# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(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)))<=>p(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__EQ__ZERO', ch4s_reals_REALu_u_POSu_u_EQu_u_ZERO)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/real/REAL__POS__EQ__ZERO', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/real/REAL__POS__EQ__ZERO', aHLu_FALSITY)).
fof(14, axiom,![X4]:(s(t_bool,t)=s(t_bool,X4)<=>p(s(t_bool,X4))),file('i/f/real/REAL__POS__EQ__ZERO', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(30, axiom,![X13]:![X1]:(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X13))))|p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X13),s(t_h4s_realaxs_real,X1))))),file('i/f/real/REAL__POS__EQ__ZERO', ah4s_reals_REALu_u_LEu_u_TOTAL)).
fof(31, axiom,![X13]:![X1]:((p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X1),s(t_h4s_realaxs_real,X13))))&p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X13),s(t_h4s_realaxs_real,X1)))))<=>s(t_h4s_realaxs_real,X1)=s(t_h4s_realaxs_real,X13)),file('i/f/real/REAL__POS__EQ__ZERO', ah4s_reals_REALu_u_LEu_u_ANTISYM)).
fof(32, 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__EQ__ZERO', ah4s_reals_posu_u_def)).
fof(33, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/real/REAL__POS__EQ__ZERO', aHLu_BOOLu_CASES)).
fof(34, axiom,![X6]:![X2]:![X3]:s(X6,h4s_bools_cond(s(t_bool,t),s(X6,X3),s(X6,X2)))=s(X6,X3),file('i/f/real/REAL__POS__EQ__ZERO', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(35, axiom,![X6]:![X2]:![X3]:s(X6,h4s_bools_cond(s(t_bool,f),s(X6,X3),s(X6,X2)))=s(X6,X2),file('i/f/real/REAL__POS__EQ__ZERO', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
