# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numeralu_u_bits_idiv2),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numeralu_u_bits_isuc),s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_arithmetics_zero),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ch4s_numeralu_u_bits_NUMERALu_u_iDIV2u_c1)).
fof(8, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_arithmetics_ALTu_u_ZERO)).
fof(9, axiom,![X12]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X12),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_arithmetics_ADDu_u_0)).
fof(15, axiom,![X12]:s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,X12)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_arithmetics_ADD1)).
fof(18, axiom,s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numerals_numeralu_u_sucu_c0)).
fof(19, axiom,s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numerals_numeralu_u_distribu_c13)).
fof(22, axiom,![X14]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,X14),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numerals_numeralu_u_addu_c1)).
fof(24, axiom,![X14]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numerals_numeralu_u_ltu_c2)).
fof(28, axiom,![X14]:![X12]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X12))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X14)))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numerals_numeralu_u_ltu_c5)).
fof(33, axiom,![X14]:s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_div2),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X14),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/numeral_bit/NUMERAL__iDIV2_c1', ah4s_arithmetics_DIV2u_u_def)).
fof(35, axiom,s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numeralu_u_bits_isuc)=s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numeralu_u_bits_iSUC0)).
fof(36, axiom,s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_numeralu_u_bits_idiv2)=s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_arithmetics_div2),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numeralu_u_bits_iDIV20)).
fof(38, axiom,~(p(s(t_bool,f))),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', aHLu_FALSITY)).
fof(50, axiom,![X19]:![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X14))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X19),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_arithmetics_LESSu_u_DIVu_u_EQu_u_ZERO)).
fof(54, axiom,![X14]:![X12]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X12)))))=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,X14),s(t_h4s_nums_num,X12))))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numerals_numeralu_u_distribu_c2)).
fof(55, axiom,![X14]:![X12]: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,X14))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X12)))))))=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,X14),s(t_h4s_nums_num,X12))))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numerals_numeralu_u_addu_c2)).
fof(71, axiom,![X14]:s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_arithmetics_zero),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numerals_internalu_u_multu_u_characterisationu_c0)).
# SZS output end CNFRefutation
