# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,X1)<=>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,X1))))),file('i/f/integer/INT__ABS__EQ__ID', ch4s_integers_INTu_u_ABSu_u_EQu_u_ID)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/integer/INT__ABS__EQ__ID', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__ABS__EQ__ID', aHLu_FALSITY)).
fof(9, axiom,![X3]:(s(t_bool,t)=s(t_bool,X3)<=>p(s(t_bool,X3))),file('i/f/integer/INT__ABS__EQ__ID', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(13, axiom,![X5]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5)))),file('i/f/integer/INT__ABS__EQ__ID', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(14, axiom,![X5]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_nums_0))))<=>s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/integer/INT__ABS__EQ__ID', ah4s_arithmetics_LESSu_u_EQu_u_0)).
fof(16, axiom,![X4]: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,X4)))))=s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X4),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__ABS__EQ__ID', ah4s_integers_INTu_u_NEGu_u_GE0)).
fof(17, axiom,![X5]:![X6]: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,X6))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X5)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X5))),file('i/f/integer/INT__ABS__EQ__ID', ah4s_integers_INTu_u_LE)).
fof(18, axiom,![X1]:(?[X5]:(s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X5)))&~(s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,h4s_nums_0)))|(?[X5]:(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,X5)))))&~(s(t_h4s_nums_num,X5)=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__ABS__EQ__ID', ah4s_integers_INTu_u_NUMu_u_CASES)).
fof(19, axiom,![X5]:s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X5)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X5))),file('i/f/integer/INT__ABS__EQ__ID', ah4s_integers_INTu_u_ABSu_u_NUM)).
fof(20, axiom,![X1]:(s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X1)))<=>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__ABS__EQ__ID', ah4s_integers_INTu_u_NEGu_u_SAMEu_u_EQ)).
fof(21, axiom,![X1]:s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X1)))))=s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X1))),file('i/f/integer/INT__ABS__EQ__ID', ah4s_integers_INTu_u_ABSu_u_NEG)).
fof(24, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/integer/INT__ABS__EQ__ID', aHLu_BOOLu_CASES)).
fof(25, axiom,![X5]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X5))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/integer/INT__ABS__EQ__ID', ah4s_numerals_numeralu_u_lteu_c1)).
# SZS output end CNFRefutation
