# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X2))))=>s(t_h4s_nums_num,happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_predu_u_sets_produ_u_set),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_insert(s(t_h4s_nums_num,X1),s(t_fun(t_h4s_nums_num,t_bool),X2)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_predu_u_sets_produ_u_set),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_delete(s(t_fun(t_h4s_nums_num,t_bool),X2),s(t_h4s_nums_num,X1)))))))),file('i/f/pred_set/PROD__SET__THM_c1', ch4s_predu_u_sets_PRODu_u_SETu_u_THMu_c1)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/PROD__SET__THM_c1', aHLu_TRUTH)).
fof(8, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/pred_set/PROD__SET__THM_c1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X8]:![X2]:![X5]:![X15]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X8,t_bool),X2))))=>s(t_h4s_nums_num,happ(s(t_fun(t_fun(X8,t_bool),t_h4s_nums_num),h4s_predu_u_sets_produ_u_image(s(t_fun(X8,t_h4s_nums_num),X5))),s(t_fun(X8,t_bool),h4s_predu_u_sets_insert(s(X8,X15),s(t_fun(X8,t_bool),X2)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,happ(s(t_fun(X8,t_h4s_nums_num),X5),s(X8,X15))),s(t_h4s_nums_num,happ(s(t_fun(t_fun(X8,t_bool),t_h4s_nums_num),h4s_predu_u_sets_produ_u_image(s(t_fun(X8,t_h4s_nums_num),X5))),s(t_fun(X8,t_bool),h4s_predu_u_sets_delete(s(t_fun(X8,t_bool),X2),s(X8,X15)))))))),file('i/f/pred_set/PROD__SET__THM_c1', ah4s_predu_u_sets_PRODu_u_IMAGEu_u_THMu_c1)).
fof(12, axiom,![X8]:![X1]:s(X8,happ(s(t_fun(X8,X8),h4s_combins_i),s(X8,X1)))=s(X8,X1),file('i/f/pred_set/PROD__SET__THM_c1', ah4s_combins_Iu_u_THM)).
fof(13, axiom,s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_predu_u_sets_produ_u_set)=s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_predu_u_sets_produ_u_image(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_combins_i))),file('i/f/pred_set/PROD__SET__THM_c1', ah4s_predu_u_sets_PRODu_u_SETu_u_DEF)).
# SZS output end CNFRefutation
