# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/transc/SQRT__EVEN__POW2', aHLu_TRUTH)).
fof(9, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/transc/SQRT__EVEN__POW2', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(10, axiom,![X10]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X10)))))),file('i/f/transc/SQRT__EVEN__POW2', ah4s_primu_u_recs_LESSu_u_0)).
fof(11, axiom,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,h4s_nums_suc(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/transc/SQRT__EVEN__POW2', ah4s_arithmetics_TWO)).
fof(12, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X11),file('i/f/transc/SQRT__EVEN__POW2', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(13, axiom,![X10]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),file('i/f/transc/SQRT__EVEN__POW2', ah4s_arithmetics_MULTu_u_SYM)).
fof(14, axiom,![X10]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X10))))<=>?[X11]:s(t_h4s_nums_num,X10)=s(t_h4s_nums_num,h4s_arithmetics_u_2a(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,X11)))),file('i/f/transc/SQRT__EVEN__POW2', ah4s_arithmetics_EVENu_u_EXISTS)).
fof(15, axiom,![X10]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10))))=>![X12]:(s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X10)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X10)))))),file('i/f/transc/SQRT__EVEN__POW2', ah4s_arithmetics_DIVISION)).
fof(16, axiom,![X10]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10))))=>![X12]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X10))),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/transc/SQRT__EVEN__POW2', ah4s_arithmetics_MODu_u_EQu_u_0)).
fof(17, axiom,![X10]:p(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_ofu_u_num(s(t_h4s_nums_num,X10)))))),file('i/f/transc/SQRT__EVEN__POW2', ah4s_reals_REALu_u_POS)).
fof(18, axiom,![X6]:(p(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))))=>![X10]:p(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_pow(s(t_h4s_realaxs_real,X6),s(t_h4s_nums_num,X10))))))),file('i/f/transc/SQRT__EVEN__POW2', ah4s_reals_POWu_u_POS)).
fof(19, axiom,![X6]:![X10]:![X11]:s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X6),s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X10)))=s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X6),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10))))),file('i/f/transc/SQRT__EVEN__POW2', ah4s_reals_REALu_u_POWu_u_POW)).
fof(20, axiom,![X13]:![X6]:((p(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))))&(p(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,X13))))&s(t_h4s_realaxs_real,h4s_reals_pow(s(t_h4s_realaxs_real,X13),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,X6)))=>s(t_h4s_realaxs_real,h4s_transcs_sqrt(s(t_h4s_realaxs_real,X6)))=s(t_h4s_realaxs_real,X13)),file('i/f/transc/SQRT__EVEN__POW2', ah4s_transcs_SQRTu_u_POSu_u_UNIQ)).
fof(21, conjecture,![X10]:(p(s(t_bool,h4s_arithmetics_even(s(t_h4s_nums_num,X10))))=>s(t_h4s_realaxs_real,h4s_transcs_sqrt(s(t_h4s_realaxs_real,h4s_reals_pow(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,X10)))))=s(t_h4s_realaxs_real,h4s_reals_pow(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,h4s_arithmetics_div(s(t_h4s_nums_num,X10),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/transc/SQRT__EVEN__POW2', ch4s_transcs_SQRTu_u_EVENu_u_POW2)).
# SZS output end CNFRefutation
