# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_measures_measureu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))&s(t_fun(t_fun(X2,t_bool),t_bool),h4s_measures_measurableu_u_sets(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3)))=s(t_fun(t_fun(X2,t_bool),t_bool),h4s_predu_u_sets_pow(s(t_fun(X2,t_bool),h4s_measures_mu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X2,X1),X4),s(t_fun(t_fun(X2,X1),t_bool),h4s_measures_measurable(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),h4s_pairs_u_2c(s(t_fun(X2,t_bool),h4s_measures_mu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))),s(t_fun(t_fun(X2,t_bool),t_bool),h4s_measures_measurableu_u_sets(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),h4s_pairs_u_2c(s(t_fun(X1,t_bool),h4s_predu_u_sets_image(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),h4s_measures_mu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_predu_u_sets_pow(s(t_fun(X1,t_bool),h4s_predu_u_sets_image(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),h4s_measures_mu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))))))))))))),file('i/f/measure/MEASURABLE__POW__TO__POW__IMAGE', ch4s_measures_MEASURABLEu_u_POWu_u_TOu_u_POWu_u_IMAGE)).
fof(6, axiom,![X1]:![X2]:![X12]:![X3]:![X4]:((p(s(t_bool,h4s_measures_measureu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))&(p(s(t_bool,h4s_bools_in(s(t_fun(X2,X1),X4),s(t_fun(t_fun(X2,X1),t_bool),h4s_measures_measurable(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),h4s_pairs_u_2c(s(t_fun(X2,t_bool),h4s_measures_mu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))),s(t_fun(t_fun(X2,t_bool),t_bool),h4s_measures_measurableu_u_sets(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),h4s_pairs_u_2c(s(t_fun(X1,t_bool),X12),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_predu_u_sets_pow(s(t_fun(X1,t_bool),X12))))))))))&~(s(t_fun(X1,t_bool),X12)=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X2,X1),X4),s(t_fun(t_fun(X2,X1),t_bool),h4s_measures_measurable(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),h4s_pairs_u_2c(s(t_fun(X2,t_bool),h4s_measures_mu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))),s(t_fun(t_fun(X2,t_bool),t_bool),h4s_measures_measurableu_u_sets(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),h4s_pairs_u_2c(s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X12),s(t_fun(X1,t_bool),h4s_predu_u_sets_image(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),h4s_measures_mu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))))),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_predu_u_sets_pow(s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X12),s(t_fun(X1,t_bool),h4s_predu_u_sets_image(s(t_fun(X2,X1),X4),s(t_fun(X2,t_bool),h4s_measures_mu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))))))))))))))),file('i/f/measure/MEASURABLE__POW__TO__POW__IMAGE', ah4s_measures_MEASURABLEu_u_RANGEu_u_REDUCE)).
fof(7, axiom,![X2]:![X1]:![X3]:![X4]:((p(s(t_bool,h4s_measures_measureu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))&s(t_fun(t_fun(X2,t_bool),t_bool),h4s_measures_measurableu_u_sets(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3)))=s(t_fun(t_fun(X2,t_bool),t_bool),h4s_predu_u_sets_pow(s(t_fun(X2,t_bool),h4s_measures_mu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X2,X1),X4),s(t_fun(t_fun(X2,X1),t_bool),h4s_measures_measurable(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),h4s_pairs_u_2c(s(t_fun(X2,t_bool),h4s_measures_mu_u_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))),s(t_fun(t_fun(X2,t_bool),t_bool),h4s_measures_measurableu_u_sets(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X2,t_bool),t_bool),t_fun(t_fun(X2,t_bool),t_h4s_realaxs_real))),X3))))),s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),h4s_pairs_u_2c(s(t_fun(X1,t_bool),h4s_predu_u_sets_univ),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_predu_u_sets_pow(s(t_fun(X1,t_bool),h4s_predu_u_sets_univ))))))))))),file('i/f/measure/MEASURABLE__POW__TO__POW__IMAGE', ah4s_measures_MEASURABLEu_u_POWu_u_TOu_u_POW)).
fof(8, axiom,![X2]:![X12]:s(t_fun(X2,t_bool),h4s_predu_u_sets_inter(s(t_fun(X2,t_bool),h4s_predu_u_sets_univ),s(t_fun(X2,t_bool),X12)))=s(t_fun(X2,t_bool),X12),file('i/f/measure/MEASURABLE__POW__TO__POW__IMAGE', ah4s_predu_u_sets_INTERu_u_UNIVu_c0)).
fof(9, axiom,![X2]:~(s(t_fun(X2,t_bool),h4s_predu_u_sets_univ)=s(t_fun(X2,t_bool),h4s_predu_u_sets_empty)),file('i/f/measure/MEASURABLE__POW__TO__POW__IMAGE', ah4s_utilu_u_probs_UNIVu_u_NEQu_u_EMPTY)).
# SZS output end CNFRefutation
