# 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(X3,t_fun(X3,t_bool)),X9),s(t_fun(X3,X4),X8),s(t_fun(X4,X3),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,X6),X11),s(t_fun(X6,X5),X12))))=>![X13]:![X14]:![X15]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X13),s(t_fun(X1,X2),X14),s(t_fun(X2,X1),X15))))=>![X16]:![X17]:![X18]:s(X2,happ(s(t_fun(X6,X2),happ(s(t_fun(X4,t_fun(X6,X2)),h4s_pairs_curry(s(t_fun(t_h4s_pairs_prod(X4,X6),X2),X16))),s(X4,X17))),s(X6,X18)))=s(X2,happ(s(t_fun(X1,X2),X14),s(X1,happ(s(t_fun(X5,X1),happ(s(t_fun(X3,t_fun(X5,X1)),h4s_pairs_curry(s(t_fun(t_h4s_pairs_prod(X3,X5),X1),happ(s(t_fun(t_fun(t_h4s_pairs_prod(X4,X6),X2),t_fun(t_h4s_pairs_prod(X3,X5),X1)),h4s_quotients_u_2du_2du_3e(s(t_fun(t_h4s_pairs_prod(X3,X5),t_h4s_pairs_prod(X4,X6)),h4s_pairs_u_23u_23(s(t_fun(X3,X4),X8),s(t_fun(X5,X6),X11))),s(t_fun(X2,X1),X15))),s(t_fun(t_h4s_pairs_prod(X4,X6),X2),X16))))),s(X3,happ(s(t_fun(X4,X3),X7),s(X4,X17))))),s(X5,happ(s(t_fun(X6,X5),X12),s(X6,X18)))))))))),file('i/f/quotient_pair/CURRY__PRS', ch4s_quotientu_u_pairs_CURRYu_u_PRS)).
fof(5, axiom,![X27]:![X28]:((p(s(t_bool,X28))=>p(s(t_bool,X27)))=>((p(s(t_bool,X27))=>p(s(t_bool,X28)))=>s(t_bool,X28)=s(t_bool,X27))),file('i/f/quotient_pair/CURRY__PRS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(17, axiom,![X5]:![X3]:![X23]:![X24]:![X25]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X25),s(t_fun(X3,X5),X24),s(t_fun(X5,X3),X23))))<=>(![X17]:s(X5,happ(s(t_fun(X3,X5),X24),s(X3,happ(s(t_fun(X5,X3),X23),s(X5,X17)))))=s(X5,X17)&(![X17]:p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X25),s(X3,happ(s(t_fun(X5,X3),X23),s(X5,X17))))),s(X3,happ(s(t_fun(X5,X3),X23),s(X5,X17))))))&![X30]:![X31]:(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X25),s(X3,X30))),s(X3,X31))))<=>(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X25),s(X3,X30))),s(X3,X30))))&(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X25),s(X3,X31))),s(X3,X31))))&s(X5,happ(s(t_fun(X3,X5),X24),s(X3,X30)))=s(X5,happ(s(t_fun(X3,X5),X24),s(X3,X31))))))))),file('i/f/quotient_pair/CURRY__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(31, axiom,![X4]:![X5]:![X1]:![X3]:![X22]:![X42]:![X21]:![X16]:s(X4,happ(s(t_fun(X3,X4),happ(s(t_fun(t_fun(X1,X5),t_fun(X3,X4)),h4s_quotients_u_2du_2du_3e(s(t_fun(X3,X1),X16),s(t_fun(X5,X4),X21))),s(t_fun(X1,X5),X42))),s(X3,X22)))=s(X4,happ(s(t_fun(X5,X4),X21),s(X5,happ(s(t_fun(X1,X5),X42),s(X1,happ(s(t_fun(X3,X1),X16),s(X3,X22))))))),file('i/f/quotient_pair/CURRY__PRS', ah4s_quotients_FUNu_u_MAPu_u_THM)).
fof(36, axiom,![X1]:![X3]:![X5]:![X29]:![X22]:![X16]:s(X1,happ(s(t_fun(X5,X1),happ(s(t_fun(X3,t_fun(X5,X1)),h4s_pairs_curry(s(t_fun(t_h4s_pairs_prod(X3,X5),X1),X16))),s(X3,X22))),s(X5,X29)))=s(X1,happ(s(t_fun(t_h4s_pairs_prod(X3,X5),X1),X16),s(t_h4s_pairs_prod(X3,X5),h4s_pairs_u_2c(s(X3,X22),s(X5,X29))))),file('i/f/quotient_pair/CURRY__PRS', ah4s_pairs_CURRYu_u_DEF)).
fof(40, axiom,![X5]:![X3]:![X4]:![X1]:![X29]:![X22]:![X21]:![X16]:s(t_h4s_pairs_prod(X5,X4),happ(s(t_fun(t_h4s_pairs_prod(X3,X1),t_h4s_pairs_prod(X5,X4)),h4s_pairs_u_23u_23(s(t_fun(X3,X5),X16),s(t_fun(X1,X4),X21))),s(t_h4s_pairs_prod(X3,X1),h4s_pairs_u_2c(s(X3,X22),s(X1,X29)))))=s(t_h4s_pairs_prod(X5,X4),h4s_pairs_u_2c(s(X5,happ(s(t_fun(X3,X5),X16),s(X3,X22))),s(X4,happ(s(t_fun(X1,X4),X21),s(X1,X29))))),file('i/f/quotient_pair/CURRY__PRS', ah4s_pairs_PAIRu_u_MAPu_u_THM)).
# SZS output end CNFRefutation
