# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X1)))=s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1))))),file('i/f/int_arith/INT__NUM__EVEN', ch4s_intu_u_ariths_INTu_u_NUMu_u_EVEN)).
fof(2, axiom,![X2]:![X3]:((p(s(t_bool,X3))=>p(s(t_bool,X2)))=>((p(s(t_bool,X2))=>p(s(t_bool,X3)))=>s(t_bool,X3)=s(t_bool,X2))),file('i/f/int_arith/INT__NUM__EVEN', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(24, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_odd(s(t_h4s_nums_num,X1))))<=>~(p(s(t_bool,h4s_integers_intu_u_divides(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(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_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))))),file('i/f/int_arith/INT__NUM__EVEN', ah4s_intu_u_ariths_INTu_u_NUMu_u_ODD)).
fof(40, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X1))))=>?[X17]: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,X17)))),file('i/f/int_arith/INT__NUM__EVEN', ah4s_arithmetics_EVENu_u_ODDu_u_EXISTSu_c0)).
fof(42, axiom,![X1]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/int_arith/INT__NUM__EVEN', ah4s_numerals_numeralu_u_distribu_c17)).
fof(44, axiom,![X1]:![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X17))),file('i/f/int_arith/INT__NUM__EVEN', ah4s_arithmetics_MULTu_u_COMM)).
fof(45, axiom,s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,t),file('i/f/int_arith/INT__NUM__EVEN', ah4s_arithmetics_EVEN0u_c0)).
fof(46, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))))<=>~(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X1)))))),file('i/f/int_arith/INT__NUM__EVEN', ah4s_arithmetics_EVEN0u_c1)).
fof(49, axiom,![X17]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/int_arith/INT__NUM__EVEN', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
fof(50, 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/int_arith/INT__NUM__EVEN', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(54, 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/int_arith/INT__NUM__EVEN', ah4s_arithmetics_TWO)).
fof(57, 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/int_arith/INT__NUM__EVEN', ah4s_arithmetics_ONE)).
fof(60, axiom,![X1]: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,X1)))))=s(t_bool,t),file('i/f/int_arith/INT__NUM__EVEN', ah4s_numerals_numeralu_u_ltu_c1)).
fof(62, axiom,~(p(s(t_bool,f))),file('i/f/int_arith/INT__NUM__EVEN', aHLu_FALSITY)).
fof(68, axiom,![X7]:(s(t_bool,X7)=s(t_bool,f)<=>~(p(s(t_bool,X7)))),file('i/f/int_arith/INT__NUM__EVEN', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(77, 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/int_arith/INT__NUM__EVEN', ah4s_arithmetics_ODDu_u_EVEN)).
fof(79, axiom,p(s(t_bool,t)),file('i/f/int_arith/INT__NUM__EVEN', aHLu_TRUTH)).
# SZS output end CNFRefutation
