# 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),X2),s(t_h4s_extreals_extreal,X3))))&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_lt(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/sup__lt', ch4s_extreals_supu_u_lt)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/extreal/sup__lt', aHLu_FALSITY)).
fof(26, axiom,![X1]:![X3]:(p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X3),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,X3)))))),file('i/f/extreal/sup__lt', ah4s_extreals_extrealu_u_ltu_u_def)).
fof(27, axiom,![X19]:![X1]:![X3]:((p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X3),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,X19)))))=>p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X3),s(t_h4s_extreals_extreal,X19))))),file('i/f/extreal/sup__lt', ah4s_extreals_lteu_u_trans)).
fof(28, axiom,![X3]:![X14]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X14),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,h4s_extreals_extrealu_u_sup(s(t_fun(t_h4s_extreals_extreal,t_bool),X14))))))),file('i/f/extreal/sup__lt', ah4s_extreals_leu_u_supu_u_imp)).
fof(29, axiom,![X3]:![X14]:(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),X14))),s(t_h4s_extreals_extreal,X3))))<=>![X1]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X14),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,X3)))))),file('i/f/extreal/sup__lt', ah4s_extreals_supu_u_le)).
fof(31, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/extreal/sup__lt', aHLu_BOOLu_CASES)).
fof(33, axiom,p(s(t_bool,t)),file('i/f/extreal/sup__lt', aHLu_TRUTH)).
fof(35, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/extreal/sup__lt', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
