# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(![X4]:![X5]:![X6]:?[X7]:?[X8]:?[X9]:(s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X2),t_h4s_lists_list(X1)),X3),s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),X4),s(t_h4s_lists_list(X2),X5))),s(t_h4s_lists_list(X2),X6)))))=s(t_h4s_lists_list(X1),h4s_lists_append(s(t_h4s_lists_list(X1),h4s_lists_append(s(t_h4s_lists_list(X1),X7),s(t_h4s_lists_list(X1),X8))),s(t_h4s_lists_list(X1),X9)))&s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X2),t_h4s_lists_list(X1)),X3),s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),X4),s(t_h4s_lists_list(X2),X6))),s(t_h4s_lists_list(X2),X5)))))=s(t_h4s_lists_list(X1),h4s_lists_append(s(t_h4s_lists_list(X1),h4s_lists_append(s(t_h4s_lists_list(X1),X7),s(t_h4s_lists_list(X1),X9))),s(t_h4s_lists_list(X1),X8))))=>![X10]:![X11]:(p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X2),t_bool),happ(s(t_fun(t_h4s_lists_list(X2),t_fun(t_h4s_lists_list(X2),t_bool)),h4s_sortings_perm),s(t_h4s_lists_list(X2),X10))),s(t_h4s_lists_list(X2),X11))))=>p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),happ(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_bool)),h4s_sortings_perm),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X2),t_h4s_lists_list(X1)),X3),s(t_h4s_lists_list(X2),X10))))),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X2),t_h4s_lists_list(X1)),X3),s(t_h4s_lists_list(X2),X11)))))))),file('i/f/sorting/PERM__lifts__monotonicities', ch4s_sortings_PERMu_u_liftsu_u_monotonicities)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/sorting/PERM__lifts__monotonicities', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/sorting/PERM__lifts__monotonicities', aHLu_FALSITY)).
fof(6, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)<=>p(s(t_bool,X12))),file('i/f/sorting/PERM__lifts__monotonicities', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X2]:p(s(t_bool,h4s_relations_transitive(s(t_fun(t_h4s_lists_list(X2),t_fun(t_h4s_lists_list(X2),t_bool)),h4s_sortings_perm)))),file('i/f/sorting/PERM__lifts__monotonicities', ah4s_sortings_PERMu_u_transitive)).
fof(8, axiom,![X2]:![X13]:![X14]:p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X2),t_bool),happ(s(t_fun(t_h4s_lists_list(X2),t_fun(t_h4s_lists_list(X2),t_bool)),h4s_sortings_perm),s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),X14),s(t_h4s_lists_list(X2),X13))))),s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),X13),s(t_h4s_lists_list(X2),X14)))))),file('i/f/sorting/PERM__lifts__monotonicities', ah4s_sortings_PERMu_u_APPEND)).
fof(9, axiom,![X1]:![X2]:![X3]:![X15]:((![X4]:![X5]:![X6]:p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X15),s(X1,happ(s(t_fun(t_h4s_lists_list(X2),X1),X3),s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),X4),s(t_h4s_lists_list(X2),X5))),s(t_h4s_lists_list(X2),X6))))))),s(X1,happ(s(t_fun(t_h4s_lists_list(X2),X1),X3),s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),X4),s(t_h4s_lists_list(X2),X6))),s(t_h4s_lists_list(X2),X5))))))))&p(s(t_bool,h4s_relations_transitive(s(t_fun(X1,t_fun(X1,t_bool)),X15)))))=>![X10]:![X11]:(p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X2),t_bool),happ(s(t_fun(t_h4s_lists_list(X2),t_fun(t_h4s_lists_list(X2),t_bool)),h4s_sortings_perm),s(t_h4s_lists_list(X2),X10))),s(t_h4s_lists_list(X2),X11))))=>p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X15),s(X1,happ(s(t_fun(t_h4s_lists_list(X2),X1),X3),s(t_h4s_lists_list(X2),X10))))),s(X1,happ(s(t_fun(t_h4s_lists_list(X2),X1),X3),s(t_h4s_lists_list(X2),X11)))))))),file('i/f/sorting/PERM__lifts__monotonicities', ah4s_sortings_PERMu_u_liftsu_u_transitiveu_u_relations)).
fof(12, axiom,![X2]:![X19]:![X13]:![X14]:s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),X14),s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),X13),s(t_h4s_lists_list(X2),X19)))))=s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),X14),s(t_h4s_lists_list(X2),X13))),s(t_h4s_lists_list(X2),X19))),file('i/f/sorting/PERM__lifts__monotonicities', ah4s_lists_APPENDu_u_ASSOC)).
fof(13, axiom,![X2]:![X13]:![X14]:![X20]:s(t_bool,happ(s(t_fun(t_h4s_lists_list(X2),t_bool),happ(s(t_fun(t_h4s_lists_list(X2),t_fun(t_h4s_lists_list(X2),t_bool)),h4s_sortings_perm),s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),X20),s(t_h4s_lists_list(X2),X14))))),s(t_h4s_lists_list(X2),h4s_lists_append(s(t_h4s_lists_list(X2),X20),s(t_h4s_lists_list(X2),X13)))))=s(t_bool,happ(s(t_fun(t_h4s_lists_list(X2),t_bool),happ(s(t_fun(t_h4s_lists_list(X2),t_fun(t_h4s_lists_list(X2),t_bool)),h4s_sortings_perm),s(t_h4s_lists_list(X2),X14))),s(t_h4s_lists_list(X2),X13))),file('i/f/sorting/PERM__lifts__monotonicities', ah4s_sortings_PERMu_u_APPENDu_u_IFFu_c0)).
fof(14, axiom,![X12]:(s(t_bool,X12)=s(t_bool,t)|s(t_bool,X12)=s(t_bool,f0)),file('i/f/sorting/PERM__lifts__monotonicities', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
