# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/integer/INT__LT__REDUCE_c1', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__LT__REDUCE_c1', 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/integer/INT__LT__REDUCE_c1', aHLu_BOOLu_CASES)).
fof(6, 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/integer/INT__LT__REDUCE_c1', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(16, axiom,![X8]:![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,X8)))))=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,X8))))),file('i/f/integer/INT__LT__REDUCE_c1', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(17, 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/integer/INT__LT__REDUCE_c1', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(46, axiom,![X8]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X8)))))),file('i/f/integer/INT__LT__REDUCE_c1', ah4s_primu_u_recs_LESSu_u_0)).
fof(48, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__LT__REDUCE_c1', ah4s_arithmetics_ALTu_u_ZERO)).
fof(60, axiom,![X8]:![X11]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X8))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11)))))))=s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X11))))))),file('i/f/integer/INT__LT__REDUCE_c1', ah4s_numerals_numeralu_u_addu_c2)).
fof(77, 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/integer/INT__LT__REDUCE_c1', ah4s_arithmetics_TWO)).
fof(79, 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/integer/INT__LT__REDUCE_c1', ah4s_arithmetics_ONE)).
fof(90, axiom,![X8]:![X11]: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,X11))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X8))),file('i/f/integer/INT__LT__REDUCE_c1', ah4s_integers_INTu_u_LT)).
fof(95, axiom,![X8]:![X20]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X8))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,X20)),file('i/f/integer/INT__LT__REDUCE_c1', ah4s_arithmetics_LESSu_u_MOD)).
fof(129, axiom,![X6]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,X6),file('i/f/integer/INT__LT__REDUCE_c1', ah4s_numerals_iZ0)).
fof(133, conjecture,![X8]: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_bit2(s(t_h4s_nums_num,X8)))))))))=s(t_bool,t),file('i/f/integer/INT__LT__REDUCE_c1', ch4s_integers_INTu_u_LTu_u_REDUCEu_c1)).
# SZS output end CNFRefutation
