# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),s(t_fun(X1,t_bool),X2)))),file('i/f/pred_set/EMPTY__SUBSET', ch4s_predu_u_sets_EMPTYu_u_SUBSET)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/EMPTY__SUBSET', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/EMPTY__SUBSET', aHLu_FALSITY)).
fof(9, axiom,![X1]:![X6]:~(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/EMPTY__SUBSET', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(10, axiom,![X1]:![X5]:![X2]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X5))))<=>![X6]:(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X2))))=>p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X5)))))),file('i/f/pred_set/EMPTY__SUBSET', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(11, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/pred_set/EMPTY__SUBSET', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
