# 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,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)))),file('i/f/real/ABS__ZERO', ch4s_reals_ABSu_u_ZERO)).
fof(4, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/real/ABS__ZERO', aHLu_BOOLu_CASES)).
fof(11, axiom,![X5]:![X3]:![X4]:s(X5,h4s_bools_cond(s(t_bool,t),s(X5,X4),s(X5,X3)))=s(X5,X4),file('i/f/real/ABS__ZERO', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(12, axiom,![X5]:![X3]:![X4]:s(X5,h4s_bools_cond(s(t_bool,f),s(X5,X4),s(X5,X3)))=s(X5,X3),file('i/f/real/ABS__ZERO', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(13, axiom,![X1]:(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(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,X1)=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__ZERO', ah4s_reals_REALu_u_NEGu_u_EQ0)).
fof(14, 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__ZERO', ah4s_reals_abs0)).
# SZS output end CNFRefutation
