# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:![X8]:![X9]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X4,t_fun(X4,t_bool)),X9),s(t_fun(X4,X1),X8),s(t_fun(X1,X4),X7))))=>![X10]:![X11]:![X12]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X5,t_fun(X5,t_bool)),X10),s(t_fun(X5,X2),X11),s(t_fun(X2,X5),X12))))=>![X13]:![X14]:![X15]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X6,t_fun(X6,t_bool)),X13),s(t_fun(X6,X3),X14),s(t_fun(X3,X6),X15))))=>![X16]:![X17]:(p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(X4,X5),X6),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(X4,X5),X6),t_fun(t_fun(t_h4s_pairs_prod(X4,X5),X6),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(t_h4s_pairs_prod(X4,X5),t_fun(t_h4s_pairs_prod(X4,X5),t_bool)),h4s_quotientu_u_pairs_u_23u_23u_23(s(t_fun(X4,t_fun(X4,t_bool)),X9),s(t_fun(X5,t_fun(X5,t_bool)),X10))),s(t_fun(X6,t_fun(X6,t_bool)),X13))),s(t_fun(t_h4s_pairs_prod(X4,X5),X6),X16))),s(t_fun(t_h4s_pairs_prod(X4,X5),X6),X17))))=>p(s(t_bool,happ(s(t_fun(t_fun(X4,t_fun(X5,X6)),t_bool),happ(s(t_fun(t_fun(X4,t_fun(X5,X6)),t_fun(t_fun(X4,t_fun(X5,X6)),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X4,t_fun(X4,t_bool)),X9),s(t_fun(t_fun(X5,X6),t_fun(t_fun(X5,X6),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X5,t_fun(X5,t_bool)),X10),s(t_fun(X6,t_fun(X6,t_bool)),X13))))),s(t_fun(X4,t_fun(X5,X6)),h4s_pairs_curry(s(t_fun(t_h4s_pairs_prod(X4,X5),X6),X16))))),s(t_fun(X4,t_fun(X5,X6)),h4s_pairs_curry(s(t_fun(t_h4s_pairs_prod(X4,X5),X6),X17)))))))))),file('i/f/quotient_pair/CURRY__RSP', ch4s_quotientu_u_pairs_CURRYu_u_RSP)).
fof(3, axiom,![X6]:![X4]:![X5]:![X23]:![X22]:![X20]:s(X6,happ(s(t_fun(X5,X6),happ(s(t_fun(X4,t_fun(X5,X6)),h4s_pairs_curry(s(t_fun(t_h4s_pairs_prod(X4,X5),X6),X20))),s(X4,X22))),s(X5,X23)))=s(X6,happ(s(t_fun(t_h4s_pairs_prod(X4,X5),X6),X20),s(t_h4s_pairs_prod(X4,X5),h4s_pairs_u_2c(s(X4,X22),s(X5,X23))))),file('i/f/quotient_pair/CURRY__RSP', ah4s_pairs_CURRYu_u_DEF)).
fof(4, axiom,![X5]:![X4]:![X21]:![X20]:![X10]:![X9]:(p(s(t_bool,happ(s(t_fun(t_fun(X4,X5),t_bool),happ(s(t_fun(t_fun(X4,X5),t_fun(t_fun(X4,X5),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X4,t_fun(X4,t_bool)),X9),s(t_fun(X5,t_fun(X5,t_bool)),X10))),s(t_fun(X4,X5),X20))),s(t_fun(X4,X5),X21))))<=>![X22]:![X23]:(p(s(t_bool,happ(s(t_fun(X4,t_bool),happ(s(t_fun(X4,t_fun(X4,t_bool)),X9),s(X4,X22))),s(X4,X23))))=>p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X10),s(X5,happ(s(t_fun(X4,X5),X20),s(X4,X22))))),s(X5,happ(s(t_fun(X4,X5),X21),s(X4,X23)))))))),file('i/f/quotient_pair/CURRY__RSP', ah4s_quotients_FUNu_u_REL)).
fof(5, axiom,![X4]:![X6]:![X5]:![X1]:![X24]:![X25]:![X26]:![X27]:![X10]:![X9]:(p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(X6,X1),t_bool),happ(s(t_fun(t_h4s_pairs_prod(X4,X5),t_fun(t_h4s_pairs_prod(X6,X1),t_bool)),h4s_quotientu_u_pairs_u_23u_23u_23(s(t_fun(X4,t_fun(X6,t_bool)),X9),s(t_fun(X5,t_fun(X1,t_bool)),X10))),s(t_h4s_pairs_prod(X4,X5),h4s_pairs_u_2c(s(X4,X27),s(X5,X26))))),s(t_h4s_pairs_prod(X6,X1),h4s_pairs_u_2c(s(X6,X25),s(X1,X24))))))<=>(p(s(t_bool,happ(s(t_fun(X6,t_bool),happ(s(t_fun(X4,t_fun(X6,t_bool)),X9),s(X4,X27))),s(X6,X25))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X5,t_fun(X1,t_bool)),X10),s(X5,X26))),s(X1,X24)))))),file('i/f/quotient_pair/CURRY__RSP', ah4s_quotientu_u_pairs_PAIRu_u_RELu_u_THM)).
# SZS output end CNFRefutation
