# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,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,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_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_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/HALF__CANCEL', ch4s_utilu_u_probs_HALFu_u_CANCEL)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/util_prob/HALF__CANCEL', aHLu_FALSITY)).
fof(35, axiom,![X13]:![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,X13)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))),file('i/f/util_prob/HALF__CANCEL', ah4s_reals_REALu_u_OFu_u_NUMu_u_LE)).
fof(38, axiom,![X13]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/util_prob/HALF__CANCEL', ah4s_numerals_numeralu_u_distribu_c17)).
fof(39, axiom,![X6]:(~(s(t_h4s_realaxs_real,X6)=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_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_realaxs_inv(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)))))))),file('i/f/util_prob/HALF__CANCEL', ah4s_reals_REALu_u_MULu_u_RINV)).
fof(40, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,X6)))=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,X6))),file('i/f/util_prob/HALF__CANCEL', ah4s_reals_REALu_u_INVu_u_1OVER)).
fof(41, axiom,![X13]:s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X13)))))=s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,X13))))),file('i/f/util_prob/HALF__CANCEL', ah4s_numerals_iDUBu_u_removalu_c0)).
fof(44, axiom,![X13]:(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/util_prob/HALF__CANCEL', ah4s_numerals_numeralu_u_equ_c3)).
fof(45, 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/HALF__CANCEL', ah4s_numerals_iDUBu_u_removalu_c2)).
fof(54, axiom,p(s(t_bool,t)),file('i/f/util_prob/HALF__CANCEL', aHLu_TRUTH)).
fof(64, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/util_prob/HALF__CANCEL', aHLu_BOOLu_CASES)).
fof(66, axiom,![X13]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X13)))),file('i/f/util_prob/HALF__CANCEL', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(67, axiom,![X13]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,h4s_nums_0))))<=>s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/util_prob/HALF__CANCEL', ah4s_arithmetics_LEu_c0)).
# SZS output end CNFRefutation
