# 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(5, axiom,![X1]:![X6]:![X7]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X7),s(X1,X6)))=s(X1,X7),file('i/f/prelim/ordering__case__def_c0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(6, axiom,![X8]: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,X8)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X8))),file('i/f/prelim/ordering__case__def_c0', ah4s_numerals_numeralu_u_distribu_c21)).
fof(7, axiom,![X8]: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,X8)))))=s(t_bool,t),file('i/f/prelim/ordering__case__def_c0', ah4s_numerals_numeralu_u_ltu_c0)).
fof(8, 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]:![X9]:![X2]:![X3]:![X4]:?[X10]:((p(s(t_bool,X10))<=>s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,X9)))=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,X9),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,X9))),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,X10),s(X1,X3),s(X1,X2)))))),file('i/f/prelim/ordering__case__def_c0', ah4s_prelims_orderingu_u_CASE0)).
# SZS output end CNFRefutation
