Bom dia Rafael, tudo bem?

Acredito que o problema seja o seguinte. Pelo que vi, você está fazendo a importação no maven do Spring 4.2, porém seu bean está configurado com o schema do Spring 3.0. Experimento trocar essas três linhas:

 http://www.springframework.org/schema/mvc/spring-mvc-3.0.xsd
 http://www.springframework.org/schema/beans/spring-beans-3.0.xsd
http://www.springframework.org/schema/context/spring-context-3.0.xsd

por

http://www.springframework.org/schema/mvc/spring-mvc-4.2.xsd
http://www.springframework.org/schema/beans/spring-beans-4.2.xsd
http://www.springframework.org/schema/context/spring-context-4.2.xsd

Acredito que isso vai resolver seu problema, depois só comenta aqui no fórum se deu certo.

Abs

Fiz a troca e encontrei o seguinte erro:

GRAVE: Context initialization failed
org.springframework.beans.factory.CannotLoadBeanClassException: Cannot find class [org.springframework.web.servlet.view.InternalResourceViewResolver] for bean with name 'org.springframework.web.servlet.view.InternalResourceViewResolver#0' defined in ServletContext resource [/WEB-INF/spring-context.xml]; nested exception is java.lang.ClassNotFoundException: org.springframework.web.servlet.view.InternalResourceViewResolver
    at org.springframework.beans.factory.support.AbstractBeanFactory.resolveBeanClass(AbstractBeanFactory.java:1261)
    at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.predictBeanType(AbstractAutowireCapableBeanFactory.java:576)
    at org.springframework.beans.factory.support.AbstractBeanFactory.isFactoryBean(AbstractBeanFactory.java:1330)
    at org.springframework.beans.factory.support.AbstractBeanFactory.isFactoryBean(AbstractBeanFactory.java:896)
    at org.springframework.beans.factory.support.DefaultListableBeanFactory.preInstantiateSingletons(DefaultListableBeanFactory.java:566)
    at org.springframework.context.support.AbstractApplicationContext.finishBeanFactoryInitialization(AbstractApplicationContext.java:895)
    at org.springframework.context.support.AbstractApplicationContext.refresh(AbstractApplicationContext.java:425)
    at org.springframework.web.context.ContextLoader.createWebApplicationContext(ContextLoader.java:282)
    at org.springframework.web.context.ContextLoader.initWebApplicationContext(ContextLoader.java:204)
    at org.springframework.web.context.ContextLoaderListener.contextInitialized(ContextLoaderListener.java:47)
    at org.apache.catalina.core.StandardContext.listenerStart(StandardContext.java:4842)
    at org.apache.catalina.core.StandardContext.startInternal(StandardContext.java:5303)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1407)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1397)
    at java.util.concurrent.FutureTask.run(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
    at java.lang.Thread.run(Unknown Source)
Caused by: java.lang.ClassNotFoundException: org.springframework.web.servlet.view.InternalResourceViewResolver
    at org.apache.catalina.loader.WebappClassLoaderBase.loadClass(WebappClassLoaderBase.java:1332)
    at org.apache.catalina.loader.WebappClassLoaderBase.loadClass(WebappClassLoaderBase.java:1166)
    at org.springframework.util.ClassUtils.forName(ClassUtils.java:257)
    at org.springframework.beans.factory.support.AbstractBeanDefinition.resolveBeanClass(AbstractBeanDefinition.java:408)
    at org.springframework.beans.factory.support.AbstractBeanFactory.doResolveBeanClass(AbstractBeanFactory.java:1282)
    at org.springframework.beans.factory.support.AbstractBeanFactory.resolveBeanClass(AbstractBeanFactory.java:1253)
    ... 18 more

