# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/EVEN__MOD2', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/EVEN__MOD2', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/arithmetic/EVEN__MOD2', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_mod(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_bools_cond(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X7))),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/arithmetic/EVEN__MOD2', ah4s_arithmetics_MODu_u_2)).
fof(21, axiom,![X6]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,X6),file('i/f/arithmetic/EVEN__MOD2', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(23, axiom,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_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/EVEN__MOD2', ah4s_arithmetics_ONE)).
fof(26, axiom,s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,t),file('i/f/arithmetic/EVEN__MOD2', ah4s_arithmetics_EVEN0u_c0)).
fof(35, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/EVEN__MOD2', ah4s_arithmetics_ALTu_u_ZERO)).
fof(68, axiom,![X8]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/EVEN__MOD2', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
fof(76, axiom,![X9]:![X12]:![X13]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X13),s(X9,X12)))=s(X9,X12),file('i/f/arithmetic/EVEN__MOD2', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(104, axiom,![X26]:![X14]:![X6]:(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,X6))))),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X26)))<=>(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X26))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X6)))))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X26))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X6)))))))=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/EVEN__MOD2', ah4s_arithmetics_NUMERALu_u_MULTu_u_EQu_u_DIVu_c1)).
fof(131, axiom,![X7]:~(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7)))),file('i/f/arithmetic/EVEN__MOD2', ah4s_arithmetics_SUCu_u_NOT)).
fof(133, conjecture,![X6]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X6))))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X6),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_nums_0)),file('i/f/arithmetic/EVEN__MOD2', ch4s_arithmetics_EVENu_u_MOD2)).
# SZS output end CNFRefutation
