# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X2),X5),s(t_fun(X2,t_bool),h4s_predu_u_sets_compl(s(t_fun(X2,t_bool),X3))))),s(t_fun(X1,t_bool),X4)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X2),X5),s(t_fun(X2,t_bool),X3))))),file('i/f/util_prob/PREIMAGE__COMPL__INTER', ch4s_utilu_u_probs_PREIMAGEu_u_COMPLu_u_INTER)).
fof(4, axiom,![X1]:![X2]:![X3]:![X8]:![X5]:s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X2),X5),s(t_fun(X2,t_bool),h4s_predu_u_sets_diff(s(t_fun(X2,t_bool),X8),s(t_fun(X2,t_bool),X3)))))=s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X2),X5),s(t_fun(X2,t_bool),X8))),s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X2),X5),s(t_fun(X2,t_bool),X3))))),file('i/f/util_prob/PREIMAGE__COMPL__INTER', ah4s_utilu_u_probs_PREIMAGEu_u_DIFF)).
fof(5, axiom,![X1]:![X3]:![X8]:![X9]:s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),X8),s(t_fun(X1,t_bool),X3))),s(t_fun(X1,t_bool),X9)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X8),s(t_fun(X1,t_bool),X9))),s(t_fun(X1,t_bool),X3))),file('i/f/util_prob/PREIMAGE__COMPL__INTER', ah4s_utilu_u_probs_DIFFu_u_INTER)).
fof(6, axiom,![X2]:![X1]:![X5]:s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X2),X5),s(t_fun(X2,t_bool),h4s_predu_u_sets_univ)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_univ),file('i/f/util_prob/PREIMAGE__COMPL__INTER', ah4s_utilu_u_probs_PREIMAGEu_u_UNIV)).
fof(16, axiom,![X1]:![X8]:s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),h4s_predu_u_sets_univ),s(t_fun(X1,t_bool),X8)))=s(t_fun(X1,t_bool),X8),file('i/f/util_prob/PREIMAGE__COMPL__INTER', ah4s_predu_u_sets_INTERu_u_UNIVu_c0)).
fof(17, axiom,![X1]:![X8]:s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X8),s(t_fun(X1,t_bool),h4s_predu_u_sets_univ)))=s(t_fun(X1,t_bool),X8),file('i/f/util_prob/PREIMAGE__COMPL__INTER', ah4s_predu_u_sets_INTERu_u_UNIVu_c1)).
fof(18, axiom,![X1]:![X13]:s(t_fun(X1,t_bool),h4s_predu_u_sets_compl(s(t_fun(X1,t_bool),X13)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_diff(s(t_fun(X1,t_bool),h4s_predu_u_sets_univ),s(t_fun(X1,t_bool),X13))),file('i/f/util_prob/PREIMAGE__COMPL__INTER', ah4s_predu_u_sets_COMPLu_u_DEF)).
# SZS output end CNFRefutation
