adding RichFaces breaks my JSF project - eclipse

Question

I have a simple JSF project which works just fine; after adding RichFaces to it, it stops working properly
Environment: Eclipse IDE, JSF 2.1 (Apache MyFaces 2.1.5), Tomcat v7.0 Server (Location: workspace metadata, Server Locations: Use Tomcat installation); http://localhost:8181/ gives me the admin console, so the server is running ok
The application: a Dynamic Web Project (version 3.0) named jsf1;
under WebContent, i have a page named main.xhtml (For brevity, i won't paste the content, because things work well so far; Its a simple hello world page);
the faces-config.xml is left unchanged;
the web.xml contains:
<servlet>
<servlet-name>Faces Servlet</servlet-name>
<servlet-class>javax.faces.webapp.FacesServlet</servlet-class>
<load-on-startup>1</load-on-startup>
</servlet>
<servlet-mapping>
<servlet-name>Faces Servlet</servlet-name>
<url-pattern>/faces/*</url-pattern>
</servlet-mapping>
In Project Explorer, i right click on the project > Run As > Run on Server, and the application is accessible in a web browser at the url http://localhost:8181/jsf1/faces/main.xhtml
Adding RichFaces: i followed the instructions given at https://docs.jboss.org/richfaces/latest_3_3_X/en/devguide/html/GettingStarted.html
under WEB-INF/lib i have added all the required jars
i have appended to web.xml the following content:
<!-- Plugging the "Blue Sky" skin into the project -->
<context-param>
<param-name>org.richfaces.SKIN</param-name>
<param-value>blueSky</param-value>
</context-param>
<!-- Making the RichFaces skin spread to standard HTML controls -->
<context-param>
<param-name>org.richfaces.CONTROL_SKINNING</param-name>
<param-value>enable</param-value>
</context-param>
<!-- Defining and mapping the RichFaces filter -->
<filter>
<display-name>RichFaces Filter</display-name>
<filter-name>richfaces</filter-name>
<filter-class>org.ajax4jsf.Filter</filter-class>
</filter>
<filter-mapping>
<filter-name>richfaces</filter-name>
<servlet-name>Faces Servlet</servlet-name>
<dispatcher>REQUEST</dispatcher>
<dispatcher>FORWARD</dispatcher>
<dispatcher>INCLUDE</dispatcher>
</filter-mapping>
Now, when i run the project on server, in the console i get:
SEVERE: Exception starting filter richfaces
java.lang.ClassNotFoundException: org.ajax4jsf.Filter
I added the richfaces-impl-3.3.3.Final.jar, which contains the org.ajax4jsf.Filter class.
Now, when i run the project on server,the console contains no errors, however, the link http://localhost:8181/jsf1/faces/main.xhtml displays a blank page.
How is it possible to create a functional RichFaces application?