# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:s(t_bool,h4s_bools_in(s(X1,X3),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_bool,h4s_bools_in(s(X2,happ(s(t_fun(X1,X2),X5),s(X1,X3))),s(t_fun(X2,t_bool),X4))),file('i/f/util_prob/IN__PREIMAGE', ch4s_utilu_u_probs_INu_u_PREIMAGE)).
fof(8, axiom,![X1]:![X3]:![X14]:s(t_bool,h4s_bools_in(s(X1,X3),s(t_fun(X1,t_bool),X14)))=s(t_bool,happ(s(t_fun(X1,t_bool),X14),s(X1,X3))),file('i/f/util_prob/IN__PREIMAGE', ah4s_predu_u_sets_SPECIFICATION)).
fof(54, axiom,![X1]:![X2]:![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),X4)))=s(t_fun(X1,t_bool),h4s_combins_o(s(t_fun(X2,t_bool),X4),s(t_fun(X1,X2),X5))),file('i/f/util_prob/IN__PREIMAGE', ah4s_utilu_u_probs_PREIMAGEu_u_ALT)).
fof(78, axiom,![X2]:![X1]:![X32]:![X3]:![X8]:![X5]:s(X2,happ(s(t_fun(X32,X2),h4s_combins_o(s(t_fun(X1,X2),X5),s(t_fun(X32,X1),X8))),s(X32,X3)))=s(X2,happ(s(t_fun(X1,X2),X5),s(X1,happ(s(t_fun(X32,X1),X8),s(X32,X3))))),file('i/f/util_prob/IN__PREIMAGE', ah4s_combins_ou_u_THM)).
# SZS output end CNFRefutation
