# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(X1,h4s_prelims_orderingu_u_case(s(t_h4s_prelims_ordering,h4s_prelims_less),s(X1,X4),s(X1,X3),s(X1,X2)))=s(X1,X4),file('i/f/prelim/ordering__case__def_c0', ch4s_prelims_orderingu_u_caseu_u_defu_c0)).
fof(3, axiom,![X1]:![X6]:![X2]:![X3]:![X4]:?[X7]:((p(s(t_bool,X7))<=>s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,X6)))=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(X1,h4s_prelims_orderingu_u_case(s(t_h4s_prelims_ordering,X6),s(X1,X4),s(X1,X3),s(X1,X2)))=s(X1,h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,X6))),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(X1,X4),s(X1,h4s_bools_cond(s(t_bool,X7),s(X1,X3),s(X1,X2)))))),file('i/f/prelim/ordering__case__def_c0', ah4s_prelims_orderingu_u_CASE0)).
fof(4, axiom,s(t_h4s_prelims_ordering,h4s_prelims_less)=s(t_h4s_prelims_ordering,h4s_prelims_num2ordering(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/prelim/ordering__case__def_c0', ah4s_prelims_LESSu_u_def)).
fof(6, axiom,s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,h4s_prelims_less)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/prelim/ordering__case__def_c0', ah4s_prelims_ordering2numu_u_thmu_c0)).
fof(9, axiom,![X1]:![X8]:![X9]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X9),s(X1,X8)))=s(X1,X9),file('i/f/prelim/ordering__case__def_c0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(11, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/prelim/ordering__case__def_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(26, axiom,![X23]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X23)))))=s(t_bool,t),file('i/f/prelim/ordering__case__def_c0', ah4s_numerals_numeralu_u_ltu_c0)).
fof(27, axiom,![X23]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X23)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X23))),file('i/f/prelim/ordering__case__def_c0', ah4s_numerals_numeralu_u_distribu_c21)).
fof(28, axiom,![X24]:?[X25]:(s(t_h4s_prelims_ordering,X24)=s(t_h4s_prelims_ordering,h4s_prelims_num2ordering(s(t_h4s_nums_num,X25)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,h4s_arithmetics_numeral(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/prelim/ordering__case__def_c0', ah4s_prelims_num2orderingu_u_ONTO)).
fof(33, axiom,![X23]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X23)))))),file('i/f/prelim/ordering__case__def_c0', ah4s_primu_u_recs_LESSu_u_0)).
fof(35, axiom,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,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/prelim/ordering__case__def_c0', ah4s_arithmetics_ONE)).
fof(36, axiom,![X25]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))<=>s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,h4s_prelims_num2ordering(s(t_h4s_nums_num,X25)))))=s(t_h4s_nums_num,X25)),file('i/f/prelim/ordering__case__def_c0', ah4s_prelims_ordering2numu_u_num2ordering)).
fof(39, axiom,![X28]:![X24]:(s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,X24)))=s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,X28)))<=>s(t_h4s_prelims_ordering,X24)=s(t_h4s_prelims_ordering,X28)),file('i/f/prelim/ordering__case__def_c0', ah4s_prelims_ordering2numu_u_11)).
fof(41, axiom,![X25]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))<=>?[X24]:s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,X24)))),file('i/f/prelim/ordering__case__def_c0', ah4s_prelims_ordering2numu_u_ONTO)).
# SZS output end CNFRefutation