set 15, 2016 8:05:56 AM org.apache.catalina.core.StandardContext listenerStart
GRAVE: Exception sending context initialized event to listener instance of class org.springframework.web.context.ContextLoaderListener
org.springframework.beans.factory.CannotLoadBeanClassException: Cannot find class [org.springframework.web.servlet.view.InternalResourceViewResolver] for bean with name 'org.springframework.web.servlet.view.InternalResourceViewResolver#0' defined in ServletContext resource [/WEB-INF/spring-context.xml]; nested exception is java.lang.ClassNotFoundException: org.springframework.web.servlet.view.InternalResourceViewResolver
    at org.springframework.beans.factory.support.AbstractBeanFactory.resolveBeanClass(AbstractBeanFactory.java:1261)
    at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.predictBeanType(AbstractAutowireCapableBeanFactory.java:576)
    at org.springframework.beans.factory.support.AbstractBeanFactory.isFactoryBean(AbstractBeanFactory.java:1330)
    at org.springframework.beans.factory.support.AbstractBeanFactory.isFactoryBean(AbstractBeanFactory.java:896)
    at org.springframework.beans.factory.support.DefaultListableBeanFactory.preInstantiateSingletons(DefaultListableBeanFactory.java:566)
    at org.springframework.context.support.AbstractApplicationContext.finishBeanFactoryInitialization(AbstractApplicationContext.java:895)
    at org.springframework.context.support.AbstractApplicationContext.refresh(AbstractApplicationContext.java:425)
    at org.springframework.web.context.ContextLoader.createWebApplicationContext(ContextLoader.java:282)
    at org.springframework.web.context.ContextLoader.initWebApplicationContext(ContextLoader.java:204)
    at org.springframework.web.context.ContextLoaderListener.contextInitialized(ContextLoaderListener.java:47)
    at org.apache.catalina.core.StandardContext.listenerStart(StandardContext.java:4842)
    at org.apache.catalina.core.StandardContext.startInternal(StandardContext.java:5303)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1407)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1397)
    at java.util.concurrent.FutureTask.run(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
    at java.lang.Thread.run(Unknown Source)
Caused by: java.lang.ClassNotFoundException: org.springframework.web.servlet.view.InternalResourceViewResolver
    at org.apache.catalina.loader.WebappClassLoaderBase.loadClass(WebappClassLoaderBase.java:1332)
    at org.apache.catalina.loader.WebappClassLoaderBase.loadClass(WebappClassLoaderBase.java:1166)
    at org.springframework.util.ClassUtils.forName(ClassUtils.java:257)
    at org.springframework.beans.factory.support.AbstractBeanDefinition.resolveBeanClass(AbstractBeanDefinition.java:408)
    at org.springframework.beans.factory.support.AbstractBeanFactory.doResolveBeanClass(AbstractBeanFactory.java:1282)
    at org.springframework.beans.factory.support.AbstractBeanFactory.resolveBeanClass(AbstractBeanFactory.java:1253)
    ... 18 more

set 15, 2016 8:05:56 AM com.sun.faces.config.ConfigureListener contextInitialized
INFORMAÇÕES: Inicializando Mojarra 2.1.6 (SNAPSHOT 20111206) para o contexto '/arena'
set 15, 2016 8:05:57 AM com.sun.faces.spi.InjectionProviderFactory createInstance
INFORMAÇÕES: JSF1048: Anotações PostConstruct/PreDestroy presentes.  Os métodos ManagedBeans marcados com essas anotações informarão as anotações processadas.
3 [localhost-startStop-1] INFO org.hibernate.validator.util.Version - Hibernate Validator 4.0.2.GA
20 [localhost-startStop-1] INFO org.hibernate.validator.engine.resolver.DefaultTraversableResolver - Instantiated an instance of org.hibernate.validator.engine.resolver.JPATraversableResolver.
set 15, 2016 8:05:59 AM org.primefaces.webapp.PostConstructApplicationEventListener processEvent
INFORMAÇÕES: Running on PrimeFaces 6.0
set 15, 2016 8:05:59 AM org.richfaces.application.DefaultModule configure
ADVERTÊNCIA: There was no service org.richfaces.focus.FocusManager found
set 15, 2016 8:05:59 AM org.richfaces.cache.CacheManager getCacheFactory
INFORMAÇÕES: Selected fallback cache factory
set 15, 2016 8:05:59 AM org.richfaces.cache.lru.LRUMapCacheFactory createCache
INFORMAÇÕES: Creating LRUMap cache instance using parameters: {contextConfigLocation=/WEB-INF/spring-context.xml}
set 15, 2016 8:05:59 AM org.richfaces.cache.lru.LRUMapCacheFactory createCache
INFORMAÇÕES: Creating LRUMap cache instance of 512 items capacity
set 15, 2016 8:05:59 AM org.richfaces.application.InitializationListener onStart
INFORMAÇÕES: RichFaces Core Implementation by JBoss by Red Hat, version 4.3.7.Final
set 15, 2016 8:05:59 AM org.apache.catalina.core.StandardContext startInternal
GRAVE: One or more listeners failed to start. Full details will be found in the appropriate container log file
set 15, 2016 8:05:59 AM org.apache.catalina.core.StandardContext startInternal
GRAVE: Context [/arena] startup failed due to previous errors
set 15, 2016 8:05:59 AM org.apache.catalina.core.ApplicationContext log
INFORMAÇÕES: Closing Spring root WebApplicationContext
set 15, 2016 8:05:59 AM org.apache.catalina.loader.WebappClassLoaderBase checkThreadLocalMapForLeaks
GRAVE: The web application [arena] created a ThreadLocal with key of type [javax.faces.context.FacesContext$1] (value [javax.faces.context.FacesContext$1@2a073a80]) and a value of type [com.sun.faces.config.InitFacesContext] (value [com.sun.faces.config.InitFacesContext@57a69b38]) but failed to remove it when the web application was stopped. Threads are going to be renewed over time to try and avoid a probable memory leak.
set 15, 2016 8:06:00 AM org.apache.coyote.AbstractProtocol start
INFORMAÇÕES: Starting ProtocolHandler ["http-nio-8080"]
set 15, 2016 8:06:00 AM org.apache.coyote.AbstractProtocol start
INFORMAÇÕES: Starting ProtocolHandler ["ajp-nio-8009"]
set 15, 2016 8:06:00 AM org.apache.catalina.startup.Catalina start
INFORMAÇÕES: Server startup in 18297 ms

