# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/probability/PROB__LE__1', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/probability/PROB__LE__1', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/probability/PROB__LE__1', aHLu_BOOLu_CASES)).
fof(14, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/probability/PROB__LE__1', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(15, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/probability/PROB__LE__1', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(39, axiom,![X8]:![X6]:s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X8)))=s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X8))))),file('i/f/probability/PROB__LE__1', ah4s_reals_realu_u_sub0)).
fof(53, axiom,![X8]:![X6]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,X8)))=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_add(s(t_h4s_realaxs_real,X6),s(t_h4s_realaxs_real,X8))))),file('i/f/probability/PROB__LE__1', ah4s_reals_REALu_u_LEu_u_LNEG)).
fof(54, axiom,![X8]:![X6]:s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X6))),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,X8)))))=s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,X8),s(t_h4s_realaxs_real,X6))),file('i/f/probability/PROB__LE__1', ah4s_reals_REALu_u_LEu_u_NEG2)).
fof(59, axiom,![X7]:![X20]:![X16]:((p(s(t_bool,h4s_probabilitys_probu_u_space(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16))))&p(s(t_bool,h4s_bools_in(s(t_fun(X7,t_bool),X20),s(t_fun(t_fun(X7,t_bool),t_bool),h4s_probabilitys_events(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16)))))))=>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(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16),s(t_fun(X7,t_bool),X20))))))),file('i/f/probability/PROB__LE__1', ah4s_probabilitys_PROBu_u_POSITIVE)).
fof(60, axiom,![X7]:![X20]:![X16]:((p(s(t_bool,h4s_probabilitys_probu_u_space(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16))))&p(s(t_bool,h4s_bools_in(s(t_fun(X7,t_bool),X20),s(t_fun(t_fun(X7,t_bool),t_bool),h4s_probabilitys_events(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16)))))))=>s(t_h4s_realaxs_real,h4s_probabilitys_prob(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16),s(t_fun(X7,t_bool),h4s_predu_u_sets_diff(s(t_fun(X7,t_bool),h4s_probabilitys_pu_u_space(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16))),s(t_fun(X7,t_bool),X20)))))=s(t_h4s_realaxs_real,h4s_reals_realu_u_sub(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))))))),s(t_h4s_realaxs_real,h4s_probabilitys_prob(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16),s(t_fun(X7,t_bool),X20)))))),file('i/f/probability/PROB__LE__1', ah4s_probabilitys_PROBu_u_COMPL)).
fof(61, axiom,![X7]:![X20]:![X16]:((p(s(t_bool,h4s_probabilitys_probu_u_space(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16))))&p(s(t_bool,h4s_bools_in(s(t_fun(X7,t_bool),X20),s(t_fun(t_fun(X7,t_bool),t_bool),h4s_probabilitys_events(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16)))))))=>p(s(t_bool,h4s_bools_in(s(t_fun(X7,t_bool),h4s_predu_u_sets_diff(s(t_fun(X7,t_bool),h4s_probabilitys_pu_u_space(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16))),s(t_fun(X7,t_bool),X20))),s(t_fun(t_fun(X7,t_bool),t_bool),h4s_probabilitys_events(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16))))))),file('i/f/probability/PROB__LE__1', ah4s_probabilitys_EVENTSu_u_COMPL)).
fof(62, conjecture,![X7]:![X20]:![X16]:((p(s(t_bool,h4s_probabilitys_probu_u_space(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16))))&p(s(t_bool,h4s_bools_in(s(t_fun(X7,t_bool),X20),s(t_fun(t_fun(X7,t_bool),t_bool),h4s_probabilitys_events(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16)))))))=>p(s(t_bool,h4s_reals_realu_u_lte(s(t_h4s_realaxs_real,h4s_probabilitys_prob(s(t_h4s_pairs_prod(t_fun(X7,t_bool),t_h4s_pairs_prod(t_fun(t_fun(X7,t_bool),t_bool),t_fun(t_fun(X7,t_bool),t_h4s_realaxs_real))),X16),s(t_fun(X7,t_bool),X20))),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__LE__1', ch4s_probabilitys_PROBu_u_LEu_u_1)).
# SZS output end CNFRefutation
