# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,X1)))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X2))))),file('i/f/real/REAL__LE__SUB__RADD', ch4s_reals_REALu_u_LEu_u_SUBu_u_RADD)).
fof(2, axiom,![X2]:![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X3))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_ADDu_u_SYM)).
fof(4, axiom,![X1]:![X2]:![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,X1))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_ADDu_u_ASSOC)).
fof(5, axiom,![X1]:![X2]:![X3]:(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))<=>s(t_h4s_realaxs_real,X3)=s(t_h4s_realaxs_real,X2)),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_EQu_u_RADD)).
fof(6, 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/real/REAL__LE__SUB__RADD', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(21, axiom,![X2]:![X3]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2)))))=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,X2))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_LEu_u_ADDR)).
fof(24, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,X2))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_LEu_u_SUBu_u_LADD)).
fof(25, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_LEu_u_RADD)).
fof(26, axiom,![X2]:![X3]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))))<=>~(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X3)))))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_realu_u_lte0)).
fof(27, axiom,![X2]:![X3]: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,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2)))))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X3))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_SUBu_u_LE)).
fof(34, axiom,![X2]:![X3]:(~(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2)))))<=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X3))))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_NOTu_u_LE)).
fof(35, axiom,![X2]:![X3]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))))<=>(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))))|s(t_h4s_realaxs_real,X3)=s(t_h4s_realaxs_real,X2))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_LEu_u_LT)).
fof(37, axiom,![X2]:![X3]:s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X2))))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_realu_u_sub0)).
fof(40, axiom,![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(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,X3)))=s(t_h4s_realaxs_real,X3),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_ADDu_u_LID)).
fof(41, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,X1)))=s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X2))))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_LTu_u_SUBu_u_RADD)).
fof(46, axiom,![X1]:![X2]:![X3]:s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))))=s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1))),s(t_h4s_realaxs_real,X2))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_LTu_u_SUBu_u_LADD)).
fof(48, axiom,![X2]:![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2)))))=s(t_h4s_realaxs_real,X3),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_SUBu_u_ADD2)).
fof(50, axiom,![X2]:![X3]:s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,X3)))=s(t_h4s_realaxs_real,X2),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_ADDu_u_SUB)).
fof(65, axiom,![X3]:s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X3)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_SUBu_u_REFL)).
fof(66, axiom,![X2]:![X3]:s(t_bool,h4s_realaxs_realu_u_lt(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,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2)))))=s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X3))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_SUBu_u_LT)).
fof(72, axiom,![X2]:![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X3))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_NEGu_u_SUB)).
fof(73, axiom,![X2]:![X3]:s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,X3)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X2))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_reals_REALu_u_SUBu_u_SUB)).
fof(74, axiom,~(p(s(t_bool,f))),file('i/f/real/REAL__LE__SUB__RADD', aHLu_FALSITY)).
fof(76, axiom,![X8]:(s(t_bool,X8)=s(t_bool,f)<=>~(p(s(t_bool,X8)))),file('i/f/real/REAL__LE__SUB__RADD', ah4s_bools_EQu_u_CLAUSESu_c3)).
# SZS output end CNFRefutation
