# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]: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,X1),s(t_h4s_hrats_hrat,X2))),file('i/f/hrat/HRAT__MUL__SYM', ch4s_hrats_HRATu_u_MULu_u_SYM)).
fof(4, axiom,![X9]:![X10]:s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(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_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,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__MUL__SYM', 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__SYM', ah4s_hrats_hratu_u_QUOTIENT)).
fof(7, axiom,![X3]:![X15]:![X16]:![X17]:![X18]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X18),s(t_fun(X3,X15),X17),s(t_fun(X15,X3),X16))))=>![X5]:![X4]:(s(X15,X5)=s(X15,X4)<=>p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X18),s(X3,happ(s(t_fun(X15,X3),X16),s(X15,X5))))),s(X3,happ(s(t_fun(X15,X3),X16),s(X15,X4)))))))),file('i/f/hrat/HRAT__MUL__SYM', ah4s_quotients_EQUALSu_u_PRS)).
fof(9, axiom,![X15]:![X3]:![X16]:![X17]:![X23]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X23),s(t_fun(X3,X15),X17),s(t_fun(X15,X3),X16))))=>![X19]:![X20]:(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X23),s(X3,X19))),s(X3,X20))))=>p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X23),s(X3,X19))),s(X3,happ(s(t_fun(X15,X3),X16),s(X15,happ(s(t_fun(X3,X15),X17),s(X3,X20)))))))))),file('i/f/hrat/HRAT__MUL__SYM', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(11, 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_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),X1),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2)))))),file('i/f/hrat/HRAT__MUL__SYM', ah4s_hrats_TRATu_u_MULu_u_SYM)).
fof(12, axiom,![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))))<=>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_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)))),file('i/f/hrat/HRAT__MUL__SYM', ah4s_hrats_TRATu_u_EQu_u_EQUIV)).
# SZS output end CNFRefutation
