# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_fun(X2,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X2,X1),X3),s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)))=s(t_fun(X2,t_bool),h4s_predu_u_sets_empty),file('i/f/util_prob/PREIMAGE__EMPTY', ch4s_utilu_u_probs_PREIMAGEu_u_EMPTY)).
fof(10, axiom,![X4]:(s(t_bool,f0)=s(t_bool,X4)<=>~(p(s(t_bool,X4)))),file('i/f/util_prob/PREIMAGE__EMPTY', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(11, axiom,![X2]:![X4]:![X8]:(s(t_fun(X2,t_bool),X8)=s(t_fun(X2,t_bool),X4)<=>![X7]:s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),X8)))=s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),X4)))),file('i/f/util_prob/PREIMAGE__EMPTY', ah4s_predu_u_sets_EXTENSION)).
fof(12, axiom,![X2]:![X7]:~(p(s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),h4s_predu_u_sets_empty))))),file('i/f/util_prob/PREIMAGE__EMPTY', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(14, axiom,![X2]:![X1]:![X7]:![X8]:![X3]:s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X2,X1),X3),s(t_fun(X1,t_bool),X8)))))=s(t_bool,h4s_bools_in(s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X7))),s(t_fun(X1,t_bool),X8))),file('i/f/util_prob/PREIMAGE__EMPTY', ah4s_utilu_u_probs_INu_u_PREIMAGE)).
# SZS output end CNFRefutation
