# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:![X8]:((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))),X4))))&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))),X4)))=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))),X4))))))=>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_conditionalu_u_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))),X4),s(t_fun(X1,X2),X8),s(t_fun(X1,X3),X7),s(t_fun(X2,t_bool),X6),s(t_fun(X3,t_bool),X5))))))),file('i/f/probability/conditional__distribution__pos', ch4s_probabilitys_conditionalu_u_distributionu_u_pos)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/probability/conditional__distribution__pos', aHLu_TRUTH)).
fof(7, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)<=>p(s(t_bool,X9))),file('i/f/probability/conditional__distribution__pos', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X2]:![X1]:![X3]:![X4]:![X5]:![X6]:![X7]:![X8]:s(t_h4s_realaxs_real,h4s_probabilitys_conditionalu_u_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))),X4),s(t_fun(X1,X2),X8),s(t_fun(X1,X3),X7),s(t_fun(X2,t_bool),X6),s(t_fun(X3,t_bool),X5)))=s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_probabilitys_jointu_u_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))),X4),s(t_fun(X1,X2),X8),s(t_fun(X1,X3),X7),s(t_fun(t_h4s_pairs_prod(X2,X3),t_bool),h4s_predu_u_sets_cross(s(t_fun(X2,t_bool),X6),s(t_fun(X3,t_bool),X5))))),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))),X4),s(t_fun(X1,X3),X7),s(t_fun(X3,t_bool),X5))))),file('i/f/probability/conditional__distribution__pos', ah4s_probabilitys_conditionalu_u_distributionu_u_def)).
fof(12, axiom,![X1]:![X2]:![X3]:![X4]:![X6]:![X7]:![X8]:((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))),X4))))&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))),X4)))=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))),X4))))))=>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_jointu_u_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))),X4),s(t_fun(X1,X2),X8),s(t_fun(X1,X3),X7),s(t_fun(t_h4s_pairs_prod(X2,X3),t_bool),X6))))))),file('i/f/probability/conditional__distribution__pos', ah4s_probabilitys_jointu_u_distributionu_u_pos)).
fof(13, axiom,![X1]:![X2]:![X4]:![X6]:![X8]:((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))),X4))))&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))),X4)))=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))),X4))))))=>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))),X4),s(t_fun(X1,X2),X8),s(t_fun(X2,t_bool),X6))))))),file('i/f/probability/conditional__distribution__pos', ah4s_probabilitys_distributionu_u_pos)).
fof(14, axiom,![X15]:![X10]:s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,X10),s(t_h4s_realaxs_real,X15)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X10),s(t_h4s_realaxs_real,h4s_realaxs_inv(s(t_h4s_realaxs_real,X15))))),file('i/f/probability/conditional__distribution__pos', ah4s_reals_realu_u_div)).
fof(15, axiom,![X15]:![X10]:((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,X10))))&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,X15)))))=>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_realaxs_realu_u_mul(s(t_h4s_realaxs_real,X10),s(t_h4s_realaxs_real,X15))))))),file('i/f/probability/conditional__distribution__pos', ah4s_reals_REALu_u_LEu_u_MUL)).
fof(16, axiom,![X10]:(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,X10))))=>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_realaxs_inv(s(t_h4s_realaxs_real,X10))))))),file('i/f/probability/conditional__distribution__pos', ah4s_reals_REALu_u_LEu_u_INV)).
# SZS output end CNFRefutation
