# 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_mul(s(t_h4s_hrats_hrat,X2),s(t_h4s_hrats_hrat,X1)))))=s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(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,X1))),file('i/f/hrat/HRAT__MUL__ASSOC', ch4s_hrats_HRATu_u_MULu_u_ASSOC)).
fof(4, 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__MUL__ASSOC', ah4s_hrats_hratu_u_mul0)).
fof(5, 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__MUL__ASSOC', ah4s_hrats_hratu_u_QUOTIENT)).
fof(7, axiom,![X4]:![X16]:![X17]:![X18]:![X19]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X4,t_fun(X4,t_bool)),X19),s(t_fun(X4,X16),X18),s(t_fun(X16,X4),X17))))=>![X6]:![X5]:(s(X16,X6)=s(X16,X5)<=>p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X19),s(X4,happ(s(t_fun(X16,X4),X17),s(X16,X6))))),s(X4,happ(s(t_fun(X16,X4),X17),s(X16,X5)))))))),file('i/f/hrat/HRAT__MUL__ASSOC', ah4s_quotients_EQUALSu_u_PRS)).
fof(9, axiom,![X16]:![X4]:![X17]:![X18]:![X24]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X4,t_fun(X4,t_bool)),X24),s(t_fun(X4,X16),X18),s(t_fun(X16,X4),X17))))=>![X20]:![X21]:(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X24),s(X4,X20))),s(X4,X21))))=>p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X24),s(X4,X20))),s(X4,happ(s(t_fun(X16,X4),X17),s(X16,happ(s(t_fun(X4,X16),X18),s(X4,X21)))))))))),file('i/f/hrat/HRAT__MUL__ASSOC', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(10, axiom,![X25]:![X26]:![X27]:![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),X28))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X27))))&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),X26))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),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),h4s_hrats_tratu_u_mul(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))))),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),X27),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X25))))))),file('i/f/hrat/HRAT__MUL__ASSOC', ah4s_hrats_TRATu_u_MULu_u_WELLDEFINED2)).
fof(11, 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_mul(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_mul(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),X1)))))),file('i/f/hrat/HRAT__MUL__ASSOC', ah4s_hrats_TRATu_u_MULu_u_ASSOC)).
fof(12, axiom,![X29]:![X30]:(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),X30))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X29))))<=>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),X30)))=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)))),file('i/f/hrat/HRAT__MUL__ASSOC', ah4s_hrats_TRATu_u_EQu_u_EQUIV)).
# SZS output end CNFRefutation
