# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_quotients_equiv(s(t_fun(X1,t_fun(X1,t_bool)),X3))))=>s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_bool)),h4s_quotients_respects),s(t_fun(X1,t_fun(X1,t_bool)),X3))),s(t_fun(X1,t_bool),X2)))=s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),d_forall),s(t_fun(X1,t_bool),X2)))),file('i/f/quotient/EQUIV__RES__FORALL', ch4s_quotients_EQUIVu_u_RESu_u_FORALL)).
fof(5, axiom,![X14]:![X15]:((p(s(t_bool,X15))=>p(s(t_bool,X14)))=>((p(s(t_bool,X14))=>p(s(t_bool,X15)))=>s(t_bool,X15)=s(t_bool,X14))),file('i/f/quotient/EQUIV__RES__FORALL', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(33, axiom,![X1]:![X6]:(p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),d_forall),s(t_fun(X1,t_bool),X6))))<=>![X8]:p(s(t_bool,happ(s(t_fun(X1,t_bool),X6),s(X1,X8))))),file('i/f/quotient/EQUIV__RES__FORALL', ah4s_bools_FORALLu_u_THM)).
fof(34, axiom,![X1]:![X8]:(p(s(t_bool,happ(s(t_fun(t_fun(X1,t_bool),t_bool),d_forall),s(t_fun(X1,t_bool),X8))))<=>![X27]:s(t_bool,happ(s(t_fun(X1,t_bool),X8),s(X1,X27)))=s(t_bool,t)),file('i/f/quotient/EQUIV__RES__FORALL', ah4s_bools_FORALLu_u_DEF)).
fof(38, axiom,![X1]:![X6]:![X2]:(p(s(t_bool,h4s_bools_resu_u_forall(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X6))))<=>![X8]:(p(s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),X2))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X6),s(X1,X8)))))),file('i/f/quotient/EQUIV__RES__FORALL', ah4s_resu_u_quans_RESu_u_FORALL)).
fof(47, axiom,![X1]:![X8]:![X11]:s(t_bool,h4s_bools_in(s(X1,X8),s(t_fun(X1,t_bool),happ(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(X1,t_bool)),h4s_quotients_respects),s(t_fun(X1,t_fun(X1,t_bool)),X11)))))=s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X11),s(X1,X8))),s(X1,X8))),file('i/f/quotient/EQUIV__RES__FORALL', ah4s_quotients_INu_u_RESPECTS)).
fof(49, axiom,![X1]:![X3]:(p(s(t_bool,h4s_quotients_equiv(s(t_fun(X1,t_fun(X1,t_bool)),X3))))<=>![X8]:![X12]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X3),s(X1,X8))),s(X1,X12))))<=>s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X3),s(X1,X8)))=s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X3),s(X1,X12))))),file('i/f/quotient/EQUIV__RES__FORALL', ah4s_quotients_EQUIVu_u_def)).
# SZS output end CNFRefutation
