# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,X1)))))),file('i/f/real/ABS__LE', ch4s_reals_ABSu_u_LE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/real/ABS__LE', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/real/ABS__LE', aHLu_FALSITY)).
fof(9, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/real/ABS__LE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(10, axiom,![X1]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X1)))),file('i/f/real/ABS__LE', ah4s_reals_REALu_u_LEu_u_REFL)).
fof(11, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/real/ABS__LE', aHLu_BOOLu_CASES)).
fof(12, axiom,![X5]:![X1]:(~(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X5)))))<=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X5),s(t_h4s_realaxs_real,X1))))),file('i/f/real/ABS__LE', ah4s_reals_REALu_u_NOTu_u_LE)).
fof(13, axiom,![X5]:![X1]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X5))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X5))))),file('i/f/real/ABS__LE', ah4s_reals_REALu_u_LTu_u_IMPu_u_LE)).
fof(14, axiom,![X1]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X1)))))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/real/ABS__LE', ah4s_reals_REALu_u_LEu_u_NEGR)).
fof(15, axiom,![X1]:s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,X1)))=s(t_h4s_realaxs_real,h4s_bools_cond(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X1))))),file('i/f/real/ABS__LE', ah4s_reals_abs0)).
fof(16, axiom,![X6]:![X2]:![X3]:s(X6,h4s_bools_cond(s(t_bool,t),s(X6,X3),s(X6,X2)))=s(X6,X3),file('i/f/real/ABS__LE', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(17, axiom,![X6]:![X2]:![X3]:s(X6,h4s_bools_cond(s(t_bool,f),s(X6,X3),s(X6,X2)))=s(X6,X2),file('i/f/real/ABS__LE', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
