# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', 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__ODD__EXISTS_c0', aHLu_BOOLu_CASES)).
fof(10, axiom,![X7]: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,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/arithmetic/EVEN__ODD__EXISTS_c0', ah4s_arithmetics_TIMES2)).
fof(11, axiom,![X7]:p(s(t_bool,h4s_arithmetics_odd(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,X7)))))))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', ah4s_arithmetics_ODDu_u_DOUBLE)).
fof(13, 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__ODD__EXISTS_c0', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(14, axiom,![X7]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X7))))<=>~(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X7)))))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', ah4s_arithmetics_EVENu_u_ODD)).
fof(15, axiom,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_suc(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__ODD__EXISTS_c0', ah4s_arithmetics_TWO)).
fof(16, 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__ODD__EXISTS_c0', ah4s_arithmetics_ONE)).
fof(17, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', ah4s_arithmetics_ALTu_u_ZERO)).
fof(19, axiom,![X7]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X7))))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(20, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(27, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X11),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(34, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_bit1(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,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', ah4s_arithmetics_BIT10)).
fof(54, axiom,s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,f),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', ah4s_arithmetics_ODD0u_c0)).
fof(58, axiom,![X7]:?[X11]:(s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_nums_num,X11)))|s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_nums_num,X11))),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__ODD__EXISTS_c0', ah4s_arithmetics_ODDu_u_ORu_u_EVEN)).
fof(63, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(120, axiom,![X19]:![X7]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X19)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X19))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', ah4s_arithmetics_ADDu_u_ASSOC)).
fof(133, conjecture,![X7]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X7))))=>?[X11]:s(t_h4s_nums_num,X7)=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,X11)))),file('i/f/arithmetic/EVEN__ODD__EXISTS_c0', ch4s_arithmetics_EVENu_u_ODDu_u_EXISTSu_c0)).
# SZS output end CNFRefutation
