# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X1))))=>?[X2]:s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_suc(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)))))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c1', ch4s_arithmetics_EVENu_u_ODDu_u_EXISTSu_c1)).
fof(9, axiom,![X2]:(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c1', ah4s_arithmetics_numu_u_CASES)).
fof(17, axiom,![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/EVEN__ODD__EXISTS_c1', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
fof(22, axiom,![X1]:![X2]:(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X1)<=>(s(t_h4s_nums_num,X2)=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,X1)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c1', ah4s_arithmetics_MULTu_u_EQu_u_ID)).
fof(29, axiom,![X5]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,X5),file('i/f/arithmetic/EVEN__ODD__EXISTS_c1', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(35, axiom,![X1]:p(s(t_bool,h4s_arithmetics_even(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)))))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c1', ah4s_arithmetics_EVENu_u_DOUBLE)).
fof(38, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X1))))=>?[X2]:s(t_h4s_nums_num,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,X2)))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c1', ah4s_arithmetics_EVENu_u_ODDu_u_EXISTSu_c0)).
fof(40, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/EVEN__ODD__EXISTS_c1', ah4s_arithmetics_ALTu_u_ZERO)).
fof(45, axiom,![X11]:![X12]:((p(s(t_bool,X12))=>p(s(t_bool,X11)))=>((p(s(t_bool,X11))=>p(s(t_bool,X12)))=>s(t_bool,X12)=s(t_bool,X11))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c1', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(60, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X1))))<=>~(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c1', ah4s_arithmetics_EVENu_u_ODD)).
fof(61, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))))<=>~(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c1', ah4s_arithmetics_ODD0u_c1)).
# SZS output end CNFRefutation
