# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:~(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X2),s(t_h4s_hrats_hrat,X1)))=s(t_h4s_hrats_hrat,X2)),file('i/f/hrat/HRAT__NOZERO', ch4s_hrats_HRATu_u_NOZERO)).
fof(4, axiom,p(s(t_bool,h4s_quotients_quotient(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_hrats_tratu_u_eq),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_hrats_hrat),h4s_hrats_hratu_u_abs),s(t_fun(t_h4s_hrats_hrat,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_hrats_hratu_u_rep)))),file('i/f/hrat/HRAT__NOZERO', ah4s_hrats_hratu_u_QUOTIENT)).
fof(5, axiom,![X9]:![X10]:s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X10),s(t_h4s_hrats_hrat,X9)))=s(t_h4s_hrats_hrat,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_hrats_hrat),h4s_hrats_hratu_u_abs),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_hrats_hrat,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_hrats_hratu_u_rep),s(t_h4s_hrats_hrat,X10))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_hrats_hrat,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_hrats_hratu_u_rep),s(t_h4s_hrats_hrat,X9))))))),file('i/f/hrat/HRAT__NOZERO', ah4s_hrats_hratu_u_add0)).
fof(6, axiom,![X3]:![X11]:![X12]:![X13]:![X14]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X14),s(t_fun(X3,X11),X13),s(t_fun(X11,X3),X12))))=>![X5]:![X4]:(s(X11,X5)=s(X11,X4)<=>p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X14),s(X3,happ(s(t_fun(X11,X3),X12),s(X11,X5))))),s(X3,happ(s(t_fun(X11,X3),X12),s(X11,X4)))))))),file('i/f/hrat/HRAT__NOZERO', ah4s_quotients_EQUALSu_u_PRS)).
fof(8, axiom,![X11]:![X3]:![X12]:![X13]:![X19]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X19),s(t_fun(X3,X11),X13),s(t_fun(X11,X3),X12))))=>![X15]:![X16]:(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X19),s(X3,X15))),s(X3,X16))))=>p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X19),s(X3,X15))),s(X3,happ(s(t_fun(X11,X3),X12),s(X11,happ(s(t_fun(X3,X11),X13),s(X3,X16)))))))))),file('i/f/hrat/HRAT__NOZERO', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(10, axiom,![X24]:![X25]:(p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_hrats_tratu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X25))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X24))))<=>s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_hrats_tratu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X25)))=s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_hrats_tratu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X24)))),file('i/f/hrat/HRAT__NOZERO', ah4s_hrats_TRATu_u_EQu_u_EQUIV)).
fof(11, axiom,![X26]:![X27]:![X28]:![X29]:((p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_hrats_tratu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X29))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X28))))&p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_hrats_tratu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X27))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X26)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_hrats_tratu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X29),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X27))))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X28),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X26))))))),file('i/f/hrat/HRAT__NOZERO', ah4s_hrats_TRATu_u_ADDu_u_WELLDEFINED2)).
fof(12, axiom,![X1]:![X2]:~(p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_hrats_tratu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1))))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2))))),file('i/f/hrat/HRAT__NOZERO', ah4s_hrats_TRATu_u_NOZERO)).
# SZS output end CNFRefutation
