PapersTree-like Resolution proves the unsatisfiability of a CNF $\varphi$ by giving a decision tree for the falsified clause problem. The leaves of the free form a partition of $\{0,1\}^n$ into “monochromatic” subcubes, each of which is a strengthening of a negation of a term of $\varphi$.
We consider the HITTING proof system, in which a CNF is refuted by giving a partition of $\{0,1\}^n$ into monochromatic subcubes, and analyze its relation to other proof systems. We also consider a linear analog of HITTING which is a generalization of Tree-like Resolution over linear forms.
The work is part of a three paper series. The first part is about partitions of $\mathbb{F}_q^n$ into affine subspaces, and the second part is about partitions of $\{0,1\}^n$ into subcubes.
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