# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_0)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_0),file('i/f/realax/REAL__INV__0', ch4s_realaxs_REALu_u_INVu_u_0)).
fof(5, axiom,![X6]:![X10]:![X11]:![X12]:![X8]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X6,t_fun(X6,t_bool)),X8),s(t_fun(X6,X10),X12),s(t_fun(X10,X6),X11))))=>![X5]:![X7]:(s(X10,X5)=s(X10,X7)<=>p(s(t_bool,happ(s(t_fun(X6,t_bool),happ(s(t_fun(X6,t_fun(X6,t_bool)),X8),s(X6,happ(s(t_fun(X10,X6),X11),s(X10,X5))))),s(X6,happ(s(t_fun(X10,X6),X11),s(X10,X7)))))))),file('i/f/realax/REAL__INV__0', ah4s_quotients_EQUALSu_u_PRS)).
fof(7, axiom,![X10]:![X6]:![X11]:![X12]:![X17]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X6,t_fun(X6,t_bool)),X17),s(t_fun(X6,X10),X12),s(t_fun(X10,X6),X11))))=>![X13]:![X14]:(p(s(t_bool,happ(s(t_fun(X6,t_bool),happ(s(t_fun(X6,t_fun(X6,t_bool)),X17),s(X6,X13))),s(X6,X14))))=>p(s(t_bool,happ(s(t_fun(X6,t_bool),happ(s(t_fun(X6,t_fun(X6,t_bool)),X17),s(X6,X13))),s(X6,happ(s(t_fun(X10,X6),X11),s(X10,happ(s(t_fun(X6,X10),X12),s(X6,X14)))))))))),file('i/f/realax/REAL__INV__0', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(8, axiom,![X18]:![X19]:(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),X19))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X18))))<=>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),X19)))=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),X18)))),file('i/f/realax/REAL__INV__0', ah4s_realaxs_TREALu_u_EQu_u_EQUIV)).
fof(9, axiom,s(t_h4s_realaxs_real,h4s_realaxs_realu_u_0)=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_0))),file('i/f/realax/REAL__INV__0', ah4s_realaxs_realu_u_00)).
fof(10, 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__INV__0', ah4s_realaxs_realu_u_QUOTIENT)).
fof(11, axiom,![X20]:s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,X20)))=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_inv(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,X20))))))),file('i/f/realax/REAL__INV__0', ah4s_realaxs_realu_u_inv)).
fof(12, axiom,![X14]:![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),X13))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X14))))=>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),h4s_realaxs_trealu_u_inv(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),h4s_realaxs_trealu_u_inv(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X14))))))),file('i/f/realax/REAL__INV__0', ah4s_realaxs_TREALu_u_INVu_u_WELLDEF)).
fof(14, axiom,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),h4s_realaxs_trealu_u_inv(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_0))))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_0)))),file('i/f/realax/REAL__INV__0', ah4s_realaxs_TREALu_u_INVu_u_0)).
# SZS output end CNFRefutation
