# 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_abs(s(t_h4s_integers_int,X2)))<=>((s(t_h4s_integers_int,X2)=s(t_h4s_integers_int,X1)&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,X1)))))|(s(t_h4s_integers_int,X2)=s(t_h4s_integers_int,h4s_integers_intu_u_neg(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_c1', ch4s_integers_INTu_u_ABSu_u_EQu_c1)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__ABS__EQ_c1', aHLu_FALSITY)).
fof(9, axiom,![X3]:((p(s(t_bool,X3))=>p(s(t_bool,f)))<=>s(t_bool,X3)=s(t_bool,f)),file('i/f/integer/INT__ABS__EQ_c1', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(36, axiom,![X4]:s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X4)))))=s(t_h4s_integers_int,X4),file('i/f/integer/INT__ABS__EQ_c1', ah4s_integers_INTu_u_NEGNEG)).
fof(43, axiom,![X2]:(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X2)))=s(t_h4s_integers_int,X2)<=>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,X2))))),file('i/f/integer/INT__ABS__EQ_c1', ah4s_integers_INTu_u_ABSu_u_EQu_u_ID)).
fof(46, axiom,![X1]:![X2]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X2))))),s(t_h4s_integers_int,X1))))<=>(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X1))),s(t_h4s_integers_int,X2))))|p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1)))))),file('i/f/integer/INT__ABS__EQ_c1', ah4s_integers_INTu_u_ABSu_u_LEu_c2)).
fof(49, axiom,![X1]:![X2]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X2))))))<=>(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X2))))|p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X1)))))))),file('i/f/integer/INT__ABS__EQ_c1', ah4s_integers_INTu_u_ABSu_u_LEu_c1)).
fof(53, axiom,![X18]:![X4]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X18))))<=>~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X18),s(t_h4s_integers_int,X4)))))),file('i/f/integer/INT__ABS__EQ_c1', ah4s_integers_intu_u_le0)).
fof(54, 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_c1', ah4s_integers_INTu_u_NEGu_u_GE0)).
fof(55, axiom,![X18]:![X4]:(~(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X18)))))<=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X18),s(t_h4s_integers_int,X4))))),file('i/f/integer/INT__ABS__EQ_c1', ah4s_integers_INTu_u_NOTu_u_LE)).
fof(56, axiom,![X18]:![X4]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X18))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X18))))|s(t_h4s_integers_int,X4)=s(t_h4s_integers_int,X18))),file('i/f/integer/INT__ABS__EQ_c1', ah4s_integers_INTu_u_LEu_u_LT)).
fof(59, axiom,![X2]:s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X2)))))=s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X2))),file('i/f/integer/INT__ABS__EQ_c1', ah4s_integers_INTu_u_ABSu_u_NEG)).
fof(63, axiom,![X1]:![X2]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X2))),s(t_h4s_integers_int,X1))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))&p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X1))),s(t_h4s_integers_int,X2)))))),file('i/f/integer/INT__ABS__EQ_c1', ah4s_integers_INTu_u_ABSu_u_LTu_c0)).
fof(70, 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__ABS__EQ_c1', ah4s_integers_INTu_u_NEGu_u_0)).
fof(71, axiom,![X4]: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_neg(s(t_h4s_integers_int,X4)))))=s(t_bool,h4s_integers_intu_u_lt(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_c1', ah4s_integers_INTu_u_NEGu_u_GT0)).
fof(76, axiom,![X12]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X12)))),file('i/f/integer/INT__ABS__EQ_c1', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(80, 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_c1', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
