  We study the probe of the gauge-phobic (or nearly gauge-phobic) heavy Higgs
bosons (GPHB) at high energy hadron colliders including the 14 TeV LHC and the
50 TeV Super Proton-Proton Collider (SppC). We take the process $pp\to t\bar t
t\bar t$, and study it at the hadron level including simulating the jet
formation and top quark tagging (with jet substructure). We show that, for a
GPHB with $M^{}_H<800$ GeV, $M^{}_H$ can be determined by adjusting the value
of $M^{}_H$ in the theoretical $p^{}_T(b_1)$ distribution to fit the observed
$p^{}_T(b_1)$ distribution, and the resonance peak can be seen at the SppC for
$M^{}_H$=800 GeV and 1 TeV.
