diff --git a/compiler/rustc_trait_selection/src/traits/fulfill.rs b/compiler/rustc_trait_selection/src/traits/fulfill.rs
index cf9d9315f60..c5429ccb46b 100644
--- a/compiler/rustc_trait_selection/src/traits/fulfill.rs
+++ b/compiler/rustc_trait_selection/src/traits/fulfill.rs
@@ -671,7 +671,7 @@ impl<'a, 'tcx> FulfillProcessor<'a, 'tcx> {
         stalled_on: &mut Vec<TyOrConstInferVar<'tcx>>,
     ) -> ProcessResult<PendingPredicateObligation<'tcx>, FulfillmentErrorCode<'tcx>> {
         let infcx = self.selcx.infcx;
-        if obligation.predicate.is_global() {
+        if obligation.predicate.is_global() && !self.selcx.is_intercrate() {
             // no type variables present, can use evaluation for better caching.
             // FIXME: consider caching errors too.
             if infcx.predicate_must_hold_considering_regions(obligation) {
@@ -725,7 +725,7 @@ impl<'a, 'tcx> FulfillProcessor<'a, 'tcx> {
     ) -> ProcessResult<PendingPredicateObligation<'tcx>, FulfillmentErrorCode<'tcx>> {
         let tcx = self.selcx.tcx();
 
-        if obligation.predicate.is_global() {
+        if obligation.predicate.is_global() && !self.selcx.is_intercrate() {
             // no type variables present, can use evaluation for better caching.
             // FIXME: consider caching errors too.
             if self.selcx.infcx.predicate_must_hold_considering_regions(obligation) {
diff --git a/tests/ui/coherence/coherence-doesnt-use-infcx-evaluate.rs b/tests/ui/coherence/coherence-doesnt-use-infcx-evaluate.rs
new file mode 100644
index 00000000000..063826f1d54
--- /dev/null
+++ b/tests/ui/coherence/coherence-doesnt-use-infcx-evaluate.rs
@@ -0,0 +1,24 @@
+// check-pass
+// issue: 113415
+
+// Makes sure that coherence doesn't call any of the `predicate_may_hold`-esque fns,
+// since they are using a different infcx which doesn't preserve the intercrate flag.
+
+#![feature(specialization)]
+//~^ WARN the feature `specialization` is incomplete
+
+trait Assoc {
+    type Output;
+}
+
+default impl<T> Assoc for T {
+    type Output = bool;
+}
+
+impl Assoc for u8 {}
+
+trait Foo {}
+impl Foo for u32 {}
+impl Foo for <u8 as Assoc>::Output {}
+
+fn main() {}
diff --git a/tests/ui/coherence/coherence-doesnt-use-infcx-evaluate.stderr b/tests/ui/coherence/coherence-doesnt-use-infcx-evaluate.stderr
new file mode 100644
index 00000000000..56eb21cd20f
--- /dev/null
+++ b/tests/ui/coherence/coherence-doesnt-use-infcx-evaluate.stderr
@@ -0,0 +1,12 @@
+warning: the feature `specialization` is incomplete and may not be safe to use and/or cause compiler crashes
+  --> $DIR/coherence-doesnt-use-infcx-evaluate.rs:7:12
+   |
+LL | #![feature(specialization)]
+   |            ^^^^^^^^^^^^^^
+   |
+   = note: see issue #31844 <https://github.com/rust-lang/rust/issues/31844> for more information
+   = help: consider using `min_specialization` instead, which is more stable and complete
+   = note: `#[warn(incomplete_features)]` on by default
+
+warning: 1 warning emitted
+