# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_sup(s(t_fun(t_h4s_extreals_extreal,t_bool),X2))))))<=>![X3]:(![X4]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X2),s(t_h4s_extreals_extreal,X4))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X4),s(t_h4s_extreals_extreal,X3)))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X3)))))),file('i/f/extreal/le__sup', ch4s_extreals_leu_u_sup)).
fof(2, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/extreal/le__sup', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(23, axiom,![X1]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_neginf),s(t_h4s_extreals_extreal,X1)))),file('i/f/extreal/le__sup', ah4s_extreals_leu_u_inftyu_c0)).
fof(26, axiom,![X4]:![X3]:![X1]:((p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X3))))&p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X4)))))=>p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X4))))),file('i/f/extreal/le__sup', ah4s_extreals_letu_u_trans)).
fof(27, axiom,![X3]:![X1]:(p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,X3))))<=>~(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X1)))))),file('i/f/extreal/le__sup', ah4s_extreals_extrealu_u_ltu_u_def)).
fof(37, axiom,![X1]:![X2]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X2),s(t_h4s_extreals_extreal,X1))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_sup(s(t_fun(t_h4s_extreals_extreal,t_bool),X2))))))),file('i/f/extreal/le__sup', ah4s_extreals_leu_u_supu_u_imp)).
fof(38, axiom,![X1]:![X2]:(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,h4s_extreals_extrealu_u_sup(s(t_fun(t_h4s_extreals_extreal,t_bool),X2))),s(t_h4s_extreals_extreal,X1))))<=>![X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X2),s(t_h4s_extreals_extreal,X3))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X1)))))),file('i/f/extreal/le__sup', ah4s_extreals_supu_u_le)).
fof(42, axiom,p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,h4s_extreals_neginf),s(t_h4s_extreals_extreal,h4s_extreals_posinf)))),file('i/f/extreal/le__sup', ah4s_extreals_ltu_u_inftyu_c2)).
fof(47, axiom,![X1]:~(p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,h4s_extreals_neginf))))),file('i/f/extreal/le__sup', ah4s_extreals_ltu_u_inftyu_c3)).
# SZS output end CNFRefutation
