# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_inv(s(t_h4s_hrats_hrat,X1))),s(t_h4s_hrats_hrat,X1)))=s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1),file('i/f/hrat/HRAT__MUL__LINV', ch4s_hrats_HRATu_u_MULu_u_LINV)).
fof(3, axiom,s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1)=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_1))),file('i/f/hrat/HRAT__MUL__LINV', ah4s_hrats_hratu_u_10)).
fof(4, axiom,![X5]:![X6]:s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,X6),s(t_h4s_hrats_hrat,X5)))=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,X6))),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,X5))))))),file('i/f/hrat/HRAT__MUL__LINV', ah4s_hrats_hratu_u_mul0)).
fof(5, axiom,![X6]:s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_inv(s(t_h4s_hrats_hrat,X6)))=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_inv(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,X6))))))),file('i/f/hrat/HRAT__MUL__LINV', ah4s_hrats_hratu_u_inv0)).
fof(7, axiom,![X2]:![X11]:(![X4]:![X3]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X11),s(X2,X4))),s(X2,X3))))<=>s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X11),s(X2,X4)))=s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X11),s(X2,X3))))<=>(![X4]:p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X11),s(X2,X4))),s(X2,X4))))&(![X4]:![X3]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X11),s(X2,X4))),s(X2,X3))))=>p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X11),s(X2,X3))),s(X2,X4)))))&![X4]:![X3]:![X12]:((p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X11),s(X2,X4))),s(X2,X3))))&p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X11),s(X2,X3))),s(X2,X12)))))=>p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X11),s(X2,X4))),s(X2,X12)))))))),file('i/f/hrat/HRAT__MUL__LINV', ah4s_quotients_EQUIVu_u_REFLu_u_SYMu_u_TRANS)).
fof(8, axiom,![X1]: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),h4s_hrats_tratu_u_inv(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),X1))))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_1)))),file('i/f/hrat/HRAT__MUL__LINV', ah4s_hrats_TRATu_u_MULu_u_LINV)).
fof(9, axiom,![X13]:![X14]:![X15]:![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),X16))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X15))))&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),X14))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X13)))))=>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),X16),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X14))))),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),X15),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X13))))))),file('i/f/hrat/HRAT__MUL__LINV', ah4s_hrats_TRATu_u_MULu_u_WELLDEFINED2)).
fof(10, 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__LINV', ah4s_hrats_hratu_u_QUOTIENT)).
fof(13, axiom,![X17]:![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),X18))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X17))))<=>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),X18)))=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)))),file('i/f/hrat/HRAT__MUL__LINV', ah4s_hrats_TRATu_u_EQu_u_EQUIV)).
fof(14, axiom,![X2]:![X22]:![X23]:![X24]:![X11]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X11),s(t_fun(X2,X22),X24),s(t_fun(X22,X2),X23))))=>![X4]:![X3]:(s(X22,X4)=s(X22,X3)<=>p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X11),s(X2,happ(s(t_fun(X22,X2),X23),s(X22,X4))))),s(X2,happ(s(t_fun(X22,X2),X23),s(X22,X3)))))))),file('i/f/hrat/HRAT__MUL__LINV', ah4s_quotients_EQUALSu_u_PRS)).
fof(16, axiom,![X22]:![X2]:![X23]:![X24]:![X29]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X29),s(t_fun(X2,X22),X24),s(t_fun(X22,X2),X23))))=>![X25]:![X26]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X29),s(X2,X25))),s(X2,X26))))=>p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X29),s(X2,X25))),s(X2,happ(s(t_fun(X22,X2),X23),s(X22,happ(s(t_fun(X2,X22),X24),s(X2,X26)))))))))),file('i/f/hrat/HRAT__MUL__LINV', ah4s_quotients_REPu_u_ABSu_u_RSP)).
# SZS output end CNFRefutation
