# 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),X3),s(t_fun(X1,t_bool),h4s_combins_k(s(t_bool,X2))))))<=>(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))|p(s(t_bool,X2)))),file('i/f/util_prob/SUBSET__K', ch4s_utilu_u_probs_SUBSETu_u_K)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/util_prob/SUBSET__K', 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/SUBSET__K', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(28, 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/SUBSET__K', ah4s_predu_u_sets_SUBSETu_u_DEF)).
fof(29, axiom,![X1]:![X3]:~(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/util_prob/SUBSET__K', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(30, 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/SUBSET__K', ah4s_combins_Ku_u_DEF)).
fof(31, 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/SUBSET__K', ah4s_predu_u_sets_SPECIFICATION)).
fof(33, axiom,p(s(t_bool,t)),file('i/f/util_prob/SUBSET__K', aHLu_TRUTH)).
fof(35, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/util_prob/SUBSET__K', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
