# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(t_fun(X1,X2),t_bool),h4s_measures_measurable(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X4),s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))),s(t_fun(t_fun(X1,X2),t_bool),h4s_measures_measurable(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X4),s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),h4s_measures_sigma(s(t_fun(X2,t_bool),h4s_measures_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))),s(t_fun(t_fun(X2,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3)))))))))),file('i/f/measure/MEASURABLE__SUBSET', ch4s_measures_MEASURABLEu_u_SUBSET)).
fof(6, axiom,![X1]:![X5]:![X13]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X13),s(t_fun(X1,t_bool),X5))))<=>![X6]:(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X13))))=>p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X5)))))),file('i/f/measure/MEASURABLE__SUBSET', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(7, axiom,![X2]:![X1]:![X14]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(t_fun(X1,X2),X14),s(t_fun(t_fun(X1,X2),t_bool),h4s_measures_measurable(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X4),s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))))))<=>(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)),X4))))&(p(s(t_bool,h4s_measures_sigmau_u_algebra(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))))&(p(s(t_bool,h4s_bools_in(s(t_fun(X1,X2),X14),s(t_fun(t_fun(X1,X2),t_bool),h4s_utilu_u_probs_funset(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)),X4))),s(t_fun(X2,t_bool),h4s_measures_space(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))))))))&![X13]:(p(s(t_bool,h4s_bools_in(s(t_fun(X2,t_bool),X13),s(t_fun(t_fun(X2,t_bool),t_bool),h4s_measures_subsets(s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),X3))))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X2),X14),s(t_fun(X2,t_bool),X13))),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)),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)),X4))))))))))),file('i/f/measure/MEASURABLE__SUBSET', ah4s_measures_INu_u_MEASURABLE)).
fof(8, axiom,![X1]:![X2]:![X15]:![X14]:![X3]:![X4]:((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)),X4))))&(p(s(t_bool,h4s_measures_subsetu_u_class(s(t_fun(X2,t_bool),X15),s(t_fun(t_fun(X2,t_bool),t_bool),X3))))&(p(s(t_bool,h4s_bools_in(s(t_fun(X1,X2),X14),s(t_fun(t_fun(X1,X2),t_bool),h4s_utilu_u_probs_funset(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)),X4))),s(t_fun(X2,t_bool),X15))))))&![X13]:(p(s(t_bool,h4s_bools_in(s(t_fun(X2,t_bool),X13),s(t_fun(t_fun(X2,t_bool),t_bool),X3))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X2),X14),s(t_fun(X2,t_bool),X13))),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)),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)),X4))))))))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X1,X2),X14),s(t_fun(t_fun(X1,X2),t_bool),h4s_measures_measurable(s(t_h4s_pairs_prod(t_fun(X1,t_bool),t_fun(t_fun(X1,t_bool),t_bool)),X4),s(t_h4s_pairs_prod(t_fun(X2,t_bool),t_fun(t_fun(X2,t_bool),t_bool)),h4s_measures_sigma(s(t_fun(X2,t_bool),X15),s(t_fun(t_fun(X2,t_bool),t_bool),X3))))))))),file('i/f/measure/MEASURABLE__SUBSET', ah4s_measures_MEASURABLEu_u_SIGMA)).
fof(9, axiom,![X1]:![X16]:(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)),X16))))<=>(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)),X16))),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)),X16))))))&(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)),X16))))))&(![X13]:(p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X13),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)),X16))))))=>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)),X16))),s(t_fun(X1,t_bool),X13))),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)),X16)))))))&![X17]:((p(s(t_bool,h4s_utilu_u_probs_countable(s(t_fun(t_fun(X1,t_bool),t_bool),X17))))&p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(t_fun(X1,t_bool),t_bool),X17),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)),X16)))))))=>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),X17))),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)),X16))))))))))),file('i/f/measure/MEASURABLE__SUBSET', ah4s_measures_SIGMAu_u_ALGEBRA)).
# SZS output end CNFRefutation
