# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:![X4]:s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),happ(s(t_fun(t_fun(t_h4s_lists_list(X1),t_bool),t_fun(t_h4s_lists_list(X1),t_bool)),X2),s(t_fun(t_h4s_lists_list(X1),t_bool),X3))),s(t_h4s_lists_list(X1),X4)))=s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X3),s(t_h4s_lists_list(X1),X4)))=>![X3]:s(t_bool,h4s_bools_resu_u_exists(s(t_fun(t_h4s_lists_list(X1),t_bool),h4s_encodevars_ofu_u_length(s(t_h4s_nums_num,h4s_nums_0))),s(t_fun(t_h4s_lists_list(X1),t_bool),happ(s(t_fun(t_fun(t_h4s_lists_list(X1),t_bool),t_fun(t_h4s_lists_list(X1),t_bool)),X2),s(t_fun(t_h4s_lists_list(X1),t_bool),X3)))))=s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X3),s(t_h4s_lists_list(X1),h4s_lists_nil)))),file('i/f/EncodeVar/of__length__exists__zero', ch4s_EncodeVars_ofu_u_lengthu_u_existsu_u_zero)).
fof(2, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/EncodeVar/of__length__exists__zero', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(4, axiom,![X9]:![X10]:![X11]:![X12]:(![X8]:s(X10,happ(s(t_fun(X9,X10),X11),s(X9,X8)))=s(X10,happ(s(t_fun(X9,X10),X12),s(X9,X8)))=>s(t_fun(X9,X10),X11)=s(t_fun(X9,X10),X12)),file('i/f/EncodeVar/of__length__exists__zero', aHLu_EXT)).
fof(6, axiom,![X1]:![X15]:(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X15)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_lists_list(X1),X15)=s(t_h4s_lists_list(X1),h4s_lists_nil)),file('i/f/EncodeVar/of__length__exists__zero', ah4s_lists_LENGTHu_u_NIL)).
fof(7, axiom,![X1]:![X16]:![X15]:(p(s(t_bool,h4s_bools_in(s(t_h4s_lists_list(X1),X15),s(t_fun(t_h4s_lists_list(X1),t_bool),h4s_encodevars_ofu_u_length(s(t_h4s_nums_num,X16))))))<=>s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X15)))=s(t_h4s_nums_num,X16)),file('i/f/EncodeVar/of__length__exists__zero', ah4s_EncodeVars_ofu_u_lengthu_u_def)).
fof(8, axiom,![X1]:![X11]:![X14]:(p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(X1,t_bool),X14),s(t_fun(X1,t_bool),X11))))<=>?[X8]:(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X14))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X11),s(X1,X8)))))),file('i/f/EncodeVar/of__length__exists__zero', ah4s_bools_RESu_u_EXISTSu_u_THM)).
# SZS output end CNFRefutation
