Is parametrized maximum independent clauses problem in FPT? Parametrized maximum independent clauses problem:
Input : A r-CNFSAT formula F having n variables and m clauses, k
Ques  : Does there exists at least k clauses such that they are mutually independent i.e. no variable occurs more than once in all these clauses combined.
Parameter : k
I would like to know whether this problem is in FPT or not. In both situations, an idea to proceed forward will be appreciated.
The problem is known as r-Set Packing:
Instance: A collection $\mathcal{C}$ of subsets of size at most $r$ of a finite set $S$ and an integer $k$.
Parameter: $k$
Question: Is there a subcollection $\mathcal{C'} \subseteq \mathcal{C}$ which consists of at least $k$ mutually disjoint subsets?

For unbounded $r$, the problem is W[1]-hard by an easy reduction from Independent Set (see for example [1]).
However, for constant $r$, the problem becomes fixed parameter tractable (see for example [2]).

[1]: Rodney G. Downey, Michael R. Fellows: Parameterized Complexity. Springer, 1999.
[2]: Michael R. Fellows, Christian Knauer, Naomi Nishimura, Prabhakar Ragde, Frances A. Rosamond, Ulrike Stege, Dimitrios M. Thilikos, Sue Whitesides: Faster Fixed-Parameter Tractable Algorithms for Matching and Packing Problems. Algorithmica 52(2): 167-176 (2008)