Give JAD (http://www.varaneckas.com/jad) a try.
The problematic code that you show is equivalent to the following:
1) Class class$schema$system$s322D2AAD7A06BA82525CDB874D86D59A$TypeSystemHolder;
2) ClassLoader loader = class$schema$system$s322D2AAD7A06BA82525CDB874D86D59A$TypeSystemHolder.getClassLoader();
3) Class type = Class.forName("org.apache.xmlbeans.impl.schema.SchemaTypeSystemImpl", true, loader);
4) Constructor ctor = type.getConstructor(Class.class);
5) Object obj = ctor.newInstance(TypeSystemHolder.class);
6) SchemaTypeSystem result = (SchemaTypeSystem) obj;
7) return result;
The part you are having trouble with is line 1, which represents a local variable or a field (possibly static). The Java compiler converts the expression 'TypeSystemHolder.class' into an invocation of getClass storing the result in a static field. This initialization happens once in each class that references 'TypeSystemHolder.class' and the compiler replaces each callsite that uses this expression with a field access.
Most decompilers fail to translate this idiom back to the original call to 'TypeSystemHolder.class' but JAD handles this quite well. Additionally, there is a plug-in that integrates JAD (and others) into Eclipse (http://jadclipse.sourceforge.net).
Unfortunately, decompilers do not handle every code sequence generated by a compiler so some manual rewriting is always required. For example, the Java compiler may generate code for one exception handling block that overlaps with code for another exception handling block. Decompilers are unable to separate this back into two catch blocks. In this case, one usually sees goto statements littered throughout the code (not valid Java) or the decompiler simply gives up on that method.
Also, you are correct that this is generated code. Specifically, it is from the XmlBeans compiler, which parses xn XML Schema and generates binding classes for Java; allowing one to serailize and deserialize XML documents conforming to that schema. If you have access to the schema it would be better to incorporate XmlBeans into your build instead of decompiling these classes.