# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),X4),s(X1,X3))))=>p(s(t_bool,h4s_llists_exists(s(t_fun(X1,t_bool),X4),s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X3),s(t_h4s_llists_llist(X1),X2))))))),file('i/f/llist/exists__rules_c0', ch4s_llists_existsu_u_rulesu_c0)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/llist/exists__rules_c0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/llist/exists__rules_c0', aHLu_FALSITY)).
fof(5, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/llist/exists__rules_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X1]:![X9]:![X12]:(p(s(t_bool,h4s_llists_exists(s(t_fun(X1,t_bool),X9),s(t_h4s_llists_llist(X1),X12))))<=>![X13]:(![X14]:((?[X3]:?[X2]:(s(t_h4s_llists_llist(X1),X14)=s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X3),s(t_h4s_llists_llist(X1),X2)))&p(s(t_bool,happ(s(t_fun(X1,t_bool),X9),s(X1,X3)))))|?[X3]:?[X2]:(s(t_h4s_llists_llist(X1),X14)=s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X3),s(t_h4s_llists_llist(X1),X2)))&p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X13),s(t_h4s_llists_llist(X1),X2))))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X13),s(t_h4s_llists_llist(X1),X14)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_llists_llist(X1),t_bool),X13),s(t_h4s_llists_llist(X1),X12)))))),file('i/f/llist/exists__rules_c0', ah4s_llists_existsu_u_def)).
fof(13, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t0)|s(t_bool,X2)=s(t_bool,f)),file('i/f/llist/exists__rules_c0', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
