# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,X1)))=s(t_h4s_realaxs_real,X1)<=>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,X1))))),file('i/f/real/ABS__REFL', ch4s_reals_ABSu_u_REFL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/real/ABS__REFL', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/real/ABS__REFL', aHLu_FALSITY)).
fof(12, axiom,![X4]:(s(t_bool,t)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/real/ABS__REFL', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(14, axiom,![X4]:(s(t_bool,X4)=s(t_bool,f)<=>~(p(s(t_bool,X4)))),file('i/f/real/ABS__REFL', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(15, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/real/ABS__REFL', aHLu_BOOLu_CASES)).
fof(17, axiom,![X7]:![X8]:(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X8)))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,X7)))<=>s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X7)),file('i/f/real/ABS__REFL', ah4s_reals_REALu_u_INJ)).
fof(18, axiom,![X1]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X1)))),file('i/f/real/ABS__REFL', ah4s_reals_REALu_u_LEu_u_REFL)).
fof(19, axiom,![X1]:s(t_h4s_realaxs_real,h4s_reals_abs(s(t_h4s_realaxs_real,X1)))=s(t_h4s_realaxs_real,h4s_bools_cond(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,X1))),s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X1))))),file('i/f/real/ABS__REFL', ah4s_reals_abs0)).
fof(20, axiom,![X6]:![X1]:(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X1),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,X6)=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X1)))),file('i/f/real/ABS__REFL', ah4s_reals_REALu_u_RNEGu_u_UNIQ)).
fof(21, axiom,![X6]:![X1]:(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X1),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,X1)=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)=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/real/ABS__REFL', ah4s_reals_REALu_u_ENTIRE)).
fof(22, axiom,![X1]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X1)))=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,X1))),file('i/f/real/ABS__REFL', ah4s_reals_REALu_u_DOUBLE)).
fof(23, axiom,![X7]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X7)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/real/ABS__REFL', ah4s_numerals_numeralu_u_distribu_c17)).
fof(24, axiom,![X7]:(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/real/ABS__REFL', ah4s_numerals_numeralu_u_equ_c3)).
fof(25, axiom,![X5]:![X2]:![X3]:s(X5,h4s_bools_cond(s(t_bool,t),s(X5,X3),s(X5,X2)))=s(X5,X3),file('i/f/real/ABS__REFL', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(26, axiom,![X5]:![X2]:![X3]:s(X5,h4s_bools_cond(s(t_bool,f),s(X5,X3),s(X5,X2)))=s(X5,X2),file('i/f/real/ABS__REFL', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
