# 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(13, axiom,![X2]:![X3]:(s(t_fun(X2,t_bool),X3)=s(t_fun(X2,t_bool),h4s_predu_u_sets_empty)|?[X8]:?[X5]:(s(t_fun(X2,t_bool),X3)=s(t_fun(X2,t_bool),h4s_predu_u_sets_insert(s(X2,X8),s(t_fun(X2,t_bool),X5)))&~(p(s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X5))))))),file('i/f/pred_set/IMAGE__EQ__EMPTY', ah4s_predu_u_sets_SETu_u_CASES)).
fof(14, axiom,![X2]:![X8]:![X3]:~(s(t_fun(X2,t_bool),h4s_predu_u_sets_insert(s(X2,X8),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_NOTu_u_INSERTu_u_EMPTY)).
fof(15, 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(17, axiom,![X1]:![X2]:![X8]:![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),h4s_predu_u_sets_insert(s(X2,X8),s(t_fun(X2,t_bool),X3)))))=s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(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_INSERT)).
# SZS output end CNFRefutation
