# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:~(s(t_h4s_lists_list(X1),X3)=s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X2))),s(t_h4s_lists_list(X1),X3)))),file('i/f/list/CONS__ACYCLIC_c0', ch4s_lists_CONSu_u_ACYCLICu_c0)).
fof(31, axiom,![X1]:![X31]:![X20]:(?[X2]:(s(X1,X2)=s(X1,X31)&p(s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X2)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X31))))),file('i/f/list/CONS__ACYCLIC_c0', ah4s_bools_UNWINDu_u_THM2)).
fof(47, axiom,![X1]:![X11]:![X33]:s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X33))),s(t_h4s_lists_list(X1),X11)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X11))))),file('i/f/list/CONS__ACYCLIC_c0', ah4s_lists_LENGTH0u_c1)).
fof(65, axiom,p(s(t_bool,t)),file('i/f/list/CONS__ACYCLIC_c0', aHLu_TRUTH)).
fof(68, axiom,![X11]:(s(t_bool,X11)=s(t_bool,t)<=>p(s(t_bool,X11))),file('i/f/list/CONS__ACYCLIC_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(80, axiom,![X37]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X37),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X37),file('i/f/list/CONS__ACYCLIC_c0', ah4s_arithmetics_ADDu_u_0)).
fof(84, axiom,![X35]:![X37]:s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X37))),s(t_h4s_nums_num,X35)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X37))),s(t_h4s_nums_num,X35))),file('i/f/list/CONS__ACYCLIC_c0', ah4s_arithmetics_LESSu_u_EQ)).
fof(85, axiom,![X1]:![X6]:![X31]:s(X1,happ(s(t_fun(t_h4s_nums_num,X1),h4s_indu_u_types_fcons(s(X1,X31),s(t_fun(t_h4s_nums_num,X1),X6))),s(t_h4s_nums_num,h4s_nums_0)))=s(X1,X31),file('i/f/list/CONS__ACYCLIC_c0', ah4s_indu_u_types_FCONS0u_c0)).
fof(88, axiom,![X35]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X35)))),file('i/f/list/CONS__ACYCLIC_c0', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(93, axiom,![X27]:![X35]:![X37]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X37),s(t_h4s_nums_num,X35))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X37),s(t_h4s_nums_num,X27)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X35),s(t_h4s_nums_num,X27))),file('i/f/list/CONS__ACYCLIC_c0', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(101, axiom,![X35]:![X37]:(~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X37))),s(t_h4s_nums_num,X35)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X35),s(t_h4s_nums_num,X37))))),file('i/f/list/CONS__ACYCLIC_c0', ah4s_arithmetics_NOTu_u_LESS)).
# SZS output end CNFRefutation
