# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/pred_set/inj__image__countable__IFF', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f0))),file('i/f/pred_set/inj__image__countable__IFF', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f0)),file('i/f/pred_set/inj__image__countable__IFF', aHLu_BOOLu_CASES)).
fof(8, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/pred_set/inj__image__countable__IFF', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(14, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/pred_set/inj__image__countable__IFF', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(32, axiom,![X21]:![X7]:![X22]:![X23]:![X1]:![X24]:![X5]:![X4]:((p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X7,X21),X4),s(t_fun(X7,t_bool),X24),s(t_fun(X21,t_bool),X1))))&p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X21,X22),X5),s(t_fun(X21,t_bool),X1),s(t_fun(X22,t_bool),X23)))))=>p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X7,X22),h4s_combins_o(s(t_fun(X21,X22),X5),s(t_fun(X7,X21),X4))),s(t_fun(X7,t_bool),X24),s(t_fun(X22,t_bool),X23))))),file('i/f/pred_set/inj__image__countable__IFF', ah4s_predu_u_sets_INJu_u_COMPOSE)).
fof(33, axiom,![X7]:![X24]:(p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X7,t_bool),X24))))<=>?[X4]:p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X7,t_h4s_nums_num),X4),s(t_fun(X7,t_bool),X24),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ))))),file('i/f/pred_set/inj__image__countable__IFF', ah4s_predu_u_sets_countableu_u_def)).
fof(34, axiom,![X21]:![X7]:![X24]:![X4]:(p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X7,t_bool),X24))))=>p(s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X21,t_bool),h4s_predu_u_sets_image(s(t_fun(X7,X21),X4),s(t_fun(X7,t_bool),X24))))))),file('i/f/pred_set/inj__image__countable__IFF', ah4s_predu_u_sets_imageu_u_countable)).
fof(35, conjecture,![X21]:![X7]:![X24]:![X4]:(p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(X7,X21),X4),s(t_fun(X7,t_bool),X24),s(t_fun(X21,t_bool),h4s_predu_u_sets_image(s(t_fun(X7,X21),X4),s(t_fun(X7,t_bool),X24))))))=>s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X21,t_bool),h4s_predu_u_sets_image(s(t_fun(X7,X21),X4),s(t_fun(X7,t_bool),X24)))))=s(t_bool,h4s_predu_u_sets_countable(s(t_fun(X7,t_bool),X24)))),file('i/f/pred_set/inj__image__countable__IFF', ch4s_predu_u_sets_inju_u_imageu_u_countableu_u_IFF)).
# SZS output end CNFRefutation
