# 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(31, axiom,![X2]:![X9]:~(p(s(t_bool,h4s_bools_in(s(X2,X9),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(39, axiom,![X2]:![X12]:![X3]:(s(t_fun(X2,t_bool),X3)=s(t_fun(X2,t_bool),X12)<=>![X9]:s(t_bool,h4s_bools_in(s(X2,X9),s(t_fun(X2,t_bool),X3)))=s(t_bool,h4s_bools_in(s(X2,X9),s(t_fun(X2,t_bool),X12)))),file('i/f/util_prob/FUNSET__EMPTY', ah4s_predu_u_sets_EXTENSION)).
fof(40, axiom,![X2]:![X9]:![X21]:s(t_bool,h4s_bools_in(s(X2,X9),s(t_fun(X2,t_bool),X21)))=s(t_bool,happ(s(t_fun(X2,t_bool),X21),s(X2,X9))),file('i/f/util_prob/FUNSET__EMPTY', ah4s_predu_u_sets_SPECIFICATION)).
fof(52, axiom,~(p(s(t_bool,f0))),file('i/f/util_prob/FUNSET__EMPTY', aHLu_FALSITY)).
fof(56, axiom,![X12]:(s(t_bool,X12)=s(t_bool,f0)<=>~(p(s(t_bool,X12)))),file('i/f/util_prob/FUNSET__EMPTY', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(67, axiom,![X2]:![X1]:![X4]:![X20]:![X21]:(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),X21),s(t_fun(X1,t_bool),X20))))))<=>![X9]:(p(s(t_bool,h4s_bools_in(s(X2,X9),s(t_fun(X2,t_bool),X21))))=>p(s(t_bool,h4s_bools_in(s(X1,happ(s(t_fun(X2,X1),X4),s(X2,X9))),s(t_fun(X1,t_bool),X20)))))),file('i/f/util_prob/FUNSET__EMPTY', ah4s_utilu_u_probs_INu_u_FUNSET)).
fof(68, axiom,![X2]:![X1]:![X20]:![X21]:![X9]:(p(s(t_bool,happ(s(t_fun(t_fun(X2,X1),t_bool),h4s_utilu_u_probs_funset(s(t_fun(X2,t_bool),X21),s(t_fun(X1,t_bool),X20))),s(t_fun(X2,X1),X9))))<=>![X27]:(p(s(t_bool,h4s_bools_in(s(X2,X27),s(t_fun(X2,t_bool),X21))))=>p(s(t_bool,h4s_bools_in(s(X1,happ(s(t_fun(X2,X1),X9),s(X2,X27))),s(t_fun(X1,t_bool),X20)))))),file('i/f/util_prob/FUNSET__EMPTY', ah4s_utilu_u_probs_FUNSETu_u_def)).
# SZS output end CNFRefutation
