# 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),h4s_lists_cons(s(X1,X4),s(t_h4s_lists_list(X1),X5)))))))),file('i/f/list/EXISTS__LIST', ch4s_lists_EXISTSu_u_LIST)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/list/EXISTS__LIST', aHLu_FALSITY)).
fof(23, axiom,![X1]:![X9]:s(t_bool,d_exists(s(t_fun(X1,t_bool),X9)))=s(t_bool,happ(s(t_fun(X1,t_bool),X9),s(X1,h4s_mins_u_40(s(t_fun(X1,t_bool),X9))))),file('i/f/list/EXISTS__LIST', ah4s_bools_EXISTSu_u_DEF)).
fof(24, axiom,![X1]:![X9]:![X2]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),X2),s(X1,X9))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),X2),s(X1,h4s_mins_u_40(s(t_fun(X1,t_bool),X2))))))),file('i/f/list/EXISTS__LIST', ah4s_bools_SELECTu_u_AX)).
fof(25, axiom,![X1]:![X3]:(s(t_h4s_lists_list(X1),X3)=s(t_h4s_lists_list(X1),h4s_lists_nil)|?[X4]:?[X5]:s(t_h4s_lists_list(X1),X3)=s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X4),s(t_h4s_lists_list(X1),X5)))),file('i/f/list/EXISTS__LIST', ah4s_lists_listu_u_CASES)).
fof(26, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t0)|s(t_bool,X5)=s(t_bool,f)),file('i/f/list/EXISTS__LIST', aHLu_BOOLu_CASES)).
fof(27, axiom,p(s(t_bool,t0)),file('i/f/list/EXISTS__LIST', aHLu_TRUTH)).
fof(29, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t0)<=>p(s(t_bool,X5))),file('i/f/list/EXISTS__LIST', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
