# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:((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_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)))=s(t_fun(t_fun(X1,t_bool),t_bool),h4s_predu_u_sets_pow(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_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_realaxs_real,h4s_probabilitys_distribution(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,X2),X5),s(t_fun(X2,t_bool),X4))))))),file('i/f/probability/distribution__pos', ch4s_probabilitys_distributionu_u_pos)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/probability/distribution__pos', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/probability/distribution__pos', aHLu_FALSITY)).
fof(5, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/probability/distribution__pos', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(8, axiom,![X1]:![X6]:![X14]:p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X6),s(t_fun(X1,t_bool),X14))),s(t_fun(X1,t_bool),X14)))),file('i/f/probability/distribution__pos', ah4s_predu_u_sets_INTERu_u_SUBSETu_c1)).
fof(9, axiom,![X1]:![X14]:![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),X14),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_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),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),X14))))))),file('i/f/probability/distribution__pos', ah4s_probabilitys_PROBu_u_POSITIVE)).
fof(11, axiom,![X1]:![X2]:![X3]:![X5]:![X13]:s(t_h4s_realaxs_real,h4s_probabilitys_distribution(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(X2,X1),X5),s(t_fun(X1,t_bool),X13)))=s(t_h4s_realaxs_real,h4s_probabilitys_prob(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(X2,t_bool),h4s_predu_u_sets_inter(s(t_fun(X2,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X2,X1),X5),s(t_fun(X1,t_bool),X13))),s(t_fun(X2,t_bool),h4s_probabilitys_pu_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/probability/distribution__pos', ah4s_probabilitys_distributionu_u_def)).
fof(12, axiom,![X1]:![X15]:![X16]:s(t_bool,h4s_bools_in(s(t_fun(X1,t_bool),X16),s(t_fun(t_fun(X1,t_bool),t_bool),h4s_predu_u_sets_pow(s(t_fun(X1,t_bool),X15)))))=s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X16),s(t_fun(X1,t_bool),X15))),file('i/f/probability/distribution__pos', ah4s_predu_u_sets_INu_u_POW)).
fof(13, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/probability/distribution__pos', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