Segue meu Web.xml:

<?xml version="1.0" encoding="UTF-8"?>
<web-app xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://java.sun.com/xml/ns/javaee" xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd" id="WebApp_ID" version="3.0">


    <display-name>ESC</display-name>

    <servlet>
        <servlet-name>dispatcher</servlet-name>
        <servlet-class>
            org.springframework.web.servlet.DispatcherServlet
        </servlet-class>
        <load-on-startup>1</load-on-startup>
    </servlet>

    <servlet-mapping>
        <servlet-name>dispatcher</servlet-name>
        <url-pattern>/</url-pattern>
    </servlet-mapping>

    <context-param>
        <param-name>contextConfigLocation</param-name>
        <param-value>/WEB-INF/spring-context.xml</param-value>
    </context-param>

    <listener>
        <listener-class>
            org.springframework.web.context.ContextLoaderListener
        </listener-class>
    </listener>
</web-app>

Resolvi um problema com as dependências, agora estou com o seguinte erro:

GRAVE: Error configuring application listener of class org.springframework.web.context.ContextLoaderListener
java.lang.ClassNotFoundException: org.springframework.web.context.ContextLoaderListener
    at org.apache.catalina.loader.WebappClassLoaderBase.loadClass(WebappClassLoaderBase.java:1332)
    at org.apache.catalina.loader.WebappClassLoaderBase.loadClass(WebappClassLoaderBase.java:1166)
    at org.apache.catalina.core.DefaultInstanceManager.loadClass(DefaultInstanceManager.java:518)
    at org.apache.catalina.core.DefaultInstanceManager.loadClassMaybePrivileged(DefaultInstanceManager.java:499)
    at org.apache.catalina.core.DefaultInstanceManager.newInstance(DefaultInstanceManager.java:118)
    at org.apache.catalina.core.StandardContext.listenerStart(StandardContext.java:4764)
    at org.apache.catalina.core.StandardContext.startInternal(StandardContext.java:5303)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:147)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1407)
    at org.apache.catalina.core.ContainerBase$StartChild.call(ContainerBase.java:1397)
    at java.util.concurrent.FutureTask.run(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
    at java.lang.Thread.run(Unknown Source)

set 15, 2016 8:35:20 AM org.apache.catalina.core.StandardContext listenerStart
GRAVE: Skipped installing application listeners due to previous error(s)
set 15, 2016 8:35:20 AM org.apache.catalina.core.StandardContext startInternal
GRAVE: One or more listeners failed to start. Full details will be found in the appropriate container log file
set 15, 2016 8:35:20 AM org.apache.catalina.core.StandardContext startInternal
GRAVE: Context [/arena] startup failed due to previous errors
set 15, 2016 8:35:20 AM org.apache.coyote.AbstractProtocol start
INFORMAÇÕES: Starting ProtocolHandler ["http-nio-8080"]
set 15, 2016 8:35:20 AM org.apache.coyote.AbstractProtocol start
INFORMAÇÕES: Starting ProtocolHandler ["ajp-nio-8009"]
set 15, 2016 8:35:20 AM org.apache.catalina.startup.Catalina start
INFORMAÇÕES: Server startup in 718 ms

