# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((![X3]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_nums_num,t_h4s_extreals_extreal),X2),s(t_h4s_nums_num,X3))),s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_nums_num,t_h4s_extreals_extreal),X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,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),h4s_predu_u_sets_image(s(t_fun(t_h4s_nums_num,t_h4s_extreals_extreal),X2),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ)))))))))=>?[X3]:p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X1),s(t_h4s_extreals_extreal,happ(s(t_fun(t_h4s_nums_num,t_h4s_extreals_extreal),X2),s(t_h4s_nums_num,X3))))))),file('i/f/extreal/sup__le__mono', ch4s_extreals_supu_u_leu_u_mono)).
fof(22, axiom,![X14]:![X15]:(p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X14))))<=>~(p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X14),s(t_h4s_extreals_extreal,X15)))))),file('i/f/extreal/sup__le__mono', ah4s_extreals_extrealu_u_ltu_u_def)).
fof(23, axiom,![X14]:![X15]:(p(s(t_bool,h4s_extreals_extrealu_u_lt(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X14))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X15),s(t_h4s_extreals_extreal,X14))))),file('i/f/extreal/sup__le__mono', ah4s_extreals_ltu_u_impu_u_le)).
fof(24, axiom,![X15]:![X12]:(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),X12))),s(t_h4s_extreals_extreal,X15))))<=>![X14]:(p(s(t_bool,happ(s(t_fun(t_h4s_extreals_extreal,t_bool),X12),s(t_h4s_extreals_extreal,X14))))=>p(s(t_bool,h4s_extreals_extrealu_u_le(s(t_h4s_extreals_extreal,X14),s(t_h4s_extreals_extreal,X15)))))),file('i/f/extreal/sup__le__mono', ah4s_extreals_supu_u_le)).
fof(25, axiom,![X21]:![X13]:![X14]:![X22]:![X2]:(p(s(t_bool,h4s_bools_in(s(X21,X14),s(t_fun(X21,t_bool),h4s_predu_u_sets_image(s(t_fun(X13,X21),X2),s(t_fun(X13,t_bool),X22))))))<=>?[X15]:(s(X21,X14)=s(X21,happ(s(t_fun(X13,X21),X2),s(X13,X15)))&p(s(t_bool,h4s_bools_in(s(X13,X15),s(t_fun(X13,t_bool),X22)))))),file('i/f/extreal/sup__le__mono', ah4s_predu_u_sets_INu_u_IMAGE)).
fof(26, axiom,![X13]:![X15]:![X19]:s(t_bool,h4s_bools_in(s(X13,X15),s(t_fun(X13,t_bool),X19)))=s(t_bool,happ(s(t_fun(X13,t_bool),X19),s(X13,X15))),file('i/f/extreal/sup__le__mono', ah4s_predu_u_sets_SPECIFICATION)).
# SZS output end CNFRefutation
