# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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))))&![X2]: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,X2))))))))=>![X3]:p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X1),s(t_h4s_extreals_extreal,X3))))),file('i/f/extreal/extreal__induction', ch4s_extreals_extrealu_u_induction)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/extreal/extreal__induction', aHLu_TRUTH)).
fof(7, axiom,![X8]:(s(t_bool,t)=s(t_bool,X8)<=>p(s(t_bool,X8))),file('i/f/extreal/extreal__induction', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(13, axiom,![X8]:(s(t_bool,f)=s(t_bool,X8)<=>~(p(s(t_bool,X8)))),file('i/f/extreal/extreal__induction', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(51, axiom,![X28]:(s(t_h4s_extreals_extreal,X28)=s(t_h4s_extreals_extreal,h4s_extreals_neginf)|(s(t_h4s_extreals_extreal,X28)=s(t_h4s_extreals_extreal,h4s_extreals_posinf)|?[X2]:s(t_h4s_extreals_extreal,X28)=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))))),file('i/f/extreal/extreal__induction', ah4s_extreals_extrealu_u_nchotomy)).
fof(61, axiom,s(t_h4s_extreals_extreal,h4s_extreals_posinf)=s(t_h4s_extreals_extreal,h4s_extreals_u_20u_40indu_u_typeextreal1),file('i/f/extreal/extreal__induction', ah4s_extreals_PosInf0)).
fof(65, axiom,s(t_h4s_extreals_extreal,h4s_extreals_neginf)=s(t_h4s_extreals_extreal,h4s_extreals_u_20u_40indu_u_typeextreal0),file('i/f/extreal/extreal__induction', ah4s_extreals_NegInf0)).
fof(68, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/extreal/extreal__induction', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
