# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]: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_bit2(s(t_h4s_nums_num,X1)))))))=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,X1))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ch4s_numeralu_u_bits_NUMERALu_u_iDIV2u_c5)).
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_c5', ah4s_arithmetics_ALTu_u_ZERO)).
fof(9, axiom,![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X13),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_arithmetics_ADDu_u_0)).
fof(16, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_bit1(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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),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_c5', ah4s_arithmetics_BIT10)).
fof(18, axiom,![X1]:![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),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,X1)))))=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_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(19, axiom,![X13]: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,X13)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),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_c5', ah4s_arithmetics_ADD1)).
fof(20, axiom,![X1]: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,X1)))=s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X1),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_c5', ah4s_arithmetics_DIV2u_u_def)).
fof(21, 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_c5', ah4s_numerals_numeralu_u_sucu_c0)).
fof(22, 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_c5', ah4s_numerals_numeralu_u_distribu_c13)).
fof(23, axiom,![X1]:![X13]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X13)))))))=s(t_h4s_nums_num,h4s_arithmetics_bit1(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_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X13))))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_numerals_numeralu_u_addu_c4)).
fof(26, axiom,![X1]:![X13]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X13))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1)))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_numerals_numeralu_u_ltu_c5)).
fof(27, 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_c5', ah4s_numeralu_u_bits_iSUC0)).
fof(28, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),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,X1))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_arithmetics_TIMES2)).
fof(31, axiom,![X1]:![X13]: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,X13)))))))=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,X13))))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_numerals_numeralu_u_addu_c2)).
fof(32, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_numerals_numeralu_u_lteu_c2)).
fof(34, 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_c5', ah4s_numeralu_u_bits_iDIV20)).
fof(35, axiom,p(s(t_bool,t)),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', aHLu_TRUTH)).
fof(36, axiom,~(p(s(t_bool,f))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', aHLu_FALSITY)).
fof(44, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)<=>p(s(t_bool,X9))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(46, axiom,![X16]:![X1]:![X17]:(?[X18]:(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X18)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X1)))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X16)),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_arithmetics_DIVu_u_UNIQUE)).
fof(51, axiom,![X1]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_numerals_numeralu_u_ltu_c2)).
fof(55, axiom,![X1]: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,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,X1),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_numerals_numeralu_u_addu_c1)).
fof(56, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_numerals_numeralu_u_lteu_c1)).
fof(58, axiom,![X1]:![X13]: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,X13)))))=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,X13))))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_numerals_numeralu_u_distribu_c2)).
fof(61, axiom,![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))=>(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1)))=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_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_arithmetics_DIVMODu_u_ID)).
fof(66, axiom,![X1]:![X13]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X13))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_arithmetics_NOTu_u_LESS)).
fof(67, axiom,![X1]:![X13]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X13))),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_arithmetics_MULTu_u_COMM)).
fof(71, axiom,![X1]:s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_zero),file('i/f/numeral_bit/NUMERAL__iDIV2_c5', ah4s_numerals_internalu_u_multu_u_characterisationu_c0)).
# SZS output end CNFRefutation
