# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_llists_llist(X1),t_fun(t_h4s_nums_num,t_bool)),X2),s(t_h4s_llists_llist(X1),h4s_llists_lnil))),s(t_h4s_nums_num,h4s_nums_0))))&![X3]:![X4]:![X5]:(p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_llists_llist(X1),t_fun(t_h4s_nums_num,t_bool)),X2),s(t_h4s_llists_llist(X1),X5))),s(t_h4s_nums_num,X4))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_llists_llist(X1),t_fun(t_h4s_nums_num,t_bool)),X2),s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X3),s(t_h4s_llists_llist(X1),X5))))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4))))))))=>![X6]:![X7]:(p(s(t_bool,h4s_llists_llengthu_u_rel(s(t_h4s_llists_llist(X1),X6),s(t_h4s_nums_num,X7))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_llists_llist(X1),t_fun(t_h4s_nums_num,t_bool)),X2),s(t_h4s_llists_llist(X1),X6))),s(t_h4s_nums_num,X7)))))),file('i/f/llist/llength__rel__ind', ch4s_llists_llengthu_u_relu_u_ind)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/llist/llength__rel__ind', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/llist/llength__rel__ind', aHLu_FALSITY)).
fof(5, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/llist/llength__rel__ind', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X1]:![X12]:![X16]:(p(s(t_bool,h4s_llists_llengthu_u_rel(s(t_h4s_llists_llist(X1),X12),s(t_h4s_nums_num,X16))))<=>![X2]:(![X17]:![X18]:(((s(t_h4s_llists_llist(X1),X17)=s(t_h4s_llists_llist(X1),h4s_llists_lnil)&s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,h4s_nums_0))|?[X3]:?[X4]:?[X5]:(s(t_h4s_llists_llist(X1),X17)=s(t_h4s_llists_llist(X1),h4s_llists_lcons(s(X1,X3),s(t_h4s_llists_llist(X1),X5)))&(s(t_h4s_nums_num,X18)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X4)))&p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_llists_llist(X1),t_fun(t_h4s_nums_num,t_bool)),X2),s(t_h4s_llists_llist(X1),X5))),s(t_h4s_nums_num,X4)))))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_llists_llist(X1),t_fun(t_h4s_nums_num,t_bool)),X2),s(t_h4s_llists_llist(X1),X17))),s(t_h4s_nums_num,X18)))))=>p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_llists_llist(X1),t_fun(t_h4s_nums_num,t_bool)),X2),s(t_h4s_llists_llist(X1),X12))),s(t_h4s_nums_num,X16)))))),file('i/f/llist/llength__rel__ind', ah4s_llists_llengthu_u_relu_u_def)).
fof(13, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t0)|s(t_bool,X5)=s(t_bool,f)),file('i/f/llist/llength__rel__ind', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