Parece que ele não esta encontrando as dependencias.

meu pom.xml:

        <!-- Spring MVC -->
        <!-- https://mvnrepository.com/artifact/org.springframework/spring-core -->
<dependency>
    <groupId>org.springframework</groupId>
    <artifactId>spring-core</artifactId>
    <version>4.0.3.RELEASE</version>
</dependency>

        <!-- https://mvnrepository.com/artifact/org.springframework/spring-web -->
<dependency>
    <groupId>org.springframework</groupId>
    <artifactId>spring-web</artifactId>
    <version>4.0.3.RELEASE</version>
</dependency>

        <!-- https://mvnrepository.com/artifact/org.springframework/spring-webmvc -->
<dependency>
    <groupId>org.springframework</groupId>
    <artifactId>spring-webmvc</artifactId>
    <version>4.0.3.RELEASE</version>
</dependency>

    <dependency>
        <groupId>org.springframework</groupId>
        <artifactId>spring-context</artifactId>
        <version>4.0.3.RELEASE</version>
    </dependency>

spring-context:

<beans xmlns="http://www.springframework.org/schema/beans"
    xmlns:context="http://www.springframework.org/schema/context"
    xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
    xsi:schemaLocation="
http://www.springframework.org/schema/beans
http://www.springframework.org/schema/beans/spring-beans-4.0.xsd
http://www.springframework.org/schema/context
http://www.springframework.org/schema/context/spring-context-4.0.xsd
http://www.springframework.org/schema/mvc
http://www.springframework.org/schema/mvc/spring-mvc-4.0.xsd">

    <context:component-scan base-package="br.com.arena.controller" />

    <bean
        class="org.springframework.web.servlet.view.InternalResourceViewResolver">
        <property name="prefix">
            <value>/WEB-INF/views/</value>
        </property>
        <property name="suffix">
            <value>.jsp</value>
        </property>
    </bean>
</beans>

web.xml:

<?xml version="1.0" encoding="UTF-8"?>
<web-app xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://java.sun.com/xml/ns/javaee" xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd" id="WebApp_ID" version="3.0">


    <display-name>SGT</display-name>

    <servlet>
        <servlet-name>dispatcher</servlet-name>
        <servlet-class>
            org.springframework.web.servlet.DispatcherServlet
        </servlet-class>
        <load-on-startup>1</load-on-startup>
    </servlet>

    <servlet-mapping>
        <servlet-name>dispatcher</servlet-name>
        <url-pattern>/</url-pattern>
    </servlet-mapping>

    <context-param>
        <param-name>contextConfigLocation</param-name>
        <param-value>/WEB-INF/spring-context.xml</param-value>
    </context-param>

    <listener>
        <listener-class>
            org.springframework.web.context.ContextLoaderListener
        </listener-class>
    </listener>
</web-app>

Resolvi! Muito obrigado a quem ajudou.

Minha configuração final ficou a seguinte:

web.xml:

<?xml version="1.0" encoding="UTF-8"?>
<web-app xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://java.sun.com/xml/ns/javaee" xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd" id="WebApp_ID" version="3.0">


    <display-name>SGT</display-name>
      <welcome-file-list>
    <welcome-file>index.html</welcome-file>
    <welcome-file>index.htm</welcome-file>
    <welcome-file>index.jsp</welcome-file>
    <welcome-file>default.html</welcome-file>
    <welcome-file>default.htm</welcome-file>
    <welcome-file>default.jsp</welcome-file>
  </welcome-file-list>

<!-- Declaracao do servlet do Spring MVC abaixo-->
    <servlet>
        <servlet-name>spring mvc</servlet-name>
        <servlet-class>org.springframework.web.servlet.DispatcherServlet</servlet-class>
        <init-param>
            <param-name>contextConfigLocation</param-name>
            <param-value>/WEB-INF/spring-context.xml</param-value>
        </init-param>
    </servlet>

    <servlet-mapping>
        <servlet-name>spring mvc</servlet-name>
        <url-pattern>/</url-pattern>
    </servlet-mapping>

</web-app>

O resto se manteve igual a minha ultima publicação.