# 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,X1))),s(t_h4s_hrats_hrat,X2)))),file('i/f/hreal/CUT__NONEMPTY', ch4s_hreals_CUTu_u_NONEMPTY)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/hreal/CUT__NONEMPTY', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/hreal/CUT__NONEMPTY', aHLu_FALSITY)).
fof(6, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/hreal/CUT__NONEMPTY', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X1]:p(s(t_bool,h4s_hreals_isacut(s(t_fun(t_h4s_hrats_hrat,t_bool),h4s_hreals_cut(s(t_h4s_hreals_hreal,X1)))))),file('i/f/hreal/CUT__NONEMPTY', ah4s_hreals_CUTu_u_ISACUT)).
fof(8, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/hreal/CUT__NONEMPTY', aHLu_BOOLu_CASES)).
fof(10, axiom,![X9]:(p(s(t_bool,h4s_hreals_isacut(s(t_fun(t_h4s_hrats_hrat,t_bool),X9))))<=>(?[X2]:p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X9),s(t_h4s_hrats_hrat,X2))))&(?[X2]:~(p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X9),s(t_h4s_hrats_hrat,X2)))))&(![X2]:![X10]:((p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X9),s(t_h4s_hrats_hrat,X2))))&p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,X10),s(t_h4s_hrats_hrat,X2)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X9),s(t_h4s_hrats_hrat,X10)))))&![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X9),s(t_h4s_hrats_hrat,X2))))=>?[X10]:(p(s(t_bool,happ(s(t_fun(t_h4s_hrats_hrat,t_bool),X9),s(t_h4s_hrats_hrat,X10))))&p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,X2),s(t_h4s_hrats_hrat,X10)))))))))),file('i/f/hreal/CUT__NONEMPTY', ah4s_hreals_isacut0)).
# SZS output end CNFRefutation
