# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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_increasing(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__INCREASING', ch4s_measures_MEASUREu_u_SPACEu_u_INCREASING)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/measure/MEASURE__SPACE__INCREASING', aHLu_TRUTH)).
fof(5, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/measure/MEASURE__SPACE__INCREASING', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X1]:![X2]:((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)),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_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))))))=>p(s(t_bool,h4s_measures_increasing(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__INCREASING', ah4s_measures_ADDITIVEu_u_INCREASING)).
fof(8, axiom,![X1]:![X7]:(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)),X7))))<=>(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)),X7))))&![X8]:((p(s(t_bool,h4s_utilu_u_probs_countable(s(t_fun(t_fun(X1,t_bool),t_bool),X8))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(t_fun(X1,t_bool),t_bool),X8),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)),X7)))))))=>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),X8))),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)),X7))))))))),file('i/f/measure/MEASURE__SPACE__INCREASING', ah4s_measures_sigmau_u_algebrau_u_def)).
fof(9, 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__INCREASING', ah4s_measures_measureu_u_spaceu_u_def)).
fof(10, 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_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__INCREASING', ah4s_measures_MEASUREu_u_SPACEu_u_ADDITIVE)).
fof(11, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/measure/MEASURE__SPACE__INCREASING', aHLu_BOOLu_CASES)).
fof(12, axiom,~(p(s(t_bool,f))),file('i/f/measure/MEASURE__SPACE__INCREASING', aHLu_FALSITY)).
# SZS output end CNFRefutation
