# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_combins_o(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_numu_u_fromu_u_hexu_u_list),s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_h4s_nums_num)),h4s_numposreps_numu_u_tou_u_hexu_u_list)))=s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_combins_i),file('i/f/numposrep/num__hex__list', ch4s_numposreps_numu_u_hexu_u_list)).
fof(3, axiom,![X1]:![X3]:s(X1,happ(s(t_fun(X1,X1),h4s_combins_i),s(X1,X3)))=s(X1,X3),file('i/f/numposrep/num__hex__list', ah4s_combins_Iu_u_THM)).
fof(4, axiom,![X4]:![X1]:![X5]:![X3]:![X6]:![X7]:s(X4,happ(s(t_fun(X5,X4),h4s_combins_o(s(t_fun(X1,X4),X7),s(t_fun(X5,X1),X6))),s(X5,X3)))=s(X4,happ(s(t_fun(X1,X4),X7),s(X1,happ(s(t_fun(X5,X1),X6),s(X5,X3))))),file('i/f/numposrep/num__hex__list', ah4s_combins_ou_u_THM)).
fof(7, axiom,s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_h4s_nums_num)),h4s_numposreps_numu_u_tou_u_hexu_u_list)=s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_h4s_nums_num)),h4s_numposreps_n2l(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))),file('i/f/numposrep/num__hex__list', ah4s_numposreps_numu_u_tou_u_hexu_u_listu_u_def)).
fof(8, axiom,s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_numu_u_fromu_u_hexu_u_list)=s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))),file('i/f/numposrep/num__hex__list', ah4s_numposreps_numu_u_fromu_u_hexu_u_listu_u_def)).
fof(9, axiom,![X8]:![X9]:![X7]:![X6]:(![X3]:s(X9,happ(s(t_fun(X8,X9),X7),s(X8,X3)))=s(X9,happ(s(t_fun(X8,X9),X6),s(X8,X3)))=>s(t_fun(X8,X9),X7)=s(t_fun(X8,X9),X6)),file('i/f/numposrep/num__hex__list', aHLu_EXT)).
fof(15, axiom,![X14]:![X15]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X15))))=>s(t_h4s_nums_num,happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_nums_num),h4s_numposreps_l2n(s(t_h4s_nums_num,X15))),s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_h4s_lists_list(t_h4s_nums_num)),h4s_numposreps_n2l(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X14)))))=s(t_h4s_nums_num,X14)),file('i/f/numposrep/num__hex__list', ah4s_numposreps_l2nu_u_n2l)).
fof(16, axiom,![X14]:![X16]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X16))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X14)))))),file('i/f/numposrep/num__hex__list', ah4s_numerals_numeralu_u_ltu_c5)).
fof(18, axiom,![X17]:![X18]:((p(s(t_bool,X18))=>p(s(t_bool,X17)))=>((p(s(t_bool,X17))=>p(s(t_bool,X18)))=>s(t_bool,X18)=s(t_bool,X17))),file('i/f/numposrep/num__hex__list', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(33, axiom,![X14]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numposrep/num__hex__list', ah4s_numerals_numeralu_u_ltu_c2)).
fof(34, axiom,![X14]:![X16]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X16)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X16))),file('i/f/numposrep/num__hex__list', ah4s_numerals_numeralu_u_distribu_c22)).
fof(35, axiom,![X14]:![X16]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X14)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X16))))),file('i/f/numposrep/num__hex__list', ah4s_arithmetics_NOTu_u_LESS)).
fof(36, axiom,~(p(s(t_bool,f))),file('i/f/numposrep/num__hex__list', aHLu_FALSITY)).
fof(37, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)|s(t_bool,X10)=s(t_bool,f)),file('i/f/numposrep/num__hex__list', aHLu_BOOLu_CASES)).
fof(38, axiom,(~(p(s(t_bool,f)))<=>p(s(t_bool,t))),file('i/f/numposrep/num__hex__list', ah4s_bools_NOTu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
