# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_integers_intu_u_le(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,X1))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(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,X2)))))))))))=s(t_bool,f),file('i/f/integer/INT__LE__REDUCE_c9', ch4s_integers_INTu_u_LEu_u_REDUCEu_c9)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__LE__REDUCE_c9', aHLu_FALSITY)).
fof(14, axiom,![X5]:(s(t_bool,f)=s(t_bool,X5)<=>~(p(s(t_bool,X5)))),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(31, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/integer/INT__LE__REDUCE_c9', aHLu_BOOLu_CASES)).
fof(34, 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__LE__REDUCE_c9', ah4s_numerals_numeralu_u_lteu_c1)).
fof(36, axiom,![X1]:![X2]: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,X1))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2)))))))=s(t_bool,f),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c3)).
fof(38, axiom,![X1]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(41, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2))))),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_arithmetics_NOTu_u_LEQ)).
fof(42, axiom,![X1]:![X2]:(~(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X2)))))),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(43, axiom,![X9]:![X7]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X9))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X9))))|s(t_h4s_integers_int,X7)=s(t_h4s_integers_int,X9))),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_integers_INTu_u_LEu_u_CALCULATE)).
fof(47, axiom,s(t_h4s_integers_int,h4s_integers_intu_u_neg(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_nums_0))),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_integers_INTu_u_NEGu_u_0)).
fof(51, axiom,![X1]:![X2]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2))))))<=>(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))|~(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c2)).
fof(55, axiom,![X1]:![X2]: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,X1))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(56, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X7),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_arithmetics_NUMERALu_u_DEF)).
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/integer/INT__LE__REDUCE_c9', ah4s_arithmetics_ONE)).
fof(64, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_numerals_numeralu_u_distribu_c27)).
fof(66, axiom,s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/integer/INT__LE__REDUCE_c9', ah4s_numerals_numeralu_u_sucu_c0)).
fof(75, axiom,p(s(t_bool,t)),file('i/f/integer/INT__LE__REDUCE_c9', aHLu_TRUTH)).
# SZS output end CNFRefutation
