# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_sortings_sorted(s(t_fun(X1,t_fun(X1,t_bool)),h4s_relations_invu_u_image(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_fun(X1,t_h4s_nums_num),X4))),s(t_h4s_lists_list(X1),X3))))&p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_map(s(t_fun(X1,t_h4s_nums_num),X4),s(t_h4s_lists_list(X1),X3))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_richu_u_lists_countu_u_list(s(t_h4s_nums_num,X2)))))))=>s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_map(s(t_fun(X1,t_h4s_nums_num),X4),s(t_h4s_lists_list(X1),X3)))=s(t_h4s_lists_list(t_h4s_nums_num),h4s_richu_u_lists_countu_u_list(s(t_h4s_nums_num,X2)))),file('i/f/sorting/sorted__perm__count__list', ch4s_sortings_sortedu_u_permu_u_countu_u_list)).
fof(2, axiom,~(p(s(t_bool,f0))),file('i/f/sorting/sorted__perm__count__list', aHLu_FALSITY)).
fof(13, axiom,![X10]:((p(s(t_bool,X10))=>p(s(t_bool,f0)))<=>s(t_bool,X10)=s(t_bool,f0)),file('i/f/sorting/sorted__perm__count__list', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(28, axiom,![X2]:p(s(t_bool,h4s_sortings_sorted(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_h4s_lists_list(t_h4s_nums_num),h4s_richu_u_lists_countu_u_list(s(t_h4s_nums_num,X2)))))),file('i/f/sorting/sorted__perm__count__list', ah4s_sortings_sortedu_u_countu_u_list)).
fof(29, axiom,![X25]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X25)))=s(t_h4s_nums_num,X25),file('i/f/sorting/sorted__perm__count__list', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(30, axiom,![X2]:![X25]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X25))),file('i/f/sorting/sorted__perm__count__list', ah4s_arithmetics_ADDu_u_SYM)).
fof(31, axiom,![X24]:![X2]:![X25]:((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_h4s_nums_num,X25))),s(t_h4s_nums_num,X2))))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X24)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_h4s_nums_num,X25))),s(t_h4s_nums_num,X24))))),file('i/f/sorting/sorted__perm__count__list', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(32, axiom,![X2]:p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_nums_num,X2)))),file('i/f/sorting/sorted__perm__count__list', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(33, axiom,![X24]:![X2]:![X25]:s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X24)))))=s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X24))),file('i/f/sorting/sorted__perm__count__list', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(34, axiom,![X2]:![X25]:(~(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_h4s_nums_num,X25))),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,X25))))),file('i/f/sorting/sorted__perm__count__list', ah4s_arithmetics_NOTu_u_LEQ)).
fof(35, axiom,![X2]:![X25]:(~(s(t_h4s_nums_num,X25)=s(t_h4s_nums_num,X2))<=>(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X25))))),s(t_h4s_nums_num,X2))))|p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_arithmetics_u_3cu_3d),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,X25)))))),file('i/f/sorting/sorted__perm__count__list', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(39, axiom,![X9]:![X26]:((p(s(t_bool,h4s_relations_transitive(s(t_fun(X9,t_fun(X9,t_bool)),X26))))&p(s(t_bool,h4s_relations_antisymmetric(s(t_fun(X9,t_fun(X9,t_bool)),X26)))))=>![X27]:![X28]:((p(s(t_bool,h4s_sortings_sorted(s(t_fun(X9,t_fun(X9,t_bool)),X26),s(t_h4s_lists_list(X9),X27))))&(p(s(t_bool,h4s_sortings_sorted(s(t_fun(X9,t_fun(X9,t_bool)),X26),s(t_h4s_lists_list(X9),X28))))&p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X9),X27),s(t_h4s_lists_list(X9),X28))))))=>s(t_h4s_lists_list(X9),X27)=s(t_h4s_lists_list(X9),X28))),file('i/f/sorting/sorted__perm__count__list', ah4s_sortings_SORTEDu_u_PERMu_u_EQ)).
fof(40, axiom,![X9]:![X1]:![X3]:![X4]:![X26]:(p(s(t_bool,h4s_relations_transitive(s(t_fun(X9,t_fun(X9,t_bool)),X26))))=>s(t_bool,h4s_sortings_sorted(s(t_fun(X9,t_fun(X9,t_bool)),X26),s(t_h4s_lists_list(X9),h4s_lists_map(s(t_fun(X1,X9),X4),s(t_h4s_lists_list(X1),X3)))))=s(t_bool,h4s_sortings_sorted(s(t_fun(X1,t_fun(X1,t_bool)),h4s_relations_invu_u_image(s(t_fun(X9,t_fun(X9,t_bool)),X26),s(t_fun(X1,X9),X4))),s(t_h4s_lists_list(X1),X3)))),file('i/f/sorting/sorted__perm__count__list', ah4s_sortings_sortedu_u_map)).
fof(41, axiom,![X9]:![X26]:(p(s(t_bool,h4s_relations_transitive(s(t_fun(X9,t_fun(X9,t_bool)),X26))))<=>![X8]:![X11]:![X29]:((p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X26),s(X9,X8))),s(X9,X11))))&p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X26),s(X9,X11))),s(X9,X29)))))=>p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X26),s(X9,X8))),s(X9,X29)))))),file('i/f/sorting/sorted__perm__count__list', ah4s_relations_transitiveu_u_def)).
fof(45, axiom,![X9]:![X26]:(p(s(t_bool,h4s_relations_antisymmetric(s(t_fun(X9,t_fun(X9,t_bool)),X26))))<=>![X8]:![X11]:((p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X26),s(X9,X8))),s(X9,X11))))&p(s(t_bool,happ(s(t_fun(X9,t_bool),happ(s(t_fun(X9,t_fun(X9,t_bool)),X26),s(X9,X11))),s(X9,X8)))))=>s(X9,X8)=s(X9,X11))),file('i/f/sorting/sorted__perm__count__list', ah4s_relations_antisymmetricu_u_def)).
fof(46, axiom,p(s(t_bool,t)),file('i/f/sorting/sorted__perm__count__list', aHLu_TRUTH)).
fof(49, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)<=>p(s(t_bool,X10))),file('i/f/sorting/sorted__perm__count__list', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
