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The problem of specifying high-level knowledge bases for planning becomes a hard task in realistic environments. This knowledge is usually handcrafted and is hard to keep updated, even for system experts. Recent approaches have shown the success of classical planning at synthesizing action models even when all intermediate states are missing. These approaches can synthesize action schemas in Planning Domain Definition Language (PDDL) from a set of execution traces each consisting, at least, of an initial and final state. In this paper, we propose a new algorithm to unsupervisedly synthesize STRIPS action models with a classical planner when action signatures are unknown. In addition, we contribute with a compilation to classical planning that mitigates the problem of learning static predicates in the action model preconditions, exploits the capabilities of SAT planners with parallel encodings to compute action schemas and validate all instances. Our system is flexible in that it supports the inclusion of partial input information that may speed up the search. We show through several experiments how learned action models generalize over unseen planning instances.