs.
 		a := ft.limits[v.Args[0].ID]
 		b := ft.limits[v.Args[1].ID]
-		return ft.unsignedMin(v, maxU(a.umin, b.umin))
+		return ft.unsignedMinMax(v,
+			maxU(a.umin, b.umin),
+			1<<bits.Len64(a.umax|b.umax)-1)
 	case OpXor64, OpXor32, OpXor16, OpXor8:
 		// XOR can't flip bits that are proved to be zero in both inputs.
 		a := ft.limits[v.Args[0].ID]
diff --git a/test/prove.go b/test/prove.go
index 2d5d181aa9..8e65404431 100644
--- a/test/prove.go
+++ b/test/prove.go
@@ -1408,6 +1408,24 @@ func xor64(a, b uint64, ensureBothBranchesCouldHappen bool) int {
 	return int(z)
 }
 
+func or64(a, b uint64, ensureBothBranchesCouldHappen bool) int {
+	a &= 0xff
+	b &= 0xfff
+
+	z := a | b
+
+	if ensureBothBranchesCouldHappen {
+		if z > 0xfff { // ERROR "Disproved Less64U$"
+			return 42
+		}
+	} else {
+		if z <= 0xfff { // ERROR "Proved Leq64U$"
+			return 1337
+		}
+	}
+	return int(z)
+}
+
 //go:noinline
 func useInt(a int) {
 }