  As with a Bell inequality, Hardy's paradox manifests a contradiction between
the prediction given by quantum theory and local-hidden variable theories. In
this work, we give two generalizations of Hardy's arguments for manifesting
such a paradox to an arbitrary, but symmetric Bell scenario involving two
observers. Our constructions recover that of Meng et al. [Phys. Rev. A. 98,
062103 (2018)] and that first discussed by Cabello [Phys. Rev. A 65, 032108
(2002)] as special cases. Among the two constructions, one can be naturally
interpreted as a demonstration of the failure of the transitivity of
implications (FTI). Moreover, a special case of which is equivalent to a
ladder-proof-type argument for Hardy's paradox. Through a suitably generalized
notion of success probability called degree of success, we provide evidence
showing that the FTI-based formulation exhibits a higher degree of success
compared with all other existing proposals. Moreover, this advantage seems to
persist even if we allow imperfections in realizing the zero-probability
constraints in such paradoxes. Explicit quantum strategies realizing several of
these proofs of nonlocality without inequalities are provided.
