# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_bool),X3))))))&~(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X4),s(X1,X2))),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_bool),X3))))))))=>s(t_h4s_nums_num,h4s_predu_u_sets_produ_u_set(s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),X3)))))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,happ(s(t_fun(X1,t_h4s_nums_num),X4),s(X1,X2))),s(t_h4s_nums_num,h4s_predu_u_sets_produ_u_set(s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,t_h4s_nums_num),X4),s(t_fun(X1,t_bool),X3)))))))),file('i/f/pred_set/PROD__SET__IMAGE__REDUCTION', ch4s_predu_u_sets_PRODu_u_SETu_u_IMAGEu_u_REDUCTION)).
fof(14, axiom,![X2]:![X3]:(p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(t_h4s_nums_num,t_bool),X3))))=>s(t_h4s_nums_num,h4s_predu_u_sets_produ_u_set(s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_insert(s(t_h4s_nums_num,X2),s(t_fun(t_h4s_nums_num,t_bool),X3)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_predu_u_sets_produ_u_set(s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_delete(s(t_fun(t_h4s_nums_num,t_bool),X3),s(t_h4s_nums_num,X2)))))))),file('i/f/pred_set/PROD__SET__IMAGE__REDUCTION', ah4s_predu_u_sets_PRODu_u_SETu_u_THMu_c1)).
fof(15, axiom,![X9]:![X1]:![X2]:![X3]:![X4]:s(t_fun(X9,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,X9),X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X2),s(t_fun(X1,t_bool),X3)))))=s(t_fun(X9,t_bool),h4s_predu_u_sets_insert(s(X9,happ(s(t_fun(X1,X9),X4),s(X1,X2))),s(t_fun(X9,t_bool),h4s_predu_u_sets_image(s(t_fun(X1,X9),X4),s(t_fun(X1,t_bool),X3))))),file('i/f/pred_set/PROD__SET__IMAGE__REDUCTION', ah4s_predu_u_sets_IMAGEu_u_INSERT)).
fof(18, axiom,![X1]:![X2]:![X3]:(~(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X3)))))<=>s(t_fun(X1,t_bool),h4s_predu_u_sets_delete(s(t_fun(X1,t_bool),X3),s(X1,X2)))=s(t_fun(X1,t_bool),X3)),file('i/f/pred_set/PROD__SET__IMAGE__REDUCTION', ah4s_predu_u_sets_DELETEu_u_NONu_u_ELEMENT)).
# SZS output end CNFRefutation
