# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_nums_num,h4s_bits_lowestu_u_setu_u_bit(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1)))))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_bits_lowestu_u_setu_u_bit(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))))))),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ch4s_numeralu_u_bits_LOWESTu_u_SETu_u_BITu_u_computeu_c0)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', aHLu_FALSITY)).
fof(9, axiom,![X4]:((p(s(t_bool,X4))=>p(s(t_bool,f)))<=>s(t_bool,X4)=s(t_bool,f)),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(12, axiom,![X1]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X11))),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_arithmetics_ADDu_u_SYM)).
fof(15, axiom,![X1]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X1))),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(16, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1)))))))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_numerals_numeralu_u_div2u_c2)).
fof(17, axiom,![X1]:(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))=>s(t_h4s_nums_num,h4s_bits_lowestu_u_setu_u_bit(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_u_2b(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_bits_lowestu_u_setu_u_bit(s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,X1)))))))))),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_numeralu_u_bits_LOWESTu_u_SETu_u_BIT)).
fof(18, axiom,![X1]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11)))))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X11))))))),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_numerals_numeralu_u_distribu_c2)).
fof(19, axiom,![X1]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_numerals_numeralu_u_distribu_c17)).
fof(21, axiom,![X1]:s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X1))),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_numerals_numeralu_u_distribu_c32)).
fof(23, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X1),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_numerals_numeralu_u_distribu_c1)).
fof(24, axiom,![X1]:(s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1)))<=>p(s(t_bool,f))),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_numerals_numeralu_u_equ_c2)).
fof(26, axiom,![X1]:![X11]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11)))))))=s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X11))))))),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_numerals_numeralu_u_addu_c2)).
fof(27, axiom,![X1]:~(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1))))))),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_numerals_numeralu_u_evenoddu_c4)).
fof(34, axiom,![X5]:![X2]:![X3]:s(X5,h4s_bools_cond(s(t_bool,f),s(X5,X3),s(X5,X2)))=s(X5,X2),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_bools_boolu_u_caseu_u_thmu_c1)).
fof(35, axiom,![X1]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,X1),file('i/f/numeral_bit/LOWEST__SET__BIT__compute_c0', ah4s_numerals_numeralu_u_addu_c0)).
# SZS output end CNFRefutation
