# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_measures_measureu_u_space(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))),X2))))&p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X3),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))),X2)))))))=>p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),h4s_measures_mu_u_space(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))),X2))))))),file('i/f/measure/MEASURE__SPACE__SUBSET__MSPACE', ch4s_measures_MEASUREu_u_SPACEu_u_SUBSETu_u_MSPACE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/measure/MEASURE__SPACE__SUBSET__MSPACE', aHLu_TRUTH)).
fof(5, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/measure/MEASURE__SPACE__SUBSET__MSPACE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X1]:![X12]:![X13]:(p(s(t_bool,h4s_measures_subsetu_u_class(s(t_fun(X1,t_bool),X13),s(t_fun(t_fun(X1,t_bool),t_bool),X12))))<=>![X11]:(p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X11),s(t_fun(t_fun(X1,t_bool),t_bool),X12))))=>p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X11),s(t_fun(X1,t_bool),X13)))))),file('i/f/measure/MEASURE__SPACE__SUBSET__MSPACE', ah4s_measures_subsetu_u_classu_u_def)).
fof(10, axiom,![X1]:![X14]:(p(s(t_bool,h4s_measures_sigmau_u_algebra(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14))))<=>(p(s(t_bool,h4s_measures_algebra(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14))))&![X15]:((p(s(t_bool,h4s_utilu_u_probs_countable(s(t_fun(t_fun(X1,t_bool),t_bool),X15))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(t_fun(X1,t_bool),t_bool),X15),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14)))))))=>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),X15))),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14))))))))),file('i/f/measure/MEASURE__SPACE__SUBSET__MSPACE', ah4s_measures_sigmau_u_algebrau_u_def)).
fof(11, axiom,![X1]:![X2]:(p(s(t_bool,h4s_measures_measureu_u_space(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))),X2))))<=>(p(s(t_bool,h4s_measures_sigmau_u_algebra(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_measures_mu_u_space(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))),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))),X2))))))))&(p(s(t_bool,h4s_measures_positive(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))),X2))))&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))),X2))))))),file('i/f/measure/MEASURE__SPACE__SUBSET__MSPACE', ah4s_measures_measureu_u_spaceu_u_def)).
fof(12, axiom,![X1]:![X9]:![X11]:s(t_fun(X1,t_bool),h4s_measures_space(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),X11),s(t_fun(t_fun(X1,t_bool),t_bool),X9)))))=s(t_fun(X1,t_bool),X11),file('i/f/measure/MEASURE__SPACE__SUBSET__MSPACE', ah4s_measures_spaceu_u_def)).
fof(13, axiom,![X1]:![X9]:![X11]:s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_subsets(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),X11),s(t_fun(t_fun(X1,t_bool),t_bool),X9)))))=s(t_fun(t_fun(X1,t_bool),t_bool),X9),file('i/f/measure/MEASURE__SPACE__SUBSET__MSPACE', ah4s_measures_subsetsu_u_def)).
fof(15, axiom,![X1]:![X14]:(p(s(t_bool,h4s_measures_algebra(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14))))<=>(p(s(t_bool,h4s_measures_subsetu_u_class(s(t_fun(X1,t_bool),h4s_measures_space(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14))),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14))))))&(p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14))))))&(![X20]:(p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X20),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14))))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),h4s_measures_space(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14))),s(t_fun(X1,t_bool),X20))),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14)))))))&![X20]:![X4]:((p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X20),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14))))))&p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X4),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14)))))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),h4s_predu_u_sets_union(s(t_fun(X1,t_bool),X20),s(t_fun(X1,t_bool),X4))),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X14))))))))))),file('i/f/measure/MEASURE__SPACE__SUBSET__MSPACE', ah4s_measures_algebrau_u_def)).
fof(16, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/measure/MEASURE__SPACE__SUBSET__MSPACE', aHLu_BOOLu_CASES)).
fof(18, axiom,~(p(s(t_bool,f))),file('i/f/measure/MEASURE__SPACE__SUBSET__MSPACE', aHLu_FALSITY)).
# SZS output end CNFRefutation
