# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X2),s(t_h4s_realaxs_real,X1)))))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X3),s(t_h4s_realaxs_real,X2))),s(t_h4s_realaxs_real,X1))),file('i/f/realax/REAL__MUL__ASSOC', ch4s_realaxs_REALu_u_MULu_u_ASSOC)).
fof(4, axiom,![X8]:![X9]:s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X9),s(t_h4s_realaxs_real,X8)))=s(t_h4s_realaxs_real,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_h4s_realaxs_real),h4s_realaxs_realu_u_abs),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_mul(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),happ(s(t_fun(t_h4s_realaxs_real,t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal)),h4s_realaxs_realu_u_rep),s(t_h4s_realaxs_real,X9))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),happ(s(t_fun(t_h4s_realaxs_real,t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal)),h4s_realaxs_realu_u_rep),s(t_h4s_realaxs_real,X8))))))),file('i/f/realax/REAL__MUL__ASSOC', ah4s_realaxs_realu_u_mul0)).
fof(5, axiom,p(s(t_bool,h4s_quotients_quotient(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_h4s_realaxs_real),h4s_realaxs_realu_u_abs),s(t_fun(t_h4s_realaxs_real,t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal)),h4s_realaxs_realu_u_rep)))),file('i/f/realax/REAL__MUL__ASSOC', ah4s_realaxs_realu_u_QUOTIENT)).
fof(7, axiom,![X4]:![X14]:![X15]:![X16]:![X17]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X4,t_fun(X4,t_bool)),X17),s(t_fun(X4,X14),X16),s(t_fun(X14,X4),X15))))=>![X3]:![X2]:(s(X14,X3)=s(X14,X2)<=>p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X17),s(X4,happ(s(t_fun(X14,X4),X15),s(X14,X3))))),s(X4,happ(s(t_fun(X14,X4),X15),s(X14,X2)))))))),file('i/f/realax/REAL__MUL__ASSOC', ah4s_quotients_EQUALSu_u_PRS)).
fof(9, axiom,![X14]:![X4]:![X15]:![X16]:![X22]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X4,t_fun(X4,t_bool)),X22),s(t_fun(X4,X14),X16),s(t_fun(X14,X4),X15))))=>![X18]:![X19]:(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X22),s(X4,X18))),s(X4,X19))))=>p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X22),s(X4,X18))),s(X4,happ(s(t_fun(X14,X4),X15),s(X14,happ(s(t_fun(X4,X14),X16),s(X4,X19)))))))))),file('i/f/realax/REAL__MUL__ASSOC', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(10, axiom,![X1]:![X2]:![X3]:s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_mul(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X3),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_mul(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X2),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X1)))))=s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_mul(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_mul(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X3),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X2))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X1))),file('i/f/realax/REAL__MUL__ASSOC', ah4s_realaxs_TREALu_u_MULu_u_ASSOC)).
fof(11, axiom,![X21]:![X20]:![X19]:![X18]:((p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X18))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X19))))&p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X20))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X21)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_mul(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X18),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X20))))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),h4s_realaxs_trealu_u_mul(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X19),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X21))))))),file('i/f/realax/REAL__MUL__ASSOC', ah4s_realaxs_TREALu_u_MULu_u_WELLDEF)).
fof(12, axiom,![X23]:![X24]:(p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X24))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X23))))<=>s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X24)))=s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X23)))),file('i/f/realax/REAL__MUL__ASSOC', ah4s_realaxs_TREALu_u_EQu_u_EQUIV)).
fof(13, axiom,![X23]:![X24]:(s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X24)=s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X23)=>p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_fun(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),t_bool)),h4s_realaxs_trealu_u_eq),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X24))),s(t_h4s_pairs_prod(t_h4s_hreals_hreal,t_h4s_hreals_hreal),X23))))),file('i/f/realax/REAL__MUL__ASSOC', ah4s_realaxs_TREALu_u_EQu_u_AP)).
# SZS output end CNFRefutation
