# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(t_fun(X2,X1),X4),s(t_fun(t_fun(X2,X1),t_bool),h4s_utilu_u_probs_funset(s(t_fun(X2,t_bool),X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))))<=>s(t_fun(X2,t_bool),X3)=s(t_fun(X2,t_bool),h4s_predu_u_sets_empty)),file('i/f/util_prob/FUNSET__EMPTY', ch4s_utilu_u_probs_FUNSETu_u_EMPTY)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/util_prob/FUNSET__EMPTY', aHLu_FALSITY)).
fof(11, axiom,![X5]:(s(t_bool,f0)=s(t_bool,X5)<=>~(p(s(t_bool,X5)))),file('i/f/util_prob/FUNSET__EMPTY', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(14, axiom,![X2]:![X5]:![X3]:(s(t_fun(X2,t_bool),X3)=s(t_fun(X2,t_bool),X5)<=>![X8]:s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X3)))=s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X5)))),file('i/f/util_prob/FUNSET__EMPTY', ah4s_predu_u_sets_EXTENSION)).
fof(15, axiom,![X2]:![X8]:~(p(s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),h4s_predu_u_sets_empty))))),file('i/f/util_prob/FUNSET__EMPTY', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(17, axiom,![X2]:![X1]:![X4]:![X16]:![X17]:(p(s(t_bool,h4s_bools_in(s(t_fun(X2,X1),X4),s(t_fun(t_fun(X2,X1),t_bool),h4s_utilu_u_probs_funset(s(t_fun(X2,t_bool),X17),s(t_fun(X1,t_bool),X16))))))<=>![X8]:(p(s(t_bool,h4s_bools_in(s(X2,X8),s(t_fun(X2,t_bool),X17))))=>p(s(t_bool,h4s_bools_in(s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X8))),s(t_fun(X1,t_bool),X16)))))),file('i/f/util_prob/FUNSET__EMPTY', ah4s_utilu_u_probs_INu_u_FUNSET)).
# SZS output end CNFRefutation
