# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(s(t_fun(X1,t_bool),h4s_predu_u_sets_image(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),X3)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)<=>s(t_fun(X2,t_bool),X3)=s(t_fun(X2,t_bool),h4s_predu_u_sets_empty)),file('i/f/pred_set/IMAGE__EQ__EMPTY', ch4s_predu_u_sets_IMAGEu_u_EQu_u_EMPTY)).
fof(31, axiom,![X2]:![X3]:(?[X8]:p(s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X3))))<=>~(s(t_fun(X2,t_bool),X3)=s(t_fun(X2,t_bool),h4s_predu_u_sets_empty))),file('i/f/pred_set/IMAGE__EQ__EMPTY', ah4s_predu_u_sets_MEMBERu_u_NOTu_u_EMPTY)).
fof(32, axiom,![X2]:![X8]:s(t_bool,happ(s(t_fun(X2,t_bool),h4s_predu_u_sets_empty),s(X2,X8)))=s(t_bool,f0),file('i/f/pred_set/IMAGE__EQ__EMPTY', ah4s_predu_u_sets_EMPTYu_u_DEF)).
fof(35, axiom,![X1]:![X2]:![X8]:![X3]:(p(s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X3))))=>![X4]:p(s(t_bool,h4s_bools_in(s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X8))),s(t_fun(X1,t_bool),h4s_predu_u_sets_image(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),X3))))))),file('i/f/pred_set/IMAGE__EQ__EMPTY', ah4s_predu_u_sets_IMAGEu_u_IN)).
fof(37, axiom,![X2]:![X1]:![X4]:s(t_fun(X1,t_bool),h4s_predu_u_sets_image(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),h4s_predu_u_sets_empty)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),file('i/f/pred_set/IMAGE__EQ__EMPTY', ah4s_predu_u_sets_IMAGEu_u_EMPTY)).
fof(40, axiom,![X2]:![X8]:![X23]:s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X23)))=s(t_bool,happ(s(t_fun(X2,t_bool),X23),s(X2,X8))),file('i/f/pred_set/IMAGE__EQ__EMPTY', ah4s_bools_INu_u_DEF)).
fof(41, axiom,~(p(s(t_bool,f0))),file('i/f/pred_set/IMAGE__EQ__EMPTY', aHLu_FALSITY)).
# SZS output end CNFRefutation
