# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:p(s(t_bool,h4s_operators_monoid(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_append),s(t_h4s_lists_list(X1),h4s_lists_nil)))),file('i/f/rich_list/MONOID__APPEND__NIL', ch4s_richu_u_lists_MONOIDu_u_APPENDu_u_NIL)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/rich_list/MONOID__APPEND__NIL', aHLu_TRUTH)).
fof(8, axiom,![X1]:![X8]:![X9]:![X10]:s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_append),s(t_h4s_lists_list(X1),X10))),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_append),s(t_h4s_lists_list(X1),X9))),s(t_h4s_lists_list(X1),X8)))))=s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_append),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_append),s(t_h4s_lists_list(X1),X10))),s(t_h4s_lists_list(X1),X9))))),s(t_h4s_lists_list(X1),X8))),file('i/f/rich_list/MONOID__APPEND__NIL', ah4s_lists_APPENDu_u_ASSOC)).
fof(9, axiom,![X1]:![X6]:![X11]:(p(s(t_bool,h4s_operators_monoid(s(t_fun(X1,t_fun(X1,X1)),X6),s(X1,X11))))<=>(p(s(t_bool,h4s_operators_assoc(s(t_fun(X1,t_fun(X1,X1)),X6))))&(p(s(t_bool,h4s_operators_rightu_u_id(s(t_fun(X1,t_fun(X1,X1)),X6),s(X1,X11))))&p(s(t_bool,h4s_operators_leftu_u_id(s(t_fun(X1,t_fun(X1,X1)),X6),s(X1,X11))))))),file('i/f/rich_list/MONOID__APPEND__NIL', ah4s_operators_MONOIDu_u_DEF)).
fof(10, axiom,![X1]:![X12]:s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_append),s(t_h4s_lists_list(X1),h4s_lists_nil))),s(t_h4s_lists_list(X1),X12)))=s(t_h4s_lists_list(X1),X12),file('i/f/rich_list/MONOID__APPEND__NIL', ah4s_lists_APPEND0u_c0)).
fof(11, axiom,![X1]:![X12]:s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_append),s(t_h4s_lists_list(X1),X12))),s(t_h4s_lists_list(X1),h4s_lists_nil)))=s(t_h4s_lists_list(X1),X12),file('i/f/rich_list/MONOID__APPEND__NIL', ah4s_richu_u_lists_APPENDu_u_NILu_c0)).
fof(12, axiom,![X1]:![X6]:(p(s(t_bool,h4s_operators_assoc(s(t_fun(X1,t_fun(X1,X1)),X6))))<=>![X3]:![X13]:![X14]:s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),X6),s(X1,X3))),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),X6),s(X1,X13))),s(X1,X14)))))=s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),X6),s(X1,happ(s(t_fun(X1,X1),happ(s(t_fun(X1,t_fun(X1,X1)),X6),s(X1,X3))),s(X1,X13))))),s(X1,X14)))),file('i/f/rich_list/MONOID__APPEND__NIL', ah4s_operators_ASSOCu_u_DEF)).
fof(13, axiom,![X15]:![X1]:![X6]:![X11]:(p(s(t_bool,h4s_operators_rightu_u_id(s(t_fun(X1,t_fun(X15,X1)),X6),s(X15,X11))))<=>![X3]:s(X1,happ(s(t_fun(X15,X1),happ(s(t_fun(X1,t_fun(X15,X1)),X6),s(X1,X3))),s(X15,X11)))=s(X1,X3)),file('i/f/rich_list/MONOID__APPEND__NIL', ah4s_operators_RIGHTu_u_IDu_u_DEF)).
fof(14, axiom,![X1]:![X15]:![X6]:![X11]:(p(s(t_bool,h4s_operators_leftu_u_id(s(t_fun(X1,t_fun(X15,X15)),X6),s(X1,X11))))<=>![X3]:s(X15,happ(s(t_fun(X15,X15),happ(s(t_fun(X1,t_fun(X15,X15)),X6),s(X1,X11))),s(X15,X3)))=s(X15,X3)),file('i/f/rich_list/MONOID__APPEND__NIL', ah4s_operators_LEFTu_u_IDu_u_DEF)).
fof(15, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/rich_list/MONOID__APPEND__NIL', aHLu_BOOLu_CASES)).
fof(16, axiom,~(p(s(t_bool,f))),file('i/f/rich_list/MONOID__APPEND__NIL', aHLu_FALSITY)).
# SZS output end CNFRefutation
