# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),X3))))<=>(p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),h4s_lists_nil))))&![X4]:![X5]:(p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),X5))))=>p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X4))),s(t_h4s_lists_list(X1),X5))))))))),file('i/f/list/FORALL__LIST0', ch4s_lists_FORALLu_u_LIST0)).
fof(3, axiom,![X1]:![X2]:((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),h4s_lists_nil))))&![X3]:(p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),X3))))=>![X6]:p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X6))),s(t_h4s_lists_list(X1),X3))))))))=>![X3]:p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),X3))))),file('i/f/list/FORALL__LIST0', ah4s_lists_listu_u_induction0)).
fof(15, axiom,![X5]:(s(t_bool,X5)=s(t_bool,f)<=>~(p(s(t_bool,X5)))),file('i/f/list/FORALL__LIST0', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(57, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t0)|s(t_bool,X5)=s(t_bool,f)),file('i/f/list/FORALL__LIST0', aHLu_BOOLu_CASES)).
fof(63, axiom,p(s(t_bool,t0)),file('i/f/list/FORALL__LIST0', aHLu_TRUTH)).
fof(66, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t0)<=>p(s(t_bool,X5))),file('i/f/list/FORALL__LIST0', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
