# 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_extreals_extreal,t_bool),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_h4s_extreals_extreal,t_bool)),X1),s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_normal),s(t_h4s_realaxs_real,X2))))),s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_normal),s(t_h4s_realaxs_real,X3))))))&(![X4]:p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_h4s_extreals_extreal,t_bool)),X1),s(t_h4s_extreals_extreal,h4s_extreals_posinf))),s(t_h4s_extreals_extreal,X4))))&(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_h4s_extreals_extreal,t_bool)),X1),s(t_h4s_extreals_extreal,h4s_extreals_neginf))),s(t_h4s_extreals_extreal,h4s_extreals_posinf))))&(![X5]:p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_h4s_extreals_extreal,t_bool)),X1),s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_normal),s(t_h4s_realaxs_real,X5))))),s(t_h4s_extreals_extreal,h4s_extreals_posinf))))&(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_h4s_extreals_extreal,t_bool)),X1),s(t_h4s_extreals_extreal,h4s_extreals_neginf))),s(t_h4s_extreals_extreal,h4s_extreals_neginf))))&(![X6]:p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_h4s_extreals_extreal,t_bool)),X1),s(t_h4s_extreals_extreal,h4s_extreals_neginf))),s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_normal),s(t_h4s_realaxs_real,X6))))))&![X7]:p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_h4s_extreals_extreal,t_bool)),X1),s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_normal),s(t_h4s_realaxs_real,X7))))),s(t_h4s_extreals_extreal,h4s_extreals_neginf))))))))))=>![X8]:![X9]:p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),happ(s(t_fun(t_h4s_extreals_extreal,t_fun(t_h4s_extreals_extreal,t_bool)),X1),s(t_h4s_extreals_extreal,X8))),s(t_h4s_extreals_extreal,X9))))),file('i/f/extreal/extreal__add__ind', ch4s_extreals_extrealu_u_addu_u_ind)).
fof(4, axiom,![X1]:((p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X1),s(t_h4s_extreals_extreal,h4s_extreals_neginf))))&(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X1),s(t_h4s_extreals_extreal,h4s_extreals_posinf))))&![X12]:p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X1),s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_normal),s(t_h4s_realaxs_real,X12))))))))=>![X13]:p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X1),s(t_h4s_extreals_extreal,X13))))),file('i/f/extreal/extreal__add__ind', ah4s_extreals_extrealu_u_induction)).
fof(7, axiom,![X14]:(s(t_bool,f)=s(t_bool,X14)<=>~(p(s(t_bool,X14)))),file('i/f/extreal/extreal__add__ind', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(28, axiom,![X29]:(s(t_h4s_extreals_extreal,X29)=s(t_h4s_extreals_extreal,h4s_extreals_neginf)|(s(t_h4s_extreals_extreal,X29)=s(t_h4s_extreals_extreal,h4s_extreals_posinf)|?[X12]:s(t_h4s_extreals_extreal,X29)=s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_realaxs_real,t_h4s_extreals_extreal),h4s_extreals_normal),s(t_h4s_realaxs_real,X12))))),file('i/f/extreal/extreal__add__ind', ah4s_extreals_extrealu_u_nchotomy)).
fof(72, axiom,p(s(t_bool,t)),file('i/f/extreal/extreal__add__ind', aHLu_TRUTH)).
fof(75, axiom,![X14]:(s(t_bool,t)=s(t_bool,X14)<=>p(s(t_bool,X14))),file('i/f/extreal/extreal__add__ind', ah4s_bools_EQu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
