# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),t_bool),X2),s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),h4s_indu_u_types_zbot))))&![X3]:![X4]:![X5]:(![X6]:p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),t_bool),X2),s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(X1,t_bool))),X5),s(t_h4s_nums_num,X6))))))=>p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),t_bool),X2),s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),h4s_indu_u_types_zconstr(s(t_h4s_nums_num,X3),s(X1,X4),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(X1,t_bool))),X5))))))))=>![X7]:(p(s(t_bool,h4s_indu_u_types_zrecspace(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X7))))=>p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),t_bool),X2),s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X7)))))),file('i/f/ind_type/ZRECSPACE__ind', ch4s_indu_u_types_ZRECSPACEu_u_ind)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/ind_type/ZRECSPACE__ind', aHLu_TRUTH)).
fof(4, 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/ind_type/ZRECSPACE__ind', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(12, axiom,![X1]:![X13]:(p(s(t_bool,h4s_indu_u_types_zrecspace(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X13))))<=>![X2]:(![X22]:((s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X22)=s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),h4s_indu_u_types_zbot)|?[X3]:?[X4]:?[X5]:(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X22)=s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),h4s_indu_u_types_zconstr(s(t_h4s_nums_num,X3),s(X1,X4),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(X1,t_bool))),X5)))&![X6]:p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),t_bool),X2),s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(X1,t_bool))),X5),s(t_h4s_nums_num,X6))))))))=>p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),t_bool),X2),s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X22)))))=>p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),t_bool),X2),s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X13)))))),file('i/f/ind_type/ZRECSPACE__ind', ah4s_indu_u_types_ZRECSPACEu_u_def)).
fof(13, axiom,![X10]:(s(t_bool,X10)=s(t_bool,t)|s(t_bool,X10)=s(t_bool,f)),file('i/f/ind_type/ZRECSPACE__ind', aHLu_BOOLu_CASES)).
fof(14, axiom,~(p(s(t_bool,f))),file('i/f/ind_type/ZRECSPACE__ind', aHLu_FALSITY)).
# SZS output end CNFRefutation
