# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/topology/METRIC__POS', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/topology/METRIC__POS', aHLu_FALSITY)).
fof(6, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/topology/METRIC__POS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/topology/METRIC__POS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(10, axiom,![X6]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(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,X6),file('i/f/topology/METRIC__POS', ah4s_reals_REALu_u_ADDu_u_LID)).
fof(11, axiom,![X10]:![X6]:(~(p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X10)))))<=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X10),s(t_h4s_realaxs_real,X6))))),file('i/f/topology/METRIC__POS', ah4s_reals_REALu_u_NOTu_u_LE)).
fof(12, axiom,![X11]:![X10]:![X6]:![X12]:((p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X6))))&p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X10),s(t_h4s_realaxs_real,X11)))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X12),s(t_h4s_realaxs_real,X10))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X11))))))),file('i/f/topology/METRIC__POS', ah4s_reals_REALu_u_LTu_u_ADD2)).
fof(13, axiom,![X9]:![X13]:(p(s(t_bool,h4s_topologys_ismet(s(t_fun(t_h4s_pairs_prod(X9,X9),t_h4s_realaxs_real),X13))))<=>(![X6]:![X10]:(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X9,X9),t_h4s_realaxs_real),X13),s(t_h4s_pairs_prod(X9,X9),h4s_pairs_u_2c(s(X9,X6),s(X9,X10)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>s(X9,X6)=s(X9,X10))&![X6]:![X10]:![X11]:p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X9,X9),t_h4s_realaxs_real),X13),s(t_h4s_pairs_prod(X9,X9),h4s_pairs_u_2c(s(X9,X10),s(X9,X11))))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X9,X9),t_h4s_realaxs_real),X13),s(t_h4s_pairs_prod(X9,X9),h4s_pairs_u_2c(s(X9,X6),s(X9,X10))))),s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X9,X9),t_h4s_realaxs_real),X13),s(t_h4s_pairs_prod(X9,X9),h4s_pairs_u_2c(s(X9,X6),s(X9,X11)))))))))))),file('i/f/topology/METRIC__POS', ah4s_topologys_ismet0)).
fof(14, axiom,![X9]:![X13]:p(s(t_bool,h4s_topologys_ismet(s(t_fun(t_h4s_pairs_prod(X9,X9),t_h4s_realaxs_real),h4s_topologys_dist(s(t_h4s_topologys_metric(X9),X13)))))),file('i/f/topology/METRIC__POS', ah4s_topologys_METRICu_u_ISMET)).
fof(15, axiom,![X9]:![X10]:![X6]:![X13]:(s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(X9,X9),t_h4s_realaxs_real),h4s_topologys_dist(s(t_h4s_topologys_metric(X9),X13))),s(t_h4s_pairs_prod(X9,X9),h4s_pairs_u_2c(s(X9,X6),s(X9,X10)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>s(X9,X6)=s(X9,X10)),file('i/f/topology/METRIC__POS', ah4s_topologys_METRICu_u_ZERO)).
fof(16, conjecture,![X9]:![X10]:![X6]:![X13]: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,happ(s(t_fun(t_h4s_pairs_prod(X9,X9),t_h4s_realaxs_real),h4s_topologys_dist(s(t_h4s_topologys_metric(X9),X13))),s(t_h4s_pairs_prod(X9,X9),h4s_pairs_u_2c(s(X9,X6),s(X9,X10)))))))),file('i/f/topology/METRIC__POS', ch4s_topologys_METRICu_u_POS)).
# SZS output end CNFRefutation
