# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,X3))),s(t_h4s_hrats_hrat,X2))))&p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,X1),s(t_h4s_hrats_hrat,X2)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,X3))),s(t_h4s_hrats_hrat,X1))))),file('i/f/hreal/CUT__DOWN', ch4s_hreals_CUTu_u_DOWN)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/hreal/CUT__DOWN', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/hreal/CUT__DOWN', aHLu_FALSITY)).
fof(6, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/hreal/CUT__DOWN', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X6]:(p(s(t_bool,h4s_hreals_isacut(s(t_fun(t_h4s_hrats_hrat,t_bool),X6))))<=>(?[X2]:p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X6),s(t_h4s_hrats_hrat,X2))))&(?[X2]:~(p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X6),s(t_h4s_hrats_hrat,X2)))))&(![X2]:![X1]:((p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X6),s(t_h4s_hrats_hrat,X2))))&p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,X1),s(t_h4s_hrats_hrat,X2)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X6),s(t_h4s_hrats_hrat,X1)))))&![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X6),s(t_h4s_hrats_hrat,X2))))=>?[X1]:(p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X6),s(t_h4s_hrats_hrat,X1))))&p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,X2),s(t_h4s_hrats_hrat,X1)))))))))),file('i/f/hreal/CUT__DOWN', ah4s_hreals_isacut0)).
fof(8, axiom,![X3]:p(s(t_bool,h4s_hreals_isacut(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,X3)))))),file('i/f/hreal/CUT__DOWN', ah4s_hreals_CUTu_u_ISACUT)).
fof(9, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/hreal/CUT__DOWN', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
