# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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))))=>![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),X3))))))))=>![X5]:p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),X5))))),file('i/f/list/list__INDUCT', ch4s_lists_listu_u_INDUCT)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/list/list__INDUCT', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/list/list__INDUCT', aHLu_FALSITY)).
fof(4, 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))))=>![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),X5))))))))=>![X5]:p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),X5))))),file('i/f/list/list__INDUCT', ah4s_lists_listu_u_induction0)).
fof(11, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t0)<=>p(s(t_bool,X3))),file('i/f/list/list__INDUCT', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(22, axiom,![X3]:(s(t_bool,X3)=s(t_bool,f)<=>~(p(s(t_bool,X3)))),file('i/f/list/list__INDUCT', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(57, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t0)|s(t_bool,X3)=s(t_bool,f)),file('i/f/list/list__INDUCT', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
