# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]: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_pow(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))))))))),s(t_h4s_nums_num,X1)))))),file('i/f/util_prob/POW__HALF__POS', ch4s_utilu_u_probs_POWu_u_HALFu_u_POS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/util_prob/POW__HALF__POS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/util_prob/POW__HALF__POS', aHLu_FALSITY)).
fof(21, axiom,![X4]:(s(t_bool,t)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/util_prob/POW__HALF__POS', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(23, axiom,![X4]:(s(t_bool,f)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/util_prob/POW__HALF__POS', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(45, axiom,![X6]:![X1]:(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,X6))))=>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_pow(s(t_h4s_realaxs_real,X6),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))))))),file('i/f/util_prob/POW__HALF__POS', ah4s_reals_POWu_u_POSu_u_LT)).
fof(46, axiom,![X13]:![X6]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X13))))<=>~(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X13),s(t_h4s_realaxs_real,X6)))))),file('i/f/util_prob/POW__HALF__POS', ah4s_reals_realu_u_lt)).
fof(47, 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/util_prob/POW__HALF__POS', ah4s_utilu_u_probs_HALFu_u_POS)).
fof(48, axiom,![X6]:s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X6),s(t_h4s_nums_num,h4s_nums_0)))=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/util_prob/POW__HALF__POS', ah4s_reals_pow0u_c0)).
fof(50, axiom,![X1]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/util_prob/POW__HALF__POS', ah4s_numerals_numeralu_u_distribu_c17)).
fof(51, axiom,![X1]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/util_prob/POW__HALF__POS', ah4s_numerals_numeralu_u_equ_c1)).
fof(52, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),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,X6),file('i/f/util_prob/POW__HALF__POS', ah4s_reals_REALu_u_MULu_u_RID)).
fof(57, axiom,![X1]:![X14]: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,X14))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X1))),file('i/f/util_prob/POW__HALF__POS', ah4s_reals_REALu_u_OFu_u_NUMu_u_LE)).
fof(58, axiom,![X1]:![X14]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X14))),s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X1))))),file('i/f/util_prob/POW__HALF__POS', ah4s_reals_REALu_u_OFu_u_NUMu_u_MUL)).
fof(60, axiom,![X1]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,X1),file('i/f/util_prob/POW__HALF__POS', ah4s_numerals_numeralu_u_addu_c0)).
fof(61, axiom,s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_nums_num,h4s_arithmetics_zero),file('i/f/util_prob/POW__HALF__POS', ah4s_numerals_iDUBu_u_removalu_c2)).
fof(62, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_zero),file('i/f/util_prob/POW__HALF__POS', ah4s_numerals_numeralu_u_multu_c0)).
fof(63, axiom,![X13]:![X6]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X13))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X13),s(t_h4s_realaxs_real,X6)))))<=>s(t_h4s_realaxs_real,X6)=s(t_h4s_realaxs_real,X13)),file('i/f/util_prob/POW__HALF__POS', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(68, axiom,![X1]:![X14]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X14)))=s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X14))))),s(t_h4s_nums_num,X14))))),file('i/f/util_prob/POW__HALF__POS', ah4s_numerals_numeralu_u_multu_c2)).
fof(69, axiom,![X14]:(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/util_prob/POW__HALF__POS', ah4s_arithmetics_numu_u_CASES)).
fof(72, axiom,![X1]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0))))<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/util_prob/POW__HALF__POS', ah4s_arithmetics_LEu_c0)).
# SZS output end CNFRefutation
