# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/pred_set/infinite__pow__uncountable', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/infinite__pow__uncountable', aHLu_FALSITY)).
fof(6, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/pred_set/infinite__pow__uncountable', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/pred_set/infinite__pow__uncountable', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(28, axiom,![X9]:~(s(t_fun(X9,t_bool),h4s_predu_u_sets_univ)=s(t_fun(X9,t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/infinite__pow__uncountable', ah4s_predu_u_sets_UNIVu_u_NOTu_u_EMPTY)).
fof(29, axiom,![X20]:![X9]:![X21]:![X22]:![X1]:![X23]:![X5]:![X4]:((p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X9,X20),X4),s(t_fun(X9,t_bool),X23),s(t_fun(X20,t_bool),X1))))&p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X20,X21),X5),s(t_fun(X20,t_bool),X1),s(t_fun(X21,t_bool),X22)))))=>p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X9,X21),h4s_combins_o(s(t_fun(X20,X21),X5),s(t_fun(X9,X20),X4))),s(t_fun(X9,t_bool),X23),s(t_fun(X21,t_bool),X22))))),file('i/f/pred_set/infinite__pow__uncountable', ah4s_predu_u_sets_SURJu_u_COMPOSE)).
fof(30, axiom,![X9]:![X23]:~(s(t_fun(t_fun(X9,t_bool),t_bool),h4s_predu_u_sets_pow(s(t_fun(X9,t_bool),X23)))=s(t_fun(t_fun(X9,t_bool),t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/infinite__pow__uncountable', ah4s_predu_u_sets_POWu_u_EMPTY)).
fof(31, axiom,![X20]:![X9]:![X1]:![X23]:![X4]:(p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X9,X20),X4),s(t_fun(X9,t_bool),X23),s(t_fun(X20,t_bool),X1))))=>(s(t_fun(X9,t_bool),X23)=s(t_fun(X9,t_bool),h4s_predu_u_sets_empty)|?[X24]:p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X20,X9),X24),s(t_fun(X20,t_bool),X1),s(t_fun(X9,t_bool),X23)))))),file('i/f/pred_set/infinite__pow__uncountable', ah4s_predu_u_sets_inju_u_surj)).
fof(32, axiom,![X9]:![X23]:(~(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X9,t_bool),X23)))))<=>?[X4]:p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(t_h4s_nums_num,X9),X4),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ),s(t_fun(X9,t_bool),X23))))),file('i/f/pred_set/infinite__pow__uncountable', ah4s_predu_u_sets_infiniteu_u_numu_u_inj)).
fof(33, axiom,![X9]:![X23]:(p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X9,t_bool),X23))))<=>(s(t_fun(X9,t_bool),X23)=s(t_fun(X9,t_bool),h4s_predu_u_sets_empty)|?[X4]:p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(t_h4s_nums_num,X9),X4),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ),s(t_fun(X9,t_bool),X23)))))),file('i/f/pred_set/infinite__pow__uncountable', ah4s_predu_u_sets_countableu_u_surj)).
fof(34, axiom,![X9]:![X23]:~(?[X4]:p(s(t_bool,h4s_predu_u_sets_surj(s(t_fun(X9,t_fun(X9,t_bool)),X4),s(t_fun(X9,t_bool),X23),s(t_fun(t_fun(X9,t_bool),t_bool),h4s_predu_u_sets_pow(s(t_fun(X9,t_bool),X23))))))),file('i/f/pred_set/infinite__pow__uncountable', ah4s_predu_u_sets_powu_u_nou_u_surj)).
fof(35, conjecture,![X9]:![X23]:(~(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X9,t_bool),X23)))))=>~(p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(t_fun(X9,t_bool),t_bool),h4s_predu_u_sets_pow(s(t_fun(X9,t_bool),X23)))))))),file('i/f/pred_set/infinite__pow__uncountable', ch4s_predu_u_sets_infiniteu_u_powu_u_uncountable)).
# SZS output end CNFRefutation
