# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X7),s(t_fun(X1,X2),X6),s(t_fun(X2,X1),X5))))=>![X8]:![X9]:![X10]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X8),s(t_fun(X3,X4),X9),s(t_fun(X4,X3),X10))))=>![X11]:![X12]:s(t_h4s_pairs_prod(X2,X4),h4s_pairs_u_2c(s(X2,X11),s(X4,X12)))=s(t_h4s_pairs_prod(X2,X4),happ(s(t_fun(t_h4s_pairs_prod(X1,X3),t_h4s_pairs_prod(X2,X4)),h4s_pairs_u_23u_23(s(t_fun(X1,X2),X6),s(t_fun(X3,X4),X9))),s(t_h4s_pairs_prod(X1,X3),h4s_pairs_u_2c(s(X1,happ(s(t_fun(X2,X1),X5),s(X2,X11))),s(X3,happ(s(t_fun(X4,X3),X10),s(X4,X12))))))))),file('i/f/quotient_pair/COMMA__PRS', ch4s_quotientu_u_pairs_COMMAu_u_PRS)).
fof(5, axiom,![X3]:![X1]:![X18]:![X19]:![X20]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X1,t_fun(X1,t_bool)),X20),s(t_fun(X1,X3),X19),s(t_fun(X3,X1),X18))))<=>(![X11]:s(X3,happ(s(t_fun(X1,X3),X19),s(X1,happ(s(t_fun(X3,X1),X18),s(X3,X11)))))=s(X3,X11)&(![X11]:p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X20),s(X1,happ(s(t_fun(X3,X1),X18),s(X3,X11))))),s(X1,happ(s(t_fun(X3,X1),X18),s(X3,X11))))))&![X22]:![X23]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X20),s(X1,X22))),s(X1,X23))))<=>(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X20),s(X1,X22))),s(X1,X22))))&(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X20),s(X1,X23))),s(X1,X23))))&s(X3,happ(s(t_fun(X1,X3),X19),s(X1,X22)))=s(X3,happ(s(t_fun(X1,X3),X19),s(X1,X23))))))))),file('i/f/quotient_pair/COMMA__PRS', ah4s_quotients_QUOTIENTu_u_def)).
fof(6, axiom,![X24]:![X25]:((p(s(t_bool,X25))=>p(s(t_bool,X24)))=>((p(s(t_bool,X24))=>p(s(t_bool,X25)))=>s(t_bool,X25)=s(t_bool,X24))),file('i/f/quotient_pair/COMMA__PRS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(35, axiom,![X3]:![X1]:![X4]:![X2]:![X26]:![X17]:![X16]:![X15]:s(t_h4s_pairs_prod(X3,X4),happ(s(t_fun(t_h4s_pairs_prod(X1,X2),t_h4s_pairs_prod(X3,X4)),h4s_pairs_u_23u_23(s(t_fun(X1,X3),X15),s(t_fun(X2,X4),X16))),s(t_h4s_pairs_prod(X1,X2),h4s_pairs_u_2c(s(X1,X17),s(X2,X26)))))=s(t_h4s_pairs_prod(X3,X4),h4s_pairs_u_2c(s(X3,happ(s(t_fun(X1,X3),X15),s(X1,X17))),s(X4,happ(s(t_fun(X2,X4),X16),s(X2,X26))))),file('i/f/quotient_pair/COMMA__PRS', ah4s_pairs_PAIRu_u_MAPu_u_THM)).
# SZS output end CNFRefutation
