# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>s(X1,h4s_lists_hd(s(t_h4s_lists_list(X1),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,X2)))))=s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/list/HD__GENLIST__COR', ch4s_lists_HDu_u_GENLISTu_u_COR)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/list/HD__GENLIST__COR', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/list/HD__GENLIST__COR', aHLu_FALSITY)).
fof(4, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f0)),file('i/f/list/HD__GENLIST__COR', aHLu_BOOLu_CASES)).
fof(7, 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/list/HD__GENLIST__COR', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(13, axiom,![X1]:![X2]:![X3]:s(X1,h4s_lists_hd(s(t_h4s_lists_list(X1),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))))=s(X1,happ(s(t_fun(t_h4s_nums_num,X1),X3),s(t_h4s_nums_num,h4s_nums_0))),file('i/f/list/HD__GENLIST__COR', ah4s_lists_HDu_u_GENLIST)).
fof(14, axiom,![X11]:(s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_0)|?[X2]:s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))),file('i/f/list/HD__GENLIST__COR', ah4s_arithmetics_numu_u_CASES)).
fof(15, axiom,![X2]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X2))))),file('i/f/list/HD__GENLIST__COR', ah4s_primu_u_recs_LESSu_u_REFL)).
# SZS output end CNFRefutation
