# 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,~(p(s(t_bool,f))),file('i/f/numposrep/num__hex__list', aHLu_FALSITY)).
fof(5, axiom,![X2]:![X3]:![X4]:![X5]:(![X6]:s(X3,happ(s(t_fun(X2,X3),X4),s(X2,X6)))=s(X3,happ(s(t_fun(X2,X3),X5),s(X2,X6)))=>s(t_fun(X2,X3),X4)=s(t_fun(X2,X3),X5)),file('i/f/numposrep/num__hex__list', aHLu_EXT)).
fof(11, axiom,![X9]:![X10]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X10)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X10))),file('i/f/numposrep/num__hex__list', ah4s_numerals_numeralu_u_distribu_c22)).
fof(12, axiom,![X9]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),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(13, axiom,![X7]:![X6]:s(X7,happ(s(t_fun(X7,X7),h4s_combins_i),s(X7,X6)))=s(X7,X6),file('i/f/numposrep/num__hex__list', ah4s_combins_Iu_u_THM)).
fof(14, axiom,![X8]:![X7]:![X11]:![X6]:![X5]:![X4]:s(X8,happ(s(t_fun(X11,X8),h4s_combins_o(s(t_fun(X7,X8),X4),s(t_fun(X11,X7),X5))),s(X11,X6)))=s(X8,happ(s(t_fun(X7,X8),X4),s(X7,happ(s(t_fun(X11,X7),X5),s(X11,X6))))),file('i/f/numposrep/num__hex__list', ah4s_combins_ou_u_THM)).
fof(15, 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(16, 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(17, axiom,![X9]:![X12]:(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,X12))))=>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,X12))),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,X12))),s(t_h4s_nums_num,X9)))))=s(t_h4s_nums_num,X9)),file('i/f/numposrep/num__hex__list', ah4s_numposreps_l2nu_u_n2l)).
fof(18, axiom,![X9]:![X10]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X10))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X9)))))),file('i/f/numposrep/num__hex__list', ah4s_numerals_numeralu_u_ltu_c5)).
# SZS output end CNFRefutation
