IntelliJ can't find javax.servlet.* - spring

Question

I am currently facing a strange issue where IntelliJ can't process my code. Something like this:
#Configuration
#EnableWebSecurity
public class SecurityConfig extends WebSecurityConfigurerAdapter {
...
#Override
protected void configure(HttpSecurity http) throws Exception {
http
.addFilterBefore(authenticationFilter(), UsernamePasswordAuthenticationFilter.class);
}
...
}
where authenticationFilter returns an instance of GenericFilterBean. This code compiles using Gradle just fine, but IntelliJ complains that my AuthenticationFilter and UsernamePasswordAuthenticationFilter.class don't match the required parameters javax.servlet.Filter and Class<? extends javax.servlet.Filter>.
Upon further inspection, it seems that the class file that defines GenericFilterBean doesn't see the javax.servlet package so in my file, it doesn't know what it is.
Another interesting thing is that spring-ws-core has a dependency on spring-web:4.0.9.RELEASE and my code depends on spring-web:4.3.2.RELEASE, and when I look at the classes inside the 4.3.2 references, it can see javax.servlet, i.e. GenericFilterBean on 4.0.9 breaks, but on 4.3.2 works.
Also, if I do
if (authenticationFilter() instanceof Filter);
if (new UsernameAuthenticationFilter() instanceof Filter);
IntelliJ says I could replace both with != null.
When I run gradlew dependencies, I can see dependencies like org.springframework:spring-beans:4.0.9.RELEASE -> 4.3.2.RELEASE, but IntelliJ displays both in the Gradle Projects view and in the project references.
My project has a multi-project gradle build and the 4.0.9 dependencies are on the subprojects.
What I tried
refreshing the gradle dependencies (through IntelliJ)
invalidating IntelliJ caches
cleaning the project (gradlew clean)
reopening IntelliJ
reinstalling IntelliJ
restarting my computer
Temporary solution
As suggested by #Jens, I added compile('javax.servlet:javax.servlet-api:3.1.0') to allprojects and now IntelliJ can parse it correcly, although it would be better not to have "hacky" dependencies on the build file.