# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X4),s(X1,X2))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X4))))&~(s(X1,X3)=s(X1,X2)))),file('i/f/pred_set/IN__DELETE', ch4s_predu_u_sets_INu_u_DELETE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/pred_set/IN__DELETE', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/pred_set/IN__DELETE', aHLu_FALSITY)).
fof(4, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/pred_set/IN__DELETE', aHLu_BOOLu_CASES)).
fof(6, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/pred_set/IN__DELETE', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(11, axiom,![X1]:![X3]:~(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/IN__DELETE', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(12, axiom,![X1]:![X3]:![X5]:![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X5))))))<=>(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X4))))&~(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X5))))))),file('i/f/pred_set/IN__DELETE', ah4s_predu_u_sets_INu_u_DIFF)).
fof(13, axiom,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),X4))))))<=>(s(X1,X3)=s(X1,X2)|p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X4)))))),file('i/f/pred_set/IN__DELETE', ah4s_predu_u_sets_INu_u_INSERT)).
fof(14, axiom,![X1]:![X3]:![X4]:s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X4),s(X1,X3)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/IN__DELETE', ah4s_predu_u_sets_DELETEu_u_DEF)).
# SZS output end CNFRefutation
