# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(X2,t_fun(X1,t_bool)),X4),s(t_h4s_lists_list(X2),X3),s(t_h4s_lists_list(X1),h4s_lists_nil))))<=>s(t_h4s_lists_list(X2),X3)=s(t_h4s_lists_list(X2),h4s_lists_nil)),file('i/f/list/EVERY2__THM_c2', ch4s_lists_EVERY2u_u_THMu_c2)).
fof(2, 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/list/EVERY2__THM_c2', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(30, axiom,![X8]:![X22]:![X10]:![X23]:(p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(X8,t_fun(X22,t_bool)),X23),s(t_h4s_lists_list(X8),h4s_lists_nil),s(t_h4s_lists_list(X22),X10))))<=>s(t_h4s_lists_list(X22),X10)=s(t_h4s_lists_list(X22),h4s_lists_nil)),file('i/f/list/EVERY2__THM_c2', ah4s_lists_LISTu_u_RELu_u_NILu_c0)).
fof(36, axiom,![X8]:![X22]:![X34]:![X35]:![X23]:s(t_bool,h4s_lists_listu_u_rel(s(t_fun(X8,t_fun(X22,t_bool)),X23),s(t_h4s_lists_list(X8),h4s_lists_nil),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,X35))),s(t_h4s_lists_list(X22),X34)))))=s(t_bool,f),file('i/f/list/EVERY2__THM_c2', ah4s_lists_LISTu_u_RELu_u_defu_c2)).
fof(37, axiom,![X8]:![X22]:![X36]:![X37]:![X23]:(p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(X8,t_fun(X22,t_bool)),X23),s(t_h4s_lists_list(X8),X37),s(t_h4s_lists_list(X22),X36))))<=>((s(t_h4s_lists_list(X8),X37)=s(t_h4s_lists_list(X8),h4s_lists_nil)&s(t_h4s_lists_list(X22),X36)=s(t_h4s_lists_list(X22),h4s_lists_nil))|?[X32]:?[X33]:?[X6]:?[X5]:(s(t_h4s_lists_list(X8),X37)=s(t_h4s_lists_list(X8),happ(s(t_fun(t_h4s_lists_list(X8),t_h4s_lists_list(X8)),happ(s(t_fun(X8,t_fun(t_h4s_lists_list(X8),t_h4s_lists_list(X8))),h4s_lists_cons),s(X8,X32))),s(t_h4s_lists_list(X8),X6)))&(s(t_h4s_lists_list(X22),X36)=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,X33))),s(t_h4s_lists_list(X22),X5)))&(p(s(t_bool,happ(s(t_fun(X22,t_bool),happ(s(t_fun(X8,t_fun(X22,t_bool)),X23),s(X8,X32))),s(X22,X33))))&p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(X8,t_fun(X22,t_bool)),X23),s(t_h4s_lists_list(X8),X6),s(t_h4s_lists_list(X22),X5))))))))),file('i/f/list/EVERY2__THM_c2', ah4s_lists_LISTu_u_RELu_u_cases)).
fof(58, axiom,p(s(t_bool,t)),file('i/f/list/EVERY2__THM_c2', aHLu_TRUTH)).
fof(59, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/list/EVERY2__THM_c2', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
