# 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),happ(s(t_fun(t_bool,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,![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(32, axiom,![X1]:![X6]:![X22]:(p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(X1,t_bool),X22),s(t_fun(X1,t_bool),X6))))<=>![X3]:(p(s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X22))))=>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(33, 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(38, axiom,![X26]:![X1]:![X3]:![X27]:s(X1,happ(s(t_fun(X26,X1),happ(s(t_fun(X1,t_fun(X26,X1)),h4s_combins_k),s(X1,X3))),s(X26,X27)))=s(X1,X3),file('i/f/util_prob/SUBSET__K', ah4s_combins_Ku_u_DEF)).
fof(40, axiom,![X1]:![X6]:![X22]:(s(t_fun(X1,t_bool),X22)=s(t_fun(X1,t_bool),X6)<=>![X3]:s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X22)))=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_EXTENSION)).
fof(41, axiom,![X1]:![X3]:![X14]:s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X14)))=s(t_bool,happ(s(t_fun(X1,t_bool),X14),s(X1,X3))),file('i/f/util_prob/SUBSET__K', ah4s_predu_u_sets_SPECIFICATION)).
# SZS output end CNFRefutation
