# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((![X4]:![X5]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),X3),s(X1,X4))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X2),s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X4),s(t_h4s_llists_llist(X1),X5)))))))&![X4]:![X5]:(p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X2),s(t_h4s_llists_llist(X1),X5))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X2),s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X4),s(t_h4s_llists_llist(X1),X5))))))))=>![X6]:(p(s(t_bool,h4s_llists_exists(s(t_fun(X1,t_bool),X3),s(t_h4s_llists_llist(X1),X6))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X2),s(t_h4s_llists_llist(X1),X6)))))),file('i/f/llist/exists__ind', ch4s_llists_existsu_u_ind)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/llist/exists__ind', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/llist/exists__ind', aHLu_FALSITY)).
fof(5, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/llist/exists__ind', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X1]:![X11]:![X14]:(p(s(t_bool,h4s_llists_exists(s(t_fun(X1,t_bool),X11),s(t_h4s_llists_llist(X1),X14))))<=>![X2]:(![X15]:((?[X4]:?[X5]:(s(t_h4s_llists_llist(X1),X15)=s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X4),s(t_h4s_llists_llist(X1),X5)))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X11),s(X1,X4)))))|?[X4]:?[X5]:(s(t_h4s_llists_llist(X1),X15)=s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X4),s(t_h4s_llists_llist(X1),X5)))&p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X2),s(t_h4s_llists_llist(X1),X5))))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X2),s(t_h4s_llists_llist(X1),X15)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X2),s(t_h4s_llists_llist(X1),X14)))))),file('i/f/llist/exists__ind', ah4s_llists_existsu_u_def)).
fof(13, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t0)|s(t_bool,X5)=s(t_bool,f)),file('i/f/llist/exists__ind', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
