# 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,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,X1))),file('i/f/integer/INT__ABS__NUM', ch4s_integers_INTu_u_ABSu_u_NUM)).
fof(3, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/integer/INT__ABS__NUM', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(22, axiom,![X1]:(~(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,h4s_nums_0))))<=>p(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,X1))))))),file('i/f/integer/INT__ABS__NUM', ah4s_integers_INTu_u_LTu_u_NZ)).
fof(23, axiom,![X1]:s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X1)))=s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(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))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X1))),s(t_h4s_integers_int,X1))),file('i/f/integer/INT__ABS__NUM', ah4s_integers_INTu_u_ABS)).
fof(24, axiom,![X11]: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,h4s_integers_abs(s(t_h4s_integers_int,X11)))))),file('i/f/integer/INT__ABS__NUM', ah4s_integers_INTu_u_ABSu_u_POS)).
fof(27, axiom,![X3]:![X4]:(~(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X3)))))<=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X4))))),file('i/f/integer/INT__ABS__NUM', ah4s_integers_INTu_u_NOTu_u_LE)).
fof(29, axiom,![X2]:![X5]:![X6]:s(X2,h4s_bools_cond(s(t_bool,f),s(X2,X6),s(X2,X5)))=s(X2,X5),file('i/f/integer/INT__ABS__NUM', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(30, axiom,![X2]:![X5]:![X6]:s(X2,h4s_bools_cond(s(t_bool,t),s(X2,X6),s(X2,X5)))=s(X2,X6),file('i/f/integer/INT__ABS__NUM', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(31, axiom,![X2]:![X12]:![X3]:![X13]:![X4]:![X18]:![X19]:((s(t_bool,X19)=s(t_bool,X18)&((p(s(t_bool,X18))=>s(X2,X4)=s(X2,X13))&(~(p(s(t_bool,X18)))=>s(X2,X3)=s(X2,X12))))=>s(X2,h4s_bools_cond(s(t_bool,X19),s(X2,X4),s(X2,X3)))=s(X2,h4s_bools_cond(s(t_bool,X18),s(X2,X13),s(X2,X12)))),file('i/f/integer/INT__ABS__NUM', ah4s_bools_CONDu_u_CONG)).
fof(39, axiom,![X4]:p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X4)))),file('i/f/integer/INT__ABS__NUM', ah4s_integers_INTu_u_LEu_u_REFL)).
fof(40, axiom,![X21]:(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,X21))))=>?[X1]:s(t_h4s_integers_int,X21)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))),file('i/f/integer/INT__ABS__NUM', ah4s_integers_NUMu_u_POSINTu_u_EXISTS)).
fof(41, axiom,![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,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))),file('i/f/integer/INT__ABS__NUM', ah4s_integers_INTu_u_POS)).
# SZS output end CNFRefutation
