# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_fun(X2,X1),X4),s(t_fun(X1,X2),X3))))=>![X6]:![X7]:![X8]:![X9]:((p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X6))),s(X2,X7))))&p(s(t_bool,happ(s(t_fun(t_fun(X2,t_bool),t_bool),happ(s(t_fun(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_equals))),s(t_fun(X2,t_bool),X8))),s(t_fun(X2,t_bool),X9)))))=>s(t_bool,h4s_bools_in(s(X2,X6),s(t_fun(X2,t_bool),X8)))=s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),X9))))),file('i/f/quotient_pred_set/IN__RSP', ch4s_quotientu_u_predu_u_sets_INu_u_RSP)).
fof(5, axiom,![X2]:![X11]:![X14]:s(t_bool,h4s_bools_in(s(X2,X11),s(t_fun(X2,t_bool),X14)))=s(t_bool,happ(s(t_fun(X2,t_bool),X14),s(X2,X11))),file('i/f/quotient_pred_set/IN__RSP', ah4s_predu_u_sets_SPECIFICATION)).
fof(6, axiom,![X2]:![X13]:![X12]:![X5]:(p(s(t_bool,happ(s(t_fun(t_fun(X2,t_bool),t_bool),happ(s(t_fun(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_fun(t_bool,t_fun(t_bool,t_bool)),d_equals))),s(t_fun(X2,t_bool),X12))),s(t_fun(X2,t_bool),X13))))<=>![X11]:![X10]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X11))),s(X2,X10))))=>s(t_bool,h4s_bools_in(s(X2,X11),s(t_fun(X2,t_bool),X12)))=s(t_bool,h4s_bools_in(s(X2,X10),s(t_fun(X2,t_bool),X13))))),file('i/f/quotient_pred_set/IN__RSP', ah4s_quotientu_u_predu_u_sets_SETu_u_REL)).
fof(18, axiom,![X22]:![X23]:((p(s(t_bool,X23))=>p(s(t_bool,X22)))=>((p(s(t_bool,X22))=>p(s(t_bool,X23)))=>s(t_bool,X23)=s(t_bool,X22))),file('i/f/quotient_pred_set/IN__RSP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(40, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_fun(X2,X1),X4),s(t_fun(X1,X2),X3))))<=>(![X19]:s(X1,happ(s(t_fun(X2,X1),X4),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X19)))))=s(X1,X19)&(![X19]:p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X19))))),s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X19))))))&![X24]:![X12]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X24))),s(X2,X12))))<=>(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X24))),s(X2,X24))))&(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(X2,X12))),s(X2,X12))))&s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X24)))=s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X12))))))))),file('i/f/quotient_pred_set/IN__RSP', ah4s_quotients_QUOTIENTu_u_def)).
# SZS output end CNFRefutation
