# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_fun(X2,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,X2),X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))=s(t_fun(X2,t_bool),h4s_predu_u_sets_empty),file('i/f/pred_set/IMAGE__EMPTY', ch4s_predu_u_sets_IMAGEu_u_EMPTY)).
fof(3, axiom,![X1]:![X5]:~(p(s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/pred_set/IMAGE__EMPTY', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(4, 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/IMAGE__EMPTY', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(21, axiom,![X2]:![X1]:![X4]:![X17]:![X3]:(p(s(t_bool,h4s_bools_in(s(X2,X4),s(t_fun(X2,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,X2),X3),s(t_fun(X1,t_bool),X17))))))<=>?[X5]:(s(X2,X4)=s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X5)))&p(s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),X17)))))),file('i/f/pred_set/IMAGE__EMPTY', ah4s_predu_u_sets_INu_u_IMAGE)).
fof(26, axiom,![X1]:![X5]:![X20]:s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),X20)))=s(t_bool,happ(s(t_fun(X1,t_bool),X20),s(X1,X5))),file('i/f/pred_set/IMAGE__EMPTY', ah4s_bools_INu_u_DEF)).
fof(27, axiom,![X1]:![X8]:![X17]:(s(t_fun(X1,t_bool),X17)=s(t_fun(X1,t_bool),X8)<=>![X5]:s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),X17)))=s(t_bool,h4s_bools_in(s(X1,X5),s(t_fun(X1,t_bool),X8)))),file('i/f/pred_set/IMAGE__EMPTY', ah4s_predu_u_sets_EXTENSION)).
# SZS output end CNFRefutation
