# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_measures_countablyu_u_additive(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X3))))&(p(s(t_bool,h4s_bools_in(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X4),s(t_fun(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),t_bool),h4s_utilu_u_probs_funset(s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_measurableu_u_sets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X3))))))))&(![X5]:![X6]:(~(s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,X6))=>p(s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(X1,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X4),s(t_h4s_nums_num,X5))),s(t_fun(X1,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X4),s(t_h4s_nums_num,X6)))))))&(s(t_fun(X1,t_bool),X2)=s(t_fun(X1,t_bool),h4s_predu_u_sets_bigunion(s(t_fun(t_fun(X1,t_bool),t_bool),h4s_predu_u_sets_image(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X4),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ)))))&p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X2),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_measurableu_u_sets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X3))))))))))=>p(s(t_bool,h4s_seqs_sums(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),h4s_combins_o(s(t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real),h4s_measures_measure(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X3))),s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X4))),s(t_h4s_realaxs_real,happ(s(t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real),h4s_measures_measure(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X3))),s(t_fun(X1,t_bool),X2))))))),file('i/f/measure/COUNTABLY__ADDITIVE', ch4s_measures_COUNTABLYu_u_ADDITIVE)).
fof(2, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/measure/COUNTABLY__ADDITIVE', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(18, axiom,![X1]:![X3]:(p(s(t_bool,h4s_measures_countablyu_u_additive(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X3))))<=>![X4]:((p(s(t_bool,h4s_bools_in(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X4),s(t_fun(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),t_bool),h4s_utilu_u_probs_funset(s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_measurableu_u_sets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X3))))))))&(![X5]:![X6]:(~(s(t_h4s_nums_num,X5)=s(t_h4s_nums_num,X6))=>p(s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(X1,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X4),s(t_h4s_nums_num,X5))),s(t_fun(X1,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X4),s(t_h4s_nums_num,X6)))))))&p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),h4s_predu_u_sets_bigunion(s(t_fun(t_fun(X1,t_bool),t_bool),h4s_predu_u_sets_image(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X4),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ))))),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_measurableu_u_sets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X3))))))))=>p(s(t_bool,h4s_seqs_sums(s(t_fun(t_h4s_nums_num,t_h4s_realaxs_real),h4s_combins_o(s(t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real),h4s_measures_measure(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X3))),s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X4))),s(t_h4s_realaxs_real,happ(s(t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real),h4s_measures_measure(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X1,t_bool),t_bool),t_fun(t_fun(X1,t_bool),t_h4s_realaxs_real))),X3))),s(t_fun(X1,t_bool),h4s_predu_u_sets_bigunion(s(t_fun(t_fun(X1,t_bool),t_bool),h4s_predu_u_sets_image(s(t_fun(t_h4s_nums_num,t_fun(X1,t_bool)),X4),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ)))))))))))),file('i/f/measure/COUNTABLY__ADDITIVE', ah4s_measures_countablyu_u_additiveu_u_def)).
# SZS output end CNFRefutation
