# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(![X3]:![X4]:s(t_h4s_realaxs_real,happ(s(t_fun(X1,t_h4s_realaxs_real),happ(s(t_fun(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))),t_fun(X1,t_h4s_realaxs_real)),X2),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(X1,X4)))=s(t_h4s_realaxs_real,h4s_probabilitys_prob(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_insert(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))))=>![X3]:((p(s(t_bool,h4s_probabilitys_probu_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))),X3))))&(![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_probabilitys_pu_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))),X3))))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_probabilitys_events(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_predu_u_sets_finite(s(t_fun(X1,t_bool),h4s_probabilitys_pu_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))),X3))))))))=>s(t_h4s_realaxs_real,h4s_realu_u_sigmas_realu_u_sumu_u_image(s(t_fun(X1,t_h4s_realaxs_real),happ(s(t_fun(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))),t_fun(X1,t_h4s_realaxs_real)),X2),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_probabilitys_pu_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))),X3)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),file('i/f/probability/PROB__REAL__SUM__IMAGE__SPACE', ch4s_probabilitys_PROBu_u_REALu_u_SUMu_u_IMAGEu_u_SPACE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/probability/PROB__REAL__SUM__IMAGE__SPACE', aHLu_TRUTH)).
fof(10, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/probability/PROB__REAL__SUM__IMAGE__SPACE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X1]:![X3]:(p(s(t_bool,h4s_probabilitys_probu_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))),X3))))=>s(t_h4s_realaxs_real,h4s_probabilitys_prob(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_probabilitys_pu_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))),X3)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))),file('i/f/probability/PROB__REAL__SUM__IMAGE__SPACE', ah4s_probabilitys_PROBu_u_UNIV)).
fof(14, axiom,![X1]:![X3]:(p(s(t_bool,h4s_probabilitys_probu_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))),X3))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),h4s_probabilitys_pu_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))),X3))),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_probabilitys_events(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))))))),file('i/f/probability/PROB__REAL__SUM__IMAGE__SPACE', ah4s_probabilitys_EVENTSu_u_SPACE)).
fof(15, axiom,![X1]:![X2]:(![X3]:![X4]:s(t_h4s_realaxs_real,happ(s(t_fun(X1,t_h4s_realaxs_real),happ(s(t_fun(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))),t_fun(X1,t_h4s_realaxs_real)),X2),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(X1,X4)))=s(t_h4s_realaxs_real,h4s_probabilitys_prob(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_insert(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))))=>![X12]:![X3]:((p(s(t_bool,h4s_probabilitys_probu_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))),X3))))&(p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X12),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_probabilitys_events(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(X1,X4),s(t_fun(X1,t_bool),X12))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),h4s_predu_u_sets_insert(s(X1,X4),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_probabilitys_events(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_predu_u_sets_finite(s(t_fun(X1,t_bool),X12)))))))=>s(t_h4s_realaxs_real,h4s_probabilitys_prob(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),X12)))=s(t_h4s_realaxs_real,h4s_realu_u_sigmas_realu_u_sumu_u_image(s(t_fun(X1,t_h4s_realaxs_real),happ(s(t_fun(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))),t_fun(X1,t_h4s_realaxs_real)),X2),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),X12))))),file('i/f/probability/PROB__REAL__SUM__IMAGE__SPACE', ah4s_probabilitys_PROBu_u_REALu_u_SUMu_u_IMAGE)).
# SZS output end CNFRefutation
