A central goal of this paper is to present a new account of the long-standing observations which have been unanswered in the development of the minimalist theory(Chomsky, 1995, 2000, 2001, 2006, 2013): (a) how to interpret/evaluate the English matrix clause under the conception that a phase is interpreted/evaluated at the next(high) strong phase (Chomsky, 2000), (b) how to value the uninterpretable([uF]) ϕ-features of C and T in the derivations without resorting to interpretability in that the valued [uF] features are indistinguishable from inherently interpretable features after turning into interpretable features, (c) how T-to-C movement undergoes under syntactic implementation of the Chomsky(2013)'s labeling system. In this paper we claim that the GP phase recognition algorithm can answer these questions, which says that the Spell-Out applies at the relevant phase level if all labels of projections are encoded and some prominent features(ϕ-features, force features)are shared by the [uF] ϕ-features of CP and TP. Thus the Spell-Out applies in the TP level of the English matrix clause through ϕ-feature sharing between Subject and TP after CP deletion. In wh-clauses or inversion clauses the Spell Out applies at the CP level in which T-to-C is obligatory in order for [uF] ϕ-features to share the prominent features between two lexical categories. (Youngsan University ‧ Silla University)