# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_llists_llist(X1),h4s_llists_lfilter(s(t_fun(X1,t_bool),X2),s(t_h4s_llists_llist(X1),h4s_llists_lnil)))=s(t_h4s_llists_llist(X1),h4s_llists_lnil),file('i/f/llist/LFILTER__THM_c0', ch4s_llists_LFILTERu_u_THMu_c0)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/llist/LFILTER__THM_c0', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/llist/LFILTER__THM_c0', aHLu_BOOLu_CASES)).
fof(13, axiom,![X1]:![X7]:![X8]:s(X1,h4s_bools_cond(s(t_bool,t),s(X1,X8),s(X1,X7)))=s(X1,X8),file('i/f/llist/LFILTER__THM_c0', ah4s_bools_boolu_u_caseu_u_thmu_c0)).
fof(15, axiom,![X1]:s(t_h4s_options_option(X1),h4s_llists_lhd(s(t_h4s_llists_llist(X1),h4s_llists_lnil)))=s(t_h4s_options_option(X1),h4s_options_none),file('i/f/llist/LFILTER__THM_c0', ah4s_llists_LHDu_u_THMu_c0)).
fof(16, axiom,![X1]:s(t_h4s_options_option(t_h4s_llists_llist(X1)),h4s_llists_ltl(s(t_h4s_llists_llist(X1),h4s_llists_lnil)))=s(t_h4s_options_option(t_h4s_llists_llist(X1)),h4s_options_none),file('i/f/llist/LFILTER__THM_c0', ah4s_llists_LTLu_u_THMu_c0)).
fof(17, axiom,![X1]:![X2]:s(t_bool,h4s_llists_exists(s(t_fun(X1,t_bool),X2),s(t_h4s_llists_llist(X1),h4s_llists_lnil)))=s(t_bool,f),file('i/f/llist/LFILTER__THM_c0', ah4s_llists_existsu_u_thmu_c0)).
fof(18, axiom,![X1]:![X12]:![X2]:?[X13]:((p(s(t_bool,X13))<=>~(p(s(t_bool,h4s_llists_exists(s(t_fun(X1,t_bool),X2),s(t_h4s_llists_llist(X1),X12))))))&s(t_h4s_llists_llist(X1),h4s_llists_lfilter(s(t_fun(X1,t_bool),X2),s(t_h4s_llists_llist(X1),X12)))=s(t_h4s_llists_llist(X1),h4s_bools_cond(s(t_bool,X13),s(t_h4s_llists_llist(X1),h4s_llists_lnil),s(t_h4s_llists_llist(X1),h4s_bools_cond(s(t_bool,happ(s(t_fun(X1,t_bool),X2),s(X1,h4s_options_the(s(t_h4s_options_option(X1),h4s_llists_lhd(s(t_h4s_llists_llist(X1),X12))))))),s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,h4s_options_the(s(t_h4s_options_option(X1),h4s_llists_lhd(s(t_h4s_llists_llist(X1),X12))))),s(t_h4s_llists_llist(X1),h4s_llists_lfilter(s(t_fun(X1,t_bool),X2),s(t_h4s_llists_llist(X1),h4s_options_the(s(t_h4s_options_option(t_h4s_llists_llist(X1)),h4s_llists_ltl(s(t_h4s_llists_llist(X1),X12))))))))),s(t_h4s_llists_llist(X1),h4s_llists_lfilter(s(t_fun(X1,t_bool),X2),s(t_h4s_llists_llist(X1),h4s_options_the(s(t_h4s_options_option(t_h4s_llists_llist(X1)),h4s_llists_ltl(s(t_h4s_llists_llist(X1),X12)))))))))))),file('i/f/llist/LFILTER__THM_c0', ah4s_llists_LFILTER0)).
# SZS output end CNFRefutation
