# 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,h4s_arithmetics_zero)))=s(t_h4s_nums_num,h4s_arithmetics_zero),file('i/f/numeral_bit/NUMERAL__iDIV2_c0', ch4s_numeralu_u_bits_NUMERALu_u_iDIV2u_c0)).
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_c0', ah4s_arithmetics_ALTu_u_ZERO)).
fof(13, axiom,![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,X14),file('i/f/numeral_bit/NUMERAL__iDIV2_c0', ah4s_numerals_numeralu_u_distribu_c0)).
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_c0', ah4s_numerals_numeralu_u_sucu_c0)).
fof(20, axiom,![X14]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X14))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/numeral_bit/NUMERAL__iDIV2_c0', ah4s_numerals_numeralu_u_distribu_c27)).
fof(25, axiom,![X14]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(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_c0', ah4s_numerals_numeralu_u_lteu_c1)).
fof(26, axiom,![X14]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(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_c0', ah4s_numerals_numeralu_u_lteu_c2)).
fof(31, axiom,![X14]:s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),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,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),h4s_nums_suc),s(t_h4s_nums_num,h4s_nums_0))))))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c0', ah4s_arithmetics_BIT20)).
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_c0', ah4s_arithmetics_DIV2u_u_def)).
fof(35, 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_c0', ah4s_numeralu_u_bits_iDIV20)).
fof(37, axiom,~(p(s(t_bool,f))),file('i/f/numeral_bit/NUMERAL__iDIV2_c0', aHLu_FALSITY)).
fof(49, 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_c0', ah4s_arithmetics_LESSu_u_DIVu_u_EQu_u_ZERO)).
fof(62, axiom,![X14]:![X12]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X14)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X12))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c0', ah4s_arithmetics_NOTu_u_LESS)).
# SZS output end CNFRefutation
