# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),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_bit1(s(t_h4s_nums_num,X1)))))))))=s(t_bool,t),file('i/f/integer/INT__LT__REDUCE_c0', ch4s_integers_INTu_u_LTu_u_REDUCEu_c0)).
fof(9, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/integer/INT__LT__REDUCE_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(18, axiom,![X1]:![X9]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X9))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X1))),file('i/f/integer/INT__LT__REDUCE_c0', ah4s_integers_INTu_u_LT)).
fof(23, axiom,![X4]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X4)))=s(t_h4s_nums_num,X4),file('i/f/integer/INT__LT__REDUCE_c0', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(24, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__LT__REDUCE_c0', aHLu_FALSITY)).
fof(28, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/integer/INT__LT__REDUCE_c0', ah4s_numerals_numeralu_u_lteu_c1)).
fof(36, axiom,![X1]:![X9]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X9))))),file('i/f/integer/INT__LT__REDUCE_c0', ah4s_arithmetics_NOTu_u_LESS)).
fof(55, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__LT__REDUCE_c0', ah4s_arithmetics_ALTu_u_ZERO)).
# SZS output end CNFRefutation
