# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(6, axiom,![X7]:![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X6))),file('i/f/util_prob/REAL__MUL__IDEMPOT', ah4s_reals_REALu_u_MULu_u_SYM)).
fof(25, axiom,s(t_h4s_realaxs_real,h4s_realaxs_realu_u_1)=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/REAL__MUL__IDEMPOT', ah4s_reals_REALu_u_1)).
fof(26, axiom,s(t_h4s_realaxs_real,h4s_realaxs_realu_u_0)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/util_prob/REAL__MUL__IDEMPOT', ah4s_reals_REALu_u_0)).
fof(27, axiom,![X6]:(~(s(t_h4s_realaxs_real,X6)=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_0))=>s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,X6)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_1)),file('i/f/util_prob/REAL__MUL__IDEMPOT', ah4s_realaxs_REALu_u_MULu_u_LINV)).
fof(36, axiom,![X8]:![X7]:![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X8)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X7))),s(t_h4s_realaxs_real,X8))),file('i/f/util_prob/REAL__MUL__IDEMPOT', ah4s_reals_REALu_u_MULu_u_ASSOC)).
fof(43, 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/REAL__MUL__IDEMPOT', ah4s_reals_REALu_u_MULu_u_RID)).
fof(116, 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_nums_0)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/util_prob/REAL__MUL__IDEMPOT', ah4s_reals_REALu_u_MULu_u_RZERO)).
fof(129, axiom,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,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/util_prob/REAL__MUL__IDEMPOT', ah4s_arithmetics_ONE)).
fof(133, conjecture,![X19]:(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X19),s(t_h4s_realaxs_real,X19)))=s(t_h4s_realaxs_real,X19)<=>(s(t_h4s_realaxs_real,X19)=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)=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/REAL__MUL__IDEMPOT', ch4s_utilu_u_probs_REALu_u_MULu_u_IDEMPOT)).
# SZS output end CNFRefutation
