# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:![X4]:![X5]:![X6]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_fun(X1,t_bool))),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_fun(X1,t_bool)))),X2),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_fun(X1,t_bool)),X4))),s(X1,X5))),s(X1,X6))))<=>((p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X5))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X6)))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X4),s(X1,X5))),s(X1,X6))))))=>![X7]:(![X3]:![X4]:![X5]:s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_bool))),X7),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_fun(X1,t_bool)),X4))),s(X1,X5)))=s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),h4s_quotients_respects(s(t_fun(X1,t_fun(X1,t_bool)),X4))),s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_fun(X1,t_bool))),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_fun(X1,t_bool)))),X2),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_fun(X1,t_bool)),X4))),s(X1,X5)))))=>![X8]:(![X3]:![X5]:s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X8),s(t_fun(X1,t_bool),X3))),s(X1,X5)))=s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X5)))=>![X3]:![X4]:(p(s(t_bool,h4s_quotients_resu_u_existsu_u_equiv(s(t_fun(X1,t_fun(X1,t_bool)),X4),s(t_fun(X1,t_bool),X3))))<=>(p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(X1,t_bool),h4s_quotients_respects(s(t_fun(X1,t_fun(X1,t_bool)),X4))),s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X8),s(t_fun(X1,t_bool),X3))))))&p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),h4s_quotients_respects(s(t_fun(X1,t_fun(X1,t_bool)),X4))),s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X8),s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_bool))),X7),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_fun(X1,t_bool)),X4))))))))))))),file('i/f/quotient/RES__EXISTS__EQUIV0', ch4s_quotients_RESu_u_EXISTSu_u_EQUIV0)).
fof(2, axiom,![X1]:![X2]:(![X5]:![X9]:![X10]:![X6]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_fun(X1,t_bool))),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_fun(X1,t_bool)))),X2),s(t_fun(X1,t_bool),X5))),s(t_fun(X1,t_fun(X1,t_bool)),X9))),s(X1,X10))),s(X1,X6))))<=>((p(s(t_bool,happ(s(t_fun(X1,t_bool),X5),s(X1,X10))))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X5),s(X1,X6)))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X9),s(X1,X10))),s(X1,X6))))))=>![X7]:(![X5]:![X9]:![X10]:s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_bool))),X7),s(t_fun(X1,t_bool),X5))),s(t_fun(X1,t_fun(X1,t_bool)),X9))),s(X1,X10)))=s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),h4s_quotients_respects(s(t_fun(X1,t_fun(X1,t_bool)),X9))),s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_fun(X1,t_bool))),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_fun(X1,t_bool)))),X2),s(t_fun(X1,t_bool),X5))),s(t_fun(X1,t_fun(X1,t_bool)),X9))),s(X1,X10)))))=>![X8]:(![X5]:![X9]:s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X8),s(t_fun(X1,t_bool),X5))),s(X1,X9)))=s(t_bool,happ(s(t_fun(X1,t_bool),X5),s(X1,X9)))=>![X5]:![X9]:(p(s(t_bool,h4s_quotients_resu_u_existsu_u_equiv(s(t_fun(X1,t_fun(X1,t_bool)),X5),s(t_fun(X1,t_bool),X9))))<=>(p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(X1,t_bool),h4s_quotients_respects(s(t_fun(X1,t_fun(X1,t_bool)),X5))),s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X8),s(t_fun(X1,t_bool),X9))))))&p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),h4s_quotients_respects(s(t_fun(X1,t_fun(X1,t_bool)),X5))),s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),X8),s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_bool)),happ(s(t_fun(t_fun(X1,t_bool),t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_bool))),X7),s(t_fun(X1,t_bool),X9))),s(t_fun(X1,t_fun(X1,t_bool)),X5))))))))))))),file('i/f/quotient/RES__EXISTS__EQUIV0', ah4s_quotients_RESu_u_EXISTSu_u_EQUIVu_u_DEF)).
fof(3, axiom,![X11]:![X12]:![X13]:![X14]:(![X5]:s(X12,happ(s(t_fun(X11,X12),X13),s(X11,X5)))=s(X12,happ(s(t_fun(X11,X12),X14),s(X11,X5)))=>s(t_fun(X11,X12),X13)=s(t_fun(X11,X12),X14)),file('i/f/quotient/RES__EXISTS__EQUIV0', aHLu_EXT)).
# SZS output end CNFRefutation
