# 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),h4s_predu_u_sets_image(s(t_fun(t_h4s_nums_num,X1),X2),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ)))))),file('i/f/pred_set/countable__image__nats', ch4s_predu_u_sets_countableu_u_imageu_u_nats)).
fof(2, axiom,~(p(s(t_bool,f0))),file('i/f/pred_set/countable__image__nats', aHLu_FALSITY)).
fof(22, axiom,![X1]:![X19]:(p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X1,t_bool),X19))))<=>?[X2]:p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X1,t_h4s_nums_num),X2),s(t_fun(X1,t_bool),X19),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ))))),file('i/f/pred_set/countable__image__nats', ah4s_predu_u_sets_countableu_u_def)).
fof(23, axiom,![X20]:![X1]:![X19]:![X2]:p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X1,X20),X2),s(t_fun(X1,t_bool),X19),s(t_fun(X20,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,X20),X2),s(t_fun(X1,t_bool),X19)))))),file('i/f/pred_set/countable__image__nats', ah4s_predu_u_sets_SURJu_u_IMAGE)).
fof(25, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f0)),file('i/f/pred_set/countable__image__nats', aHLu_BOOLu_CASES)).
fof(26, axiom,![X1]:![X20]:![X5]:![X19]:![X2]:(p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X1,X20),X2),s(t_fun(X1,t_bool),X19),s(t_fun(X20,t_bool),X5))))=>?[X17]:(p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X20,X1),X17),s(t_fun(X20,t_bool),X5),s(t_fun(X1,t_bool),X19))))&![X18]:(p(s(t_bool,h4s_bools_in(s(X20,X18),s(t_fun(X20,t_bool),X5))))=>s(X20,happ(s(t_fun(X1,X20),X2),s(X1,happ(s(t_fun(X20,X1),X17),s(X20,X18)))))=s(X20,X18)))),file('i/f/pred_set/countable__image__nats', ah4s_predu_u_sets_SURJu_u_INJu_u_INV)).
fof(28, axiom,p(s(t_bool,t)),file('i/f/pred_set/countable__image__nats', aHLu_TRUTH)).
fof(30, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/pred_set/countable__image__nats', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
