# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(~(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_lists_listu_u_tou_u_set(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)))))))))<=>(~(s(X1,X2)=s(X1,X4))&~(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X1),X3))))))))),file('i/f/HolSmt/NOT__MEM__CONS', ch4s_HolSmts_NOTu_u_MEMu_u_CONS)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/HolSmt/NOT__MEM__CONS', aHLu_FALSITY)).
fof(4, 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/HolSmt/NOT__MEM__CONS', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(9, axiom,![X3]:(s(t_bool,f)=s(t_bool,X3)<=>~(p(s(t_bool,X3)))),file('i/f/HolSmt/NOT__MEM__CONS', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(37, axiom,(p(s(t_bool,f))<=>![X3]:p(s(t_bool,X3))),file('i/f/HolSmt/NOT__MEM__CONS', ah4s_bools_Fu_u_DEF)).
fof(62, axiom,![X1]:![X9]:![X2]:![X30]:(p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X9),s(t_fun(X1,t_bool),X30))))))<=>(s(X1,X2)=s(X1,X9)|p(s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X30)))))),file('i/f/HolSmt/NOT__MEM__CONS', ah4s_predu_u_sets_INu_u_INSERT)).
fof(65, axiom,![X1]:![X2]:![X31]:s(t_bool,h4s_bools_in(s(X1,X2),s(t_fun(X1,t_bool),X31)))=s(t_bool,happ(s(t_fun(X1,t_bool),X31),s(X1,X2))),file('i/f/HolSmt/NOT__MEM__CONS', ah4s_bools_INu_u_DEF)).
fof(71, axiom,![X22]:![X3]:![X4]:s(t_fun(X22,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X22),happ(s(t_fun(t_h4s_lists_list(X22),t_h4s_lists_list(X22)),happ(s(t_fun(X22,t_fun(t_h4s_lists_list(X22),t_h4s_lists_list(X22))),h4s_lists_cons),s(X22,X4))),s(t_h4s_lists_list(X22),X3)))))=s(t_fun(X22,t_bool),h4s_predu_u_sets_insert(s(X22,X4),s(t_fun(X22,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X22),X3))))),file('i/f/HolSmt/NOT__MEM__CONS', ah4s_lists_LISTu_u_TOu_u_SET0u_c1)).
fof(77, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t0)|s(t_bool,X3)=s(t_bool,f)),file('i/f/HolSmt/NOT__MEM__CONS', aHLu_BOOLu_CASES)).
fof(78, axiom,![X3]:((p(s(t_bool,f))=>p(s(t_bool,X3)))<=>p(s(t_bool,t0))),file('i/f/HolSmt/NOT__MEM__CONS', ah4s_bools_IMPu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
