# 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))))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),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_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))),file('i/f/bit/ODD__MOD2__LEM', ch4s_bits_ODDu_u_MOD2u_u_LEM)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/bit/ODD__MOD2__LEM', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/bit/ODD__MOD2__LEM', aHLu_FALSITY)).
fof(4, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/bit/ODD__MOD2__LEM', aHLu_BOOLu_CASES)).
fof(12, axiom,![X2]:(s(t_bool,t)=s(t_bool,X2)<=>p(s(t_bool,X2))),file('i/f/bit/ODD__MOD2__LEM', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(14, axiom,![X2]:(s(t_bool,f)=s(t_bool,X2)<=>~(p(s(t_bool,X2)))),file('i/f/bit/ODD__MOD2__LEM', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(15, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),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,X1))),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/bit/ODD__MOD2__LEM', ah4s_arithmetics_MODu_u_2)).
fof(16, axiom,![X1]:(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1)))<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/bit/ODD__MOD2__LEM', ah4s_numerals_numeralu_u_distribu_c18)).
fof(17, axiom,![X1]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/bit/ODD__MOD2__LEM', ah4s_numerals_numeralu_u_equ_c1)).
fof(18, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X1))))<=>~(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X1)))))),file('i/f/bit/ODD__MOD2__LEM', ah4s_arithmetics_ODDu_u_EVEN)).
fof(19, axiom,![X5]:![X3]:![X4]:s(X5,h4s_bools_cond(s(t_bool,t),s(X5,X4),s(X5,X3)))=s(X5,X4),file('i/f/bit/ODD__MOD2__LEM', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(20, axiom,![X5]:![X3]:![X4]:s(X5,h4s_bools_cond(s(t_bool,f),s(X5,X4),s(X5,X3)))=s(X5,X3),file('i/f/bit/ODD__MOD2__LEM', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
