# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X3),s(X1,X2)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)<=>~(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_relations_rdom(s(t_fun(X1,t_fun(X1,t_bool)),X3)))))))),file('i/f/tc/NOT__IN__RDOM', ch4s_tcs_NOTu_u_INu_u_RDOM)).
fof(2, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/tc/NOT__IN__RDOM', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(3, axiom,![X1]:![X2]:![X6]:s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X6)))=s(t_bool,happ(s(t_fun(X1,t_bool),X6),s(X1,X2))),file('i/f/tc/NOT__IN__RDOM', ah4s_predu_u_sets_SPECIFICATION)).
fof(4, axiom,![X1]:![X2]:~(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/tc/NOT__IN__RDOM', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(5, axiom,![X1]:![X7]:![X2]:![X8]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),h4s_relations_rdom(s(t_fun(X1,t_fun(X7,t_bool)),X8))),s(X1,X2))))<=>?[X9]:p(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X1,t_fun(X7,t_bool)),X8),s(X1,X2))),s(X7,X9))))),file('i/f/tc/NOT__IN__RDOM', ah4s_relations_RDOMu_u_DEF)).
fof(6, axiom,![X10]:![X11]:![X12]:![X13]:(![X2]:s(X11,happ(s(t_fun(X10,X11),X12),s(X10,X2)))=s(X11,happ(s(t_fun(X10,X11),X13),s(X10,X2)))=>s(t_fun(X10,X11),X12)=s(t_fun(X10,X11),X13)),file('i/f/tc/NOT__IN__RDOM', aHLu_EXT)).
# SZS output end CNFRefutation
