# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X2))))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),X3),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X4))),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X2))))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),X3),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),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_numeral(s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,X4))))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),X3),s(t_h4s_nums_num,X5))),s(t_bool,f0))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X4))),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1))))),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ch4s_numeralu_u_bits_NUMERALu_u_BITu_u_MODFu_c2)).
fof(4, axiom,![X1]:![X7]:![X2]:![X3]:![X4]:![X5]:s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),X3),s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_numeralu_u_bits_bitu_u_modf(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),X3),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X7),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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),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_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,X4))),s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),X3),s(t_h4s_nums_num,X5))),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_odd),s(t_h4s_nums_num,X7))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1))))),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_numeralu_u_bits_BITu_u_MODFu_u_defu_c1)).
fof(16, axiom,![X2]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X15))),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_arithmetics_ADDu_u_COMM)).
fof(19, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X7),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(26, axiom,![X21]:(s(t_bool,X21)=s(t_bool,t)|s(t_bool,X21)=s(t_bool,f0)),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', aHLu_BOOLu_CASES)).
fof(31, axiom,![X21]:((p(s(t_bool,X21))=>p(s(t_bool,f0)))<=>s(t_bool,X21)=s(t_bool,f0)),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(33, axiom,![X21]:(s(t_bool,f0)=s(t_bool,X21)<=>~(p(s(t_bool,X21)))),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(35, axiom,![X7]:s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X7))),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_numerals_iDUB0)).
fof(36, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_arithmetics_ALTu_u_ZERO)).
fof(37, axiom,![X2]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X2)))))=s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X2))),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_numerals_numeralu_u_sucu_c1)).
fof(43, axiom,~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),h4s_arithmetics_odd),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_numerals_numeralu_u_distribu_c34)).
fof(52, axiom,![X2]: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,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X2))),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_arithmetics_TIMES2)).
fof(57, axiom,![X27]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X27),s(t_h4s_nums_num,X2))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X27),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_arithmetics_LESSu_u_DIVu_u_EQu_u_ZERO)).
fof(61, axiom,![X2]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(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,X2))),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(65, axiom,p(s(t_bool,t)),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', aHLu_TRUTH)).
fof(69, axiom,![X2]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X2)))))=s(t_bool,t),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_numerals_numeralu_u_ltu_c1)).
fof(71, axiom,![X2]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X2)))))=s(t_bool,t),file('i/f/numeral_bit/NUMERAL__BIT__MODF_c2', ah4s_numerals_numeralu_u_ltu_c0)).
# SZS output end CNFRefutation
