# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X1))))=>![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_sumu_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),X1),s(t_h4s_nums_num,X2)))))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(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_sumu_u_set),s(t_fun(t_h4s_nums_num,t_bool),X1))),s(t_h4s_nums_num,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_sumu_u_set),s(t_fun(t_h4s_nums_num,t_bool),X1)))))),file('i/f/pred_set/SUM__SET__DELETE', ch4s_predu_u_sets_SUMu_u_SETu_u_DELETE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/SUM__SET__DELETE', aHLu_TRUTH)).
fof(9, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)<=>p(s(t_bool,X9))),file('i/f/pred_set/SUM__SET__DELETE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X8]:![X1]:![X5]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(X8,t_bool),X1))))=>![X2]:s(t_h4s_nums_num,happ(s(t_fun(t_fun(X8,t_bool),t_h4s_nums_num),h4s_predu_u_sets_sumu_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),X1),s(X8,X2)))))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_bools_in(s(X8,X2),s(t_fun(X8,t_bool),X1))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,happ(s(t_fun(t_fun(X8,t_bool),t_h4s_nums_num),h4s_predu_u_sets_sumu_u_image(s(t_fun(X8,t_h4s_nums_num),X5))),s(t_fun(X8,t_bool),X1))),s(t_h4s_nums_num,happ(s(t_fun(X8,t_h4s_nums_num),X5),s(X8,X2))))),s(t_h4s_nums_num,happ(s(t_fun(t_fun(X8,t_bool),t_h4s_nums_num),h4s_predu_u_sets_sumu_u_image(s(t_fun(X8,t_h4s_nums_num),X5))),s(t_fun(X8,t_bool),X1)))))),file('i/f/pred_set/SUM__SET__DELETE', ah4s_predu_u_sets_SUMu_u_IMAGEu_u_DELETE)).
fof(14, axiom,![X18]:![X8]:![X10]:![X7]:s(X8,happ(s(t_fun(X18,X8),happ(s(t_fun(X8,t_fun(X18,X8)),h4s_combins_k),s(X8,X7))),s(X18,X10)))=s(X8,X7),file('i/f/pred_set/SUM__SET__DELETE', ah4s_combins_Ku_u_THM)).
fof(15, axiom,![X19]:![X18]:![X8]:![X7]:![X6]:![X5]:s(X19,happ(s(t_fun(X8,X19),h4s_combins_s(s(t_fun(X8,t_fun(X18,X19)),X5),s(t_fun(X8,X18),X6))),s(X8,X7)))=s(X19,happ(s(t_fun(X18,X19),happ(s(t_fun(X8,t_fun(X18,X19)),X5),s(X8,X7))),s(X18,happ(s(t_fun(X8,X18),X6),s(X8,X7))))),file('i/f/pred_set/SUM__SET__DELETE', ah4s_combins_Su_u_THM)).
fof(16, axiom,![X8]:s(t_fun(X8,X8),h4s_combins_i)=s(t_fun(X8,X8),h4s_combins_s(s(t_fun(X8,t_fun(t_fun(X8,X8),X8)),h4s_combins_k),s(t_fun(X8,t_fun(X8,X8)),h4s_combins_k))),file('i/f/pred_set/SUM__SET__DELETE', ah4s_combins_Iu_u_DEF)).
fof(17, axiom,s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_predu_u_sets_sumu_u_set)=s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_h4s_nums_num),h4s_predu_u_sets_sumu_u_image(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_combins_i))),file('i/f/pred_set/SUM__SET__DELETE', ah4s_predu_u_sets_SUMu_u_SETu_u_DEF)).
# SZS output end CNFRefutation
