# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(s(t_h4s_options_option(t_h4s_lists_list(X1)),h4s_llists_ltake(s(t_h4s_nums_num,X2),s(t_h4s_llists_llist(X1),h4s_llists_lnil)))=s(t_h4s_options_option(t_h4s_lists_list(X1)),h4s_options_none)<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))),file('i/f/llist/LTAKE__NIL__EQ__NONE', ch4s_llists_LTAKEu_u_NILu_u_EQu_u_NONE)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/llist/LTAKE__NIL__EQ__NONE', aHLu_FALSITY)).
fof(11, axiom,![X5]:(s(t_bool,f)=s(t_bool,X5)<=>~(p(s(t_bool,X5)))),file('i/f/llist/LTAKE__NIL__EQ__NONE', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(12, axiom,![X7]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/llist/LTAKE__NIL__EQ__NONE', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(13, axiom,![X7]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7)))))),file('i/f/llist/LTAKE__NIL__EQ__NONE', ah4s_primu_u_recs_LESSu_u_0)).
fof(16, axiom,![X2]:(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)|?[X7]:s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7)))),file('i/f/llist/LTAKE__NIL__EQ__NONE', ah4s_arithmetics_numu_u_CASES)).
fof(17, axiom,![X9]:![X7]:s(t_h4s_options_option(t_h4s_lists_list(X9)),h4s_llists_ltake(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))),s(t_h4s_llists_llist(X9),h4s_llists_lnil)))=s(t_h4s_options_option(t_h4s_lists_list(X9)),h4s_options_none),file('i/f/llist/LTAKE__NIL__EQ__NONE', ah4s_llists_LTAKEu_u_THMu_c1)).
fof(18, axiom,![X1]:![X10]:s(t_h4s_options_option(t_h4s_lists_list(X1)),h4s_llists_ltake(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_llists_llist(X1),X10)))=s(t_h4s_options_option(t_h4s_lists_list(X1)),h4s_options_some(s(t_h4s_lists_list(X1),h4s_lists_nil))),file('i/f/llist/LTAKE__NIL__EQ__NONE', ah4s_llists_LTAKE0u_c0)).
fof(19, axiom,![X1]:![X6]:~(s(t_h4s_options_option(X1),h4s_options_none)=s(t_h4s_options_option(X1),h4s_options_some(s(X1,X6)))),file('i/f/llist/LTAKE__NIL__EQ__NONE', ah4s_options_NOTu_u_NONEu_u_SOME)).
# SZS output end CNFRefutation
