# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(?[X2]:(s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2)))&~(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)))|(?[X2]:(s(t_h4s_integers_int,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_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0)))|s(t_h4s_integers_int,X1)=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__NUM__CASES', ch4s_integers_INTu_u_NUMu_u_CASES)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/integer/INT__NUM__CASES', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__NUM__CASES', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/integer/INT__NUM__CASES', aHLu_BOOLu_CASES)).
fof(23, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/integer/INT__NUM__CASES', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(38, axiom,![X8]: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_neg(s(t_h4s_integers_int,X8)))))=s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X8),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__NUM__CASES', ah4s_integers_INTu_u_NEGu_u_GE0)).
fof(39, axiom,![X2]:![X15]: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,X15))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X2))),file('i/f/integer/INT__NUM__CASES', ah4s_integers_INTu_u_LE)).
fof(41, axiom,![X16]:(p(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,X16))))=>?[X2]:s(t_h4s_integers_int,X16)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2)))),file('i/f/integer/INT__NUM__CASES', ah4s_integers_NUMu_u_POSINTu_u_EXISTS)).
fof(42, axiom,![X16]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X16),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))=>?[X2]:s(t_h4s_integers_int,X16)=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)))))),file('i/f/integer/INT__NUM__CASES', ah4s_integers_NUMu_u_NEGINTu_u_EXISTS)).
fof(43, axiom,![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),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__NUM__CASES', ah4s_arithmetics_LESSu_u_EQu_u_0)).
fof(44, axiom,![X9]:![X8]:(~(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X9)))))<=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X9),s(t_h4s_integers_int,X8))))),file('i/f/integer/INT__NUM__CASES', ah4s_integers_INTu_u_NOTu_u_LE)).
fof(45, axiom,![X9]:![X8]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X9))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X9))))|s(t_h4s_integers_int,X8)=s(t_h4s_integers_int,X9))),file('i/f/integer/INT__NUM__CASES', ah4s_integers_INTu_u_LEu_u_LT)).
# SZS output end CNFRefutation
