# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]: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_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,X1)))))))=s(t_bool,t),file('i/f/integer/INT__LE__REDUCE_c1', ch4s_integers_INTu_u_LEu_u_REDUCEu_c1)).
fof(19, axiom,p(s(t_bool,t)),file('i/f/integer/INT__LE__REDUCE_c1', aHLu_TRUTH)).
fof(20, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/integer/INT__LE__REDUCE_c1', aHLu_BOOLu_CASES)).
fof(27, axiom,![X4]:(s(t_bool,t)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/integer/INT__LE__REDUCE_c1', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(29, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__LE__REDUCE_c1', aHLu_FALSITY)).
fof(35, axiom,![X4]:(s(t_bool,f)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/integer/INT__LE__REDUCE_c1', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(42, 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_c1', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(45, axiom,![X1]:![X15]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),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,X15))))),file('i/f/integer/INT__LE__REDUCE_c1', ah4s_arithmetics_NOTu_u_LEQ)).
fof(46, axiom,![X1]:![X15]:(~(s(t_h4s_nums_num,X15)=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,X15))),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,X15)))))),file('i/f/integer/INT__LE__REDUCE_c1', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(47, axiom,![X8]:![X6]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X8))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X8))))|s(t_h4s_integers_int,X6)=s(t_h4s_integers_int,X8))),file('i/f/integer/INT__LE__REDUCE_c1', ah4s_integers_INTu_u_LEu_u_CALCULATE)).
fof(48, 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_c1', ah4s_integers_INTu_u_NEGu_u_0)).
fof(52, axiom,![X1]:![X15]: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,X15)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X15))),file('i/f/integer/INT__LE__REDUCE_c1', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(54, axiom,![X1]:![X15]:(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,X15))))))<=>(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))|~(s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/integer/INT__LE__REDUCE_c1', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c2)).
fof(55, axiom,![X1]:![X15]: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,X15)))))))=s(t_bool,f),file('i/f/integer/INT__LE__REDUCE_c1', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c3)).
fof(56, 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__LE__REDUCE_c1', 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_c1', 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_c1', ah4s_numerals_numeralu_u_distribu_c27)).
fof(70, 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_c1', ah4s_numerals_numeralu_u_sucu_c0)).
fof(80, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer/INT__LE__REDUCE_c1', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
