# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,X3),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,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,X3),s(t_h4s_hrats_hrat,X2))),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,X3),s(t_h4s_hrats_hrat,X1))))),file('i/f/hrat/HRAT__LDISTRIB', ch4s_hrats_HRATu_u_LDISTRIB)).
fof(4, axiom,![X10]:![X11]:s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,X11),s(t_h4s_hrats_hrat,X10)))=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,X11))),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))))))),file('i/f/hrat/HRAT__LDISTRIB', ah4s_hrats_hratu_u_add0)).
fof(5, axiom,![X10]:![X11]:s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,X11),s(t_h4s_hrats_hrat,X10)))=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_mul(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,X11))),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))))))),file('i/f/hrat/HRAT__LDISTRIB', ah4s_hrats_hratu_u_mul0)).
fof(6, 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__LDISTRIB', ah4s_hrats_hratu_u_QUOTIENT)).
fof(8, axiom,![X16]:![X17]:![X18]:![X19]:((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),X19))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X18))))&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),X17))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X16)))))=>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),X19),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X17))))),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),X18),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X16))))))),file('i/f/hrat/HRAT__LDISTRIB', ah4s_hrats_TRATu_u_ADDu_u_WELLDEFINED2)).
fof(9, axiom,![X1]:![X2]:![X3]: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_mul(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3),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),h4s_hrats_tratu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_mul(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3),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),h4s_hrats_tratu_u_mul(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1)))))))),file('i/f/hrat/HRAT__LDISTRIB', ah4s_hrats_TRATu_u_LDISTRIB)).
fof(10, axiom,![X20]:![X21]:(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),X21))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X20))))<=>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),X21)))=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),X20)))),file('i/f/hrat/HRAT__LDISTRIB', ah4s_hrats_TRATu_u_EQu_u_EQUIV)).
fof(11, axiom,![X16]:![X17]:![X18]:![X19]:((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),X19))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X18))))&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),X17))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X16)))))=>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_mul(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X19),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X17))))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_mul(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X18),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X16))))))),file('i/f/hrat/HRAT__LDISTRIB', ah4s_hrats_TRATu_u_MULu_u_WELLDEFINED2)).
fof(12, axiom,![X4]:![X22]:![X23]:![X24]:![X25]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X4,t_fun(X4,t_bool)),X25),s(t_fun(X4,X22),X24),s(t_fun(X22,X4),X23))))=>![X6]:![X5]:(s(X22,X6)=s(X22,X5)<=>p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X25),s(X4,happ(s(t_fun(X22,X4),X23),s(X22,X6))))),s(X4,happ(s(t_fun(X22,X4),X23),s(X22,X5)))))))),file('i/f/hrat/HRAT__LDISTRIB', ah4s_quotients_EQUALSu_u_PRS)).
fof(14, axiom,![X22]:![X4]:![X23]:![X24]:![X30]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X4,t_fun(X4,t_bool)),X30),s(t_fun(X4,X22),X24),s(t_fun(X22,X4),X23))))=>![X26]:![X27]:(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X30),s(X4,X26))),s(X4,X27))))=>p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X30),s(X4,X26))),s(X4,happ(s(t_fun(X22,X4),X23),s(X22,happ(s(t_fun(X4,X22),X24),s(X4,X27)))))))))),file('i/f/hrat/HRAT__LDISTRIB', ah4s_quotients_REPu_u_ABSu_u_RSP)).
# SZS output end CNFRefutation
