# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,X2))),s(t_h4s_hrats_hrat,X1))))=>?[X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,X2))),s(t_h4s_hrats_hrat,X3))))&p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,X1),s(t_h4s_hrats_hrat,X3)))))),file('i/f/hreal/CUT__UP', ch4s_hreals_CUTu_u_UP)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/hreal/CUT__UP', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/hreal/CUT__UP', aHLu_FALSITY)).
fof(6, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/hreal/CUT__UP', 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))))<=>(?[X1]:p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X6),s(t_h4s_hrats_hrat,X1))))&(?[X1]:~(p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X6),s(t_h4s_hrats_hrat,X1)))))&(![X1]:![X3]:((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,X3),s(t_h4s_hrats_hrat,X1)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X6),s(t_h4s_hrats_hrat,X3)))))&![X1]:(p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X6),s(t_h4s_hrats_hrat,X1))))=>?[X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X6),s(t_h4s_hrats_hrat,X3))))&p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,X1),s(t_h4s_hrats_hrat,X3)))))))))),file('i/f/hreal/CUT__UP', ah4s_hreals_isacut0)).
fof(8, axiom,![X2]:p(s(t_bool,h4s_hreals_isacut(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,X2)))))),file('i/f/hreal/CUT__UP', 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__UP', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
