# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(5, 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(6, 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(16, 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(20, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),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_c1', ah4s_arithmetics_BIT20)).
fof(21, axiom,![X11]:![X12]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_arithmetics_NOTu_u_LESS)).
fof(29, axiom,![X15]:![X11]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X11))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X11)))=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(38, 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(43, axiom,![X11]: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,X11)))=s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X11),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(45, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,X11),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numerals_numeralu_u_distribu_c0)).
fof(54, 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(66, 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(71, axiom,![X11]:![X12]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,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,X11),s(t_h4s_nums_num,X12))))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numerals_numeralu_u_distribu_c2)).
fof(98, axiom,![X11]:![X12]:(~(s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,X11))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,X11))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(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,X11))),s(t_h4s_nums_num,X12)))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(115, axiom,![X6]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,X6),file('i/f/numeral_bit/NUMERAL__iDIV2_c1', ah4s_numerals_iZ0)).
fof(133, 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)).
# SZS output end CNFRefutation
