# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1))))=>p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X1))))))),file('i/f/realax/REAL__LT__IADD', ch4s_realaxs_REALu_u_LTu_u_IADD)).
fof(3, axiom,![X7]:![X8]:![X9]:![X10]:![X11]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X8,t_fun(X8,t_bool)),X11),s(t_fun(X8,X7),X10),s(t_fun(X7,X8),X9))))=>![X12]:![X13]:(p(s(t_bool,happ(s(t_fun(X8,t_bool),happ(s(t_fun(X8,t_fun(X8,t_bool)),X11),s(X8,X12))),s(X8,X13))))=>p(s(t_bool,happ(s(t_fun(X8,t_bool),happ(s(t_fun(X8,t_fun(X8,t_bool)),X11),s(X8,X12))),s(X8,happ(s(t_fun(X7,X8),X9),s(X7,happ(s(t_fun(X8,X7),X10),s(X8,X13)))))))))),file('i/f/realax/REAL__LT__IADD', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(6, axiom,![X18]:![X19]:s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,X19),s(t_h4s_realaxs_real,X18)))=s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),happ(s(t_fun(t_h4s_realaxs_real,t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal)),h4s_realaxs_realu_u_rep),s(t_h4s_realaxs_real,X19))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),happ(s(t_fun(t_h4s_realaxs_real,t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal)),h4s_realaxs_realu_u_rep),s(t_h4s_realaxs_real,X18))))),file('i/f/realax/REAL__LT__IADD', ah4s_realaxs_realu_u_lt0)).
fof(7, axiom,![X18]:![X19]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X19),s(t_h4s_realaxs_real,X18)))=s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_h4s_realaxs_real),h4s_realaxs_realu_u_abs),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_add(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),happ(s(t_fun(t_h4s_realaxs_real,t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal)),h4s_realaxs_realu_u_rep),s(t_h4s_realaxs_real,X19))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),happ(s(t_fun(t_h4s_realaxs_real,t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal)),h4s_realaxs_realu_u_rep),s(t_h4s_realaxs_real,X18))))))),file('i/f/realax/REAL__LT__IADD', ah4s_realaxs_realu_u_add0)).
fof(8, axiom,p(s(t_bool,h4s_quotients_quotient(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_h4s_realaxs_real),h4s_realaxs_realu_u_abs),s(t_fun(t_h4s_realaxs_real,t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal)),h4s_realaxs_realu_u_rep)))),file('i/f/realax/REAL__LT__IADD', ah4s_realaxs_realu_u_QUOTIENT)).
fof(13, axiom,![X29]:![X30]:(p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X30))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X29))))<=>s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X30)))=s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X29)))),file('i/f/realax/REAL__LT__IADD', ah4s_realaxs_TREALu_u_EQu_u_EQUIV)).
fof(15, axiom,![X31]:![X32]:![X13]:![X12]:((p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X12))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X13))))&p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X32))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X31)))))=>s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X12),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X32)))=s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X13),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X31)))),file('i/f/realax/REAL__LT__IADD', ah4s_realaxs_TREALu_u_LTu_u_WELLDEF)).
fof(20, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X2),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X1))))=>p(s(t_bool,h4s_realaxs_trealu_u_lt(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_add(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X3),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X2))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_add(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X3),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X1))))))),file('i/f/realax/REAL__LT__IADD', ah4s_realaxs_TREALu_u_LTu_u_ADD)).
# SZS output end CNFRefutation
