# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X1,t_bool),X2))))<=>(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)|?[X3]:p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(t_h4s_nums_num,X1),X3),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ),s(t_fun(X1,t_bool),X2)))))),file('i/f/pred_set/countable__surj', ch4s_predu_u_sets_countableu_u_surj)).
fof(42, axiom,![X1]:![X20]:![X9]:![X2]:![X3]:(p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X1,X20),X3),s(t_fun(X1,t_bool),X2),s(t_fun(X20,t_bool),X9))))<=>s(t_fun(X20,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,X20),X3),s(t_fun(X1,t_bool),X2)))=s(t_fun(X20,t_bool),X9)),file('i/f/pred_set/countable__surj', ah4s_predu_u_sets_IMAGEu_u_SURJ)).
fof(45, axiom,![X20]:![X1]:![X9]:![X2]:![X3]:(p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,X20),X3),s(t_fun(X1,t_bool),X2),s(t_fun(X20,t_bool),X9))))=>(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)|?[X25]:p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X20,X1),X25),s(t_fun(X20,t_bool),X9),s(t_fun(X1,t_bool),X2)))))),file('i/f/pred_set/countable__surj', ah4s_predu_u_sets_inju_u_surj)).
fof(50, axiom,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X1,t_bool),X2))))<=>?[X3]:p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,t_h4s_nums_num),X3),s(t_fun(X1,t_bool),X2),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ))))),file('i/f/pred_set/countable__surj', ah4s_predu_u_sets_countableu_u_def)).
fof(51, axiom,![X1]:![X3]:p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X1,t_bool),h4s_predu_u_sets_image(s(t_fun(t_h4s_nums_num,X1),X3),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ)))))),file('i/f/pred_set/countable__surj', ah4s_predu_u_sets_countableu_u_imageu_u_nats)).
fof(68, axiom,![X1]:![X15]:~(p(s(t_bool,h4s_bools_in(s(X1,X15),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/countable__surj', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(71, axiom,![X20]:![X1]:![X9]:![X2]:![X3]:(p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,X20),X3),s(t_fun(X1,t_bool),X2),s(t_fun(X20,t_bool),X9))))<=>(![X15]:(p(s(t_bool,h4s_bools_in(s(X1,X15),s(t_fun(X1,t_bool),X2))))=>p(s(t_bool,h4s_bools_in(s(X20,happ(s(t_fun(X1,X20),X3),s(X1,X15))),s(t_fun(X20,t_bool),X9)))))&![X15]:![X17]:((p(s(t_bool,h4s_bools_in(s(X1,X15),s(t_fun(X1,t_bool),X2))))&p(s(t_bool,h4s_bools_in(s(X1,X17),s(t_fun(X1,t_bool),X2)))))=>(s(X20,happ(s(t_fun(X1,X20),X3),s(X1,X15)))=s(X20,happ(s(t_fun(X1,X20),X3),s(X1,X17)))=>s(X1,X15)=s(X1,X17))))),file('i/f/pred_set/countable__surj', ah4s_predu_u_sets_INJu_u_DEF)).
# SZS output end CNFRefutation
