# 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,h4s_integers_intu_u_ofu_u_num(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__EQ0', ch4s_integers_INTu_u_ABSu_u_EQ0)).
fof(4, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/integer/INT__ABS__EQ0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(27, axiom,![X17]:s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X17)))=s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X17),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,X17))),s(t_h4s_integers_int,X17))),file('i/f/integer/INT__ABS__EQ0', ah4s_integers_INTu_u_ABS)).
fof(30, axiom,![X17]: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,X17)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X17))),file('i/f/integer/INT__ABS__EQ0', ah4s_integers_INTu_u_ABSu_u_NUM)).
fof(36, axiom,![X17]:![X18]: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,X18))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X17)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X17))),file('i/f/integer/INT__ABS__EQ0', ah4s_integers_INTu_u_LE)).
fof(38, axiom,![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X6)))))=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__EQ0', ah4s_integers_INTu_u_ADDu_u_RINV)).
fof(46, axiom,![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X6),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,X6),file('i/f/integer/INT__ABS__EQ0', ah4s_integers_INTu_u_ADDu_u_RID)).
fof(48, axiom,![X17]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X17)))),file('i/f/integer/INT__ABS__EQ0', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(52, 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,X8),s(t_h4s_integers_int,X6))))),file('i/f/integer/INT__ABS__EQ0', ah4s_integers_INTu_u_NOTu_u_LE)).
fof(53, axiom,![X6]:p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X6)))),file('i/f/integer/INT__ABS__EQ0', ah4s_integers_INTu_u_LEu_u_REFL)).
fof(64, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__ABS__EQ0', aHLu_FALSITY)).
fof(73, axiom,![X12]:((p(s(t_bool,X12))=>p(s(t_bool,f)))<=>s(t_bool,X12)=s(t_bool,f)),file('i/f/integer/INT__ABS__EQ0', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(74, axiom,![X12]:(s(t_bool,X12)=s(t_bool,f)<=>~(p(s(t_bool,X12)))),file('i/f/integer/INT__ABS__EQ0', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(77, axiom,![X7]:![X9]:![X10]:s(X7,h4s_bools_cond(s(t_bool,f),s(X7,X10),s(X7,X9)))=s(X7,X9),file('i/f/integer/INT__ABS__EQ0', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(78, axiom,![X7]:![X9]:![X10]:s(X7,h4s_bools_cond(s(t_bool,t),s(X7,X10),s(X7,X9)))=s(X7,X10),file('i/f/integer/INT__ABS__EQ0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(79, axiom,![X9]:![X10]:![X31]:(p(s(t_bool,h4s_bools_cond(s(t_bool,X31),s(t_bool,X10),s(t_bool,X9))))<=>((~(p(s(t_bool,X31)))|p(s(t_bool,X10)))&(p(s(t_bool,X31))|p(s(t_bool,X9))))),file('i/f/integer/INT__ABS__EQ0', ah4s_bools_CONDu_u_EXPAND)).
# SZS output end CNFRefutation
