# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,p(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_u_2f(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ch4s_reals_REALu_u_THIRDSu_u_BETWEENu_c2)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', aHLu_FALSITY)).
fof(3, axiom,![X1]:![X2]:((p(s(t_bool,X2))=>p(s(t_bool,X1)))=>((p(s(t_bool,X1))=>p(s(t_bool,X2)))=>s(t_bool,X2)=s(t_bool,X1))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(7, axiom,![X3]:((p(s(t_bool,X3))=>p(s(t_bool,f)))<=>s(t_bool,X3)=s(t_bool,f)),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(10, axiom,p(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_u_2f(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_HALFu_u_BETWEENu_c0)).
fof(22, axiom,![X6]:![X8]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X6))))<=>~(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X8)))))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_realu_u_lt)).
fof(24, axiom,![X6]:![X8]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X6))))|p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X8))))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_LEu_u_TOTAL)).
fof(32, axiom,![X14]:![X6]:![X8]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X6))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X14)))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X14))))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_LETu_u_TRANS)).
fof(35, axiom,![X6]:![X8]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X6))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X6))))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_LTu_u_IMPu_u_LE)).
fof(37, axiom,![X6]:![X8]:(~(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X6)))))<=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X8))))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_NOTu_u_LT)).
fof(40, axiom,![X17]:![X18]:(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X18)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X17)))<=>s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,X17)),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_INJ)).
fof(42, axiom,![X19]: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_u_2f(s(t_h4s_realaxs_real,X19),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))=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,X19))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_LTu_u_HALF1)).
fof(44, axiom,![X17]:![X19]:(~(s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,h4s_nums_0))=>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_u_2f(s(t_h4s_realaxs_real,X19),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X17)))))))=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,X19)))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_LTu_u_FRACTIONu_u_0)).
fof(54, axiom,![X8]:(~(s(t_h4s_realaxs_real,X8)=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_u_2f(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X8)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_DIVu_u_REFL)).
fof(58, axiom,![X17]:![X18]: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,X18))),s(t_h4s_realaxs_real,h4s_reals_realu_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/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_LE)).
fof(60, axiom,![X17]:![X18]: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,X18))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X17)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X17))))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_ADD)).
fof(63, axiom,![X6]:![X8]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X6)))))=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,X6))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_reals_REALu_u_LEu_u_ADDR)).
fof(66, axiom,![X17]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_numerals_numeralu_u_distribu_c27)).
fof(70, axiom,![X17]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X17)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X17))),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(71, axiom,![X17]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_numerals_numeralu_u_lteu_c1)).
fof(79, axiom,![X17]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/real/REAL__THIRDS__BETWEEN_c2', ah4s_numerals_numeralu_u_lteu_c2)).
# SZS output end CNFRefutation
