# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),h4s_utilu_u_probs_schroederu_u_close(s(t_fun(X1,X1),X3),s(t_fun(X1,t_bool),X2)))))),file('i/f/util_prob/SCHROEDER__CLOSE__SUBSET', ch4s_utilu_u_probs_SCHROEDERu_u_CLOSEu_u_SUBSET)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/util_prob/SCHROEDER__CLOSE__SUBSET', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/util_prob/SCHROEDER__CLOSE__SUBSET', aHLu_FALSITY)).
fof(6, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/util_prob/SCHROEDER__CLOSE__SUBSET', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X1]:![X5]:![X2]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X2),s(t_fun(X1,t_bool),X5))))<=>![X4]:(p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X2))))=>p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X5)))))),file('i/f/util_prob/SCHROEDER__CLOSE__SUBSET', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(12, axiom,![X1]:![X4]:![X15]:s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),X15)))=s(t_bool,happ(s(t_fun(X1,t_bool),X15),s(X1,X4))),file('i/f/util_prob/SCHROEDER__CLOSE__SUBSET', ah4s_predu_u_sets_SPECIFICATION)).
fof(13, axiom,![X1]:![X4]:![X2]:![X3]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),h4s_utilu_u_probs_schroederu_u_close(s(t_fun(X1,X1),X3),s(t_fun(X1,t_bool),X2))),s(X1,X4))))<=>?[X16]:p(s(t_bool,h4s_bools_in(s(X1,X4),s(t_fun(X1,t_bool),h4s_arithmetics_funpow(s(t_fun(t_fun(X1,t_bool),t_fun(X1,t_bool)),h4s_predu_u_sets_image(s(t_fun(X1,X1),X3))),s(t_h4s_nums_num,X16),s(t_fun(X1,t_bool),X2))))))),file('i/f/util_prob/SCHROEDER__CLOSE__SUBSET', ah4s_utilu_u_probs_schroederu_u_closeu_u_def)).
fof(14, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f0)),file('i/f/util_prob/SCHROEDER__CLOSE__SUBSET', aHLu_BOOLu_CASES)).
fof(15, axiom,![X1]:![X4]:![X3]:s(X1,h4s_arithmetics_funpow(s(t_fun(X1,X1),X3),s(t_h4s_nums_num,h4s_nums_0),s(X1,X4)))=s(X1,X4),file('i/f/util_prob/SCHROEDER__CLOSE__SUBSET', ah4s_arithmetics_FUNPOW0u_c0)).
# SZS output end CNFRefutation
