# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_bools_in(s(t_fun(X1,X2),X3),s(t_fun(t_fun(X1,X2),t_bool),h4s_utilu_u_probs_funset(s(t_fun(X1,t_bool),X5),s(t_fun(X2,t_bool),X4))))))<=>![X6]:(p(s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X5))))=>p(s(t_bool,h4s_bools_in(s(X2,happ(s(t_fun(X1,X2),X3),s(X1,X6))),s(t_fun(X2,t_bool),X4)))))),file('i/f/util_prob/IN__FUNSET', ch4s_utilu_u_probs_INu_u_FUNSET)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/util_prob/IN__FUNSET', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/util_prob/IN__FUNSET', aHLu_FALSITY)).
fof(8, axiom,![X1]:![X2]:![X4]:![X5]:![X6]:(p(s(t_bool,happ(s(t_fun(t_fun(X1,X2),t_bool),h4s_utilu_u_probs_funset(s(t_fun(X1,t_bool),X5),s(t_fun(X2,t_bool),X4))),s(t_fun(X1,X2),X6))))<=>![X13]:(p(s(t_bool,h4s_bools_in(s(X1,X13),s(t_fun(X1,t_bool),X5))))=>p(s(t_bool,h4s_bools_in(s(X2,happ(s(t_fun(X1,X2),X6),s(X1,X13))),s(t_fun(X2,t_bool),X4)))))),file('i/f/util_prob/IN__FUNSET', ah4s_utilu_u_probs_FUNSETu_u_def)).
fof(11, axiom,![X1]:![X6]:![X5]:s(t_bool,h4s_bools_in(s(X1,X6),s(t_fun(X1,t_bool),X5)))=s(t_bool,happ(s(t_fun(X1,t_bool),X5),s(X1,X6))),file('i/f/util_prob/IN__FUNSET', ah4s_predu_u_sets_SPECIFICATION)).
fof(12, axiom,![X17]:(s(t_bool,X17)=s(t_bool,t)|s(t_bool,X17)=s(t_bool,f0)),file('i/f/util_prob/IN__FUNSET', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
