# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/bitstring/el__sign__extend', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/bitstring/el__sign__extend', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/bitstring/el__sign__extend', aHLu_BOOLu_CASES)).
fof(14, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/bitstring/el__sign__extend', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(15, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,t),s(X9,X8),s(X9,X7)))=s(X9,X8),file('i/f/bitstring/el__sign__extend', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(16, axiom,![X9]:![X7]:![X8]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X8),s(X9,X7)))=s(X9,X7),file('i/f/bitstring/el__sign__extend', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(22, axiom,![X18]:![X9]:![X10]:![X6]:s(X9,happ(s(t_fun(X18,X9),h4s_combins_k(s(X9,X6))),s(X18,X10)))=s(X9,X6),file('i/f/bitstring/el__sign__extend', ah4s_combins_Ku_u_THM)).
fof(24, axiom,![X20]:![X19]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X20)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X19))),file('i/f/bitstring/el__sign__extend', ah4s_arithmetics_ADDu_u_SYM)).
fof(27, axiom,![X20]:![X19]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X20)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X19))))),file('i/f/bitstring/el__sign__extend', ah4s_arithmetics_NOTu_u_LESS)).
fof(34, axiom,![X21]:![X20]:![X19]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X20))),s(t_h4s_nums_num,X21)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X21))))),file('i/f/bitstring/el__sign__extend', ah4s_arithmetics_SUBu_u_RIGHTu_u_LESSu_u_EQ)).
fof(35, axiom,![X21]:![X20]:![X19]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X21)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X21))),s(t_h4s_nums_num,X20))),file('i/f/bitstring/el__sign__extend', ah4s_arithmetics_SUBu_u_LEFTu_u_LESS)).
fof(38, axiom,![X9]:s(t_fun(t_h4s_lists_list(X9),X9),h4s_lists_el(s(t_h4s_nums_num,h4s_nums_0)))=s(t_fun(t_h4s_lists_list(X9),X9),h4s_lists_hd),file('i/f/bitstring/el__sign__extend', ah4s_lists_ELu_u_restrictedu_c0)).
fof(39, axiom,![X9]:![X20]:![X4]:s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X9),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,X9),X4),s(t_h4s_nums_num,X20)))))=s(t_h4s_nums_num,X20),file('i/f/bitstring/el__sign__extend', ah4s_lists_LENGTHu_u_GENLIST)).
fof(40, axiom,![X9]:![X22]:![X20]:![X23]:s(t_h4s_lists_list(X9),h4s_lists_padu_u_left(s(X9,X23),s(t_h4s_nums_num,X20),s(t_h4s_lists_list(X9),X22)))=s(t_h4s_lists_list(X9),h4s_lists_append(s(t_h4s_lists_list(X9),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,X9),h4s_combins_k(s(X9,X23))),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X9),X22))))))),s(t_h4s_lists_list(X9),X22))),file('i/f/bitstring/el__sign__extend', ah4s_lists_PADu_u_LEFT0)).
fof(41, axiom,![X9]:![X6]:![X20]:![X4]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X20))))=>s(X9,happ(s(t_fun(t_h4s_lists_list(X9),X9),h4s_lists_el(s(t_h4s_nums_num,X6))),s(t_h4s_lists_list(X9),h4s_lists_genlist(s(t_fun(t_h4s_nums_num,X9),X4),s(t_h4s_nums_num,X20)))))=s(X9,happ(s(t_fun(t_h4s_nums_num,X9),X4),s(t_h4s_nums_num,X6)))),file('i/f/bitstring/el__sign__extend', ah4s_lists_ELu_u_GENLIST)).
fof(42, axiom,![X9]:![X20]:![X24]:![X25]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X9),X25))))))=>s(X9,happ(s(t_fun(t_h4s_lists_list(X9),X9),h4s_lists_el(s(t_h4s_nums_num,X20))),s(t_h4s_lists_list(X9),h4s_lists_append(s(t_h4s_lists_list(X9),X25),s(t_h4s_lists_list(X9),X24)))))=s(X9,happ(s(t_fun(t_h4s_lists_list(X9),X9),h4s_lists_el(s(t_h4s_nums_num,X20))),s(t_h4s_lists_list(X9),X25)))),file('i/f/bitstring/el__sign__extend', ah4s_richu_u_lists_ELu_u_APPEND1)).
fof(43, axiom,![X9]:![X20]:![X25]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X9),X25))),s(t_h4s_nums_num,X20))))=>![X24]:s(X9,happ(s(t_fun(t_h4s_lists_list(X9),X9),h4s_lists_el(s(t_h4s_nums_num,X20))),s(t_h4s_lists_list(X9),h4s_lists_append(s(t_h4s_lists_list(X9),X25),s(t_h4s_lists_list(X9),X24)))))=s(X9,happ(s(t_fun(t_h4s_lists_list(X9),X9),h4s_lists_el(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X9),X25))))))),s(t_h4s_lists_list(X9),X24)))),file('i/f/bitstring/el__sign__extend', ah4s_richu_u_lists_ELu_u_APPEND2)).
fof(44, axiom,![X9]:![X26]:![X20]:s(t_h4s_lists_list(X9),h4s_bitstrings_signu_u_extend(s(t_h4s_nums_num,X20),s(t_h4s_lists_list(X9),X26)))=s(t_h4s_lists_list(X9),h4s_lists_padu_u_left(s(X9,happ(s(t_fun(t_h4s_lists_list(X9),X9),h4s_lists_hd),s(t_h4s_lists_list(X9),X26))),s(t_h4s_nums_num,X20),s(t_h4s_lists_list(X9),X26))),file('i/f/bitstring/el__sign__extend', ah4s_bitstrings_signu_u_extendu_u_def)).
fof(45, conjecture,![X9]:![X26]:![X20]:![X27]:s(X9,happ(s(t_fun(t_h4s_lists_list(X9),X9),h4s_lists_el(s(t_h4s_nums_num,X27))),s(t_h4s_lists_list(X9),h4s_bitstrings_signu_u_extend(s(t_h4s_nums_num,X20),s(t_h4s_lists_list(X9),X26)))))=s(X9,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X27),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X9),X26))))))),s(X9,happ(s(t_fun(t_h4s_lists_list(X9),X9),h4s_lists_el(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_lists_list(X9),X26))),s(X9,happ(s(t_fun(t_h4s_lists_list(X9),X9),h4s_lists_el(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X27),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X9),X26))))))))),s(t_h4s_lists_list(X9),X26))))),file('i/f/bitstring/el__sign__extend', ch4s_bitstrings_elu_u_signu_u_extend)).
# SZS output end CNFRefutation
