# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_fun(t_fun(X1,X2),t_bool),h4s_utilu_u_probs_funset(s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),s(t_fun(X2,t_bool),X3)))=s(t_fun(t_fun(X1,X2),t_bool),h4s_predu_u_sets_univ),file('i/f/util_prob/EMPTY__FUNSET', ch4s_utilu_u_probs_EMPTYu_u_FUNSET)).
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/EMPTY__FUNSET', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(7, axiom,![X1]:![X7]:p(s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),h4s_predu_u_sets_univ)))),file('i/f/util_prob/EMPTY__FUNSET', ah4s_predu_u_sets_INu_u_UNIV)).
fof(8, axiom,![X1]:![X6]:![X3]:(s(t_fun(X1,t_bool),X3)=s(t_fun(X1,t_bool),X6)<=>![X7]:s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X3)))=s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X6)))),file('i/f/util_prob/EMPTY__FUNSET', ah4s_predu_u_sets_EXTENSION)).
fof(9, axiom,![X1]:![X2]:![X12]:![X13]:![X14]:(p(s(t_bool,h4s_bools_in(s(t_fun(X1,X2),X12),s(t_fun(t_fun(X1,X2),t_bool),h4s_utilu_u_probs_funset(s(t_fun(X1,t_bool),X14),s(t_fun(X2,t_bool),X13))))))<=>![X7]:(p(s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),X14))))=>p(s(t_bool,h4s_bools_in(s(X2,happ(s(t_fun(X1,X2),X12),s(X1,X7))),s(t_fun(X2,t_bool),X13)))))),file('i/f/util_prob/EMPTY__FUNSET', ah4s_utilu_u_probs_INu_u_FUNSET)).
fof(10, axiom,![X1]:![X7]:~(p(s(t_bool,h4s_bools_in(s(X1,X7),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty))))),file('i/f/util_prob/EMPTY__FUNSET', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
# SZS output end CNFRefutation
