# 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),X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))<=>s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/SUBSET__EMPTY', ch4s_predu_u_sets_SUBSETu_u_EMPTY)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/SUBSET__EMPTY', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/SUBSET__EMPTY', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/pred_set/SUBSET__EMPTY', aHLu_BOOLu_CASES)).
fof(11, axiom,![X3]:(s(t_bool,X3)=s(t_bool,f)<=>~(p(s(t_bool,X3)))),file('i/f/pred_set/SUBSET__EMPTY', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(12, axiom,![X1]:![X3]:![X2]:(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),X3)<=>![X6]:s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X2)))=s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X3)))),file('i/f/pred_set/SUBSET__EMPTY', ah4s_predu_u_sets_EXTENSION)).
fof(13, 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/SUBSET__EMPTY', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(15, axiom,![X1]:![X3]:![X2]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X3))))<=>![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),X3)))))),file('i/f/pred_set/SUBSET__EMPTY', ah4s_predu_u_sets_SUBSETu_u_DEF)).
# SZS output end CNFRefutation
