# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,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/ordering2num__thm_c0', ch4s_prelims_ordering2numu_u_thmu_c0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/prelim/ordering2num__thm_c0', aHLu_TRUTH)).
fof(6, axiom,![X2]: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,X2)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X2))),file('i/f/prelim/ordering2num__thm_c0', ah4s_numerals_numeralu_u_distribu_c21)).
fof(7, axiom,![X2]: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,X2)))))=s(t_bool,t),file('i/f/prelim/ordering2num__thm_c0', ah4s_numerals_numeralu_u_ltu_c0)).
fof(8, axiom,![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),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,X3)))))=s(t_h4s_nums_num,X3)),file('i/f/prelim/ordering2num__thm_c0', ah4s_prelims_ordering2numu_u_num2ordering)).
fof(9, 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/ordering2num__thm_c0', ah4s_prelims_LESSu_u_def)).
# SZS output end CNFRefutation
