# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(![X5]:![X6]:s(t_h4s_sums_sum(X3,X2),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),happ(s(t_fun(X3,t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2))),X4),s(X3,X5))),s(t_h4s_lists_list(X1),X6)))=s(t_h4s_sums_sum(X3,X2),h4s_sums_inl(s(X3,X5)))=>![X5]:p(s(t_bool,h4s_inftrees_isu_u_tree(s(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),happ(s(t_fun(X3,t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2))),X4),s(X3,X5))))))),file('i/f/inftree/is__tree__rules_c0', ch4s_inftrees_isu_u_treeu_u_rulesu_c0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/inftree/is__tree__rules_c0', aHLu_TRUTH)).
fof(12, axiom,![X1]:![X3]:![X2]:![X12]:(p(s(t_bool,h4s_inftrees_isu_u_tree(s(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),X12))))<=>![X20]:(![X21]:((?[X5]:![X22]:s(t_h4s_sums_sum(X3,X2),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),X21),s(t_h4s_lists_list(X1),X22)))=s(t_h4s_sums_sum(X3,X2),h4s_sums_inl(s(X3,X5)))|?[X18]:?[X23]:(![X22]:?[X24]:((p(s(t_bool,X24))<=>s(t_h4s_lists_list(X1),X22)=s(t_h4s_lists_list(X1),h4s_lists_nil))&s(t_h4s_sums_sum(X3,X2),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),X21),s(t_h4s_lists_list(X1),X22)))=s(t_h4s_sums_sum(X3,X2),h4s_bools_cond(s(t_bool,X24),s(t_h4s_sums_sum(X3,X2),h4s_sums_inr(s(X2,X23))),s(t_h4s_sums_sum(X3,X2),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2))),X18),s(X1,h4s_lists_hd(s(t_h4s_lists_list(X1),X22))))),s(t_h4s_lists_list(X1),h4s_lists_tl(s(t_h4s_lists_list(X1),X22))))))))&![X25]:p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),t_bool),X20),s(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2))),X18),s(X1,X25))))))))=>p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),t_bool),X20),s(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),X21)))))=>p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),t_bool),X20),s(t_fun(t_h4s_lists_list(X1),t_h4s_sums_sum(X3,X2)),X12)))))),file('i/f/inftree/is__tree__rules_c0', ah4s_inftrees_isu_u_treeu_u_def)).
fof(13, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/inftree/is__tree__rules_c0', aHLu_BOOLu_CASES)).
fof(14, axiom,~(p(s(t_bool,f))),file('i/f/inftree/is__tree__rules_c0', aHLu_FALSITY)).
# SZS output end CNFRefutation
