# 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),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__LIST', ch4s_lists_FORALLu_u_LIST)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/list/FORALL__LIST', aHLu_FALSITY)).
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))))&![X5]:(p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),X5))))=>![X4]: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))))))))=>![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__LIST', ah4s_lists_listu_u_INDUCT)).
fof(36, axiom,![X5]:(s(t_bool,f)=s(t_bool,X5)<=>~(p(s(t_bool,X5)))),file('i/f/list/FORALL__LIST', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(67, axiom,p(s(t_bool,t0)),file('i/f/list/FORALL__LIST', aHLu_TRUTH)).
fof(69, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t0)<=>p(s(t_bool,X5))),file('i/f/list/FORALL__LIST', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
