We consider the quantified constraint satisfaction problem (QCSP) which is to decide, given a structure and a first-order sentence (not assumed here to be in prenex form) built from conjunction and quantification, whether or not the sentence is true on the structure. We present a proof system for certifying the falsity of QCSP instances and develop its basic theory; for instance, we provide an algorithmic interpretation of its behavior. Our proof system places the established Q-resolution proof system in a broader context, and also allows us to derive QCSP tractability results.

• 03B35 - Mechanization of proofs and logical operations
• 03F20 - Complexity of proofs
• 68T20 - Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)