# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', aHLu_FALSITY)).
fof(17, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(21, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_arithmetics_ALTu_u_ZERO)).
fof(22, axiom,![X13]:s(t_h4s_nums_num,h4s_arithmetics_bit1(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_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,h4s_nums_0))))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_arithmetics_BIT10)).
fof(24, axiom,![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X14),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_arithmetics_ADDu_u_0)).
fof(26, axiom,![X13]:![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,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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(28, axiom,![X13]:![X14]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X14))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_arithmetics_NOTu_u_LESS)).
fof(29, axiom,![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,X14)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),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_c2', ah4s_arithmetics_ADD1)).
fof(30, axiom,![X13]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X14))),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_arithmetics_MULTu_u_COMM)).
fof(32, axiom,![X13]: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,X13)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X13))),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_arithmetics_TIMES2)).
fof(35, axiom,![X13]: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,X13)))=s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X13),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_c2', ah4s_arithmetics_DIV2u_u_def)).
fof(36, axiom,![X16]:![X13]:![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,X13))),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,X13)))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,X16)),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_arithmetics_DIVu_u_UNIQUE)).
fof(41, axiom,![X13]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X13))))=>(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X13),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)))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_arithmetics_DIVMODu_u_ID)).
fof(44, 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_c2', ah4s_numerals_numeralu_u_sucu_c0)).
fof(47, axiom,![X13]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X14)))))=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,X13),s(t_h4s_nums_num,X14))))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_numerals_numeralu_u_distribu_c2)).
fof(50, 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_c2', ah4s_numerals_numeralu_u_distribu_c13)).
fof(55, axiom,![X13]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,X13),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_numerals_numeralu_u_addu_c1)).
fof(56, axiom,![X13]:![X14]: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,X13))),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,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X14))))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_numerals_numeralu_u_addu_c2)).
fof(59, axiom,![X13]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_numerals_numeralu_u_ltu_c2)).
fof(60, axiom,![X13]:![X14]:(p(s(t_bool,h4s_primu_u_recs_u_3c(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,X14))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_numerals_numeralu_u_ltu_c5)).
fof(61, axiom,![X13]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_numerals_numeralu_u_lteu_c1)).
fof(69, axiom,![X13]:s(t_h4s_nums_num,h4s_numerals_internalu_u_mult(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_arithmetics_zero),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ah4s_numerals_internalu_u_multu_u_characterisationu_c0)).
fof(71, 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_c2', ah4s_numeralu_u_bits_iSUC0)).
fof(72, 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_c2', ah4s_numeralu_u_bits_iDIV20)).
fof(73, conjecture,![X13]: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_bit1(s(t_h4s_nums_num,X13)))))=s(t_h4s_nums_num,X13),file('i/f/numeral_bit/NUMERAL__iDIV2_c2', ch4s_numeralu_u_bits_NUMERALu_u_iDIV2u_c2)).
# SZS output end CNFRefutation
