# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(X2,t_bool),X4),s(t_fun(X2,t_bool),X3))))=>p(s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(X1,t_bool),h4s_utilu_u_probs_preimage(s(t_fun(X1,X2),X5),s(t_fun(X2,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__DISJOINT', ch4s_utilu_u_probs_PREIMAGEu_u_DISJOINT)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/util_prob/PREIMAGE__DISJOINT', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f0))),file('i/f/util_prob/PREIMAGE__DISJOINT', aHLu_FALSITY)).
fof(9, axiom,![X1]:![X3]:![X4]:(p(s(t_bool,h4s_predu_u_sets_disjoint(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X3))))<=>s(t_fun(X1,t_bool),h4s_predu_u_sets_inter(s(t_fun(X1,t_bool),X4),s(t_fun(X1,t_bool),X3)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty)),file('i/f/util_prob/PREIMAGE__DISJOINT', ah4s_predu_u_sets_DISJOINTu_u_DEF)).
fof(11, 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_empty)))=s(t_fun(X1,t_bool),h4s_predu_u_sets_empty),file('i/f/util_prob/PREIMAGE__DISJOINT', ah4s_utilu_u_probs_PREIMAGEu_u_EMPTY)).
fof(12, axiom,![X1]:![X2]:![X3]:![X4]:![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_inter(s(t_fun(X2,t_bool),X4),s(t_fun(X2,t_bool),X3)))))=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),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__DISJOINT', ah4s_utilu_u_probs_PREIMAGEu_u_INTER)).
fof(14, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t0)|s(t_bool,X3)=s(t_bool,f0)),file('i/f/util_prob/PREIMAGE__DISJOINT', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
