# 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_forall(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__univ__zero', ch4s_EncodeVars_ofu_u_lengthu_u_univu_u_zero)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/EncodeVar/of__length__univ__zero', aHLu_TRUTH)).
fof(8, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)<=>p(s(t_bool,X10))),file('i/f/EncodeVar/of__length__univ__zero', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(12, axiom,![X1]:![X19]:![X7]:(![X9]:(s(X1,X9)=s(X1,X19)=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X7),s(X1,X9)))))<=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X7),s(X1,X19))))),file('i/f/EncodeVar/of__length__univ__zero', ah4s_bools_UNWINDu_u_FORALLu_u_THM2)).
fof(13, axiom,![X1]:![X7]:![X20]:(p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),X20),s(t_fun(X1,t_bool),X7))))<=>![X9]:(p(s(t_bool,h4s_bools_in(s(X1,X9),s(t_fun(X1,t_bool),X20))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X7),s(X1,X9)))))),file('i/f/EncodeVar/of__length__univ__zero', ah4s_bools_RESu_u_FORALLu_u_THM)).
fof(14, axiom,![X1]:![X21]:(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X21)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_lists_list(X1),X21)=s(t_h4s_lists_list(X1),h4s_lists_nil)),file('i/f/EncodeVar/of__length__univ__zero', ah4s_lists_LENGTHu_u_NIL)).
fof(15, axiom,![X1]:![X22]:![X21]:(p(s(t_bool,h4s_bools_in(s(t_h4s_lists_list(X1),X21),s(t_fun(t_h4s_lists_list(X1),t_bool),h4s_encodevars_ofu_u_length(s(t_h4s_nums_num,X22))))))<=>s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X21)))=s(t_h4s_nums_num,X22)),file('i/f/EncodeVar/of__length__univ__zero', ah4s_EncodeVars_ofu_u_lengthu_u_def)).
fof(16, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)|s(t_bool,X10)=s(t_bool,f)),file('i/f/EncodeVar/of__length__univ__zero', aHLu_BOOLu_CASES)).
fof(17, axiom,~(p(s(t_bool,f))),file('i/f/EncodeVar/of__length__univ__zero', aHLu_FALSITY)).
# SZS output end CNFRefutation
