# 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),h4s_combins_k(s(t_bool,X3))),s(t_fun(X1,t_bool),X2))))<=>(~(p(s(t_bool,X3)))|p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),h4s_predu_u_sets_univ),s(t_fun(X1,t_bool),X2)))))),file('i/f/util_prob/K__SUBSET', ch4s_utilu_u_probs_Ku_u_SUBSET)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/util_prob/K__SUBSET', aHLu_FALSITY)).
fof(3, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/util_prob/K__SUBSET', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(27, axiom,![X1]:![X6]:![X21]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X21),s(t_fun(X1,t_bool),X6))))<=>![X3]:(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X21))))=>p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X6)))))),file('i/f/util_prob/K__SUBSET', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(28, axiom,![X22]:![X1]:![X3]:![X23]:s(X1,happ(s(t_fun(X22,X1),h4s_combins_k(s(X1,X3))),s(X22,X23)))=s(X1,X3),file('i/f/util_prob/K__SUBSET', ah4s_combins_Ku_u_DEF)).
fof(29, axiom,![X1]:![X3]:![X7]:s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X7)))=s(t_bool,happ(s(t_fun(X1,t_bool),X7),s(X1,X3))),file('i/f/util_prob/K__SUBSET', ah4s_predu_u_sets_SPECIFICATION)).
fof(30, axiom,![X1]:![X3]:p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_univ)))),file('i/f/util_prob/K__SUBSET', ah4s_predu_u_sets_INu_u_UNIV)).
fof(31, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/util_prob/K__SUBSET', aHLu_BOOLu_CASES)).
fof(32, axiom,p(s(t_bool,t)),file('i/f/util_prob/K__SUBSET', aHLu_TRUTH)).
# SZS output end CNFRefutation
