# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_pos(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_bool,h4s_reals_realu_u_lte(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/REAL__POS__LE__ZERO', ch4s_reals_REALu_u_POSu_u_LEu_u_ZERO)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/real/REAL__POS__LE__ZERO', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/real/REAL__POS__LE__ZERO', aHLu_FALSITY)).
fof(4, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/real/REAL__POS__LE__ZERO', aHLu_BOOLu_CASES)).
fof(23, axiom,![X2]:(s(t_bool,X2)=s(t_bool,f)<=>~(p(s(t_bool,X2)))),file('i/f/real/REAL__POS__LE__ZERO', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(36, axiom,![X7]:![X1]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X7))))|p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X1))))),file('i/f/real/REAL__POS__LE__ZERO', ah4s_reals_REALu_u_LEu_u_TOTAL)).
fof(37, axiom,![X7]:![X1]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X7))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X7),s(t_h4s_realaxs_real,X1)))))<=>s(t_h4s_realaxs_real,X1)=s(t_h4s_realaxs_real,X7)),file('i/f/real/REAL__POS__LE__ZERO', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(38, axiom,![X1]:s(t_h4s_realaxs_real,h4s_reals_pos(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_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/real/REAL__POS__LE__ZERO', ah4s_reals_posu_u_def)).
fof(39, axiom,![X6]:![X3]:![X4]:s(X6,h4s_bools_cond(s(t_bool,t),s(X6,X4),s(X6,X3)))=s(X6,X4),file('i/f/real/REAL__POS__LE__ZERO', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(40, axiom,![X6]:![X3]:![X4]:s(X6,h4s_bools_cond(s(t_bool,f),s(X6,X4),s(X6,X3)))=s(X6,X3),file('i/f/real/REAL__POS__LE__ZERO', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
