# 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),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))))&(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))))&(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,h4s_extreals_neginf))))&(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,h4s_extreals_posinf))))&(![X2]: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,h4s_extreals_neginf))))&(![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,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,X3))))))&(![X2]: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,h4s_extreals_posinf))))&(![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,h4s_extreals_posinf))),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))))))&![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]:![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,X4))),s(t_h4s_extreals_extreal,X5))))),file('i/f/extreal/extreal__mul__ind', ch4s_extreals_extrealu_u_mulu_u_ind)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/extreal/extreal__mul__ind', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/extreal/extreal__mul__ind', aHLu_FALSITY)).
fof(5, axiom,![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))))))&(![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_posinf))),s(t_h4s_extreals_extreal,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,h4s_extreals_posinf))))&(![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_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))))&(![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,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,X9))))))&![X8]: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,X8))))),s(t_h4s_extreals_extreal,h4s_extreals_neginf))))))))))=>![X4]:![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,X4))),s(t_h4s_extreals_extreal,X5))))),file('i/f/extreal/extreal__mul__ind', ah4s_extreals_extrealu_u_subu_u_ind)).
fof(9, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)<=>p(s(t_bool,X12))),file('i/f/extreal/extreal__mul__ind', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(29, 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))))&![X16]: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,X16))))))))=>![X20]:p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X1),s(t_h4s_extreals_extreal,X20))))),file('i/f/extreal/extreal__mul__ind', ah4s_extreals_extrealu_u_induction)).
fof(57, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)|s(t_bool,X12)=s(t_bool,f)),file('i/f/extreal/extreal__mul__ind', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
