# 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(3, axiom,![X8]:![X9]:((p(s(t_bool,X9))=>p(s(t_bool,X8)))=>((p(s(t_bool,X8))=>p(s(t_bool,X9)))=>s(t_bool,X9)=s(t_bool,X8))),file('i/f/util_prob/PREIMAGE__EMPTY', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(38, 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(45, axiom,![X2]:![X13]:![X24]:(s(t_fun(X2,t_bool),X24)=s(t_fun(X2,t_bool),X13)<=>![X7]:s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),X24)))=s(t_bool,h4s_bools_in(s(X2,X7),s(t_fun(X2,t_bool),X13)))),file('i/f/util_prob/PREIMAGE__EMPTY', ah4s_predu_u_sets_EXTENSION)).
fof(48, axiom,![X2]:![X1]:![X7]:![X24]:![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),X24)))))=s(t_bool,h4s_bools_in(s(X1,happ(s(t_fun(X2,X1),X3),s(X2,X7))),s(t_fun(X1,t_bool),X24))),file('i/f/util_prob/PREIMAGE__EMPTY', ah4s_utilu_u_probs_INu_u_PREIMAGE)).
# SZS output end CNFRefutation
