# 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_greater),s(X1,X4),s(X1,X3),s(X1,X2)))=s(X1,X2),file('i/f/prelim/ordering__case__def_c2', ch4s_prelims_orderingu_u_caseu_u_defu_c2)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/prelim/ordering__case__def_c2', aHLu_FALSITY)).
fof(3, axiom,![X5]:![X6]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X6)))<=>s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,X6)),file('i/f/prelim/ordering__case__def_c2', ah4s_numerals_numeralu_u_distribu_c19)).
fof(4, axiom,![X5]:![X6]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X5))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X6)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X6))),file('i/f/prelim/ordering__case__def_c2', ah4s_numerals_numeralu_u_distribu_c22)).
fof(5, axiom,![X5]:![X6]:(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X6)))<=>p(s(t_bool,f))),file('i/f/prelim/ordering__case__def_c2', ah4s_numerals_numeralu_u_equ_c5)).
fof(6, axiom,![X5]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/prelim/ordering__case__def_c2', ah4s_numerals_numeralu_u_ltu_c2)).
fof(7, axiom,![X5]:![X6]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X5))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X6)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X6))),file('i/f/prelim/ordering__case__def_c2', ah4s_numerals_numeralu_u_ltu_c6)).
fof(8, axiom,![X1]:![X7]:![X2]:![X3]:![X4]:?[X8]:((p(s(t_bool,X8))<=>s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,X7)))=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,X7),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,X7))),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,X8),s(X1,X3),s(X1,X2)))))),file('i/f/prelim/ordering__case__def_c2', ah4s_prelims_orderingu_u_CASE0)).
fof(9, axiom,s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,h4s_prelims_greater)))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),file('i/f/prelim/ordering__case__def_c2', ah4s_prelims_ordering2numu_u_thmu_c2)).
fof(10, axiom,p(s(t_bool,t)),file('i/f/prelim/ordering__case__def_c2', aHLu_TRUTH)).
fof(11, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/prelim/ordering__case__def_c2', aHLu_BOOLu_CASES)).
fof(12, axiom,![X1]:![X10]:![X11]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X11),s(X1,X10)))=s(X1,X10),file('i/f/prelim/ordering__case__def_c2', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
